摘要:

Selective Free Radical Reactions with Proteins and Enzymes The Inactivation of Subtilisin Carlsberg and Subtilisin Novo BY ROGER H. BISBY, ROBERT B. CUNDALL* Chemistry Department, The University, Nottingham NG7 2RD AND GERALD E. ADAMS AND J. LESLIE REDPATH+ Cancer Research Campaign, Gray Laboratory, Mount Vernon Hospital, Northwood, Middlesex HA6 2RN Received 12th March, 1974 Reactions of the selective inorganic radical anions (SCN); and Br;, with subtilisins Nouo and Cuvlsberg lead to selective oxidation of the tryptophan, tyrosine, and histidine amino-acid residues. Inactivation studies show that most of the inactivation is caused by oxidation of one or more histidine residues. Oxidation of tryptophan residues has a minor effect upon activity but damage to tyrosine residues does not affect the activity of the two enzymes towards the small synthetic substrate N- acetyl-L-tyrosine ethyl ester.Rate constants for reactions with the radical anions and transient spectra, measured by pulse radiolysis, reflect the differences in amino-acid composition and in structure between the two enzymes. The inactivation of enzymes in dilute aqueous solution by ionising radiation has now been the subject of many studies and although the use of specific radical scaveng- ers, such as nitrous oxide and t-butanol, allows the contribution to inactivation by primary radicals (OH, H and e i ) to be assessed, the mechanism of radiation-induced inactivation of many enzymes is still uncertain. The primary radicals may react at several sites within a protein molecule, but not all of these reactions lead to inactiva- tion.Consequently the yield of inactivation is generally lower than the yield of the radicals and product analysis does not indicate which of the several alternative radical reactions is the cause of inactivation. TABLE 1 .-ESSENTIAL RESIDUES OF ENZYMES IDENTIFIED BY THE SELECTIVE INORGANIC RADICAL ANION PULSE TECHNIQUE enzyme essential residue(s) identified 1ef. ri bonuclease histidine 2 1 ysozyme tryptophan 3 trypsin histidine (tryptophan) 4 a-chymo trypsin his t idine 5 a-carboxypep tidase tyrosine (tryptophan) 7 papain cysteine, tryptophan 6 superoxide dismutase histidine 8 The interpretation of the mechanism of the inactivation by oxidising radicals is simplified by employing the reactions of some inorganic radical anions which select- ively attack some amino-acid residues.' These chemical probes may be used to U.S.A.7 present address : Department of Medical Physics, Michael Reese Hospital, Chicago, Illinois, 2210R . H . BISBY; R . B . CUNDALL, G . E . ADAMS, J . L . REDPATH 2211 identify radiation sensitive residues in enzymes and investigations, using this tech- nique, have been made with RNAase,2 ly~ozyme,~ t r y p ~ i n , ~ a-chymotryp~in,~ papain, a-carboxypeptidase and superoxide dismutase. * These experiments have identified the same amino-acid residues to be necessary for enzymic activity as have been found by conventional biochemical techniques. In these enzymes oxidative free radical attack leads to inactivation by oxidation of a single type of amino-acid residue which is involved in either catalysis or binding of the substrate by the enzyme (table 1).Subtilisins Carlsberg and Novo are two closely related serine proteases formed by strains of Bacillus subtilis. Both enzymes consist of a single polypeptide chain lacking both cysteine and cystine residues (table 2). Subtilisin Carlsberg has 274 and Novo 275 amino-acid residues. There are 84 differences in the amino-acid sequences, as well as one deletion in subtilisin Carl~berg.~ Most of the substitutions involving hydrophobic residues are conservative. Crystallographic evidence O on subtilisin Novo shows all substitutions except one occur in exterior chain segments and of the 9 inward pointing side chain substitutions, 8 are conservative. In the segments containing residues which are thought to be part of the active sites, the sequences are identical in the two enzymes.Although the subtilisins resemble the mammalian pancreatic proteases, whose radiation induced inactivation have been studied,4* in many of their properties, the primary structures of the subtilisins are completely different.g In this work, we have investigated the reactions of selective inorganic radical anions with the two subtilisins. The results reflect the known differences in composi- tion and structure, and reveal the extent of participation of histidine, tyrosine and tryptophan in the active sites. EXPERIMENTAL For pulse radiolysis, enzyme solutions contained in a quartz cell of 2cm path length were irradiated with single 0.2 p s electron pulses from a 1.8 MeV linear accelerator.The doses used were between 100 and 500 rad for kinetic studies, and about 1 krad for measure- ment of transient spectra. Details of the equipment, associated circuitry," and method of solution preparation * have been published. For inactivation measurements, enzyme solutions (0.03 mg cnr3) were irradiated with a 6oCo y-source at a dose rate of about 1 krad min-'. All solutions contained phosphate buffer (1 mmol dm-3) and, where necessary, sodium hydroxide. Crystalline subtilisins No00 and Carlsberg were used as supplied (Novo Industri A/S, Copenhagen) and were assayed by a spectrophotometric method in which N-acetyl-L- tyrosine ethyl ester (ATEE) was used as substrate.13 The sample of subtilisin Carlsberg was found to be essentially homogeneous by Sephadex G75 chromatography.Other materials were of AnalaR grade. RESULTS PULSE RADIOLYSIS In N20 saturated solutions containing an inorganic anion X- such as SCN- or Br-, radical anions, X,, are formed by reaction of OH radicals : N,O+e&-+NZ+OH+OH- X- + OH+X* + OH- x- + x---+xz. The rate constants for reaction of the radical anions, Br; and (SCN)F, with a solute were measured by observing the first order decay of their strong absorptions at22 12 SELECTIVE FREE RADICAL REACTIONS 380 and 500nrn. The derived second order rate constants for (SCN); and Br? with subtilisins Novo and Carlsberg are shown as in fig. 1. the reactions of a function of pH f PH (4 (b) FIG. 1 .-Effect of pH on the second order rate constants for reactions of radical anions with subtilisins Carisberg and Novo.(a) (SCN);; (6) Br;. 0, subtilisin Carlsberg; 0, subtilisin Novo. Salt concentration = 4 x low2 mol dm-3. Enzyme concentration = 0.2-1.0 mg ~ m - ~ . Reactions of OH, Br; and (SCN): in neutral and alkaline solutions with the two enzymes produced moderately intense transient absorption spectra shown in fig. 2. The spectra obtained from pulse radiolysis of neutral N,O-saturated solutions of subtilisins Carlsberg and Nuvu containing 4 x mol dm-3 KBr are compared in fig. 3. 1 I I I I I 3 0 0 3 5 0 400 4 5 0 5 0 0 5 5 0 6 0 0 wavelength /nm FIG. 3.-Transient spectra from pulse radiolysis of N20 saturated solutions of subtilisins Novo and Carlsberg containing 4 x 0 subtilisin Novo (1 mg ~ m - ~ ) , pH 7.1, 200 ,us after pulse ; x subtilisin Carlsberg (1 mg cnr3), pH 7.6, 100 ps after pulse.Dose = 1 krad pulse-'. mol dm-3 KBr.R. H . BISBY, R . B . CUNDALL, G . E . ADAMS, J . L. REDPATH 2213 0 . 0 1 5 h 5 0,010 8 8 0.005 a 0 - ." +J A 3 0 0 400 5 6 0 6 0 0 0.0 15 h + ." 8 0.010 8 0 . 0 0 5 -0 0 c( ." + h + .. c( 8 I- 3 0,010 + a 0 0.00 5 3 0 0 400 5 0 0 6 0 0 (4 wavelength /nm O.Ot5 0.0 I 0 0 . 0 0 5 0 0.01 5 0.0 10 0.005 0 3 0 0 4 0 0 5 0 0 600 300 400 5 0 0 6 0 0 wavelength/nm (b) FIG. 2.-Transient spectra from pulse radiolysis of N20 saturated solutions of subtilisin (a) CurZsberg (1.0-3.0 mg ~ r n - ~ ) and (b) Novo (0.5-1.0 mg ~ m - ~ ) containing : A and B, N20 alone ; A, 0 pH 7.6, 100 ps after pulse, x pH 11.1, 100 ps after pulse; B, 0 pH 6.9, 100 ps after pulse, 0 pH 11.8, 100 ps after pulse; C and D, 4 x lo-' mol dm-3 KSCN ; C, 0 pH 6.8,400 ps after pulse, 6 pH 11.2, 200 ps after pulse ; D, 0 pH 7.0, 250 ps after pulse, 0 pH 11, 300 ps after pulse; E and F, 4 x mol dm-3 KBr ; E, 0 pH 7.6, 100 ps after pulse, pH 11.2, 200 ps after pulse: F, 0 pH 7.1, 200 ps after pulse, pH 11 .O, 200 ps after pulse.Dose = 1 krad pulse-'.2214 SELECTIVE FREE RADICAL REACTIONS dose/ krad FIG. 4.-Inactivation of solutions of subtilisin Carlsberg (0.03 mg ~ m - ~ ) . (a) N20 saturated, rnol dm-3 KBr, pH 10.3 ; (c) N20 saturated, no added salt, pH 7.2 ; (d) argon saturated, no added salt, pH 7.3 ; (e) N20 saturated, mol mol dm-3 KBr, pH 7.15 ; (b) NzO saturated, dm-3 KSCN, pH 7.5 ; (f) 0, saturated, no added salt, pH 7.3.0.7 Q. 6 0.5 h s *s 0.4 0.3 > 0 .-. Y .- 5 0.2 0.1 0 I I I I I 1 6 7 8 9 1011 PH FIG. 5.-Effect of pH on Ginact for N20 saturated solutions of subtilisin Carlsberg containing 0, N 2 0 alone ; A, rnol dm-3 KBr ; 0, rnol dm-3 KSCN.R . H . BISBY, R . B . CUNDALL, G . E . ADAMS, J . L . REDPATH 2215 INACTIVATION STUDIES The inactivation curves for subtilisin Carlsberg y-irradiated in solutions equilibri- ated with oxygen, argon or nitrous oxide are shown in fig. 4. Nitrous oxide approxi- mately doubles the yield of inactivation relative to the argon-purged (oxygen-free) solution. In contrast oxygen has a slight protective effect. Fig. 4 also includes inactivation curves in the presence of added salts and N,O. Relative to the solution containing N20 alone, addition of Br- causes an increase in the rate of inactivation, whereas addition of SCN- has a protective effect upon the inactivation.In fig. 5, the G values for inactivation (Ginact) for subtilisin Carlsberg are shown for the pH range 5-1 1 in N20 saturated solutions containing mol dm-3 KSCN and are compared to Ginact in solutions containing N20 alone. The inactivation curves for subtilisin Novo in solutions containing NZO and lo-' rnol dm-3 KSCN and KBr at both neutral and alkaline pH values are shown in fig. 6. Table 3 presents values of Ginact for the two enzymes under various conditions. Exponential inactivation curves were obtained under all conditions except at pH > 10 in solutions containing SCN-. mol dm-3 KBr and 0 I I I l l I 0 2 4 6 8 1 0 1 2 0 2 4 6 8 1 0 1 2 14 (4 doselkrad (b) FIG.6.-Inactivation of N20 saturated solutions of subtilisin Now (0.03 mg ~ r n - ~ ) at (a) pH 7.0-7.1 and (b) pH 10.0. 0, N20 alone ; A, mol dm-3 KBr ; 0, rnol dm-3 KSCN. DISCUSSION REACTIVITY OF SUBTILISINS At neutral pH the rate constants for reaction of the subtilisins Carlsberg and Nouo with BrF are 1.0 and 1.3 x lo9 dm3 mol-' s-' and for (SCN), are 1.0 and 3.0 x lo8 dm3 mol-1 s-l. These are approximately the same as for free tryptophan with Br;. 0.8 x lo9 dm3 mol-' s-', and (SCN): 2.7 x 10' dm3 mol-1 s-1 which is the most reactive of the amino acids ' present in the two enzymes. The rate constants for reactions of the radical anions with both enzymes increase markedly in alkaline solution due to the increased reactivity of the ionised phenolic groups of tyrosine residues.l Free tyrosine has a pK value of 10.1 for deprotonation.Whilst the rate constants for reaction of Br; and (SCN), with free tyrosine increase at about pH 10,' the increase in reactivity of the subtilisins is displaced to a higher pH, consistent with2216 SELECTIVE FREE RADICAL REACTIONS the presence of tyrosine residues in these enzymes possessing pK values higher than Both Br; and (SCN), react more rapidly at neutral pH with subtilisin Novo than with subtilisin Carlsberg. This is consistent with the higher content of the reactive tryptophan residues in subtilisin Novo (table 2). At pH > 10 subtilisin Carlsberg becomes more reactive than subtilisin Novo because of its higher tyrosine content. 11.14 TABLE TYR AMINO ACID COMPOSITION OF SUBTILISINS Carlsberg AND NOVO amino acid Carlsberg 22 tryptophan tyrosine his tidine phenylalanine methionine lysine arginine aspartic acid asparagine t hreonine serine glutamic acid glutamine proline glycine alanine valine isoleucine leucine cysteine, cystine total 1 13 5 4 5 9 4 9 19 19 32 5 7 9 35 41 31 10 16 0 274 Novo 23 3 10 6 3 5 11 2 11 17 13 37 4 11 14 33 37 30 13 15 0 275 TRANSIENT SPECTRA The transient spectra obtained by pulse radiolysis of solutions of subtilisins Carlsberg and Novo (fig.2) contain components similar to the spectra of oxidised free amino acidsf We assign the absorption maxima at 310-320 nm and 520 nm to radicals formed by oxidation of tryptophan residues, and those below 300 nm and at 410 nm to radicals derived from tyrosine residues. With Br; , an additional absorp- tion due to histidine radicals at about 400nm may also be present.The 410nm absorption of tyrosine radicals becomes more pronounced at pH = 11 for reactions of both enzymes with (SCN), and Br; due to the high reactivity of the ionised phenolic groups of tyrosine residues. As the relative absorption due to the tyrosine product increases, those arising from the tryptophan radical at 310-320 nm and 520 nm show a complementary decrease in intensity. The absorption bands produced by oxidation of tryptophan and tyrosine are less pronounced in the transient spectra (fig. 2) of the OH radical subtilisin adducts. This is because OH radicals are less specific in their reactions than the radical anions, and can react at other sites in the protein molecule 5 9 to produce species which absorb in other spectral regions. Fig.3 shows that reaction of Br; with subtilisin Novo forms a more intense trypto- phan radical absorption than subtilisin Carlsberg. The tyrosine radical absorption is less intense in subtilisin Novo than Carlsberg. This is consistent with the different relative contents of tryptophan and tyrosine in the two enzymes (table 2).R. H . BISBY, R . B . CUNDALL, G . E . ADAMS, J . L. REDPATH 2217 Assuming that the values of the extinction coefficients which have been determined for radicals from free tryptophan (1600 dm3 mol-1 cm-l at 520 nm) and free tyrosine (2100 dm3 mol-1 cm-l at 410 nm) apply to the oxidised residues in the proteins it can be calculated that between 65 and 80 % of the (SCN); and Br; radicals react with the protein to form tyrosine or tryptophan radicals in both enzymes.INACTIVATION STUDIES The effect of N20 in the inactivation of subtilisin Carlsberg (fig. 4) shows that most of the inactivation is caused by OH radicals. This conclusion is supported by the relatively small protective effect of oxygen, which removes the reducing radicals, e: and H. These experiments show that nearly all inactivation in N20 saturated solution is due to the OH radicals and the specific inorganic radical anion technique can be applied for identification of some of the essential amino-acid residues susceptible to oxidative attack. TABLE 3 .-INACTIVATION YIELDS OF SUBTILISINS NOVO AND Carlsberg IN NzO SATURATED SOLUTIONS radical Ginact/molecule (100 eV)-1 PH Carlsherg Noco OH 0.23 0.34 WN), 0.14 0.13 Br, 7.0-7.2 0.66 0.44 OH 0.21 0.34 Br, 10.0-10.3 0.34 0.36 WN), 0.18* 0.16* * values from initial slopes of non-exponential inactivation curves.Values of Ginact for subtilisin Carlsberg inactivation by Br, and (SCN), are different and both vary with pH (table 3). Over the pH range studied Br, inactivates more efficiently than OH, whereas the presence of thiocyanate has a protective effect. At neutral pH, of the relevant free amino-acids, Br; reacts only with tryptophan, tyrosine, and histidine at rates above the limit of measurement (k > 106 dm3 mol-1 s-l). (SCN); radicals react only with tyrosine and tryptophan and the enhanced inactivation by Br2 must be due to oxidation of one or more of the histidine residues.This conclusion is consistent with the decrease in inactivation at pH of about 8 in solutions containing Br- due to the increased reactivity of tyrosine relative to histidine as pH is increased. In solutions which contain SCN-, damage to tryptophan contri- butes to the inactivation, although to a much smaller extent than that which occurs when histidine is oxidised by Br; . The decrease observed in inactivation by (SCN), as pH is increased between 7 and 9 also indicates that damage to tyrosine residues does not cause inactivation. The inactivation of subtilisin Novo (fig. 6 and table 3) exhibits the same trends in reactivity with radical anions as subtilisin Carlsberg. Similar reasoning to that used for data on the latter enzyme shows that inactivation of subtilisin No00 is also caused by oxidation of one or more histidine residues together with a minor contribution from some tryptophan residue oxidation.It is interesting to note that the additional tryptophan residues present in subtilisin Novo do not cause a decrease in Ginact, compared with subtilisin Carlsberg. This may221 8 SELECTIVE FREE RADICAL REACTIONS be because the total numbers of tyrosine and tryptophan residues are comparable in both enzymes.22 9 The substitutions involving tyrosine and tryptophan residues all occur in exterior chain segments of the two molecules and these particular residues are therefore likely to be accessible for reaction with radicals. In discussing the reactivities of the radical anions with the subtilisins, any contri- bution to reactivity arising from methionine residues can be discounted, although free methionine reacts fairly rapidly with Br; and (SCN),, because methionine owes its reactivity to its unprotonated amino group, and when part of a polypeptide chain, or the amino group is acylated, reactivity is 1ost.l The conclusions from this investigation agree with photoxidation and kinetic measurements l8 and also with the results obtained using highly selective reagents l9 which show a histidine residue to be part of the active site of subtilisins.The histi- dine residue involved is that which is associated with a reactive serine residue, analog- ous to the grouping in molecules of the vertebrate serine proteases such as trypsin and chymotrypsin.20 Biochemical studies show that tyrosine residues appear to be involved in the binding of large substrate molecules, such as clupeine, with subtilisin, but not in the binding of small synthetic substrates such as ATEE.21 The finding in this work that tyrosine residues are not essential to activity of subtilisins Carlsberg and NOVO is therefore consistent with available biochemical evidence.This work was supported by the Cancer Research Campaign. Thanks are due to Novo Industri A/S, Copenhagen, for gifts of samples of subtilisins Carlsberg and Novo. G. E. Adams, J. E. Aldrich, R. H. Bisby, R. B. Cundall, J. L. Redpath and R. L. Willson, Rud. Res., 1972, 49, 278. G. E. Adams, R. H. Bisby, R. B. Cundall, J. L. Redpath and R. L. Willson, Rud. Res., 1972,49, 290.G. E. Adams, R. L. Willson, J. E. Aldrich and R. B. Cundall, Int. J. Rud. Bid., 1969, 16, 333. G. E. Adams, J. L. Redpath, R. H. Bisby and R. B. Cundall, J.C.S. Faruday I, 1973,69,1608. G. E. Adams, K. F. Baverstock, R. B. Cundall and J. L. Redpath, Znt. J. Rud. Bid., 1974, 26, 39. J. L. Redpath, Int. J. Rud. Bid., 1972, 22, 99. ' P. B. Roberts, Int. J. Rud. Bid., 1973, 24, 143. P. B. Roberts and E. M. Fielden, Abstr. 5th L. H. Gray Memuriul Cunf, 1973. F. S. Markland and E. L. Smith in The Enzymes, Vol. 111, ed. P. D. Boyer (Academic Press, London and New York, 3rd edn., 1971), p. 561. lo J. Kraut in The Enzymes, Vol. 111, ed. P. D. Boyer (Academic Press, London and New York, 3rd edn., 1971), p. 547. G. E. Adams, J. W. Boag and B. D. Michael, Trans. Furaduy Suc., 1965,17, 349. l2 R. L. Willson, Int. J. Rud. Biul., 1970, 17, 349. l 3 G. W. Schwert and Y. Takenaka, Biochim. Biuphys. Acra, 1965, 16, 570. l4 F. S. Markland, J. Bid. Chem., 1969, 244, 694. l5 G. Scholes, P. Shaw, R. L. Willson and M. Ebert, in Pulse Radiulysis ed. M. Ebert, J. P. Keene, A. J. Swallow and J. H. Baxendale (Academic Press, London and New York, 1965), p. 151. l 6 E. Hayon and M. Simic, Intra-Science Chem. Rep., 1971, 5, 357. l7 R. A. Oosterbaan and J. A. Cohen, in Structure and Activity of Enzymes ed. T. W. Goodwin, J. I. Harris and B. S. Hartley (Academic Press, New York, 1964), p. 87. A. N. Glazer, J. Biul. Chem., 1967, 242, 433. l9 F. S. Markland, E. Shaw and E. L. Smith, Pruc. Nut. Acud. Sci. U.S.A., 1968, 61, 1440, 2o D. M. Blow in The Enzymes, Vol. 111, ed. P. D. Boyer (Academic Press, London and New York, 3rd edn., 1971), p. 196. 21 M. Oltesen, J. T. Johansen and I. Svendsen, in Structure-Function Relationships of Pruteulytic Enzymes, ed. P. Desnuelle, H. Neurath, and M. Ottesen (Munksgaard, Copenhagen, 1970), p. 175. 22 R. J. DeLange and E. L. Smith, J. Biul. Chem., 1968,243, 2134. 23 S. A. Olaitan, R. J. DeLange and E. L. Smith, J. Biul. Chem., 1968,243, 5296.

ISSN:0300-9599    

DOI:10.1039/F19747002210

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Mass Spectrometric Determination of the Dissociation Energies of the Molecules CuLi, AgLi and AuLi BY A. NEUBERT* AND K. F. ZMBOV? Institute for Nuclear Chemistry of the Kernforschungsanlage Jiilich GmbH, Postfach 365, West Germany Received 1st April, 1974 Equilibria involving gaseous species CuLi, AgLi and AuLi have been investigated using a Knudsen effusion technique combined with mass spectrometric analysis of the vapour composition. The following dissociation energies were derived by the third law procedure from the measured ion intensities, free energy functions and auxiliary data : Di(CuLi) = 189.3 & 8.8 kJ mol-1 DG(AgLi) = 173.6k6.3 kJ mol-' Di(AuLi) = 280.8 2 6.5 kJ mol-I. 'The measured dissociation energies are considerably lower than those calculated from the Pauling model of the polar bond.There has been considerable interest recently in gaseous intermetallic com- pounds.1.2 The high stability of many of these compounds has been explained in terms of the Pauling model of the polar bond. No intermetallic gaseous compound of lithium has been observed so far, although one can expect relatively stable molecules between lithium and the elements of the IB group due to the large electronegativity difference between them. The present paper describes the identification of, and the determination of the dissociation energies of the molecules CuLi, AgLi and AuLi by the Knudsen effusion method in combination with mass spectrometric analysis. EXPERIMENTAL The experiments were carried out with a double-focusing mass spectrometer MS 702 (AEI), equipped with a Knudsen cell and an ion counting detection system as described previ~usly.~ The Knudsen cells used were machined from molybdenum. They were 9.5 mm i.d., 25 mm long, had an orifice of diameter of 0.7 mm, and were heated by radiation from a tantalum filament.The temperatures were measured by an optical pyrometer which was sighted directly onto the Knudsen cell orifice. Appropriate corrections were derived from the observation of the melting plateaus of Ag and A u . ~ Two runs were performed. In the first one a mixture of Ag, Au and Li,O was evaporated using a molybdenum liner. In the gas phase silver was predominant and the measurements showed the activity of silver to be close to unity. In the second run a mixture of 300 mg Cu, 900 mg Au, 15 mg Ag, and approximately 100 mg Li,O was contained in a zirconia liner.This mixture was chosen in order to overcome the disparity in the vapour pressures of the different components. The pressure calibration was carried out by the measurement of Ag+-ion currents at various temperatures. In this case the same Knudsen cell was used from which, later on, the two samples were evaporated. j- On leave from the Boris Kidric Institute, Vinca, Belgrade, Yugoslavia. 22192220 DISSOCIATION ENERGIES The electron energy scale was calibrated by measuring the appearance potential of Ag+ using the linear extrapolation method. RESULTS AND DISCUSSION The molecular species effusing from the cell were identified by their mass-to- charge-ratio, their isotopic abundance and the intensity profile of the molecular beam.In addition to the atomic ions Li+, Cu+, Ag+ and Au+, the molecular ions CuLi+, AgLi+, AuLi+, Cui and Agi were observed. LiO+ and Li20+ were also present. (No search was made for Aui and for the asymmetric diatomic molecules of the IB elements.) The ionization potential of AuLi was found to be 1.5 eV lower than the ionization potential of Au. Because of the low intensities of the CuLi+ and AgLi+ ions, it was impossible to measure their appearance potentials. A difference appearance potential (M) - appearance potential (MLif) = 1.5 eV was therefore assumed for all these ions by analogy with AuLi. The intensities of the various ions were measured at an electron energy 5 eV above the corresponding ionization potential.The pressures were calculated using the instrument sensitivity factor obtained from the silver calibration and the ionization cross sections given by Mann.6 For molecules the additivity rule was applied and the isotopic abundances were taken into account. The pressure data obtained were used to calculate the enthalpy changes for the following reactions : MLi(g)-+M(g) + Li(g) M = CU, Ag, AU (1) M u g ) + M(g)+M,(g) + Wg) M = Ag, CU (2) MLi(g) + M'(g)-+M(g) + M'Li(g) (3) M = Cu, Ag, Au. The pressures, equilibrium constants and enthalpy change for the reaction AgLi(g) -+ Ag(g) + Li(g) are given in table 1. TABLE 1 .-VAPOUR PRESSURES, EQUILIBRIUM CONSTANTS AND ENTHALPY CHANGES FOR THE REACTION AgLi(g)-+Ag(g)+ Li(g) T/K p(Ag)/N m-2 p(Li)/(lO-,N m-2) p(AgLi)/ (lO-sN m-2) 1st run 1212 1255 1292 1330 1330 1340 1352 1369 1394 2nd run 1356 1386 1397 1400 1421 1440 0.17 0.39 0.94 1.8 2.1 2.4 3.0 3.8 4.9 0.076 0.14 0.18 0.16 0.19 0.27 0.66 2.3 4.0 8 .o 11.2 11.6 12.8 19.3 26.3 0.55 1.1 1.6 0.93 1.7 2.0 0.39 1.5 4.2 6.4 7.4 8.3 10.2 16.5 26.1 0.91 2.5 3.5 3 .O 3.6 7.1 - 8.158 - 7.430 - 7.016 - 6.079 - 5.770 - 5.696 - 5.567 - 5.409 - 5.304 - 81.63 -81.92 -82.13 - 82.26 - 82.26 - 82.30 - 82.30 - 82.38 - 82.47 average 181.2 180.3 181.6 176.6 173.2 173.6 173.6 174.5 173.2 176.4_+ 3.6 - 5.375 -82.34 172.4 - 5.080 -82.42 172.8 -4.814 -82.47 171.1 - 5.325 -82.47 177.4 - 4.701 -82.55 172.8 - 4.903 -82.63 177.4 average 174.0k 2.7 average from both runs 175.5f 3.4A .NEUBERT AND K . F . ZMBOV 2221 The equilibrium constants for the decomposition reactions (1) are presented in figure 1 and the results for the exchange reactions (2) and (3) given in tables 2 and 3.The enthalpy changes were calculated by the third-law method according to the relation AH: = -RT In K-TA(G,-H:)/T. (4) Free energy functions for the monatomic species were taken from Stull and Sinke ’ and those for the diatomic species were calculated by the usual statistical thermo- dynamic procedure from experimental or estimated parameters. The interatomic distances were calculated as sums of the Pauling single bond radii,3 and the vibrational frequencies were calculated using Goody’s correlation between electronegativity, internuclear distance and the force constant. Calculations with the help of Guggen- heimer’s relations gave essentially the same results.A IC ground state was assumed I. 60 .65 .70 .75 .80 .a5 FIG. 1 .-Equilibrium constants for the reactions MLi(g)+M(g) + Li(g), M = Cu (curve A), Ag (B), Au (0. 103 KIT TABLE 2.-EQUILIBRIUM CONSTANTS AND ENTHALPY CHANGES FOR THE EXCHANGE REACTIONS MLi(g)+ M(g)-+Li(g)+ M2k) T/K InK A,H/kJ mol M = CU 1466 1484 1486 1508 M = Ag 1212 1292 1330 1369 1394 - 0.887 - 2.5 - 1.565 5.9 - 0.73 1 - 4.6 - 1.101 0.08 average - 0.3 & 4.5 - 2.629 17.6 - 2.567 18.0 - 1.970 12.1 - 1.882 11.7 - 1.917 12.1 average 14.3+ 3.22222 DISSOCIATION ENERGIES TABLE 3.-EQUILIBRIUM CONSTANTS AND ENTHALPY CHANGES FOR THE EXCHANGE REACTIONS MWg) + M'(g)-+ M'Li(g) + M(g) T/K InK AHi/kJ mol-I 1st run M = Ag 1212 9.555 - 96.7 M' = Au 1292 8.922 - 96.7 1330 9.446 - 105.0 1369 9.522 - 109.2 1394 9.237 - 107.5 average - 103.0+ 5.9 2nd run 1356 9.710 - 110.0 1386 9.463 - 109.6 1398 9.287 - 108.8 1400 9.127 - 107.1 1421 9.252 - 110.0 1440 8.92 I - 107.5 average - 108.8+ 1.3 average from both runs - 106.2k4.9 M = Ag, M' = Cu M = Au, M' = Cu 1398 1.014 - 13.4 1400 0.598 - 8.8 1421 1.417 - 18.4 1440 1.097 - 15.1 average - 13.9+ 4.0 1398 - 8.273 95.0 1400 - 8.529 98.3 1421 - 7.835 91.6 1440 - 7.824 92.4 average 94.3+ 3.0 by analogy with liydrides and other compounds of Cu, Ag and Au.1° Table 4 lists the molecular parameters and the free energy functions for the various molecules.The good mutual agreement of results obtained in two different runs (table 1) shows that attainment of equilibrium does not depend on the composition of the condensed phase.Table 5 summarizes the measured enthalpy changes of the various reactions and the derived dissociation energies of the CuLi, AgLi and AuLi molecules. The TABLE 4.-MOLECULAR PARAMETERS AND FREE-ENERGY FUNCTIONS OF THE GASEOUS MOLECULES AuLi, AgLi, CuLi, Cu2 AND Ag, molecule AuLi AgLi CuLi Cuz Ag2 vibrational wavenumber/crir' 528.1" 499.0n 527.3" 264.56b 192.4c interatomic distance/A 2.57d 2.57d 2.40" 2.21gb 2.6gC TJK - ( GT- tf ,-JT)/Jrnol- K - 1 200 1300 1400 1 500 253.4 246.4 238.5 256.8 273.3 256.2 249.2 241.3 259.7 276.2 258.9 251.8 243.9 262.4 278.9 261.3 254.3 246.4 264.9 281.4 fl calculated according the method of Gordy [ref. ( 8 ) ] ; b ref. (1) ; C ref. (10) ; d calculated from Pauling radii.A . NEUBERT AND K . F . ZMBOV 2223 TABLE 5.-sUMMARY OF THE THIRD-LAW ENTHALPIES AND DISSOCIATION ENERGIES molecule reaction AHG/kJ mol-' ADg/kJ mol- AgLi(g) AgLW -+ + L W 175.5k3.4 175.5k 3.4 AgLi(g)+ Ag(g)+&z(g)+ LKg) 14.3k3.2 171.6+ 9.2 average 173.6f 6.3 CuLi(g) CuLi(g)-+ Cu(g)+ Li(g) 190.2+ 3.4 190.2+ 3.4 1 87.5 k 1 0.3 average 189.3+ 8.8 AuLi(g) AuLi(g)-+Au(g)+ Li(g) 281.8k2.4 281.8+ 2.4 AuLi(g)+ Ag(g)+Au(g)+AgLi(g) 106.2k4.9 279.8+ 11.2 average 280.8+ 6.5 CuLi(g)+ Cu(g)-+Cu2(g)+ Li(g) -0.3k4.5 190.1+12.6 CuLi(g) + Ag(g) -+ AgLi(g) + Cu(g) 1 3.9 k 4.0 dissociation energies of CuLi and AgLi obtained from the decomposition reactions (1) are in very good agreement with the values derived from the enthalpy changes of the reactions (2) when the known values Dg(Cu,) = 190.4k9.2 kJ mol-1 D:(Ag,) = 157.3 k9.2 kJ mol-1 are used.This justifies the calibration procedure used. Adopting the value D:(AgLi) = 173.6 kJ mol-l as a reference, the dissociation energies of CuLi and AuLi derived from the exchange reactions (3) agree well with the values from the reactions (1). While there are no other data on the stabilities of the molecules CuLi, AgLi and AuLi, it is interesting to compare the measured dissociation energies with those calculated according to the Pauling electronegativity concept. The dissociation energy of a compound AB is usually related to those of the dimers A, and B2, and the electronegativities XA and XB by Pauling's formula : Using the electronegativities calculated by Gordy and Thomas l2 XA, = 2.3, XA, = 1.8 and Xcu = 1.8 and XLi = 0.95, one obtains values of 218, 200.4 and 338.5 kJ mol-1 for the dissociation energies of CuLi, AgLi and AuLi, respectively.These values are considerably higher than the measured ones. Much better agreement with the experimental values is obtained, however, if 0.2 is subtracted from the electronegativities of Cu, Ag and Au used in the calculations. D(AB) = 3[D(A,) + D(B,)] + 96.2(XA - X,), kJ mol-I. ( 5 ) The authors thank Dr. D. Guggi for the preparation of lithium oxide. J. Drowart, in Phase Stability in Metals and Alloys, ed. P. S . Rudman, J. Stringer and R. I. Jaffee (McGraw Hill, New York, 1967), p. 305. K. A. Gingerich, J. Cryst. Growth, 1971, 9, 31. L. Pauling, The Nature of the Chemical Bond (Cornell U. P., Ithaca, New York, 3rd edn., 1960). H. Michael, A. Neubert and H.Nickel, Int. J. Appl. Rad. Isotopes, 1974, 25, 183. A. Neubert and K. F. Zmbov, High Temp. Sci., to be published. J. B. Mann, J. Chem. Phys., 1967, 46, 1646. D. R. Stull and G. C. Sinke, Thermodynamic Properties of the Elements (Adv. Chem. Series), (Amer. Chem. SOC., Washington, D.C., 1956) Vol. 18. W. Gordy, J. Chem. Phys., 1946, 14, 305. K. M. Guggenheimer, Proc. Phys. SOC., 1946,58,456. (Academic Press, New York, 1967), Vol. 1, p. 7. lo C. J. Cheetham and R. F. Barrow, Aduances in High Temperature Chemistry, ed. L. Eyring I ' M. Ackermann, F. E. Stafford and J. Drowart, J. Chem. Phys., 1960, 33, 1784. l 2 W. Gordy and W. J. 0. Thomas, J. Chern. Phys., 1956, 24, 439. Mass Spectrometric Determination of the Dissociation Energies of the Molecules CuLi, AgLi and AuLi BY A.NEUBERT* AND K. F. ZMBOV? Institute for Nuclear Chemistry of the Kernforschungsanlage Jiilich GmbH, Postfach 365, West Germany Received 1st April, 1974 Equilibria involving gaseous species CuLi, AgLi and AuLi have been investigated using a Knudsen effusion technique combined with mass spectrometric analysis of the vapour composition. The following dissociation energies were derived by the third law procedure from the measured ion intensities, free energy functions and auxiliary data : Di(CuLi) = 189.3 & 8.8 kJ mol-1 DG(AgLi) = 173.6k6.3 kJ mol-' Di(AuLi) = 280.8 2 6.5 kJ mol-I. 'The measured dissociation energies are considerably lower than those calculated from the Pauling model of the polar bond. There has been considerable interest recently in gaseous intermetallic com- pounds.1.2 The high stability of many of these compounds has been explained in terms of the Pauling model of the polar bond.No intermetallic gaseous compound of lithium has been observed so far, although one can expect relatively stable molecules between lithium and the elements of the IB group due to the large electronegativity difference between them. The present paper describes the identification of, and the determination of the dissociation energies of the molecules CuLi, AgLi and AuLi by the Knudsen effusion method in combination with mass spectrometric analysis. EXPERIMENTAL The experiments were carried out with a double-focusing mass spectrometer MS 702 (AEI), equipped with a Knudsen cell and an ion counting detection system as described previ~usly.~ The Knudsen cells used were machined from molybdenum.They were 9.5 mm i.d., 25 mm long, had an orifice of diameter of 0.7 mm, and were heated by radiation from a tantalum filament. The temperatures were measured by an optical pyrometer which was sighted directly onto the Knudsen cell orifice. Appropriate corrections were derived from the observation of the melting plateaus of Ag and A u . ~ Two runs were performed. In the first one a mixture of Ag, Au and Li,O was evaporated using a molybdenum liner. In the gas phase silver was predominant and the measurements showed the activity of silver to be close to unity. In the second run a mixture of 300 mg Cu, 900 mg Au, 15 mg Ag, and approximately 100 mg Li,O was contained in a zirconia liner.This mixture was chosen in order to overcome the disparity in the vapour pressures of the different components. The pressure calibration was carried out by the measurement of Ag+-ion currents at various temperatures. In this case the same Knudsen cell was used from which, later on, the two samples were evaporated. j- On leave from the Boris Kidric Institute, Vinca, Belgrade, Yugoslavia. 22192220 DISSOCIATION ENERGIES The electron energy scale was calibrated by measuring the appearance potential of Ag+ using the linear extrapolation method. RESULTS AND DISCUSSION The molecular species effusing from the cell were identified by their mass-to- charge-ratio, their isotopic abundance and the intensity profile of the molecular beam. In addition to the atomic ions Li+, Cu+, Ag+ and Au+, the molecular ions CuLi+, AgLi+, AuLi+, Cui and Agi were observed.LiO+ and Li20+ were also present. (No search was made for Aui and for the asymmetric diatomic molecules of the IB elements.) The ionization potential of AuLi was found to be 1.5 eV lower than the ionization potential of Au. Because of the low intensities of the CuLi+ and AgLi+ ions, it was impossible to measure their appearance potentials. A difference appearance potential (M) - appearance potential (MLif) = 1.5 eV was therefore assumed for all these ions by analogy with AuLi. The intensities of the various ions were measured at an electron energy 5 eV above the corresponding ionization potential. The pressures were calculated using the instrument sensitivity factor obtained from the silver calibration and the ionization cross sections given by Mann.6 For molecules the additivity rule was applied and the isotopic abundances were taken into account.The pressure data obtained were used to calculate the enthalpy changes for the following reactions : MLi(g)-+M(g) + Li(g) M = CU, Ag, AU (1) M u g ) + M(g)+M,(g) + Wg) M = Ag, CU (2) MLi(g) + M'(g)-+M(g) + M'Li(g) (3) M = Cu, Ag, Au. The pressures, equilibrium constants and enthalpy change for the reaction AgLi(g) -+ Ag(g) + Li(g) are given in table 1. TABLE 1 .-VAPOUR PRESSURES, EQUILIBRIUM CONSTANTS AND ENTHALPY CHANGES FOR THE REACTION AgLi(g)-+Ag(g)+ Li(g) T/K p(Ag)/N m-2 p(Li)/(lO-,N m-2) p(AgLi)/ (lO-sN m-2) 1st run 1212 1255 1292 1330 1330 1340 1352 1369 1394 2nd run 1356 1386 1397 1400 1421 1440 0.17 0.39 0.94 1.8 2.1 2.4 3.0 3.8 4.9 0.076 0.14 0.18 0.16 0.19 0.27 0.66 2.3 4.0 8 .o 11.2 11.6 12.8 19.3 26.3 0.55 1.1 1.6 0.93 1.7 2.0 0.39 1.5 4.2 6.4 7.4 8.3 10.2 16.5 26.1 0.91 2.5 3.5 3 .O 3.6 7.1 - 8.158 - 7.430 - 7.016 - 6.079 - 5.770 - 5.696 - 5.567 - 5.409 - 5.304 - 81.63 -81.92 -82.13 - 82.26 - 82.26 - 82.30 - 82.30 - 82.38 - 82.47 average 181.2 180.3 181.6 176.6 173.2 173.6 173.6 174.5 173.2 176.4_+ 3.6 - 5.375 -82.34 172.4 - 5.080 -82.42 172.8 -4.814 -82.47 171.1 - 5.325 -82.47 177.4 - 4.701 -82.55 172.8 - 4.903 -82.63 177.4 average 174.0k 2.7 average from both runs 175.5f 3.4A .NEUBERT AND K . F . ZMBOV 2221 The equilibrium constants for the decomposition reactions (1) are presented in figure 1 and the results for the exchange reactions (2) and (3) given in tables 2 and 3.The enthalpy changes were calculated by the third-law method according to the relation AH: = -RT In K-TA(G,-H:)/T. (4) Free energy functions for the monatomic species were taken from Stull and Sinke ’ and those for the diatomic species were calculated by the usual statistical thermo- dynamic procedure from experimental or estimated parameters. The interatomic distances were calculated as sums of the Pauling single bond radii,3 and the vibrational frequencies were calculated using Goody’s correlation between electronegativity, internuclear distance and the force constant. Calculations with the help of Guggen- heimer’s relations gave essentially the same results. A IC ground state was assumed I. 60 .65 .70 .75 .80 .a5 FIG.1 .-Equilibrium constants for the reactions MLi(g)+M(g) + Li(g), M = Cu (curve A), Ag (B), Au (0. 103 KIT TABLE 2.-EQUILIBRIUM CONSTANTS AND ENTHALPY CHANGES FOR THE EXCHANGE REACTIONS MLi(g)+ M(g)-+Li(g)+ M2k) T/K InK A,H/kJ mol M = CU 1466 1484 1486 1508 M = Ag 1212 1292 1330 1369 1394 - 0.887 - 2.5 - 1.565 5.9 - 0.73 1 - 4.6 - 1.101 0.08 average - 0.3 & 4.5 - 2.629 17.6 - 2.567 18.0 - 1.970 12.1 - 1.882 11.7 - 1.917 12.1 average 14.3+ 3.22222 DISSOCIATION ENERGIES TABLE 3.-EQUILIBRIUM CONSTANTS AND ENTHALPY CHANGES FOR THE EXCHANGE REACTIONS MWg) + M'(g)-+ M'Li(g) + M(g) T/K InK AHi/kJ mol-I 1st run M = Ag 1212 9.555 - 96.7 M' = Au 1292 8.922 - 96.7 1330 9.446 - 105.0 1369 9.522 - 109.2 1394 9.237 - 107.5 average - 103.0+ 5.9 2nd run 1356 9.710 - 110.0 1386 9.463 - 109.6 1398 9.287 - 108.8 1400 9.127 - 107.1 1421 9.252 - 110.0 1440 8.92 I - 107.5 average - 108.8+ 1.3 average from both runs - 106.2k4.9 M = Ag, M' = Cu M = Au, M' = Cu 1398 1.014 - 13.4 1400 0.598 - 8.8 1421 1.417 - 18.4 1440 1.097 - 15.1 average - 13.9+ 4.0 1398 - 8.273 95.0 1400 - 8.529 98.3 1421 - 7.835 91.6 1440 - 7.824 92.4 average 94.3+ 3.0 by analogy with liydrides and other compounds of Cu, Ag and Au.1° Table 4 lists the molecular parameters and the free energy functions for the various molecules. The good mutual agreement of results obtained in two different runs (table 1) shows that attainment of equilibrium does not depend on the composition of the condensed phase.Table 5 summarizes the measured enthalpy changes of the various reactions and the derived dissociation energies of the CuLi, AgLi and AuLi molecules.The TABLE 4.-MOLECULAR PARAMETERS AND FREE-ENERGY FUNCTIONS OF THE GASEOUS MOLECULES AuLi, AgLi, CuLi, Cu2 AND Ag, molecule AuLi AgLi CuLi Cuz Ag2 vibrational wavenumber/crir' 528.1" 499.0n 527.3" 264.56b 192.4c interatomic distance/A 2.57d 2.57d 2.40" 2.21gb 2.6gC TJK - ( GT- tf ,-JT)/Jrnol- K - 1 200 1300 1400 1 500 253.4 246.4 238.5 256.8 273.3 256.2 249.2 241.3 259.7 276.2 258.9 251.8 243.9 262.4 278.9 261.3 254.3 246.4 264.9 281.4 fl calculated according the method of Gordy [ref. ( 8 ) ] ; b ref. (1) ; C ref. (10) ; d calculated from Pauling radii.A . NEUBERT AND K . F . ZMBOV 2223 TABLE 5.-sUMMARY OF THE THIRD-LAW ENTHALPIES AND DISSOCIATION ENERGIES molecule reaction AHG/kJ mol-' ADg/kJ mol- AgLi(g) AgLW -+ + L W 175.5k3.4 175.5k 3.4 AgLi(g)+ Ag(g)+&z(g)+ LKg) 14.3k3.2 171.6+ 9.2 average 173.6f 6.3 CuLi(g) CuLi(g)-+ Cu(g)+ Li(g) 190.2+ 3.4 190.2+ 3.4 1 87.5 k 1 0.3 average 189.3+ 8.8 AuLi(g) AuLi(g)-+Au(g)+ Li(g) 281.8k2.4 281.8+ 2.4 AuLi(g)+ Ag(g)+Au(g)+AgLi(g) 106.2k4.9 279.8+ 11.2 average 280.8+ 6.5 CuLi(g)+ Cu(g)-+Cu2(g)+ Li(g) -0.3k4.5 190.1+12.6 CuLi(g) + Ag(g) -+ AgLi(g) + Cu(g) 1 3.9 k 4.0 dissociation energies of CuLi and AgLi obtained from the decomposition reactions (1) are in very good agreement with the values derived from the enthalpy changes of the reactions (2) when the known values Dg(Cu,) = 190.4k9.2 kJ mol-1 D:(Ag,) = 157.3 k9.2 kJ mol-1 are used.This justifies the calibration procedure used.Adopting the value D:(AgLi) = 173.6 kJ mol-l as a reference, the dissociation energies of CuLi and AuLi derived from the exchange reactions (3) agree well with the values from the reactions (1). While there are no other data on the stabilities of the molecules CuLi, AgLi and AuLi, it is interesting to compare the measured dissociation energies with those calculated according to the Pauling electronegativity concept. The dissociation energy of a compound AB is usually related to those of the dimers A, and B2, and the electronegativities XA and XB by Pauling's formula : Using the electronegativities calculated by Gordy and Thomas l2 XA, = 2.3, XA, = 1.8 and Xcu = 1.8 and XLi = 0.95, one obtains values of 218, 200.4 and 338.5 kJ mol-1 for the dissociation energies of CuLi, AgLi and AuLi, respectively. These values are considerably higher than the measured ones. Much better agreement with the experimental values is obtained, however, if 0.2 is subtracted from the electronegativities of Cu, Ag and Au used in the calculations. D(AB) = 3[D(A,) + D(B,)] + 96.2(XA - X,), kJ mol-I. ( 5 ) The authors thank Dr. D. Guggi for the preparation of lithium oxide. J. Drowart, in Phase Stability in Metals and Alloys, ed. P. S . Rudman, J. Stringer and R. I. Jaffee (McGraw Hill, New York, 1967), p. 305. K. A. Gingerich, J. Cryst. Growth, 1971, 9, 31. L. Pauling, The Nature of the Chemical Bond (Cornell U. P., Ithaca, New York, 3rd edn., 1960). H. Michael, A. Neubert and H. Nickel, Int. J. Appl. Rad. Isotopes, 1974, 25, 183. A. Neubert and K. F. Zmbov, High Temp. Sci., to be published. J. B. Mann, J. Chem. Phys., 1967, 46, 1646. D. R. Stull and G. C. Sinke, Thermodynamic Properties of the Elements (Adv. Chem. Series), (Amer. Chem. SOC., Washington, D.C., 1956) Vol. 18. W. Gordy, J. Chem. Phys., 1946, 14, 305. K. M. Guggenheimer, Proc. Phys. SOC., 1946,58,456. (Academic Press, New York, 1967), Vol. 1, p. 7. lo C. J. Cheetham and R. F. Barrow, Aduances in High Temperature Chemistry, ed. L. Eyring I ' M. Ackermann, F. E. Stafford and J. Drowart, J. Chem. Phys., 1960, 33, 1784. l 2 W. Gordy and W. J. 0. Thomas, J. Chern. Phys., 1956, 24, 439.

ISSN:0300-9599    

DOI:10.1039/F19747002219

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Heat Capacity of Nickel and Cobalt Tellurides BY KENNETH C . MILLS Division of Chemical Standards, National Physical Laboratory, Teddington, Middlesex TW 1 1 OLW Received 3rd April, 1974 Differential scanning calorimetry has been used to measure the heat capacities between 200 and 800 K of " Ni,Tez ", five compositions of the 8 Ni-Te phase, four compositions of the /3 Co-Te phase and two compositions of the y CoTez+x phase. Thermodynamic properties are given for the various phases. The recent interest 1 - 1 1 in the nickel and cobalt tellurides originates from the fact that these non-stoichiometric compounds exist over large ranges of homogeneity and undergo some interesting structural changes. Heat capacity data at high tempera- tures are needed for the cobalt and nickel tellurides to derive enthalpy and entropy values from extant Gibbs energy data and to discover if the structural changes are accompanied by changes in heat capacity.Nickel forms three types of tellurides, the P-phase (Ni3-xTe2), the y-phase (NiTe0.77) and the &phase stable between Nio -478-9 Te, - 5 2 2 (NiTe, .09) and Ni, .333Te0 -667 (NiTe,). Cobalt forms two types of tellurides, the P-phase stable between Coo .455Te0.545 (CoTe, .,) and Co0.357Teo.643 (CoTeIn8), and the y-phase, stable between Co0.333Te0.667 (CoTe,) and Co0.304Te0.696 (CoTe,. 12). In this investigation heat capacities have been determined between 200 and 800K for Ni3Te,, for five compositions of the S Ni-Te phase, and four compositions of the p Co-Te phase and for two compositions of the y Co-Te phase.As the y Ni-Te phase has not yet been obtained in a pure state, no thermodynamic data are presented here for this phase. EXPERIMENTAL MATERIALS The Ni-Te alloys and the Co-Te alloys were donated by Professor Komarek and co- workers of the University of Vienna. The sample-preparation procedure described below is that employed by Professor Komarek and his co-workers to prepare fully-annealed Ni-Te and Co-Te samples, which were free from oxygen contaminati0n.t The samples were prepared from tellurium (purity 99.99 %) and nickel sheet (purity 99.999 %) or cobalt sheet (purity 99.99 %). Weighed amounts of the elements were mixed and transferred to silica capsules which were evacuated and heated to 873 K for 24 h. The temperature of the sample was increased to 1223 K over a period of 48 h and then rapidly increased to temperatures above the liquidus temperature (approximately 1370 K) and maintained at this temperature for 24 h.Samples of the P-phase, Ni0.599Te0.401, were formed by slowly cooling the melt to 1173 K, rapidly quenching to 273 K, powdering, annealing under vacuum at 973 K for two weeks and then quenching to 273 K. Samples of the 6 Ni-Te phase and the p Co-Te phase were formed by slowly cooling to 1123 K and quenching to room temperature. These samples i- Although oxygen analyses were not carried out on the samples, great precautions were taken at every stage of the procedure to avoid any contamination with oxygen. 2224K. C. MILLS 2225 were powdered and annealed under vacuum for two weeks at 1023 K, except for the Ni0.357Te0.643 sample which was annealed for three weeks at 723 K.The samples of the y-CoTe2+, phase were formed by cooling at a rate of 1.2 K h-I to 973 K and maintaining this temperature for 24 h. They were then cooled to 773 K and quenched to room tempera- ture. The samples, Co0.33Te0.67 and Coo.32Teo.68, were powdered and anneared in vacuum for 2 weeks at 973 and 873 K, respectively, before being quenched to room temperature. This annealing procedure was then repeated for both samples. All annealed samples were then checked by X-ray analysis, the results of which showed no evidence of ordering of the vacancies in any of the samples. MEASUREMENTS The measurements of C, and ( H T - H ~ ~ ~ ) were obtained using a model 1B Perkin Elmer differential scanning calorimeter (d.s.c.).The output signal from the d.s.c. was measured with a digital voltmeter and recorded on paper tape. Readings were started at a constant temperature, Tl, to define an isothermal baseline. The temperature was then raised at a constant rate to T2 (usually 30 K above TI) where readings were continued to produce an isothermal baseline for T2. The experiment was run with the calorimeter (i) empty (ii) filled with an inert calibrant (Calorimetry Conference synthetic sapphire), (iii) filled with the material under investigation. The treatment of the data has been described by Richardson l 2 and by Mills and Richard- son.13 The primary aim of this treatment is to produce " full minus empty " curves for the calibrant and for the sample by subtracting the curve for the empty calorimeter from each of the curves for the filled calorimeter.For the " full minus empty " curves of both cali- brant and sample, the areas under the curves between TI and T2 are proportional to the enthalpy change ( H T ~ - H T ~ ) . Accurately known values of ( H T ~ - H T ~ ) for the calibrant permit calculation of the proportionality constant which was then applied to the calculation of the mean heat capacity of the sample, ( H T ~ - H T ~ ) / ( T ~ - TI). In previous investigations l 3 it has been established that mean C, values determined in this way have an accuracy of 1 %. As the ordinate of the " full minus empty " curve for a material is proportional to the heat capacity at any given temperature, then C, values may be determined at '' point temperatures ".However, C, values obtained using this dynamic technique are of lower accuracy but are of particurar use in a transformation region. RESULTS AND DISCUSSION In this paper, thermodynamic properties are given for one mole of Ni,Te,_, or Co,Te,,,, as appropriate, where x < 1. /? Ni-Te PHASE (" Ni,Te, ") The heat capacities of Ni0~599Te0~401 measured in this investigation and shown in fig. 1 are in excellent agreement with Cp values reported recently by Grsnvold et aL7 for Ni0.6Te0.4. Two transitions were observed. The first transition is associated with the transformation of a rnonoclinic structure into an orthorhombic (ricardite- type) structure. The transition temperature, 492.5 K, was obtained using the " dyna- mic technique " and is not an equilibrium value like that reported by Grsnvold et aZ.,7 viz.490.6 K. The value of AH,,,,, = 340560 J mol-', obtained from a plot of (HF - HZg8) against temperature, is lower than the value reported by Grsnvold et aZ.,' AH,,,,, = 384 J mol-l. The slight differences in the AHtrans values can be attributed to slight differences in the stoichiometry of the two samples, for Grsnvold et ai.' have noted that AHtrans values are markedly dependent upon composition. The second transition is a 1-type transition and is associated with the transforma- tion of the orthorhombic (ricardite-type) structure into a tetragonal structure. The peak in the C,(T) curve obtained in this investigation by the " dynamic technique " occurred at 613.9 K compared with the " equilibrium " transition temperature,Cp OF Ni AND Co TELLURIDES 0 ' 1 I I I 1 201 1 1 I 1 I I 2 0 0 3 0 0 400 5 0 0 600 703 800 TIK FIG.1.-The temperature dependence of Cp for the 8-phase, Nio.599Teo.401 ; a, this investigation, average C' values ; 0, this investigation, Cp values using " dynamic technique " ; x , from ref. (7). 609.4 K, recorded by Grnrnvold et aL7 The AH,,,,, of a 1-type transition can only be calculated by estimating non-transitional Cp values for the material ; using the esti- mated values due to Grarnvold et al.,7 the values AH,,,,, = 548 J mol-1 and AS,,,,, = 0.900 J K-1 mol-1 were obtained, compared with the values reported by Grarnvold et al.,7 viz. AHt,,,, = 664 J mol-1 and AS,,,,, = 1.16 J K-1 mol-I. The values of AH,,,,, obtained by Grnrnvold et aZ.7 and in this investigation are considerably higher than the value, AH,,,,, = 8 J mol-1 reported by Ste~e1s.l~ Grarnvold et aL7 have TIK 298.15 350 400 450 492.5 a 492.5 a 500 550 600 613 a 628 650 700 750 TABLE 1 .-THERMODYNAMIC PROPERTIES OF Nio.599Te0.40 1 (S;--s;98)/ Cp/J K-l mol-1 (H$-FZ&)/J mol-I J K-1 mol-* 25.08 0 0 26.07 1329 4.1 1 27.07 2 657 7.66 28.10 4 037 10.90 31.00 5 250 13.48 30.70 30.58 31.05 34.12 39.00 31.41 31.53 31.82 32.10 5 590 5 820 7 350 8 968 9 465 9 972 10 661 12 245 13 843 14.17 14.63 17.55 20.36 21.18 22.00 23.08 25.42 27.63 - CG& H ; ~ S ) T - ~ I / J K-' rno1-l 40.0 40.3 41 .O 41.9 42.8 42.8 43 .O 44.2 45.4 45.8 46.1 46.7 47.9 49.2 a Temperature of transition obtained with " dynamic technique " i.e.not an equilibrium value of the temperature.K. C. MILLS 2227 shown by an analysis of the structural changes associated with the transformation that theoretically AStrans should have a value around 0.2 R In 2 or 1.15 J K-I mol-l. Thermodynamic properties listed in table 1 for Nio. 99Teo -40 1 were derived from the experimental Cp and enthalpy data and an estimated standard entropy at 298 K, s;98 = 40 & 3 J K-l mo1-l. An additional digit beyond those significant is given in tables 1 to 4 to facilitate interpolation. 6 Ni-Te PHASE The &phase has been reported by Ettenberg et al.’ to exist between Nio .478Te0 -522 (NiTe, .09) and Nio .333Te0 -667 (NiTe,), the nickel-rich compositions having a NiAs- type, hexagonal structure and the tellurium-rich compositions having a Cd(OH),-type hexagonal structure.Carbonara and Hoch reported galvanic cell data from which FIG. 2.--The temperature dependence of C, for the 6 Ni-Te phase. Nio.465Te0.535; x , this investigation ; V , from ref. (6). Ni0.357Te0.643 : --- , @, this investigation. they concluded that at 670 K the NiAs-type structure transformed into the Cd(OH),- type structure when the tellurium content exceeded NiTe, .33. Carbonara and Hoch reported that their experiments provided no evidence for a two-phase region? where both structures could coexist. The heat capacities between 200 and 800 K were measured for the following &phase NiO .465Te0 .535 “iTe1 .1S) ; NiO .435Te0 . 5 6 5 (NiTel .3) ; NiO .417Te0.583 (NiTe1.4) ; Ni0.385Te0.615 (NiTe1.6) ; Ni0.357Te0.643 (NiTel.8)- The Cp(T) plots for Ni0.46sTeo.535 and Ni0.3~7Te0.643 are given in fig.2; the C,(T) relationships for the other compositions lie within these two curves. Westrum et aL6 measured heat capacities between 5 and 350 K for three &phase alloy compositions correspond- ing to NiTe, . ,, NiTe, . and NiTe2. The present Cp values for the range (200-300 K) are in good agreement with the values reported by Westrum et aL6 The high-temp- This term is misleading as it could lead one to conclude that a rise in the C,(T) curve would be expected at 670 K in an alloy of composition of NiTel.33, this is not so. t Carbonara and Hoch refer to this structural transition as being “ second order ”.2228 Cp OF Ni AND Co TELLURIDES erature molar Cp values of the nickel-rich &phase alloys are 1-2 % higher than the molar Cp values observed for the tellurium-rich alloys; this observation was also noted by Westrum et aL6 for low-temperature Cp measurements.No transitions were observed in the present experiments on the /I-phase Ni-Te alloys. has reported heat capacities for a single composition of the 6 Ni-Te phase, i.e. Ni0.429Te0.571 (" Ni3Te4 "). The heat capacity values obtained in these investigations for Nio.435Teo.5 6 5 (NiTe, .30) are in excellent agreement with those reported by Gramvold. However, Grarnvold noted that the heat capacities of " Ni3Te4 " were " enhanced " by up to 2 % in the temperature range 350 to 500 K and suggested that this could be caused by the disappearance of a minor configurational order.The heat capacities of NiTe,., between 350 and 500 K which were obtained in the present investigation were " enhanced " by 1 % ; however, as the experimental uncertainty associated with each individual heat capacity is also 1 %, the heat capacity data were treated to give a smooth CP(T) relationship for the entire temperature range (200-750 K). Gramvold TABLE Z.-THERMODYNAMIC PROPERTIES OF Nio.465Te0.535 AND Nio.35,Teom 643 [-(G& c p / (H+H+8)/ (s&si98)/ H;98)P1l/ c,! T / K J K-I mol-I J mol- JK-' mol-I J K-1 mol-1 J K-I mol- Ni0.465TeO. 5 3 5 298 25.73 0 0 40.1 25.37 350 26.40 1355 4.19 40.4 26.13 400 26.95 2 689 7.75 41.1 26.73 450 27.45 4049 10.96 42.1 27.25 500 27.92 5434 13.87 43.1 27.73 550 28.37 6 841 16.56 44.2 28.17 600 28.81 8 271 19.04 45.4 28.60 650 29.23 9 722 21.37 46.5 29.00 700 29.65 11 194 23.55 47.7 29.40 750 30.06 12 687 25.61 48.8 29.79 [-&G&- I(H&ffi;8)/ (sg-s2098:/ H298)T-'I/ - J mol- J K-I rno1-I J K-' mol-1 Ni0.357Te0.643 0 0 40.1 1340 4.14 40.4 2 662 7.67 41.1 4012 10.85 42.0 5 386 13.75 43.1 6784 16.41 44.2 8 203 18.88 45.3 9643 21.19 46.4 11 103 23.35 47.6 12 583 25.39 48.7 The absence of a well-defined transition in the 6 Ni-Te alloys indicates that there is very little ordering of the vacancies in these samples.Further evidence of this may be found in the low interaction energies between vacancies reported 2 s for 6 Ni-Te alloys and from the X-ray studies which showed no evidence of ordering in these samples. Tilden l5 has reported (HG-H&8) values for " NiTe " and these values were recalculated by Kelley l6 to give a Cp(T) relationship for " NiTe ".Although this composition lies outside the stability range of the &phase, the reported Cp(T) relation- ship yields molar Cp values which are within 2 % of those recorded here for the &phase. Thermodynamic properties for two 6-phase alloys, Ni0.465Te0.53 (NiTe,. , 5 ) and Ni, .357Te0.643 (NiTe,.,) are given in table 2. The Sg98 values were obtained by comparison with the Sz98 values Iisted by Westrum et al.6 for the &phase. DCo-Te PHASE Geffken et aL5 have reported that this phase exists between Coo.455Te0.545 (CoTe, .2) and C O ~ . ~ ~ ~ T ~ ~ . ~ ~ ~ (CoTe,.,), the cobalt-rich compositions having a NiAs-type, hexagonal structure and the tellurium-rich compositions having a Cd(OH),- type, hexagonal structure.Heat capacities were measured between 200 and 800 K for four P-phase alloys of the following composition, Co0.435Te0.5 6 5 (CoTel .3) ;K. C . MILLS 2229 Cp(T) relationships for Co0.435Te0,565 and Coo.3ssTeo.615 are shown in fig. 3. Although the Cp measurements for this phase show more experimental scatter than C00.417Te0.583 (CoTel.4) ; c00.4Te0.6 (CoTe1.5); C00.385Te0.615 (CoTel.6). The T/K FIG. 3.-The temperature dependence of C, for the /3 Co-Te phase; Coo.435Teo.565, ; Co0.385Te0.615, - other Cp values reported here, all four P-phase alloys had identical Cp values for a given temperature within the experimental uncertainty of & 1 %. No transitions were observed in these alloys suggesting that the vacancies in these samples are not TABLE 3.-THERMODYNAMIC PROPERTIES OF THE p Co-Te PHASE (co0.43 5TeO.5 6 5 TO COO. 3 85TeCI. 6 15) 298 350 400 450 500 550 600 650 700 750 25.13 25.77 26.38 26.99 27.61 28.22 28.83 29.44 30.06 30.67 0 1323 2 627 3 961 5 326 6 721 8 148 9 604 11 092 12 610 0 4.09 7.57 10.72 13.59 16.25 18.73 21.06 23.27 25.36 40.0 40.3 41 .o 41.9 42.9 44.0 45.2 46.3 47.4 48.6 ordered to any appreciable extent, although a transition at temperatures above 750 K cannot be ruled out. However X-ray studies revealed no evidence for the ordering of vacancies in these samples. Molar heat capacity values for any given temperature2230 Cp OF Ni AND Co TELLURIDES are similar to those obtained for 6 phase Ni-Te alloys. The thermodynamic proper- ties for B Co-Te listed in table 3 were calculated using an estimated value, Sgg8 = 40+2 J K-' mol-' which was obtained by comparison with reported Sig8 values for the Ni-Te phase and from Latimer additivity contributions. 1 y Co-Te PHASE (CoTe,+J Geffken et aL5 have reported that the y-phase is stable from COo.333Teo.66, (CoTe,) to Co0~304Te0~,96 (CoTe,.,,) and has a marcasite-type structure.Heat capacities have been measured between 200 and 750 K for two alloys ; CO,.,,T~~.~, (CoTe,.,,) and Co0.32Te0.68 (CoTe,.,,) and are shown in fig. 4. No transitions were observed in these alloys and for a given temperature the molar Cp values appear to be independent of composition within the limits of experimental uncertainty. Tellurium 30 29t 0 1 I I I i 1 1 300 400 500 600 70 0 800 x ; TIK Co0.32Te0.68, e.FIG. 4.-The temperature dependence of C, for the y Co-Te phase ; TABLE 4.-THERMODYNAMIC PROPERTIES OF THE (COO. 3 3TeO. 6 7 TO COO. 3 2TeO. 6 8 ) Co-Te PHASE (H$- Hz;8)/ (&-S;W)/ [-(G$-EZ;98)T-']/ T/K Cp/J K-' mol-l J mol- J K-I mol-' J K-I mol-I 298 350 400 450 500 550 600 650 700 750 24.94 25.63 26.14 26.56 26.93 27.26 27.57 27.86 28.14 28.42 0 1315 2 610 3 927 5 265 6 619 7 990 9 376 10 776 12 190 0 4.07 7.52 10.63 13.45 16.03 18.41 20.63 22.71 24.66 43.0 43.3 44.0 44.9 45.9 47.0 48.1 49.2 50.3 51.4K. C . MILLS 223 1 was vaporized from the Co0.32Te0.68 sample for temperatures above 700 K and this probably caused the high Cp values recorded for this material above 700 K. The thermodynamic properties of CO,.~,T~,. 67 listed in table 4 were calculated using a value of si98 = 43+3 J K-' mol-1 which was estimated by comparison with the reported Si98 values for the nickel tellurides and also from Latimer additivity contributions.I thank Professor K. Komarek for the gift of the samples, and Mr. D. G. Nunn for experimental assistance. I am grateful to Professor M. Hoch, Professor K. Komarek and Dr. M. J. Richardson for useful discussions. J. Barstad, F. Grernvold, E. Rsst and E. Vestersjs, Actu Chem. Scund., 1966, 20, 2865. M. Ettenberg, K. L. Komarek and E. Miller, J. Solid State Chem., 1970, 1, 583. K. 0. Klepp and K. L. Komarek, Monatsh., 1972,103,934. H. Haraldsen, F. Grsnvold and T. Hurlen, 2. anorg. Chem., 1956,283, 143. R. M. Geffken, K. L. Komarek and E. Miller, J. Solid State Chem., 1972, 4, 153. E. F. Westrum, Jr., C. Chou, R. E. Macho1 and F. Grsnvold, J. Chem. Phys., 1958, 28, 497. ' F. Grsnvold, N. J. Kveseth and A. Sveen, J. Chem. Thermodynamics, 1972, 4, 337. * R. S. Carbonara and M. Hoch, Monutsch., 1972, 103,695. lo S. M. Ariya, E. M. Kolbina and M. S . Apurina, Zhur. neorg. Khim., 1957, 2, 23. l 2 M. J. Richardson, J. Polymer Sci. C, 1972,38, 251. l3 K. C. Mills and M. J. Richardson, Thermochim. Acta, 1973, 6,427. l4 A. L. N. Stevels, Thesis (University of Groningen, 1969); see also Philrips Res. Rep. Suppl., 1969, No. 9. l 5 W. A. Tilden, Trans. Royal SOC. A, 1904,203, 139. K. K. Kelley, Bull. U.S. Bur. Mines, 1960, 584. 0. B. Matlasevich and V. A. Geiderikh, Zhur. fiz. Khim., 1973, 47, 277. F. Grsnvold, J. Chem. Thermodynamics, 1973, 5, 545.

ISSN:0300-9599    

DOI:10.1039/F19747002224

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Manganese(II1) and its Hydroxo- and Chloro-complexes in Aqueous Perchloric Acid : Comparison with similar Transit ion-met al( 111) Complexes BY DAVID R. ROSSEINSKY,* MICHAEL J. NIcoL,? KENNETH KITE Department of Chemistry, The University, Exeter EX4 4QD AND R. JOHN HILL $ Received 10th April, I974 At 25°C the formation constant of MnCI2+ is found by spectrophotometry to be 13.2k0.9 dm3 mol-’ at ionic strength 3.26 mol dm-3 ; for MnCIi the value is 1.1 k0.7 dm3 mol-’. Increase in the number of chloride ions in complexes results in longer wavelengths for the corresponding absorption maxima. In the absence of chloride the hydrolysis constant of MnIII at ionic strength 5.6 rnol dm-3 is found from voltammetry and potentiometry to be 1.05 f0.26 mol dm-3. Aged manganese(u1) is found to be 15-25 % polymeric, from both kinetic and e.m.f.measurements. Comparison of forma- tion constants for halogeno- and hydroxo-complexes of M3+ (first transition series) shows that a combination of charge-transfer, ligand-field and coulomb interactions underlies the observed se- quences ; the dipole moment of OH- is also a factor. The extent of interest in halide (X-) and hydroxo complexes of the trivalent cations M3+ of the first-row transition metals is evident from the growing number of measurements of stability constants K collated or being Solutions in quite concentrated HC104 have often to be used ; however, at ionic strengths I > 0.5 mol dm-3 ionic activity coefficients change but slowly with composition, and for our purposes, comparison of log K values in this range, such high electrolyte concentra- tions present few problems. Some K values are less well founded than most.That for Fe12+ cannot be obtained in HC104, since oxidation of I- occurs by a mechanism which does not give a stability constant from the rate e q ~ a t i o n . ~ For MnC12+ an estimate, from kinetics, of 8.9 dm3 mol-’ in 2 rnol dm-3 HC104 has been recalculated as 13.5 mol dm-3. This revision may well reflect only the uncertainty of the estimate. spectrophotometric value of the hydrolysis constant Khx4 mol dm-3 in I = 6 mol dm-3, was re-measured 7 a as 0.93 mol dm-3 in ionic strength 4 mol dm-3, and 0.96 mol dm-3 (at 23°C),7b Values of Kfor both of these Mn”’ complexes clearly need to be redetermined, by independent techniques if possible, and in this paper we report such measurements, first of Kh by electrochemical methods and secondly of K,, for MnC12+ by spectrophotometry.Fresh MdJ1 differs from aged MnIII in that with time, a fraction of the fresh sample forms a polymeric species which reacts slowly in some electron transfer reactions.8 It is possible to use e.m.f. data 9* l 3 to substantiate a kinetic estimate of the fraction polymerised, which has some effect on the K values. Finally we compare K values for most of the MX2+ species, and elicit the major molecular factors governing the values observed. For MnOH2+ formation the original National Institute of Metallurgy, Johannesburg ; $ Dept. of Physical Chemistry, The University, Leeds. 2232D . R . ROSSEINSKY, M . J . NICOL, K .KITE AND R . J . H I L L 2233 EXPERIMENTAL The voltammetric cell for measuring the variation of exchange current, and of e.m.f., with [H+] was used in the determination of transfer coefficient a and rate constant in 3 mol dm-3 HClO, for the electrode reaction Mnrn+ept+Mn2+. The ionic strength was now made 5.6 mol dm-3 in HC104+ NaClO, so as to accommodate a sufficiently large change of [H+], from the minimum commensurate with the stability of Mnm, 0.75moldm-3, to 5.3 rnol dmV3. The solution was made 0.1 mol dm-3 in Mn(C104)2 to suppress the dis- proportionation of M P , the concentration of which was kept at 1.89 x lo-, mol dmd3 throughout. The MnIIr, at near this concentration, was prepared at room temperature by the reaction 8y 4 MnU+ MnVII, and aged for >36 h, at which time after a prolonged period of decrease the absorbance at 470nm remained constant.Mnrrl was standardised by amperometric titration with iron(@. To determine the MnC12+ stability constant at ionic strength 3.26 mol dm-3 (a value chosen in connection with other work 8, twenty four solutions of 4 x lo-, mol dnr3 Mnnr, 3 mol dm-3 HClO4 and 0.05 mol dm-3 Mn(C104)2 containing 0.01-0.2 mol dm-3 C1-, were examined at 25.0”C in 0.2-4cm cells being Unicam SP500 spectrophotometer over the wavelength range 230-400nm, where neither Mnn nor Cl- absorb. Enhancements of absorbance occurred, which were checked with doubled [MnIn] at the two extreme [Cl-] values. For both [Cl-] values the enhancements were doubled, indicating that the absorbing complex(es) were monatomic in MnlI1.Further elaboration depended on assumptions regarding Kh. RESULTS AND DISCUSSION HYDROXO-COMPLEX The value of the exchange current io and the e.m.f. E at 25°C are given in table 1 for five different solutions at compositions differing only in [Hf] and “a+], with [H+] + “a+] constant. Notably, the transfer coefficient a is identical for both acidities, strongly implying constancy of electroactive specie^.^ The relationship between io at 5.3 mol dm-3 H+ and at 0.75 mol dm-3 H+ is log~i~(5.3)/i0(0.75)) = (1 -or) log{5.3[(Kh/mol dm-3) + 0.75]/ 0.75[(Kh/mol + 5.311. TABLE 1 .-VOLTAMMETRY AND POTENTIOMETRY ON MnrI1 SOLUTIONS AT TWO DIFFERENT [Mnrrl] = 1 . 8 9 ~ lo-, mol dm-3, [Mnn] = 0.1 mol dm-3, I = 5.60 mol dm-3, 25°C 0.75 1.008 6.993 0.249 1.006 6.998 0.255 1.010 6.976 0.257 1.009 6.994 0.256 1.008 6.957 0.248 ACIDITIES [H+]/mol dm-3 E D - log(fo/A) U mean : 1.008k 0.002 6.977+ 0.016 0.253 If: 0.004 [0.3657Ia 5.30 1.052 6.794 0.251 1.056 6.73 1 0.248 1.057 6.781 0.250 1.055 6.745 0.253 1.056 6.777 0.258 mean : 1.055+0.001 6.767k0.021 0.252a0.003 [0.2877Ia a E for HzlHC1O4, NaC104, NaCllHg2C121Hg ; 0.01 mol dm-3 NaCl.2234 FORMATION CONSTANTS O F MnrIr SPECIES This expression follows irrespective of whether Mn3' or MnOH2+ is assumed to be reduced, as it is kinetically impossible to identify the electroactive species. Indirect arguments from the mechanism invoked to explain the low value of a suggest that it is Mn3+.From table 1 the left side of the equation is 0.210+0.037, whence the value of Kh is 0.95k0.35 mol dm-3.The E values were combined with those for a cell H21HC104, NaClO,(HClO,, NaClO,, NaClIHg,Cl,IHg ([NaCl] small), to give at the two [H+] employed, E' values for the cell, H,(HC104, NaClO,(HClO,, NaClO,, Mn(ClO,),, Mn(C10,), IPt with I = 5.6 mol d ~ n - ~ throughout ([Mn"+] small). Hence (E')5.3 -(E')0.75 = RT/F ln([(K,/mol dm-3) +0.75]/[(Kh/mol dm-3) + 5.301) which was 1.374 0.002 - (1.342+0.001) V or -32Ifr3 mV, giving Kh = l.lk0.20 mol dm-3. Preliminary measurements were carried out with calomel electrodes having electrolyte which differed in composition from that of the Mn3+, Mn2+ and hydrogen electrodes. The liquid junctions introduced slightly irreproducible error ; neverthe- less, the current against voltage curves (with ct 0.249 +_ 0.005 and 0.255 f 0.004 at 0.75 and 5.3 mol dm-3 H+) gave a Kh of 1.05-&0.30 mol dm-3, and from E' differences, - 31 1 2 mV, a K,, of 1.1 kO.20 mol dm-3.Since the additional uncertainty is only slight, we include all these values to obtain a mean of Kh = I .05 p0.2, mol dm-3. While a different ratio of activity coefficients is implicitly assumed constant in going from io to E to calculate K,, the consequence is clearly within the experimental error of either method. The agreement of our value with the 0.93 obtained in a predomin- antly Mn(C104)2 medium at I = 4 mol dm-3 is satisfactory considering the difficulties of electrometry with this reactive ion, and the problems of extrapolation to zero time (to correct for polymer formation) involved in the spectroph~tometry.~ We have hitherto considered MnI" monomeric : taking account of the pdymeric fraction (below) shows that the high side of the quoted limits should be emphasized for the truly mononuclear equilibria.CHLORO-COMPLEXES By straightforward use of Beer's law and including an appropriate value of Kh, First it was assumed that MnC12+ is the Then these initial K,, values obtained from 230-290 nm data a three stage computation was employed. only chloro-complex. TABLE 2.-vALUES OF FOR Mn3++ C1-+MnCl2I- AT VARIOUS WAVELENGTHS A/nm Kcl/drn3 mol- i/nm Kc1/dm3 rnoi-' 230 12.9 255 12.5 235 15.8 265 14.7 240 12.2 270 12.4 245 12.6 275 12.7 250 12.9 mean 13.2+ 0.9 Kh = 1.0 mol dm-3 assumed were used to estimate K2,, for MnCl2++C1-+MnC1l, which is invoked to account for the higher-wavelength absorption.This gave a small K2c1 and a large E(MnC1:) which justify the original assumptions and support the actual values of K,, initially obtained (table 2). Finally a complete Beer's law expression for the total absorbance gave better values of K2c1, see table 3. The algebra, straightforward but cumbersome,D . R. ROSSEINSKY, M . J . NICOL, K . KITE AND R. J . HILL 2235 is detailed elsewhere,'O as are all individual measurements. Because the value of K,, depends on the value assumed for Kh, the calculation was repeated for a range of Kh, which established (table 4) that the dependence is not oversensitive, and is small enough to ensure that any further uncertainty introduced is smaller than that already inherent (table 2) in the parameter fitting.The Kh range almost certainly encompasses the true value for this medium. TABLE 3.-APPROXIMATE VALUES OF K2c1 FOR MnCI2++ Cl-+MnClzf AT VARIOUS WAVE- LENGTHS L/nm K 4 d m 3 mcl-I 300 0.8 320 0.3 340 1.6 360 0.5 380 2 . 3 mean 1.1 k0.7 dm3 mol-', with KCI = 13.2 dm3 mol-I The spectra observed and calculated are shown in fig. 1. If we add the longest in 10 mol dm-3 HCl, which presumably indicates wavelength maximum observed an even higher complex, the following sequence of absorbance maxima is seen : species Mn3+ MnC12+ MnCli MnCl,,(3-n)t 210 240 300 550. It is thus possible that the absorption bands are due to ligand-to-metal ion charge transfer. Our spectrophotometry results agree satisfactorily with earlier qualitative observations.I2 Again as with MnOH2+ the upper limits of K,, (13.2k0.9 dm-3 TABLE 4.-DEPENDENCE OF DERIVED Kc1 ON ASSUMED VALUES OF Kh Kh/mol dm-3 Kc1/dm3 mol-* 0.6 12.8 0.93 13.0 1 .o 13.2 1.20 14.0 mol-I) are to be emphasized when the fraction of hydrolytic polymer present is allowed for.It is unlikely that the Z = 2 mol dm-3 value, 13.5 dm3 mol-l is truly coincident with our Z = 3.26 mol dm-3 value of 13.2 dm3 mol-l, especially in view of the variation of the FeC12+ value with Z, 5.0 and 7.8 dm3 mol-l at Z = 2 and 3 mol dm-3 respectively. As we are quite certain of our limits, this conclusion reflects the uncertainty in the indirect kinetic measurement mentioned in the introduction. For Kh and K,, these are about five times larger than is commonly quoted, and they arise from the highly reactive nature of the cation.MnIII reacts, albeit slowly, ca. 1 % per day, with the solvent, and it partially polymerises (below). For Kh the effect being measured, while un- ambiguous, is not so large as to diminish these errors to the ordinary level of para- meter fitting. For K,, the MnC1; equilibrium is a marginal complication, but the effect measured is much larger, so diminishing, relatively, the errors resulting from the nature of Mn'". (CeIv and Co"' present comparable prob1ems.l 6* ') The size of the error limits calls for comment.2236 FORMATION CONSTANTS OF Mnrrr SPECIES I t 4.0 FIG. 1.-A, Calculated (+) and observed (-) values of logarithm of absorbance, A, for 0.15 mol dm-3 C1- solution ; [MnIII] = 4.00 x rnol dm-3, [MnII] = 0.05 mol dm-3, [HC104] = 3 rnol dm-3 250°C ; B, log A for MnIII without C1-, otherwise as A ; C, log(&Mnciz + /dm3 rnol cm-') ; D, log(EMnclf /dm3 mol-' cm-l).MANGANESE(III) IN PERCHLORIC ACID In the chloride catalysed oxidation of TI' by Mnrrl with rnol dm-3 < [MnII'] < mol dm-3, it was found that a multi-step mechanism could explain the obser- vations up to ca. 70 or 80 % consumption of Mn"', but thereafter the rate plots were curved. The plots could be made linear by assuming that about 10-20 % MnlI1 was present as unreactive polymer. There is clear evidence for some hydrolytic polymer- isation in the marked spectral changes occurring in MnIII for more than 24 h after preparation. Therefore in the spectrophotometric Kh determination, readings had to be extrapolated to zero time (see above).Further evidence comes from e.m.f. measurements. All our observations in this and preceding papers have been made on aged Mn"', and our conditional (3 rnol dm-3 HCIO,) standard e.m.f. was found to be 1.53550.003 V, while for fresh Mn"' the value was 1.541 V.I3 If the difference 6+3 mV is attributed to the presence of polymer in the former, the fraction of polymer is 25+ 14 %. Combining the kinetic and the e.m.f. estimated values leads to the conclusion that - 15-25 % of the Mnlrr is polymeric. The precise amount is determined by preparative conditions, since such hydrolytic equilibria are often extremely sluggish. The conditional e.m.f. values quoted here are for Mn"', 3 mol dm-3 HC104, without account of the first hydrolysis. Inclusion of Kh= 1 mol dm-3, as the value appropriate for Z = 3 rnol dm-3, gives as the conditional (3 mol dm-3 HClO,) standard e.m.f.for Mn3+(unhydrolysed) + e = Mn2+ the value 1.559 V calculated from the fresh Mn"' measurement. COMPARISON OF MX2+ FORMATION CONSTANTS OF FIRST TRANSITION SERIES METAL IONS M3+ Values are tabulated in table 5 for perchlorate solutions between 0.5 mol dm-3 and 2 mol dm-3 in ionic strength ; most have I = 1 rnol dm-3, MnOH2+ has 4 mol d~n-~. Hydrolysis constants have been converted for comparative purposes to formationD . R . ROSSEINSKY, M. J . NICOL, K. KKTE AND R. J . HILL 2237 constants by subtraction of log K, at the appropriate ionic strength. Neglecting the only slight irregularities introduced by I variations, we can immediately make two generalisations which are in almost complete accord with earlier views 6* l4 on the bonding in MOH2+ and MF2+.First, the decrease, with only one minor deviation, TABLE 5.-sELECTED VALUES a OF LOGARITHMS OF FORMATION CONSTANTS FOR M3f+ X-*MX2+ IN PERCHLORATE SOLUTION OF IONIC STRENGTH USUALLY b 1 mol dm-3 AT 25°C OH F sc 8.84 6.19 Ti 11.7 - V 11.1 - Cr 9.8 4.36)o.s - Mn 13.7)s 5.63 Fe 11.0 5.06 Co <11.8d - C1 Br I E0(M3+m2+)/V - _ . 3.07)0.5 1.21 0.34)o. 5 - - - 1.29 - - - - 0.26 0.65 -2.67)z - 5.0 C - 0.41 0.95)z - - 1.56 0.56 - 0.25 - 0.77 1.49)l.S - - 1.85 a from ref. (1) unless otherwise indicated ; log(Kx/dm3 mol-') given. b Other ionic strengths given in mol d ~ n - ~ as subscripts. C T. W. Swaddle and G. Guestalla, Znorg. Chem., 1968, 9, 1915. d G. Davies and B.Warnquist, Coord. Chem. Rev., 1970,5, 349. e Ref. (l), and J. K. Rowley and N. Sutin, J. Phys. Chem., 1970, 74, 2043. f Ref. (3). from OH- and F- to I- can be attributed to the decreases in coulomb interaction and in the X- ligand field stabilisation parameter. Very low values probably indicate outer sphere association. Secondly, in the variation with M, considering the Sc, Cr and Fe complexes for which the data are most complete, the Cr values always fall low o - - - - , \ . - 1.5 1.0 - J -0.5 k - 0 2 M - -0.5 I t I I I Ti V C r Mn Fe C o .FIG. 2.-Approximate parallelism of trends in log Kx for MX2+ and E"(M3+y2+). Data from table 5. at 25°C. A, log KOH ; B, log KCI, ; C, E".2238 FORMATION CONSTANTS OF Mn1l1 SPECIES n a plot of log K against the M atomic number, which supports the view that charge transfer interaction is important.This follows from the fact that of the three ,5'"(M3+*2+) values, that for Cr is negative. Mn3+ has the second highest, positive, E" and, again in agreement, the K values fall high relative to the Sc-Fe line. These trends are illustrated in fig. 2. The detailed dependences on ionic properties further involve the effect of replacing the originally co-ordinated OH2 by X-, and the variation of dielectric saturation with M3+-X- separation in the coulomb interaction. These variables apart from charge transfer are amenable to quite exact theoretical treatment, which however we do not pursue here. We note that the earlier l4 coincidence, of F- and OH- complexing dependences on M3+, arose from the use of Latimer's outdated quantities for fluorine reactions, and OH- complexes turn out to be more stable than F- complexes by an amount which cannot be explained solely by easier charge transfer l4 from OH-.(The anion radii are nearly identical.) However, this excess stability is readily understood as arising from the fact that OH- is 02- with an attached H-I, and a large part of the interaction is M3+02-; put alternatively, OH- has a large dipole moment, absent in F-, which enhances M3+-OH- interactions. (A similar enhancement of inter- action arising this time within the cation is found in [NO,CO~~'(NH,),]~+ SO:- ion association, which greatly exceeds that for e.g. Co2+SOi- by virtue of the cationic dipole moment in the former. Further examples are a~ailable,'~ e.g.V02+ cf. Fe2+, where the dipole moment in the V'' cation is evident in relative rate and equilibrium effects .) Stability Constants of Metal Ion Complexes, ed. L. G. Sillen and A. E. Martell (Chem. SOC. London, 1964), and Suppl. I, 1971. D. W. Carlyle and J. H. Espenson, Inorg. Chem., 1969, 8, 575. A. McAuley, M. N. Malik and J. Hill, J. Chem. SOC. A, 1970, 2641. G . S. Laurence and K. J. Ellis, J.C.S. Dalton, 1972, 2229. G. Davies and K. Kustin, Znorg. Chem., 1969, 8, 1196. H. Diebler and N. Sutin, J. Phys. Chem., 1964, 68, 174. (4 C. F. Wells and G. Davies, J. Chem. SOC. A, 1967, 1858 ; (4 V. B. Goncharik, L. P. Tikhon- ova and K. B. Yatsimirskii, Russ. J. Inorg. Chem., 1973, 18, 658. D. R. Rosseinsky and R. J. Hill, J.C.S. Dalton, 1972, 715.D. R. Rosseinsky and R. J. Hill, J.C.S. Faraday I, 1974, 70, 1140. l o R. J. Hill, Thesis (Exeter, 1971). l 1 J. A. Ibers and N. Davidson, J. Amer. Chem. SOC., 1950, 72, 4744. l 2 C. F. Wells, D. Mays and C. Barnes, J. Znorg. Nuclear Chem., 1968, 30, 1341. l 3 L. Ciavatta and M. Grimaldi, J. Inorg. Nuclear Chem., 1969, 31, 3071. l 4 D. R. Rosseinsky, Nature, 1967, 216, 791. l 5 D. R. Rosseinsky, Ann. Rep. Chem. SOC. A , 1971, 95 ; Chem. Rev., 1972, 72, 220. l 6 M. G. Adamson, F. S. Dainton and P. Glentworth, Trans. Farday Sm., 1965, 61, 700. C. F. Wells and M. Husain, Trans. Faraday Suc., 1971, 67,767. Manganese(II1) and its Hydroxo- and Chloro-complexes in Aqueous Perchloric Acid : Comparison with similar Transit ion-met al( 111) Complexes BY DAVID R.ROSSEINSKY,* MICHAEL J. NIcoL,? KENNETH KITE Department of Chemistry, The University, Exeter EX4 4QD AND R. JOHN HILL $ Received 10th April, I974 At 25°C the formation constant of MnCI2+ is found by spectrophotometry to be 13.2k0.9 dm3 mol-’ at ionic strength 3.26 mol dm-3 ; for MnCIi the value is 1.1 k0.7 dm3 mol-’. Increase in the number of chloride ions in complexes results in longer wavelengths for the corresponding absorption maxima. In the absence of chloride the hydrolysis constant of MnIII at ionic strength 5.6 rnol dm-3 is found from voltammetry and potentiometry to be 1.05 f0.26 mol dm-3. Aged manganese(u1) is found to be 15-25 % polymeric, from both kinetic and e.m.f. measurements. Comparison of forma- tion constants for halogeno- and hydroxo-complexes of M3+ (first transition series) shows that a combination of charge-transfer, ligand-field and coulomb interactions underlies the observed se- quences ; the dipole moment of OH- is also a factor.The extent of interest in halide (X-) and hydroxo complexes of the trivalent cations M3+ of the first-row transition metals is evident from the growing number of measurements of stability constants K collated or being Solutions in quite concentrated HC104 have often to be used ; however, at ionic strengths I > 0.5 mol dm-3 ionic activity coefficients change but slowly with composition, and for our purposes, comparison of log K values in this range, such high electrolyte concentra- tions present few problems. Some K values are less well founded than most. That for Fe12+ cannot be obtained in HC104, since oxidation of I- occurs by a mechanism which does not give a stability constant from the rate e q ~ a t i o n .~ For MnC12+ an estimate, from kinetics, of 8.9 dm3 mol-’ in 2 rnol dm-3 HC104 has been recalculated as 13.5 mol dm-3. This revision may well reflect only the uncertainty of the estimate. spectrophotometric value of the hydrolysis constant Khx4 mol dm-3 in I = 6 mol dm-3, was re-measured 7 a as 0.93 mol dm-3 in ionic strength 4 mol dm-3, and 0.96 mol dm-3 (at 23°C),7b Values of Kfor both of these Mn”’ complexes clearly need to be redetermined, by independent techniques if possible, and in this paper we report such measurements, first of Kh by electrochemical methods and secondly of K,, for MnC12+ by spectrophotometry.Fresh MdJ1 differs from aged MnIII in that with time, a fraction of the fresh sample forms a polymeric species which reacts slowly in some electron transfer reactions.8 It is possible to use e.m.f. data 9* l 3 to substantiate a kinetic estimate of the fraction polymerised, which has some effect on the K values. Finally we compare K values for most of the MX2+ species, and elicit the major molecular factors governing the values observed. For MnOH2+ formation the original National Institute of Metallurgy, Johannesburg ; $ Dept. of Physical Chemistry, The University, Leeds. 2232D . R . ROSSEINSKY, M . J . NICOL, K . KITE AND R . J . H I L L 2233 EXPERIMENTAL The voltammetric cell for measuring the variation of exchange current, and of e.m.f., with [H+] was used in the determination of transfer coefficient a and rate constant in 3 mol dm-3 HClO, for the electrode reaction Mnrn+ept+Mn2+.The ionic strength was now made 5.6 mol dm-3 in HC104+ NaClO, so as to accommodate a sufficiently large change of [H+], from the minimum commensurate with the stability of Mnm, 0.75moldm-3, to 5.3 rnol dmV3. The solution was made 0.1 mol dm-3 in Mn(C104)2 to suppress the dis- proportionation of M P , the concentration of which was kept at 1.89 x lo-, mol dmd3 throughout. The MnIIr, at near this concentration, was prepared at room temperature by the reaction 8y 4 MnU+ MnVII, and aged for >36 h, at which time after a prolonged period of decrease the absorbance at 470nm remained constant. Mnrrl was standardised by amperometric titration with iron(@.To determine the MnC12+ stability constant at ionic strength 3.26 mol dm-3 (a value chosen in connection with other work 8, twenty four solutions of 4 x lo-, mol dnr3 Mnnr, 3 mol dm-3 HClO4 and 0.05 mol dm-3 Mn(C104)2 containing 0.01-0.2 mol dm-3 C1-, were examined at 25.0”C in 0.2-4cm cells being Unicam SP500 spectrophotometer over the wavelength range 230-400nm, where neither Mnn nor Cl- absorb. Enhancements of absorbance occurred, which were checked with doubled [MnIn] at the two extreme [Cl-] values. For both [Cl-] values the enhancements were doubled, indicating that the absorbing complex(es) were monatomic in MnlI1. Further elaboration depended on assumptions regarding Kh. RESULTS AND DISCUSSION HYDROXO-COMPLEX The value of the exchange current io and the e.m.f.E at 25°C are given in table 1 for five different solutions at compositions differing only in [Hf] and “a+], with [H+] + “a+] constant. Notably, the transfer coefficient a is identical for both acidities, strongly implying constancy of electroactive specie^.^ The relationship between io at 5.3 mol dm-3 H+ and at 0.75 mol dm-3 H+ is log~i~(5.3)/i0(0.75)) = (1 -or) log{5.3[(Kh/mol dm-3) + 0.75]/ 0.75[(Kh/mol + 5.311. TABLE 1 .-VOLTAMMETRY AND POTENTIOMETRY ON MnrI1 SOLUTIONS AT TWO DIFFERENT [Mnrrl] = 1 . 8 9 ~ lo-, mol dm-3, [Mnn] = 0.1 mol dm-3, I = 5.60 mol dm-3, 25°C 0.75 1.008 6.993 0.249 1.006 6.998 0.255 1.010 6.976 0.257 1.009 6.994 0.256 1.008 6.957 0.248 ACIDITIES [H+]/mol dm-3 E D - log(fo/A) U mean : 1.008k 0.002 6.977+ 0.016 0.253 If: 0.004 [0.3657Ia 5.30 1.052 6.794 0.251 1.056 6.73 1 0.248 1.057 6.781 0.250 1.055 6.745 0.253 1.056 6.777 0.258 mean : 1.055+0.001 6.767k0.021 0.252a0.003 [0.2877Ia a E for HzlHC1O4, NaC104, NaCllHg2C121Hg ; 0.01 mol dm-3 NaCl.2234 FORMATION CONSTANTS O F MnrIr SPECIES This expression follows irrespective of whether Mn3' or MnOH2+ is assumed to be reduced, as it is kinetically impossible to identify the electroactive species. Indirect arguments from the mechanism invoked to explain the low value of a suggest that it is Mn3+.From table 1 the left side of the equation is 0.210+0.037, whence the value of Kh is 0.95k0.35 mol dm-3. The E values were combined with those for a cell H21HC104, NaClO,(HClO,, NaClO,, NaClIHg,Cl,IHg ([NaCl] small), to give at the two [H+] employed, E' values for the cell, H,(HC104, NaClO,(HClO,, NaClO,, Mn(ClO,),, Mn(C10,), IPt with I = 5.6 mol d ~ n - ~ throughout ([Mn"+] small).Hence (E')5.3 -(E')0.75 = RT/F ln([(K,/mol dm-3) +0.75]/[(Kh/mol dm-3) + 5.301) which was 1.374 0.002 - (1.342+0.001) V or -32Ifr3 mV, giving Kh = l.lk0.20 mol dm-3. Preliminary measurements were carried out with calomel electrodes having electrolyte which differed in composition from that of the Mn3+, Mn2+ and hydrogen electrodes. The liquid junctions introduced slightly irreproducible error ; neverthe- less, the current against voltage curves (with ct 0.249 +_ 0.005 and 0.255 f 0.004 at 0.75 and 5.3 mol dm-3 H+) gave a Kh of 1.05-&0.30 mol dm-3, and from E' differences, - 31 1 2 mV, a K,, of 1.1 kO.20 mol dm-3.Since the additional uncertainty is only slight, we include all these values to obtain a mean of Kh = I .05 p0.2, mol dm-3. While a different ratio of activity coefficients is implicitly assumed constant in going from io to E to calculate K,, the consequence is clearly within the experimental error of either method. The agreement of our value with the 0.93 obtained in a predomin- antly Mn(C104)2 medium at I = 4 mol dm-3 is satisfactory considering the difficulties of electrometry with this reactive ion, and the problems of extrapolation to zero time (to correct for polymer formation) involved in the spectroph~tometry.~ We have hitherto considered MnI" monomeric : taking account of the pdymeric fraction (below) shows that the high side of the quoted limits should be emphasized for the truly mononuclear equilibria.CHLORO-COMPLEXES By straightforward use of Beer's law and including an appropriate value of Kh, First it was assumed that MnC12+ is the Then these initial K,, values obtained from 230-290 nm data a three stage computation was employed. only chloro-complex. TABLE 2.-vALUES OF FOR Mn3++ C1-+MnCl2I- AT VARIOUS WAVELENGTHS A/nm Kcl/drn3 mol- i/nm Kc1/dm3 rnoi-' 230 12.9 255 12.5 235 15.8 265 14.7 240 12.2 270 12.4 245 12.6 275 12.7 250 12.9 mean 13.2+ 0.9 Kh = 1.0 mol dm-3 assumed were used to estimate K2,, for MnCl2++C1-+MnC1l, which is invoked to account for the higher-wavelength absorption. This gave a small K2c1 and a large E(MnC1:) which justify the original assumptions and support the actual values of K,, initially obtained (table 2).Finally a complete Beer's law expression for the total absorbance gave better values of K2c1, see table 3. The algebra, straightforward but cumbersome,D . R. ROSSEINSKY, M . J . NICOL, K . KITE AND R. J . HILL 2235 is detailed elsewhere,'O as are all individual measurements. Because the value of K,, depends on the value assumed for Kh, the calculation was repeated for a range of Kh, which established (table 4) that the dependence is not oversensitive, and is small enough to ensure that any further uncertainty introduced is smaller than that already inherent (table 2) in the parameter fitting. The Kh range almost certainly encompasses the true value for this medium. TABLE 3.-APPROXIMATE VALUES OF K2c1 FOR MnCI2++ Cl-+MnClzf AT VARIOUS WAVE- LENGTHS L/nm K 4 d m 3 mcl-I 300 0.8 320 0.3 340 1.6 360 0.5 380 2 .3 mean 1.1 k0.7 dm3 mol-', with KCI = 13.2 dm3 mol-I The spectra observed and calculated are shown in fig. 1. If we add the longest in 10 mol dm-3 HCl, which presumably indicates wavelength maximum observed an even higher complex, the following sequence of absorbance maxima is seen : species Mn3+ MnC12+ MnCli MnCl,,(3-n)t 210 240 300 550. It is thus possible that the absorption bands are due to ligand-to-metal ion charge transfer. Our spectrophotometry results agree satisfactorily with earlier qualitative observations.I2 Again as with MnOH2+ the upper limits of K,, (13.2k0.9 dm-3 TABLE 4.-DEPENDENCE OF DERIVED Kc1 ON ASSUMED VALUES OF Kh Kh/mol dm-3 Kc1/dm3 mol-* 0.6 12.8 0.93 13.0 1 .o 13.2 1.20 14.0 mol-I) are to be emphasized when the fraction of hydrolytic polymer present is allowed for.It is unlikely that the Z = 2 mol dm-3 value, 13.5 dm3 mol-l is truly coincident with our Z = 3.26 mol dm-3 value of 13.2 dm3 mol-l, especially in view of the variation of the FeC12+ value with Z, 5.0 and 7.8 dm3 mol-l at Z = 2 and 3 mol dm-3 respectively. As we are quite certain of our limits, this conclusion reflects the uncertainty in the indirect kinetic measurement mentioned in the introduction. For Kh and K,, these are about five times larger than is commonly quoted, and they arise from the highly reactive nature of the cation. MnIII reacts, albeit slowly, ca. 1 % per day, with the solvent, and it partially polymerises (below). For Kh the effect being measured, while un- ambiguous, is not so large as to diminish these errors to the ordinary level of para- meter fitting.For K,, the MnC1; equilibrium is a marginal complication, but the effect measured is much larger, so diminishing, relatively, the errors resulting from the nature of Mn'". (CeIv and Co"' present comparable prob1ems.l 6* ') The size of the error limits calls for comment.2236 FORMATION CONSTANTS OF Mnrrr SPECIES I t 4.0 FIG. 1.-A, Calculated (+) and observed (-) values of logarithm of absorbance, A, for 0.15 mol dm-3 C1- solution ; [MnIII] = 4.00 x rnol dm-3, [MnII] = 0.05 mol dm-3, [HC104] = 3 rnol dm-3 250°C ; B, log A for MnIII without C1-, otherwise as A ; C, log(&Mnciz + /dm3 rnol cm-') ; D, log(EMnclf /dm3 mol-' cm-l). MANGANESE(III) IN PERCHLORIC ACID In the chloride catalysed oxidation of TI' by Mnrrl with rnol dm-3 < [MnII'] < mol dm-3, it was found that a multi-step mechanism could explain the obser- vations up to ca.70 or 80 % consumption of Mn"', but thereafter the rate plots were curved. The plots could be made linear by assuming that about 10-20 % MnlI1 was present as unreactive polymer. There is clear evidence for some hydrolytic polymer- isation in the marked spectral changes occurring in MnIII for more than 24 h after preparation. Therefore in the spectrophotometric Kh determination, readings had to be extrapolated to zero time (see above). Further evidence comes from e.m.f. measurements. All our observations in this and preceding papers have been made on aged Mn"', and our conditional (3 rnol dm-3 HCIO,) standard e.m.f.was found to be 1.53550.003 V, while for fresh Mn"' the value was 1.541 V.I3 If the difference 6+3 mV is attributed to the presence of polymer in the former, the fraction of polymer is 25+ 14 %. Combining the kinetic and the e.m.f. estimated values leads to the conclusion that - 15-25 % of the Mnlrr is polymeric. The precise amount is determined by preparative conditions, since such hydrolytic equilibria are often extremely sluggish. The conditional e.m.f. values quoted here are for Mn"', 3 mol dm-3 HC104, without account of the first hydrolysis. Inclusion of Kh= 1 mol dm-3, as the value appropriate for Z = 3 rnol dm-3, gives as the conditional (3 mol dm-3 HClO,) standard e.m.f. for Mn3+(unhydrolysed) + e = Mn2+ the value 1.559 V calculated from the fresh Mn"' measurement.COMPARISON OF MX2+ FORMATION CONSTANTS OF FIRST TRANSITION SERIES METAL IONS M3+ Values are tabulated in table 5 for perchlorate solutions between 0.5 mol dm-3 and 2 mol dm-3 in ionic strength ; most have I = 1 rnol dm-3, MnOH2+ has 4 mol d~n-~. Hydrolysis constants have been converted for comparative purposes to formationD . R . ROSSEINSKY, M. J . NICOL, K. KKTE AND R. J . HILL 2237 constants by subtraction of log K, at the appropriate ionic strength. Neglecting the only slight irregularities introduced by I variations, we can immediately make two generalisations which are in almost complete accord with earlier views 6* l4 on the bonding in MOH2+ and MF2+. First, the decrease, with only one minor deviation, TABLE 5.-sELECTED VALUES a OF LOGARITHMS OF FORMATION CONSTANTS FOR M3f+ X-*MX2+ IN PERCHLORATE SOLUTION OF IONIC STRENGTH USUALLY b 1 mol dm-3 AT 25°C OH F sc 8.84 6.19 Ti 11.7 - V 11.1 - Cr 9.8 4.36)o.s - Mn 13.7)s 5.63 Fe 11.0 5.06 Co <11.8d - C1 Br I E0(M3+m2+)/V - _ .3.07)0.5 1.21 0.34)o. 5 - - - 1.29 - - - - 0.26 0.65 -2.67)z - 5.0 C - 0.41 0.95)z - - 1.56 0.56 - 0.25 - 0.77 1.49)l.S - - 1.85 a from ref. (1) unless otherwise indicated ; log(Kx/dm3 mol-') given. b Other ionic strengths given in mol d ~ n - ~ as subscripts. C T. W. Swaddle and G. Guestalla, Znorg. Chem., 1968, 9, 1915. d G. Davies and B. Warnquist, Coord. Chem. Rev., 1970,5, 349. e Ref. (l), and J. K. Rowley and N. Sutin, J. Phys. Chem., 1970, 74, 2043. f Ref. (3).from OH- and F- to I- can be attributed to the decreases in coulomb interaction and in the X- ligand field stabilisation parameter. Very low values probably indicate outer sphere association. Secondly, in the variation with M, considering the Sc, Cr and Fe complexes for which the data are most complete, the Cr values always fall low o - - - - , \ . - 1.5 1.0 - J -0.5 k - 0 2 M - -0.5 I t I I I Ti V C r Mn Fe C o .FIG. 2.-Approximate parallelism of trends in log Kx for MX2+ and E"(M3+y2+). Data from table 5. at 25°C. A, log KOH ; B, log KCI, ; C, E".2238 FORMATION CONSTANTS OF Mn1l1 SPECIES n a plot of log K against the M atomic number, which supports the view that charge transfer interaction is important. This follows from the fact that of the three ,5'"(M3+*2+) values, that for Cr is negative.Mn3+ has the second highest, positive, E" and, again in agreement, the K values fall high relative to the Sc-Fe line. These trends are illustrated in fig. 2. The detailed dependences on ionic properties further involve the effect of replacing the originally co-ordinated OH2 by X-, and the variation of dielectric saturation with M3+-X- separation in the coulomb interaction. These variables apart from charge transfer are amenable to quite exact theoretical treatment, which however we do not pursue here. We note that the earlier l4 coincidence, of F- and OH- complexing dependences on M3+, arose from the use of Latimer's outdated quantities for fluorine reactions, and OH- complexes turn out to be more stable than F- complexes by an amount which cannot be explained solely by easier charge transfer l4 from OH-. (The anion radii are nearly identical.) However, this excess stability is readily understood as arising from the fact that OH- is 02- with an attached H-I, and a large part of the interaction is M3+02-; put alternatively, OH- has a large dipole moment, absent in F-, which enhances M3+-OH- interactions. (A similar enhancement of inter- action arising this time within the cation is found in [NO,CO~~'(NH,),]~+ SO:- ion association, which greatly exceeds that for e.g. Co2+SOi- by virtue of the cationic dipole moment in the former. Further examples are a~ailable,'~ e.g. V02+ cf. Fe2+, where the dipole moment in the V'' cation is evident in relative rate and equilibrium effects .) Stability Constants of Metal Ion Complexes, ed. L. G. Sillen and A. E. Martell (Chem. SOC. London, 1964), and Suppl. I, 1971. D. W. Carlyle and J. H. Espenson, Inorg. Chem., 1969, 8, 575. A. McAuley, M. N. Malik and J. Hill, J. Chem. SOC. A, 1970, 2641. G . S. Laurence and K. J. Ellis, J.C.S. Dalton, 1972, 2229. G. Davies and K. Kustin, Znorg. Chem., 1969, 8, 1196. H. Diebler and N. Sutin, J. Phys. Chem., 1964, 68, 174. (4 C. F. Wells and G. Davies, J. Chem. SOC. A, 1967, 1858 ; (4 V. B. Goncharik, L. P. Tikhon- ova and K. B. Yatsimirskii, Russ. J. Inorg. Chem., 1973, 18, 658. D. R. Rosseinsky and R. J. Hill, J.C.S. Dalton, 1972, 715. D. R. Rosseinsky and R. J. Hill, J.C.S. Faraday I, 1974, 70, 1140. l o R. J. Hill, Thesis (Exeter, 1971). l 1 J. A. Ibers and N. Davidson, J. Amer. Chem. SOC., 1950, 72, 4744. l 2 C. F. Wells, D. Mays and C. Barnes, J. Znorg. Nuclear Chem., 1968, 30, 1341. l 3 L. Ciavatta and M. Grimaldi, J. Inorg. Nuclear Chem., 1969, 31, 3071. l 4 D. R. Rosseinsky, Nature, 1967, 216, 791. l 5 D. R. Rosseinsky, Ann. Rep. Chem. SOC. A , 1971, 95 ; Chem. Rev., 1972, 72, 220. l 6 M. G. Adamson, F. S. Dainton and P. Glentworth, Trans. Farday Sm., 1965, 61, 700. C. F. Wells and M. Husain, Trans. Faraday Suc., 1971, 67,767.

ISSN:0300-9599    

DOI:10.1039/F19747002232

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Influence of Pressure on the Ionization of Substituted Phenols BY SEFTON D. HAMANN" AND MAX LINTON CSIRO Applied Chemistry Laboratories, G.P.O. Box 433 1, Melbourne 3001, Australia Received 1 1 th April, 1974 Spectroscopic measurements have been made of the ionization constants of eighteen substituted phenols in water at 25°C and at 1, 500, 1O00, 1500 and 2000 bar. Ionization of the phenols is en- hanced by an increase of pressure, and the derived values of the change in partial molar volume for ionization lie between - 8 and -20 cm3 mol-'. The results are discussed in terms of the molecular structures of the phenols. One of the most pronounced and general of the chemical effects of increasing pressure is the increase in the degree of ionic dissociation of weak electrolytes in solution.The enhancement of ionization is explained by the fact that compression increases the dielectric constants of liquids and so lowers the standard free energies of dissolved ions with respect to those of neutral molecules. It is related thermodyna- mically to the decrease in total volume which accompanies ionization reactions and which arises from electrostriction of solvent around the ions that are formed. The effect has been reviewed 1-4 and a tabulation of the experimental results is given in ref. (4), tables 17-23. Here, we describe spectroscopic measurements of the ionization constants of a number of phenols in water at 25°C and at pressures up to 2000 bar (1 bar = lo5 Paz0.9869 atin). The main purpose of the experiments was to see how substituent groups in the phenols alter the pressure effect and the volume change for ionization. A later paper will report similar measurements on substituted anilines. EXPERIMENTAL SPECTROSCOPIC MEASUREMENTS PRINCIPLE OF THE METHOD The spectroscopic method of von Halban has been widely used at atmospheric pressure and was applied to substituted phenols by Robinson and coworkers.6 It is based on the fact that if the parent molecule ROH and the anion RO- of a phenol have sufficiently different optical absorption spectra, the degree of ionization c( of the phenol in a buffer solution can be estimated from the relationship D = (1 - ~ ) D R O H + UDRO - (1 1 where D denotes the optical density of the buffer solution, DROH is the optical density of an acidified solution in which the phenol is virtually unionized, and DRO- is the optical density of an alkaline solution in which it is virtually fully ionized.The three optical densities are measured at the same total concentration of phenol, and for the same wavelength, path length, temperature and pressure. The molal ionization constant KROH can then be derived from the known hydrogen ion activity ~ H + Y H + of the buffer by the formula (2) which is based on the usual assumption that the activity coefficient YROH is unity. KROH = EmH + YH + YRO - /(I - a) 22392240 IONIZATION OF PHENOLS To apply the method at high pressures calls for measurements of D, &OH and DRo-, all as functions of pressure, and for an estimate of the way in which WZH +YH + and yRo - change with pressure.APPARATUS The high pressure optical measurements were made with a manually operated Unicam SP500 spectrophotometer which had been modified by moving the photocell housing to provide a 133 mrn working space for a high pressure optical cell. The cell [see fig. 13 of ref. (4)] consisted of a temperature-controlled steel block, 89x 76x 127 mm, with a 19 rnm diameter cylindrical bore designed to take a standard 10 mm square silica optical cell sup- ported in a brass holder. The block had two optically flat silica windows mounted after the manner of Poulter ; they were 12.7 mm in diameter and 9.5 mm thick, and had a viewing diameter of 6 mm. The pressure fluid was pharmaceutical grade paraffin oil, and the pres- sure was generated by a hand pump and a screw-driven ram and measured on a calibrated Bourdon gauge.The oil surrounded the inner silica cell and was in direct contact with the aqueous solution inside it. Although this presented dangers of possible contamination of the solution and of extraction of phenol from it, we found that neither occurred to any measur- able extent over a longer time than was needed for the measurements. The optical absorb- ance of the oil and loss of transmitted light by reflection at the silica surfaces combined to limit the range of reliable measurements to wavelengths greater than 300nm. For that reason we were unable to obtain high pressure data for phenol (unsubstituted) itself. Since we had no reference cell, the method of operating the spectrophotometer differed considerably from the normal.The instrument was first modified by replacing the knobs of the " sensitivity ", " dark current " and " slit width " controls by Beckman Duodials, which allowed accurate reading, resetting and locking of the controls. Before each pressure run, appropriate slit width and sensitivity settings were determined at a number of wavelengths with pure water in the optical cell at atmospheric pressure (tests showed that raising the pressure to 2000 bar had no effect on these settings). A constant slit width was chosen such that the sensitivity control was adequate over the chosen range of wavelengths, which usually spanned the absorption peak of the phenolate ion at seven intervals of 2 to 10 nm depending on the sharpness of the peak. The phenol+ buffer solution was then placed in the cell and the optical density measured at the same wavelengths and with the same dial settings as for water, at the series of pressures 1, 500, 10o0, 1500, 2000, lo00 and 1 bar. Several minutes were allowed after each change of pressure to let the temperature of the solution return to 25°C.The final measurements at loo0 and 1 bar served as checks on possible drift in the instrument or changes in the solution : they differed by no more than 0.01 in optical density from the measurements made during compression and frequently they differed by less than 0.001, although the absolute accuracy of the instrument is only claimed to be kO.0025. The success of the above method of operation depended upon the stability of the spectro- photometer over periods of an hour or more.This stability was achieved by frequently servicing the instrument, by running it from a voltage stabilizer, by using only the tungsten lamp, and by periodically replacing the lamp, the dry batteries and the electrometer and current valves. The photocell was exposed to light as briefly as possible, MATERIALS The phenols were the purest comniercially available samples. They were recrystallized and their purity was established by their melting points and absorption spectra. All the other reagents were of analytical grade. PROCEDURE The absorption spectrum of each phenol ROH and that of its anion RO- were determined separately in dilute solutions of HCl and NaOH respectively, at 25°C and at 1,500,1000,1500 and 2000 bar. The spectrum was then measured at the same temperature and pressures in one or more buffer solutions with pH close to the pKof the phenol, so that roughly half of the phenol was ionized.The total concentration of phenol was always very much less than theS . D. HAMANN AND M. LINTON 224 1 concentration of buffer. The pH of the buffer solutions was measured at atmospheric pressure with a Radiometer 25 pH meter, standardized with at least two standard buffers made according to the specifications of the National Bureau of Standards.I* Both the positions and intensities of the absorption peaks of ROH and RO- were slightly but measurably changed by pressure, the wavelengths increasing by 1-3 nm for the phenols and decreasing by 0-2 nm for the anions between 1 and 2000 bar. These changes were allowed for in calculating a.DILATOMETRIC MEASUREMENTS The absorption peaks of unsubstituted phenol and its anion occur at wavelengths shorter than 300 nm and for that reason we were unable to measure its ionization constant in the high pressure cell (see Apparatus section above). However, for comparison with the sub- stituted phenols, we measured the volume change for ionization of phenol in water at 25°C using the dilatometric apparatus and method of Hepler, Stokes and Stokes l 1 to determine the partial molar volumes of C6HsOH and C6H50- at infinite dilution. We also made a direct measurement of the volume change which accompanies the neutralization of phenol by sodium hydroxide. The substituted phenols that we studied in the high pressure experiments are in general too insoluble in water to yield reliable values by the dilatometric method.RESULTS SPEC TRO S C 0 PIC ME AS UREM EN TS METHOD OF TREATMENT As an example of the raw experimental results, fig. 1 shows the measured spectrum of 4-nitrophenol in a phosphate buffer solution at 25°C and at 1, 1000 and 2000 bar. An increase of pressure reduces the absorption at 402 nm due to the anions RO- of the phenol and raises the absorption at wavelengths below 350 nm due to the parent molecules ROH, which have their absorption peak at 314 nm. In other words, it wavelength/nm FIG. 1.-The absorption spectrum of 4-nitrophenol (9.3 x mol kg-') in aqueous phosphate buffer (NaH2P04 : 0.01 mol kg-l ; Na2HP04 : 0.01 mol kg-l) at 25°C and 1, 1000 and 2000 bar. For the purpose of this diagram the experimental optical densities have been multiplied by the relative volumes PV/l Vof compressed water, to remove the contributions of the increases of molar concentra- tion under pressure.Pressures (in bar) given against the curves. 1-7 12242 IONIZATION OF PHENOLS shifts the equilibrium depicted at the top of the diagram to the left, indicating that compression increases the acidity of the dihydrogen phosphate ion H2PO; more than it does the acidity of the phenol. OH+HPO:-;-\ OzN O-+H,PO; in water at 25°C It can be seen from this example that to proceed from the measured spectra and the derived value of a to an estimate of the ionization constant K R o H of the phenol requires additional knowledge of the ionization constant KAiI of the buffer acid at high pressures.Expressed quantitatively, the value of mH+YH+ in eqn (2) is equal to KAHmAHYAH/mA-YA- for a buffered solution, and so (2) can be written &OH = ~ ~ ( , H ~ A H Y A H Y R ~ - / Y ~ ? A - Y A - ( I -a)* (3) Values of K A H have already been measured independently at high pressures for the three buffer acids that we used in this work : acetic acid, dihydrogen phosphate and bicarbonate. The molal ionization constant of acetic acid has been determined by conductance methods up to 3000 bar 79 12* l 3 and by e.m.f. methods up to 8000 bar,l49 l5 and the values in water at 25°C and zero ionic strength can be represented accurately over the whole pressure range by the formula l6 - A1 VAH(P - 1 bar) RT[l+ b(P- 1 bar)] 'K,, = '~,,exp (4) where P denotes the pressure and the superscripts P and 1 indicate values at pressures of P and 1 bar; R and Tare the gas constant and absolute temperature; b is a con- stant equal to 9.2 x bar-' and A' VAH is the change of partial molar volume for the ionization of acetic acid in water at 25°C and 1 bar and at zero ionic strength : A' VAH = - 11.6 cm3 mol-'.The ionization constant of dihydrogen phosphate ions has been measured under pressure by conductance, e.m.f. 14* methods and can be represented by (4) with the same value of b, but with A' VAH = -26.2 cm3 mol-l for the ionization of H,PO,. Similarly, 'KAH has been measured for bicarbonate ions by an e.m.f. method 14. 2o and is described by (4) with the same values of b, and with A' VA, = -27.9 cm3 mol-' for the ionization of HCO;.Another quantity which is needed in applying eqn (3) is the product of activity coefficients yAHyRO-/yA- which we shall denote by the symbol r. For acetic acid buffer, AH is electrically neutral and A- and RO- are both singly charged ions so that we can justifiably assume that r is close to unity and independent of pressure. How- ever, for dihydrogen phosphate and bicarbonate buffers, AH and RO- are singly charged whereas A-is doubly charged(HP0: -, CO -), and r is therefore significantly different from unity and is affected by pressure. In these cases we have taken the pressure dependence of and spectroscopic to be given by the formula 1 - 2.80211(P - 1 bar) RT[I +b(P- I bar)] -__- ( 5 ) where P is in bar, RT is in cm3 bar and I denotes the ionic strength of the solution at 1 bar in mol dm-3.The factor -2.802 I* is the theoretical value of the initial pres- sure dependence of RT In r at low pressures, calculated from the Debye equation allowing for the variation with pressure of the dielectric constant and density of water at 25°C (the numerical part is equal to Redlich's l 8 factor, k = 1.868, multiplied by 3). The term involving b corresponds to the one in (4) and corrects for the non-linearity of the pressure dependence of the dielectric constant and density; again, b has the value 9.2 x bar-'.S . D . HAMANN AND M . LINTON 2243 For a few strongly acidic phenols such as picric acid we used hydrochloric acid as the "buffer" and in these cases mH+ in eqn (2) was known and was independent of the pressure.However, we needed to estimate how the product yH+yRO- changed with pressure. We assumed that it varied in the same way as YH+YCl- in a solution of the same ionic strength, and estimated that variation from Dunn's measurements of the partial molar volume VHcl of hydrochloric acid in water at various concentrations, together with an assumed relationship where R, T, P and b have the same meanings as in (4) and A VHcl denotes the difference between the partial molar volume of HCl in the solution and its partial molar volume at zero ionic strength. NUMERICAL RESULTS Table 1 lists the phenols that we studied and the ionic strengths and natures of the buffer solutions that we used. It also shows the values we found for the ionization constants at atmospheric pressure and for the wavelengths Am and molar extinction coefficients E, of the absorption maxima of the phenolate ions at atmospheric pressure.Our values for these quantities agree well with those found by previous workers. TABLE 1 .-IONIZATION CONSTANTS AND OPTICAL ABSORPTION COEFFICIENTS OF PHENOLS IN WATER AT 25°C AND 1 BAR compound 1 phenolb 2 2-nitrophenol 3 3-nitrophenol 4 4-nitrophenol 5 2,4-dinitrophenol 6 2,5-dinitrophenol 7 2,6-dinitrophenol 8 2,4,6-trinitrophenol (picric acid) 9 4-ni tro-2-aminophenol 10 4-nitro-2,6-dibromophenol 11 12 13 14 15 16 17 IS 19 2,4-dini t ro-6-aminophenol 3,5-dinitrosalicylate ion (2nd ionization) 4-nitrosophenol (4-benzoquinone oxime) 2-methoxy -4-formylphenol 1-naphthol 2-naphthol 2,4-dinitro- 1 -naphthol 1 -hydroxy-2,4-dini tronaphthalene-7- sulphonate ion (flavianate ion, 2nd ionization) 3,5-dinitrosalicyclic acid (1st ionization) ionic strength, I! buf- mol fer a dm-3 P 0.124 P 0.124 P 0.05 A 0.06 A 0.05 A 0.022 H 1.00 P 0.05 A 0.11 A P P P C c HS H H 0.01 5 0.072 0.035 0,078 0.063 0.063 0.024 0.005 0.so ~KROH/ mol kg-I l.0Ox 10-'O 5 . 2 ~ 6 . 9 ~ 5.4x 3 . 8 ~ 10-1 8 . 5 ~ 4 . 2 ~ 10-9 8 . 9 ~ 10-5 1.8 x 10-4 3.1 x 10-4 optical absorptkn of ions RO- L / n m loglo ~m C b 287 3.41 415 3.66 390 3.19 402 4.27 360 4.25 439 3.63 432 3.90 357 4.16 443 3.92 400 4.00 4 . 3 ~ 10-5 404 3.99 4 . 2 ~ 372 3.97 4 . 7 ~ 398 4.40 3 . 2 ~ 348 4.43 4.4~ lo-'' 332 3.87 2 S x lo-'' 345 3.46 3 . 6 ~ 3941439 4.2814.29 3 . 2 ~ 428 4.16 2 . 9 ~ lo-* 333 5.04 Key : A = acetic acid/acetate, C = bicarboiiate/carbonate, H = hydrochloric acid, HS = this hydrochloric acid + sodium chloride, P = dihydrogen phosphate/monohydrogen phosphate ; value of 'KROH for phenol is from ref.(23) ; C the units of ern are dm3 cm-' mol-'.2244 IONIZATION OF PHENOLS Table 2 shows a specimen calculation of the relative ionization constant PKROH/ 'KRoH of 4-nitrophenol at high pressures. The values A l VRoH of the volume change for ionization of the phenol at I bar and zero ionic strength were calculated from the formula which has been found to hold accurately for a wide range of ionization reactions in water to at least 8000 bar l6 ; the constant b is 9.2 x lo-' bar-'. Eqn (7) was ob- tained by integrating Planck's 21 general thermodynamic relationship aRT la K = -AV ap on the assumption that the pressure dependence of AVRoH is given by A1 VRoH [ l + b ( P - l bar)12' APVROH = (9) The results for all the phenols are summarized in table 3, and table 4 compares our values of AIVRoH with some that have been measured previously.It is difficult to estimate the absolute accuracy of our results, but we think that the values in table 3 are reliable to + 5 in the last digits listed. TABLE 2.-A SPECIMEN CALCULATION OF THE RELATIVE IONIZATION CONSTANT p K ~ ~ ~ / l r c ~ ~ ~ OF 4-NITROPHENOL IN WATER AT 25°C Plbar optical densities measured at 402 nm with a path length of 1 cm a from (1) average a a al(1 -a) 'K-/'KAH from (4) pr/rr from (5) P K ~ ~ ~ / ' K ~ ~ ~ from (3) 1 0.314 0.003 0.739 0.423 0.422 0.730 1 .om 1 .ooo 1 .Ooo 50G 0.268 0.003 0.748 0.356 0.356 0.553 1.656 0.988 1.239 1000 0.226 0.003 0.754 0.297 0.298 0.425 2.630 0.977 1.496 1500 0.191 0.003 0.760 0.248 0.250 0.333 4.024 0.967 1.775 2000 0.163 0.003 0.764 0.210 0.212 0.269 5.927 0.958 2.103 A1 YRo~/crn~ mol-I c -11.1' -10.90 -10.79 -10.91 average - 10.93 Total concentration of ROH = 3.98 x rnol kg-I ; buffer = 0.0125 mol kg-' NaHzP04+ a Average values of cc for 7 wavelengths around 402 nm at each pressure.These values were b PKROHI'KROH = P[a/(l -E)lPKAHPr/'[a/(1 - E)]'KAH'r. 0.0125 rnol kg-' Na2HP04 ; ionic strength Z = 0.05 rnol dm-3. used in the subsequent calculations. C calculated from eqn (7). DILATOMETRIC MEASUREMENTS The limiting partial molar volume of phenol at infinite dilution in water at 25°C was found to be 86.17 cm3 mol-l and the corresponding value for sodium phenolate, corrected for hydrolysis, was 66.3* cm3 mol-l.Combining these values with the difference of 1.21 cm3 mol-l between the partial molar volumes of Hf and Na+ 26 gives A1 VRoH = - 18.5* cm3 mol-l for the ionization of phenol at infinite dilution. A direct measurement of the volume change for neutralization of phenol by NaOH to give a solution containing 0.002 96 mol kg-l of sodium phenolate gave the valueS . D. HAMANN A N D M. LINTON 2245 TABLE 3.-IONIZATION OF PHENOLS IN WATER UNDER PRESSURE AT 25°C compound 1 phenol 2 2-nitrophenol 3 3-nitrophenol 4 4-nitrophenol 5 2,4-dinitrophenol 6 2,5-dinitrophenol 7 2,6-dinitrophenol 8 2,4,6-trinitrophenol (picric acid) 9 4-nitro-2-aminophenol 1 0 4-nitro-2,6-dibromophenol 1 1 2,4-dinitro-6-aminophenoI 12 3,5-dinitrosalicylate ion (2nd ionization) 13 4-nitrosophenol (4-benzoquinone oxime) 14 2-methoxy-4-formylphenol 15 1 -naphthol 16 2-naphthol 17 2,4-dinitronaphthol 1 8 1 -hydroxy-2,4-dinitronaphthalene-7- sulphonate ion (flavianate ion, 2nd ionization) 19 3,5-dinitrosalicyclic acid (1st ionization) Plbar 500 1000 1500 2000 A' VROH~ cm3 mol- 1.332 1.343 1.241 1.232 1.275 1.318 1.189 1.248 1.286 1.171 1.487 1.261 1.289 1.413 1.402 1.231 1.229 1.076 1.659 1.674 1.497 1.492 1.551 1.699 1.442 1.517 1.590 1.347 2.220 1.525 1.674 1.902 1.888 1.446 1.521 1.176 2.048 2.136 1.785 1.786 1.881 2.182 1.708 1.816 1.974 1.547 3.07 1.865 2.140 2.485 2.472 1.646 1.871 1.275 - 18.4 2.491 -13.5 2.608 -14.1 2.108 -10.9 2.149 -11.0 2.270 -11.9 2.777 -14.7 1.955 -9.9 2.165 -11.3 2.378 -12.7 1.759 -8.2 4.08 -21.1 2.209 - 11.6 2.634 -14.2 3.180 -17.2 3.167 -17.1 2.032 -9.9 2.305 - 11.8 1.397 -4.6 PKROH/'KROH is the relative molal ionization constant under pressure and A~VROH is the derived change of partial molar volume for ionization at 1 bar and zero ionic strength, calculated from eqn (7).TABLE 4.-cOMPARISON OF PUBLISHED VALUES OF A' VROH FOR PHENOLS IN WATER ref. compound: phenol 3-ni trophenol 4 4 trophenol 2,s- dinitrophenol 23 - 18.7 24 - 10.3 Cv b 25 - 18.0 - 12.8 -11.3 17 - 11.3 6' e - 1 1.3 b* e this work - 18.4 - 14.1 f - 10.9f -1l.9f A1 VROH is expressed in cm3 mol-' ; a from dilatometric measurements at 30°C, at ionic strengths between 0.1 and 0.2 mol dm-3 ; b these results have not been corrected by activity coefficients or extrapolated to zero ionic strength ; C from high pressure conductivity measurements at 40°C, on a solution with [ROH] = 0.028 mol kg-' ; dfrom density measurements at 25"C, extrapolated to zero ionic strength ; e from high pressure spectroscopic measurements at 25°C in phosphate buffer of unstated ionic strength ; f from high pressure spectroscopic measurements at 25"C, corrected by activity coefficients.+ 3.87 cm3 mol-1 (corrected for hydrolysis) which, combined with A' VH20 = -22.1 1 cm3 mol-' for the ionization of gives A' VROH = - 18.24. The tables list the average of the two values. DISCUSSION It is convenient to discuss the results in terms of the standard partial molar volume changes for ionization at atmospheric pressure, A1 VROH, since these are direct meas- ures of the general high pressure behaviour of the phenols [through the empirical2246 IONIZATION OF PHENOLS relationship (7) or similar ones ' 3* **I and are related fairly directly to the structures and electrical charge states of the ionizing molecules.The first and most obvious feature of the results is that the volume changes are all negative, as they are for the hundred or so other weak electrolytes that have been examined [see tables 17-23 of ref. (4)]. This universal contraction for ionization reactions arises from electrostriction of water around the free ions. Expressed another way, the reason why pressure increases the degree of ionization of weak electrolytes is that it enhances the hydration of ions (on a macroscopic scale, by raising the dielectric constant of water) and in this way lowers their standard free energies with respect to those of the relatively unhydrated parent molecules. Drude and Nernst 29 estimated the degree of contraction for a simple model in which the solvent was treated as a continuum of dielectric constant c and the ions were assumed to be incompressible spheres of radius r i .They concluded that the volume contraction -AVc, (electro- striction) associated with the development of a charge zie on such an ion is where zi is the valence of the ion, e is the electronic charge and N is Avogadro's constant. Although refinements have been made to that e q u a t i ~ n , ~ ' ~ . 30-32 it is sufficient here to quote it in its simple form to indicate how the electrostriction might be expected to vary with the effective size and charge of the ions.The local electric field strength and consequently the electrostriction are greatest for small ions with multiple charges. PHENOL A N D NAPHTHOLS The values of A' VRoH are between - 17 and - 19 cm3 mol-' for unsubstituted phenol and 1 -naphthol and 2-naphthol, and they are therefore intermediate between the values -22.1 cm3 mol-' for the ionization of water 27 and - 1 1 cm3 mol-' for most aliphatic carboxylic acids.3* In the ionization of water the negative charge is localized on the oxygen atom of OH-, whereas in carboxylate ions it is shared equally between the two oxygen atoms of -COT. For that reason the effective radius ri of the carboxylate ion is greater and the electrostriction is correspondingly less.In the case of phenolate and naphtholate ions there is only a single oxygen atom, but some part of the charge is carried by the aromatic ring. The relative values of A*VRoH suggest that the degree of charge delocalization is less, however, than in carboxylate ions. MONOSUBSTITUTED PHENOLS For nitrophenols, delocalization of the negative charge of the anions RO- occurs to a much greater extent than for phenol itself, because of charge transference of the type represented by the valence bond structures O=(-I>=NO;. - The electron-withdrawing action of the nitro group is greatest when it is in the 2- or 4-position and that explains the sequence of values of blVRo, for compounds 1-4 in table 3. The same effect, of course, is largely responsible for the very marked differ- ences in the ionization constants lKROH of these phenols (table 1) and it is interesting to consider a possible theoretical relationship between AVRoH and '&OH.If the influence of the nitro group were simply electrostatic, it might be expected to alter the ionization constant in the manner proposed by Eucken 33 :S . D. HAMANN AND M . LINTON 2247 where 'KphOH is the ionization constant of unsubstituted phenol, p is the dipole mo- ment of the nitro group, 0 is the angle between the dipole and the C-0 bond of the phenol, r is the distance between the two groups and c is the dielectric constant of water. It follows from eqn (8) that = - 2.69(p1KROF1 - p' Kph,,,) Cll13 ITlOi- (13) where the factor 2.69 is based on the value d In E / ~ P = 4.71 x bar-l, measured by Owen ef ~ 7 1 .~ ~ for water at 25°C and 1 bar. A plot of -A* VRoH against plKRoH should therefore be a straight line with a slope'k of 2.69 cm3 mol-I. Fig. 2 shows that it is indeed so for phenol, 3-nitrophenol and 4-nitrophenol. 2-Nitrophenol (shown in brackets) deviates in a way that is understandable for an ortho derivative. PLK FIG. 2.-Plots based on eqn (12) for the ionization of mono-substituted aromatic compounds in water at 25°C. The lines have the theoretical slope of 2.69 cm3 mol-1 per pK unit. Experimental points : 0, phenols ; 0, benzoic acids ; A, phenylacetic acids. Substituents : a, H (unsubstituted) ; by 3-N02 ; c, 4-N02 ; d, 3-F ; e, 4-F ; f, 3-C1; g, 4-C1; h, 3-CH30 ; i, 4-CH30 ; j, 4-CH3.Fig. 2 also shows the data of Fischer et ~ 1 . ~ ~ for the ionization of substituted benzoic and phenylacetic acids in water at 25°C [we have recalculated A' V for these acids from eqn (7)]. Again there is remarkable agreement with the theoretical rela- tionship (1 3). Apart from the three nitrophenols, the only other monosubstituted phenol we * Any relationship, not necessarily (1 l), which supposes that the standard free energy of ionization is proportional to I /s would give the same theoretical slope.2248 IONIZATION OF PHENOLS investigated was 4-nitrosophenol, compound 13 in the tables. Its A' VRoH value lies considerably above the line for the phenols in fig. 2, but that can be explained by the fact that this compound exists in water mainly in the tautomeric form 4-benzoquinone monoxime 36 HON=-(II)=O - and so it is not comparable with true phenols.POLYSUBSTITUTED PHENOLS The effects of more than one substituent in compouiids 5-1 1, 14, 17 are only very roughly additive; there are a number of exceptions to additivity, notably 2,6- dinitrophenol, and the compounds fail to obey formula (1 3). This is hardly surprising since they all have ortho substituents and the partial molar volumes of both the parent molecules and the anions are affected by internal hydrogen bonding and steric factors as well as by simple electrostatic interactions. ANIONIC PHENOLS Compounds 12 and 18 deserve special discussion because they are negatively charged phenols which ionize to give doubly charged phenolate anions. According to (10) a change of zi from - 1 to -2 should increase electrostriction by three times as much as a change from 0 to - 1, and so A1 VROH should be correspondingly more negative for these phenols than for the others.However, that is true only if the charges are close together and act jointly on the surrounding solvent. If they are sufficiently separated in the molecule, the solvent will " see " only one at a time and A1 VRoH will then be more normal. In compound 12 the -CO, and -OH groups are about 3 A apart whereas in 18 the -SO, and -OH groups are about 6 A apart. This difference explains why A' VRoH is considerably more negative for compound 12 than for 18. SUBSTITUTED BENZOIC ACID Finally, the data listed for compound 19 relate to the first ionization of the carboxyl group of a substituted benzoic acid to give the anionic phenol 12, and so are in a different class from the other results for phenol ionizations. Understandably Al VRo, is much less negative (see the discussion of carboxylic acids and phenols in the Phenols and Naphthols section, above) and, in fact, it has the smallest value that has been observed for the ionization of any neutral weak acid.The dilatometric measurements on phenol were made in the Department of Physical and Inorganic Chemistry at the University of New England, Armidale, New South Wales, and we thank Professor R. H. Stokes and Dr. L. A. Dunn for their hospitality there and for their advice and help in that part of the work. We also thank Mr. A. J. Murphy for his help in the high pressure experiments. B.B. Owen and S. R. Brinkley, Chem. Rev., 1941, 29,461. S . D. Hamann, Physico-Chemical Eflects ofPressure (Butterworth, London, 1957). S. D. Harnann, in High Pressure Physics and Chemistry, ed. R. S. Bradiey (Academic Press, London, 1965), Vol. 2, chap. 7(ii), p. 131. S. D. Hamann, in Modern Aspects of Electrochemistry, ed. J. O'M. Bockris and B. E. Conway (Plenum, New York, 1974), Vol. 9, chap. 2, p. 47. H. von Halban and L. Ebert, Z. Phys. Chem., 1924, 112, 359.S . D . HAMANN AND M . LINTON 2249 R. A. Robinson, in The Structure of Electrolyte Solutions, ed. W. J. Hamer (Wiley, New York 1959), chap. 16, p. 253. S. D. Hamann and W. Strauss, Trans. Faraday SOC., 1955, 51, 1684. T. C. Poulter, Phys. Rev., 1932, 40, 860. * S. D. Hamann, J.Phys. Chem., 1963, 67,2233. lo R. G. Bates, J. Res. Nat. Bur. Stand. A, 1962, 66, 179. 11 L. G. Hepler, J. M. Stokes and R. H. Stokes, Trans. Faraday Soc., 1965, 61, 20. l 2 A. J. Ellis and D. W. Anderson, J. Chem. Soc., 1961, 1765. l3 D. A. Lown, H. R. Thirsk and Lord Wynne-Jones, Trans. Faraday SOC., 1970, 66, 51. l4 A. Distbche and S. Distkhe, J. Electrochem. SOC., 1965, 112, 350 ; 1967, 114, 330. P. A. Kryukov and E. D. Linov, VZNZTZ, 1969, 1102-69; 1103-69 dep. (publ. U.S.S.R. Acad. Sci., Siber. Dep., Inst. Inorg. Chem., Novosibirsk). l 6 B. S. El'yanov and S. D. Hamann, Austral. J. Chem., to be published. l7 R. C. Neuman, W. Kauzmann and A. Zipp, J. Phys. Chem., 1973, 77, 2687. l 9 L. A. Dunn, Trans. Faraday SOC., 1964, 62, 2348. 'O M. Whitfield, J. Electrochem.SOC., 1969, 116, 1042. 21 M. Planck, Ann. Phys., 1887, 32,462. 22 A. I. Biggs, Trans. Faraday SOC., 1956, 52, 35. 23 H. H. Weber and D. Nachmannsohn, Biochem. Z., 1929, 204,215. 24 E. Brander, SOC. Sci. Fennica Comm. Phys.-Math., 1932, 6(8), 42. 2 5 C. L. Liotta, A. Abidaud and H. P. Hopkins, J. Amer. Chem. Soc., 1972, 94, 8624. 26 F. J. Millero, Chem. Rev., 1971,71, 147. 27 L. A. Dunn, R. H. Stokes and L. G. Hepler, J. Phys. Chem., 1965, 69, 2808. 28 D. A. Lown, H. R. Thirsk and W. F. K. Wynne-Jones, Trans. Faraday SOC., 1968, 64, 2073 29 P. Drude and W. Nernst, 2. Phys. Chem., 1894, 15, 79. 30 E. Whalley, J. Chem. Phys., 1963,38,1400. 31 S . W. Benson and C. S. Copeland, J. Phys. Chem., 1963, 67, 1194. 32 D. E. Desnoyers, R. E. Verrell and B. E. Conway, J.Chem. Phys., 1965, 43,243. 33 A. Eucken, Angew. Chem., 1932, 45, 203. 34 B. B. Owen, R. C. Miller, C. E. Milner and H. L. Cogan, J. Phys. Chem., 1961, 65,2065. 35 A. Fischer, B. R. Mann and J. Vaughan, J. Chem. SOC., 1961, 1093. 36 R. K. Norris and S. Sternhell, Austral. J. Chem., 1966, 19, 841. 0. Redlich, J. Phys. Chem., 1963, 67, 496. eqn (7). Influence of Pressure on the Ionization of Substituted Phenols BY SEFTON D. HAMANN" AND MAX LINTON CSIRO Applied Chemistry Laboratories, G.P.O. Box 433 1, Melbourne 3001, Australia Received 1 1 th April, 1974 Spectroscopic measurements have been made of the ionization constants of eighteen substituted phenols in water at 25°C and at 1, 500, 1O00, 1500 and 2000 bar. Ionization of the phenols is en- hanced by an increase of pressure, and the derived values of the change in partial molar volume for ionization lie between - 8 and -20 cm3 mol-'.The results are discussed in terms of the molecular structures of the phenols. One of the most pronounced and general of the chemical effects of increasing pressure is the increase in the degree of ionic dissociation of weak electrolytes in solution. The enhancement of ionization is explained by the fact that compression increases the dielectric constants of liquids and so lowers the standard free energies of dissolved ions with respect to those of neutral molecules. It is related thermodyna- mically to the decrease in total volume which accompanies ionization reactions and which arises from electrostriction of solvent around the ions that are formed.The effect has been reviewed 1-4 and a tabulation of the experimental results is given in ref. (4), tables 17-23. Here, we describe spectroscopic measurements of the ionization constants of a number of phenols in water at 25°C and at pressures up to 2000 bar (1 bar = lo5 Paz0.9869 atin). The main purpose of the experiments was to see how substituent groups in the phenols alter the pressure effect and the volume change for ionization. A later paper will report similar measurements on substituted anilines. EXPERIMENTAL SPECTROSCOPIC MEASUREMENTS PRINCIPLE OF THE METHOD The spectroscopic method of von Halban has been widely used at atmospheric pressure and was applied to substituted phenols by Robinson and coworkers.6 It is based on the fact that if the parent molecule ROH and the anion RO- of a phenol have sufficiently different optical absorption spectra, the degree of ionization c( of the phenol in a buffer solution can be estimated from the relationship D = (1 - ~ ) D R O H + UDRO - (1 1 where D denotes the optical density of the buffer solution, DROH is the optical density of an acidified solution in which the phenol is virtually unionized, and DRO- is the optical density of an alkaline solution in which it is virtually fully ionized.The three optical densities are measured at the same total concentration of phenol, and for the same wavelength, path length, temperature and pressure. The molal ionization constant KROH can then be derived from the known hydrogen ion activity ~ H + Y H + of the buffer by the formula (2) which is based on the usual assumption that the activity coefficient YROH is unity.KROH = EmH + YH + YRO - /(I - a) 22392240 IONIZATION OF PHENOLS To apply the method at high pressures calls for measurements of D, &OH and DRo-, all as functions of pressure, and for an estimate of the way in which WZH +YH + and yRo - change with pressure. APPARATUS The high pressure optical measurements were made with a manually operated Unicam SP500 spectrophotometer which had been modified by moving the photocell housing to provide a 133 mrn working space for a high pressure optical cell. The cell [see fig. 13 of ref. (4)] consisted of a temperature-controlled steel block, 89x 76x 127 mm, with a 19 rnm diameter cylindrical bore designed to take a standard 10 mm square silica optical cell sup- ported in a brass holder.The block had two optically flat silica windows mounted after the manner of Poulter ; they were 12.7 mm in diameter and 9.5 mm thick, and had a viewing diameter of 6 mm. The pressure fluid was pharmaceutical grade paraffin oil, and the pres- sure was generated by a hand pump and a screw-driven ram and measured on a calibrated Bourdon gauge. The oil surrounded the inner silica cell and was in direct contact with the aqueous solution inside it. Although this presented dangers of possible contamination of the solution and of extraction of phenol from it, we found that neither occurred to any measur- able extent over a longer time than was needed for the measurements. The optical absorb- ance of the oil and loss of transmitted light by reflection at the silica surfaces combined to limit the range of reliable measurements to wavelengths greater than 300nm.For that reason we were unable to obtain high pressure data for phenol (unsubstituted) itself. Since we had no reference cell, the method of operating the spectrophotometer differed considerably from the normal. The instrument was first modified by replacing the knobs of the " sensitivity ", " dark current " and " slit width " controls by Beckman Duodials, which allowed accurate reading, resetting and locking of the controls. Before each pressure run, appropriate slit width and sensitivity settings were determined at a number of wavelengths with pure water in the optical cell at atmospheric pressure (tests showed that raising the pressure to 2000 bar had no effect on these settings). A constant slit width was chosen such that the sensitivity control was adequate over the chosen range of wavelengths, which usually spanned the absorption peak of the phenolate ion at seven intervals of 2 to 10 nm depending on the sharpness of the peak.The phenol+ buffer solution was then placed in the cell and the optical density measured at the same wavelengths and with the same dial settings as for water, at the series of pressures 1, 500, 10o0, 1500, 2000, lo00 and 1 bar. Several minutes were allowed after each change of pressure to let the temperature of the solution return to 25°C. The final measurements at loo0 and 1 bar served as checks on possible drift in the instrument or changes in the solution : they differed by no more than 0.01 in optical density from the measurements made during compression and frequently they differed by less than 0.001, although the absolute accuracy of the instrument is only claimed to be kO.0025.The success of the above method of operation depended upon the stability of the spectro- photometer over periods of an hour or more. This stability was achieved by frequently servicing the instrument, by running it from a voltage stabilizer, by using only the tungsten lamp, and by periodically replacing the lamp, the dry batteries and the electrometer and current valves. The photocell was exposed to light as briefly as possible, MATERIALS The phenols were the purest comniercially available samples. They were recrystallized and their purity was established by their melting points and absorption spectra. All the other reagents were of analytical grade.PROCEDURE The absorption spectrum of each phenol ROH and that of its anion RO- were determined separately in dilute solutions of HCl and NaOH respectively, at 25°C and at 1,500,1000,1500 and 2000 bar. The spectrum was then measured at the same temperature and pressures in one or more buffer solutions with pH close to the pKof the phenol, so that roughly half of the phenol was ionized. The total concentration of phenol was always very much less than theS . D. HAMANN AND M. LINTON 224 1 concentration of buffer. The pH of the buffer solutions was measured at atmospheric pressure with a Radiometer 25 pH meter, standardized with at least two standard buffers made according to the specifications of the National Bureau of Standards.I* Both the positions and intensities of the absorption peaks of ROH and RO- were slightly but measurably changed by pressure, the wavelengths increasing by 1-3 nm for the phenols and decreasing by 0-2 nm for the anions between 1 and 2000 bar.These changes were allowed for in calculating a. DILATOMETRIC MEASUREMENTS The absorption peaks of unsubstituted phenol and its anion occur at wavelengths shorter than 300 nm and for that reason we were unable to measure its ionization constant in the high pressure cell (see Apparatus section above). However, for comparison with the sub- stituted phenols, we measured the volume change for ionization of phenol in water at 25°C using the dilatometric apparatus and method of Hepler, Stokes and Stokes l 1 to determine the partial molar volumes of C6HsOH and C6H50- at infinite dilution.We also made a direct measurement of the volume change which accompanies the neutralization of phenol by sodium hydroxide. The substituted phenols that we studied in the high pressure experiments are in general too insoluble in water to yield reliable values by the dilatometric method. RESULTS SPEC TRO S C 0 PIC ME AS UREM EN TS METHOD OF TREATMENT As an example of the raw experimental results, fig. 1 shows the measured spectrum of 4-nitrophenol in a phosphate buffer solution at 25°C and at 1, 1000 and 2000 bar. An increase of pressure reduces the absorption at 402 nm due to the anions RO- of the phenol and raises the absorption at wavelengths below 350 nm due to the parent molecules ROH, which have their absorption peak at 314 nm.In other words, it wavelength/nm FIG. 1.-The absorption spectrum of 4-nitrophenol (9.3 x mol kg-') in aqueous phosphate buffer (NaH2P04 : 0.01 mol kg-l ; Na2HP04 : 0.01 mol kg-l) at 25°C and 1, 1000 and 2000 bar. For the purpose of this diagram the experimental optical densities have been multiplied by the relative volumes PV/l Vof compressed water, to remove the contributions of the increases of molar concentra- tion under pressure. Pressures (in bar) given against the curves. 1-7 12242 IONIZATION OF PHENOLS shifts the equilibrium depicted at the top of the diagram to the left, indicating that compression increases the acidity of the dihydrogen phosphate ion H2PO; more than it does the acidity of the phenol.OH+HPO:-;-\ OzN O-+H,PO; in water at 25°C It can be seen from this example that to proceed from the measured spectra and the derived value of a to an estimate of the ionization constant K R o H of the phenol requires additional knowledge of the ionization constant KAiI of the buffer acid at high pressures. Expressed quantitatively, the value of mH+YH+ in eqn (2) is equal to KAHmAHYAH/mA-YA- for a buffered solution, and so (2) can be written &OH = ~ ~ ( , H ~ A H Y A H Y R ~ - / Y ~ ? A - Y A - ( I -a)* (3) Values of K A H have already been measured independently at high pressures for the three buffer acids that we used in this work : acetic acid, dihydrogen phosphate and bicarbonate.The molal ionization constant of acetic acid has been determined by conductance methods up to 3000 bar 79 12* l 3 and by e.m.f. methods up to 8000 bar,l49 l5 and the values in water at 25°C and zero ionic strength can be represented accurately over the whole pressure range by the formula l6 - A1 VAH(P - 1 bar) RT[l+ b(P- 1 bar)] 'K,, = '~,,exp (4) where P denotes the pressure and the superscripts P and 1 indicate values at pressures of P and 1 bar; R and Tare the gas constant and absolute temperature; b is a con- stant equal to 9.2 x bar-' and A' VAH is the change of partial molar volume for the ionization of acetic acid in water at 25°C and 1 bar and at zero ionic strength : A' VAH = - 11.6 cm3 mol-'. The ionization constant of dihydrogen phosphate ions has been measured under pressure by conductance, e.m.f.14* methods and can be represented by (4) with the same value of b, but with A' VAH = -26.2 cm3 mol-l for the ionization of H,PO,. Similarly, 'KAH has been measured for bicarbonate ions by an e.m.f. method 14. 2o and is described by (4) with the same values of b, and with A' VA, = -27.9 cm3 mol-' for the ionization of HCO;. Another quantity which is needed in applying eqn (3) is the product of activity coefficients yAHyRO-/yA- which we shall denote by the symbol r. For acetic acid buffer, AH is electrically neutral and A- and RO- are both singly charged ions so that we can justifiably assume that r is close to unity and independent of pressure. How- ever, for dihydrogen phosphate and bicarbonate buffers, AH and RO- are singly charged whereas A-is doubly charged(HP0: -, CO -), and r is therefore significantly different from unity and is affected by pressure.In these cases we have taken the pressure dependence of and spectroscopic to be given by the formula 1 - 2.80211(P - 1 bar) RT[I +b(P- I bar)] -__- ( 5 ) where P is in bar, RT is in cm3 bar and I denotes the ionic strength of the solution at 1 bar in mol dm-3. The factor -2.802 I* is the theoretical value of the initial pres- sure dependence of RT In r at low pressures, calculated from the Debye equation allowing for the variation with pressure of the dielectric constant and density of water at 25°C (the numerical part is equal to Redlich's l 8 factor, k = 1.868, multiplied by 3). The term involving b corresponds to the one in (4) and corrects for the non-linearity of the pressure dependence of the dielectric constant and density; again, b has the value 9.2 x bar-'.S .D . HAMANN AND M . LINTON 2243 For a few strongly acidic phenols such as picric acid we used hydrochloric acid as the "buffer" and in these cases mH+ in eqn (2) was known and was independent of the pressure. However, we needed to estimate how the product yH+yRO- changed with pressure. We assumed that it varied in the same way as YH+YCl- in a solution of the same ionic strength, and estimated that variation from Dunn's measurements of the partial molar volume VHcl of hydrochloric acid in water at various concentrations, together with an assumed relationship where R, T, P and b have the same meanings as in (4) and A VHcl denotes the difference between the partial molar volume of HCl in the solution and its partial molar volume at zero ionic strength. NUMERICAL RESULTS Table 1 lists the phenols that we studied and the ionic strengths and natures of the buffer solutions that we used.It also shows the values we found for the ionization constants at atmospheric pressure and for the wavelengths Am and molar extinction coefficients E, of the absorption maxima of the phenolate ions at atmospheric pressure. Our values for these quantities agree well with those found by previous workers. TABLE 1 .-IONIZATION CONSTANTS AND OPTICAL ABSORPTION COEFFICIENTS OF PHENOLS IN WATER AT 25°C AND 1 BAR compound 1 phenolb 2 2-nitrophenol 3 3-nitrophenol 4 4-nitrophenol 5 2,4-dinitrophenol 6 2,5-dinitrophenol 7 2,6-dinitrophenol 8 2,4,6-trinitrophenol (picric acid) 9 4-ni tro-2-aminophenol 10 4-nitro-2,6-dibromophenol 11 12 13 14 15 16 17 IS 19 2,4-dini t ro-6-aminophenol 3,5-dinitrosalicylate ion (2nd ionization) 4-nitrosophenol (4-benzoquinone oxime) 2-methoxy -4-formylphenol 1-naphthol 2-naphthol 2,4-dinitro- 1 -naphthol 1 -hydroxy-2,4-dini tronaphthalene-7- sulphonate ion (flavianate ion, 2nd ionization) 3,5-dinitrosalicyclic acid (1st ionization) ionic strength, I! buf- mol fer a dm-3 P 0.124 P 0.124 P 0.05 A 0.06 A 0.05 A 0.022 H 1.00 P 0.05 A 0.11 A P P P C c HS H H 0.01 5 0.072 0.035 0,078 0.063 0.063 0.024 0.005 0.so ~KROH/ mol kg-I l.0Ox 10-'O 5 . 2 ~ 6 . 9 ~ 5.4x 3 . 8 ~ 10-1 8 . 5 ~ 4 . 2 ~ 10-9 8 . 9 ~ 10-5 1.8 x 10-4 3.1 x 10-4 optical absorptkn of ions RO- L / n m loglo ~m C b 287 3.41 415 3.66 390 3.19 402 4.27 360 4.25 439 3.63 432 3.90 357 4.16 443 3.92 400 4.00 4 .3 ~ 10-5 404 3.99 4 . 2 ~ 372 3.97 4 . 7 ~ 398 4.40 3 . 2 ~ 348 4.43 4.4~ lo-'' 332 3.87 2 S x lo-'' 345 3.46 3 . 6 ~ 3941439 4.2814.29 3 . 2 ~ 428 4.16 2 . 9 ~ lo-* 333 5.04 Key : A = acetic acid/acetate, C = bicarboiiate/carbonate, H = hydrochloric acid, HS = this hydrochloric acid + sodium chloride, P = dihydrogen phosphate/monohydrogen phosphate ; value of 'KROH for phenol is from ref. (23) ; C the units of ern are dm3 cm-' mol-'.2244 IONIZATION OF PHENOLS Table 2 shows a specimen calculation of the relative ionization constant PKROH/ 'KRoH of 4-nitrophenol at high pressures. The values A l VRoH of the volume change for ionization of the phenol at I bar and zero ionic strength were calculated from the formula which has been found to hold accurately for a wide range of ionization reactions in water to at least 8000 bar l6 ; the constant b is 9.2 x lo-' bar-'.Eqn (7) was ob- tained by integrating Planck's 21 general thermodynamic relationship aRT la K = -AV ap on the assumption that the pressure dependence of AVRoH is given by A1 VRoH [ l + b ( P - l bar)12' APVROH = (9) The results for all the phenols are summarized in table 3, and table 4 compares our values of AIVRoH with some that have been measured previously. It is difficult to estimate the absolute accuracy of our results, but we think that the values in table 3 are reliable to + 5 in the last digits listed.TABLE 2.-A SPECIMEN CALCULATION OF THE RELATIVE IONIZATION CONSTANT p K ~ ~ ~ / l r c ~ ~ ~ OF 4-NITROPHENOL IN WATER AT 25°C Plbar optical densities measured at 402 nm with a path length of 1 cm a from (1) average a a al(1 -a) 'K-/'KAH from (4) pr/rr from (5) P K ~ ~ ~ / ' K ~ ~ ~ from (3) 1 0.314 0.003 0.739 0.423 0.422 0.730 1 .om 1 .ooo 1 .Ooo 50G 0.268 0.003 0.748 0.356 0.356 0.553 1.656 0.988 1.239 1000 0.226 0.003 0.754 0.297 0.298 0.425 2.630 0.977 1.496 1500 0.191 0.003 0.760 0.248 0.250 0.333 4.024 0.967 1.775 2000 0.163 0.003 0.764 0.210 0.212 0.269 5.927 0.958 2.103 A1 YRo~/crn~ mol-I c -11.1' -10.90 -10.79 -10.91 average - 10.93 Total concentration of ROH = 3.98 x rnol kg-I ; buffer = 0.0125 mol kg-' NaHzP04+ a Average values of cc for 7 wavelengths around 402 nm at each pressure. These values were b PKROHI'KROH = P[a/(l -E)lPKAHPr/'[a/(1 - E)]'KAH'r. 0.0125 rnol kg-' Na2HP04 ; ionic strength Z = 0.05 rnol dm-3.used in the subsequent calculations. C calculated from eqn (7). DILATOMETRIC MEASUREMENTS The limiting partial molar volume of phenol at infinite dilution in water at 25°C was found to be 86.17 cm3 mol-l and the corresponding value for sodium phenolate, corrected for hydrolysis, was 66.3* cm3 mol-l. Combining these values with the difference of 1.21 cm3 mol-l between the partial molar volumes of Hf and Na+ 26 gives A1 VRoH = - 18.5* cm3 mol-l for the ionization of phenol at infinite dilution. A direct measurement of the volume change for neutralization of phenol by NaOH to give a solution containing 0.002 96 mol kg-l of sodium phenolate gave the valueS .D. HAMANN A N D M. LINTON 2245 TABLE 3.-IONIZATION OF PHENOLS IN WATER UNDER PRESSURE AT 25°C compound 1 phenol 2 2-nitrophenol 3 3-nitrophenol 4 4-nitrophenol 5 2,4-dinitrophenol 6 2,5-dinitrophenol 7 2,6-dinitrophenol 8 2,4,6-trinitrophenol (picric acid) 9 4-nitro-2-aminophenol 1 0 4-nitro-2,6-dibromophenol 1 1 2,4-dinitro-6-aminophenoI 12 3,5-dinitrosalicylate ion (2nd ionization) 13 4-nitrosophenol (4-benzoquinone oxime) 14 2-methoxy-4-formylphenol 15 1 -naphthol 16 2-naphthol 17 2,4-dinitronaphthol 1 8 1 -hydroxy-2,4-dinitronaphthalene-7- sulphonate ion (flavianate ion, 2nd ionization) 19 3,5-dinitrosalicyclic acid (1st ionization) Plbar 500 1000 1500 2000 A' VROH~ cm3 mol- 1.332 1.343 1.241 1.232 1.275 1.318 1.189 1.248 1.286 1.171 1.487 1.261 1.289 1.413 1.402 1.231 1.229 1.076 1.659 1.674 1.497 1.492 1.551 1.699 1.442 1.517 1.590 1.347 2.220 1.525 1.674 1.902 1.888 1.446 1.521 1.176 2.048 2.136 1.785 1.786 1.881 2.182 1.708 1.816 1.974 1.547 3.07 1.865 2.140 2.485 2.472 1.646 1.871 1.275 - 18.4 2.491 -13.5 2.608 -14.1 2.108 -10.9 2.149 -11.0 2.270 -11.9 2.777 -14.7 1.955 -9.9 2.165 -11.3 2.378 -12.7 1.759 -8.2 4.08 -21.1 2.209 - 11.6 2.634 -14.2 3.180 -17.2 3.167 -17.1 2.032 -9.9 2.305 - 11.8 1.397 -4.6 PKROH/'KROH is the relative molal ionization constant under pressure and A~VROH is the derived change of partial molar volume for ionization at 1 bar and zero ionic strength, calculated from eqn (7).TABLE 4.-cOMPARISON OF PUBLISHED VALUES OF A' VROH FOR PHENOLS IN WATER ref.compound: phenol 3-ni trophenol 4 4 trophenol 2,s- dinitrophenol 23 - 18.7 24 - 10.3 Cv b 25 - 18.0 - 12.8 -11.3 17 - 11.3 6' e - 1 1.3 b* e this work - 18.4 - 14.1 f - 10.9f -1l.9f A1 VROH is expressed in cm3 mol-' ; a from dilatometric measurements at 30°C, at ionic strengths between 0.1 and 0.2 mol dm-3 ; b these results have not been corrected by activity coefficients or extrapolated to zero ionic strength ; C from high pressure conductivity measurements at 40°C, on a solution with [ROH] = 0.028 mol kg-' ; dfrom density measurements at 25"C, extrapolated to zero ionic strength ; e from high pressure spectroscopic measurements at 25°C in phosphate buffer of unstated ionic strength ; f from high pressure spectroscopic measurements at 25"C, corrected by activity coefficients.+ 3.87 cm3 mol-1 (corrected for hydrolysis) which, combined with A' VH20 = -22.1 1 cm3 mol-' for the ionization of gives A' VROH = - 18.24. The tables list the average of the two values. DISCUSSION It is convenient to discuss the results in terms of the standard partial molar volume changes for ionization at atmospheric pressure, A1 VROH, since these are direct meas- ures of the general high pressure behaviour of the phenols [through the empirical2246 IONIZATION OF PHENOLS relationship (7) or similar ones ' 3* **I and are related fairly directly to the structures and electrical charge states of the ionizing molecules. The first and most obvious feature of the results is that the volume changes are all negative, as they are for the hundred or so other weak electrolytes that have been examined [see tables 17-23 of ref.(4)]. This universal contraction for ionization reactions arises from electrostriction of water around the free ions. Expressed another way, the reason why pressure increases the degree of ionization of weak electrolytes is that it enhances the hydration of ions (on a macroscopic scale, by raising the dielectric constant of water) and in this way lowers their standard free energies with respect to those of the relatively unhydrated parent molecules. Drude and Nernst 29 estimated the degree of contraction for a simple model in which the solvent was treated as a continuum of dielectric constant c and the ions were assumed to be incompressible spheres of radius r i .They concluded that the volume contraction -AVc, (electro- striction) associated with the development of a charge zie on such an ion is where zi is the valence of the ion, e is the electronic charge and N is Avogadro's constant. Although refinements have been made to that e q u a t i ~ n , ~ ' ~ . 30-32 it is sufficient here to quote it in its simple form to indicate how the electrostriction might be expected to vary with the effective size and charge of the ions. The local electric field strength and consequently the electrostriction are greatest for small ions with multiple charges. PHENOL A N D NAPHTHOLS The values of A' VRoH are between - 17 and - 19 cm3 mol-' for unsubstituted phenol and 1 -naphthol and 2-naphthol, and they are therefore intermediate between the values -22.1 cm3 mol-' for the ionization of water 27 and - 1 1 cm3 mol-' for most aliphatic carboxylic acids.3* In the ionization of water the negative charge is localized on the oxygen atom of OH-, whereas in carboxylate ions it is shared equally between the two oxygen atoms of -COT.For that reason the effective radius ri of the carboxylate ion is greater and the electrostriction is correspondingly less. In the case of phenolate and naphtholate ions there is only a single oxygen atom, but some part of the charge is carried by the aromatic ring. The relative values of A*VRoH suggest that the degree of charge delocalization is less, however, than in carboxylate ions. MONOSUBSTITUTED PHENOLS For nitrophenols, delocalization of the negative charge of the anions RO- occurs to a much greater extent than for phenol itself, because of charge transference of the type represented by the valence bond structures O=(-I>=NO;. - The electron-withdrawing action of the nitro group is greatest when it is in the 2- or 4-position and that explains the sequence of values of blVRo, for compounds 1-4 in table 3.The same effect, of course, is largely responsible for the very marked differ- ences in the ionization constants lKROH of these phenols (table 1) and it is interesting to consider a possible theoretical relationship between AVRoH and '&OH. If the influence of the nitro group were simply electrostatic, it might be expected to alter the ionization constant in the manner proposed by Eucken 33 :S . D. HAMANN AND M .LINTON 2247 where 'KphOH is the ionization constant of unsubstituted phenol, p is the dipole mo- ment of the nitro group, 0 is the angle between the dipole and the C-0 bond of the phenol, r is the distance between the two groups and c is the dielectric constant of water. It follows from eqn (8) that = - 2.69(p1KROF1 - p' Kph,,,) Cll13 ITlOi- (13) where the factor 2.69 is based on the value d In E / ~ P = 4.71 x bar-l, measured by Owen ef ~ 7 1 . ~ ~ for water at 25°C and 1 bar. A plot of -A* VRoH against plKRoH should therefore be a straight line with a slope'k of 2.69 cm3 mol-I. Fig. 2 shows that it is indeed so for phenol, 3-nitrophenol and 4-nitrophenol. 2-Nitrophenol (shown in brackets) deviates in a way that is understandable for an ortho derivative.PLK FIG. 2.-Plots based on eqn (12) for the ionization of mono-substituted aromatic compounds in water at 25°C. The lines have the theoretical slope of 2.69 cm3 mol-1 per pK unit. Experimental points : 0, phenols ; 0, benzoic acids ; A, phenylacetic acids. Substituents : a, H (unsubstituted) ; by 3-N02 ; c, 4-N02 ; d, 3-F ; e, 4-F ; f, 3-C1; g, 4-C1; h, 3-CH30 ; i, 4-CH30 ; j, 4-CH3. Fig. 2 also shows the data of Fischer et ~ 1 . ~ ~ for the ionization of substituted benzoic and phenylacetic acids in water at 25°C [we have recalculated A' V for these acids from eqn (7)]. Again there is remarkable agreement with the theoretical rela- tionship (1 3). Apart from the three nitrophenols, the only other monosubstituted phenol we * Any relationship, not necessarily (1 l), which supposes that the standard free energy of ionization is proportional to I /s would give the same theoretical slope.2248 IONIZATION OF PHENOLS investigated was 4-nitrosophenol, compound 13 in the tables.Its A' VRoH value lies considerably above the line for the phenols in fig. 2, but that can be explained by the fact that this compound exists in water mainly in the tautomeric form 4-benzoquinone monoxime 36 HON=-(II)=O - and so it is not comparable with true phenols. POLYSUBSTITUTED PHENOLS The effects of more than one substituent in compouiids 5-1 1, 14, 17 are only very roughly additive; there are a number of exceptions to additivity, notably 2,6- dinitrophenol, and the compounds fail to obey formula (1 3). This is hardly surprising since they all have ortho substituents and the partial molar volumes of both the parent molecules and the anions are affected by internal hydrogen bonding and steric factors as well as by simple electrostatic interactions.ANIONIC PHENOLS Compounds 12 and 18 deserve special discussion because they are negatively charged phenols which ionize to give doubly charged phenolate anions. According to (10) a change of zi from - 1 to -2 should increase electrostriction by three times as much as a change from 0 to - 1, and so A1 VROH should be correspondingly more negative for these phenols than for the others. However, that is true only if the charges are close together and act jointly on the surrounding solvent. If they are sufficiently separated in the molecule, the solvent will " see " only one at a time and A1 VRoH will then be more normal.In compound 12 the -CO, and -OH groups are about 3 A apart whereas in 18 the -SO, and -OH groups are about 6 A apart. This difference explains why A' VRoH is considerably more negative for compound 12 than for 18. SUBSTITUTED BENZOIC ACID Finally, the data listed for compound 19 relate to the first ionization of the carboxyl group of a substituted benzoic acid to give the anionic phenol 12, and so are in a different class from the other results for phenol ionizations. Understandably Al VRo, is much less negative (see the discussion of carboxylic acids and phenols in the Phenols and Naphthols section, above) and, in fact, it has the smallest value that has been observed for the ionization of any neutral weak acid.The dilatometric measurements on phenol were made in the Department of Physical and Inorganic Chemistry at the University of New England, Armidale, New South Wales, and we thank Professor R. H. Stokes and Dr. L. A. Dunn for their hospitality there and for their advice and help in that part of the work. We also thank Mr. A. J. Murphy for his help in the high pressure experiments. B. B. Owen and S. R. Brinkley, Chem. Rev., 1941, 29,461. S . D. Hamann, Physico-Chemical Eflects ofPressure (Butterworth, London, 1957). S. D. Harnann, in High Pressure Physics and Chemistry, ed. R. S. Bradiey (Academic Press, London, 1965), Vol. 2, chap. 7(ii), p. 131. S. D. Hamann, in Modern Aspects of Electrochemistry, ed. J. O'M. Bockris and B. E. Conway (Plenum, New York, 1974), Vol. 9, chap. 2, p. 47. H. von Halban and L. Ebert, Z. Phys. Chem., 1924, 112, 359.S . D . HAMANN AND M . LINTON 2249 R. A. Robinson, in The Structure of Electrolyte Solutions, ed. W. J. Hamer (Wiley, New York 1959), chap. 16, p. 253. S. D. Hamann and W. Strauss, Trans. Faraday SOC., 1955, 51, 1684. T. C. Poulter, Phys. Rev., 1932, 40, 860. * S. D. Hamann, J. Phys. Chem., 1963, 67,2233. lo R. G. Bates, J. Res. Nat. Bur. Stand. A, 1962, 66, 179. 11 L. G. Hepler, J. M. Stokes and R. H. Stokes, Trans. Faraday Soc., 1965, 61, 20. l 2 A. J. Ellis and D. W. Anderson, J. Chem. Soc., 1961, 1765. l3 D. A. Lown, H. R. Thirsk and Lord Wynne-Jones, Trans. Faraday SOC., 1970, 66, 51. l4 A. Distbche and S. Distkhe, J. Electrochem. SOC., 1965, 112, 350 ; 1967, 114, 330. P. A. Kryukov and E. D. Linov, VZNZTZ, 1969, 1102-69; 1103-69 dep. (publ. U.S.S.R. Acad. Sci., Siber. Dep., Inst. Inorg. Chem., Novosibirsk). l 6 B. S. El'yanov and S. D. Hamann, Austral. J. Chem., to be published. l7 R. C. Neuman, W. Kauzmann and A. Zipp, J. Phys. Chem., 1973, 77, 2687. l 9 L. A. Dunn, Trans. Faraday SOC., 1964, 62, 2348. 'O M. Whitfield, J. Electrochem. SOC., 1969, 116, 1042. 21 M. Planck, Ann. Phys., 1887, 32,462. 22 A. I. Biggs, Trans. Faraday SOC., 1956, 52, 35. 23 H. H. Weber and D. Nachmannsohn, Biochem. Z., 1929, 204,215. 24 E. Brander, SOC. Sci. Fennica Comm. Phys.-Math., 1932, 6(8), 42. 2 5 C. L. Liotta, A. Abidaud and H. P. Hopkins, J. Amer. Chem. Soc., 1972, 94, 8624. 26 F. J. Millero, Chem. Rev., 1971,71, 147. 27 L. A. Dunn, R. H. Stokes and L. G. Hepler, J. Phys. Chem., 1965, 69, 2808. 28 D. A. Lown, H. R. Thirsk and W. F. K. Wynne-Jones, Trans. Faraday SOC., 1968, 64, 2073 29 P. Drude and W. Nernst, 2. Phys. Chem., 1894, 15, 79. 30 E. Whalley, J. Chem. Phys., 1963,38,1400. 31 S . W. Benson and C. S. Copeland, J. Phys. Chem., 1963, 67, 1194. 32 D. E. Desnoyers, R. E. Verrell and B. E. Conway, J. Chem. Phys., 1965, 43,243. 33 A. Eucken, Angew. Chem., 1932, 45, 203. 34 B. B. Owen, R. C. Miller, C. E. Milner and H. L. Cogan, J. Phys. Chem., 1961, 65,2065. 35 A. Fischer, B. R. Mann and J. Vaughan, J. Chem. SOC., 1961, 1093. 36 R. K. Norris and S. Sternhell, Austral. J. Chem., 1966, 19, 841. 0. Redlich, J. Phys. Chem., 1963, 67, 496. eqn (7).

ISSN:0300-9599    

DOI:10.1039/F19747002239

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Kinetic Studies of Diatomic Free Radicals using Mass Spectrometry Part 2.-Rapid Bimolecular Reactions involving the C10 X211 Radical BY MICHAEL A. A. CLYNE‘:: AND ROBERT T. WATSON? Department of Chemistry, Queen Mary College, Mile End Road, London El 4NS Received 18th April, 1974 The kinetics of rapid bimolecular reactions involving C10, X2rI, v = 0, radicals at 298 K have been studied mass spectrometrically using molecular beam sampling from a discharge-flow system. The following rate constants (298 K, cm3 m~lecule-~ s-I) are reported : ClO+NO+Cl+NOz; kl = (1.70+0.22)~ (1) CI2P+ + 03-tC10 + 0 2 ; k2 = (1.85 0.36) x lo-’ I . (2) C10 radicals were found to be unreactive towards a range of singlet ground state molecules, up to 670 K. The reactions (1) and (2) are important rate-determining steps in the proposed C10, cycle for depletion of ozone in the stratosphere.The implications for this C10, cycle of recent measurements of rate constants involving C1, C10 and OCIO, are discussed. k i k2 The detection and determination of ground state C10 radicals using mass spectrometry, with collision-free sampling from a discharge-flow system, has been des- cribed previous1y.l This technique has been used to study the kinetics and mechan- isms of the second order decay reaction, C10 + C10-+products.2 The high sensitivity of the mass spectrometric method used has been exploited in order to measure the rate constants for a number of rapid bimolecular reactions of chlorine dioxide, OC10, with free atoms3 ; a concentration equal to 5 x 10s ~ m - ~ of OClO could be measured with signal/noise of unity.The similarly high sensitivity for measurements of 03, and of C10 radicals, in a discharge-flow system, has now been used to measure the rate constants for the rapid bimolecular reactions (1) and (2), k i k2 C1Q+NO-+C1+NQ2 ; AU19, = -39 kJ mol-I Cl2P3+ O3+C1O + O2 ; AU,”,, = - 163 kJ mol-I . (1) (2) Reaction (1) has been used as a titration reaction for the determination of absolute C10 radical concentration^,^* l 1 whilst reaction (2) has sometimes been utilized as a source of C10 radicals for kinetic studies.4* Recently, reactions (1) and (2), as well as other rapid bimolecular reactions in- volving C10 and C1, have been proposed as major steps in the C10, cycle.6* This cycle, it is suggested, depletes stratospheric ozone in atmospheres polluted by chlorine containing compounds, such as CFCl, (freons) originating from the earth’s surface, and HC1 from aerospace vehicle exhaust gases.6.The present work now provides P present address : Department of Chemistry and Lawrence Radiation Laboratory, University of California, Berkeley, California, U.S.A. 2250M. A . A . C L Y N E A N D R. T. W A T S O N 225 1 direct measurements of k , and kZ, which may be used to compute ambient concen- trations of active species in the C10, cycle. The similar NO, cycle for depletion of ozone was proposed originally in order to remedy the inadequacy of the Chapman mechanism for the production and destruction of ozone in the stratosphere, which failed to quantitatively account for the observed vertical ozone column concen- trations.' O EXPERIMENTAL The experimental system consisted of a glass discharge-flow apparatus, in which ClO radicals or Cl atoms were generated and then reacted, linked via a two-stage sampling system, to the ion source of a 90" mass spectr0meter.l An all-metal vacuum line, with careful attention to minimizing residual gases, was employed for pumping the mass spectro- meter ion source,' since the minimum detectable concentration of any species was determined in practice by the background ion current at the relevant mass peak.The details of the entire system,' and of the experimental procedures employed for studies of CI atoms and CIO radical^,^*^ have been described previously. RESULTS h i RATE OF THE REACTION NO+ClO-+NO,+Cl The measurements of the rate constant at 298 K for the reaction of NO with C10, k l , were carried out at low initial C10 concentrations, 12.0 x 10" >,[CIO]o 2 1.4 x lo1, ~ m - ~ , where second order decay of C10 was negligible,2- ClO+ClO--, products. C10 radicals were generated by addition of small concentrations of OClO to an excess (- 1 00-fold excess) of C12P+ atoms upstream of the NO + C10 reaction zone, Cl+OCl0-+2C10; k298 = (5.9k0.9) x lo-'' cm3 molecule-' s - ' .~ For the kinetic measurements of reaction (l), NO + C10-+N02 + C1, pseudo first- order conditions were used, with [NO],~[C10],, and the rate of attenuation of C10 was measured mass spectrometrically2 using m/e 51 (35C10+) : k i + d In ([ClO],/[ClO]) = k,[NO],t. (1) NO was added at a series of reaction times (2-55 ms) to the ClO radical stream, and the various values of [ClO] remaining at the mass spectrometer inlet were measured.A wide range of initial concentrations of ClO and of NO was used (23.0 x 10I2 3 [NO], 2 1.2 x 10I2 ~ m - ~ ) , giving initial stoichiometries [NO],/[ClO], from 4 to 65, with a median value of 20. Fig. 1 shows typical data for the decay of CIO in the presence of NO; good fit to first-order kinetic behaviour for [ClO] was obtained up to the highest decays observed (a factor of lo3). The lower limit of C10 concentration which could be detected (signal-to-noise of unity) was 1.5 x lo9 ~ r n - ~ , an improvement by a factor of E lo4 over detection by ultra-violet absorption spectrophotometry. Fig. 2 shows that values of -d In [ClO]/dt were directly proportional to [NO],, verifying that the rate of removal of C10 is first-order in [NO].The mean value obtained for kl from least mean squares analysis of the nineteen independent data (fig. 2) was (1.7, k0.2,) x lo-', cm3 molecule-' s-l at 298 K. Previous work by Clyne and Coxon 5 9 l 1 showed that reaction (I), between NO and C10, was rapid compared with the ClO+ClO decay reaction. Reaction (I) has been used as a flow system titration to determine 5 9 l1 absolute concentrations of C10 by detection of the null point at which the C10 absorption spectrum was just removed by addition of NO, [ClO] = [NO]. However, apart from the lower limit2252 REACTIONS OF THE c l o x2n RADICAL k f g 8 > 3 x 10-1 cm3 molecule-l s-l reported by Coxon,12 no determination of kl appears to have been made.The present result, ktg8 = (1.70+o.21) x cm3 molecule-l s-l, confirms the rapidity of reaction (1) and the validity of its use as a titration foithe measurement of ClO concentrations. It also enables the mechanism of the NO + OClO reaction to be satisfactorily reinter~reted.~ 25- 2.0 - 1 u 1.51 p time /ms FIG. 1 .-Kinetics of the NO + C10 reaction at 298 K. First order decay plots of [ClO] in the presence of various excess concentrations ~ r n - ~ ) of NO as follows: A, 2.8; 0, 6.2; M, 9.9; V, 23.2. kz RATE OF THE REACTION Cl+03+C10+02 Low concentrations of C12P+, [Cl], = 3.2 to 1 3 . 6 ~ 10l2 crn-,, flowing from the discharge-bypass,2 were reacted with 0, (diluted with 0,) at still lower concentrations (range of [O& : 3.4 to 12.4 x loll cm-,).(The decay of [Cl] through the reaction zone (<50 ms, 120 Nm-2 total pressure) was found to be less than 5 %, based on measurements of O3 consumption under different conditions (much higher [O,]) where the C1+ 0, reaction was > 99 % complete in <2 ms. ] For the kinetic measurements, pseudo first-order conditions were used with [Cl],~[O,],, and +d In ([O,],/[O,])/dt was measured from the rate of attenuation of the 0; (m/e 48) ion current : +d In ([03]o/[03])/dt = k2[ClJot. Absolute values forM. A. A . CLYNE AND R . T. WATSON 2253 [Cll0 were determined by measurement of the O3 consumption when an excess of O3 was added to the C1 atoms, [Cl], = [O,] consumed. The concentration of C1 was inadequate to generate sufficiently high concentrations of ClO for the second-order [NO]o/10’2 molecule ~ r n - ~ first-order rate constant, -d In [ClO]/dt, with [Nolo.FIG. 2.-Kinetics of the NO + C10 reaction at 298 K. Summary plot, showing variation of pseudo decay of this radical to be appreciable on the time scale used. ion current in terms of [O,] for this purpose was carried out, as described previously,l by partial conversion of O3 to NO2 by the NO+O, reaction, The calibration of 0; NO+ 03+NOz + 0 2 , time/ms FIG. 3.-Kinetics of the ClfO3 reaction at 298 K. Typical first-order decay plots of [03] in the presence of excess [Cl]. Initial concentrations (10l2 as follows: A, [Cl], = 4.00, [o& = 0.36; 0, [CI]o = 6.65, [O& = 0.70; 0, [CIIo = 10.2, [03]0 = 0.70; 0, [Cllo = 13.6; [ 0 3 ] 0 = 1.0.2254 REACTIONS OF THE c10 x2n RADICAL and then by equating [0,] reacted to the [NO,] produced in this reaction.The measurement of [Cl], was thus obtained indirectly from a calibration of NO; ion current in terms of [NO,]. The indirect nature of the measurement of [Cl], suggests that the present determination of k , may possess a greater random error than that of k,, and this possibility is reflected in the wider limits of error estimated for k 2 . 200- ,- I, a" P - c 100- . n . - . rn I W / OO 5 10 15 [Cl],/lO" atom ~ m - ~ dt with [Cll0. FIG. 4.-Kinetics of the C1+03 reaction at 298 K. Summary plot, showing variation of -d In [03]/ Fig. 3 shows typical results for the variation of log,, ([O,],/[O,]) with time, whilst the summary plot (fig.4) shows the variation of all the 12 results for the pseudo first-order rate constant - d In [03]/dt, with [Cl],. The results of 12 independent determinations gave a value for k2 of (1 .85 & 0.36) x 10-l' cm3 molecule-l s-I at 298 K. No previous determinations of k , appear to have been reported, other than a lower limit, kZg8 >. 7 x 10W3 cm3 molecule-I s-l, by Clyne and Coxon.S REACTIONS OF C1O WITH H2, CH4, C2H4, C2H2, NH3, CO AND N2O Measurements were made (at d670 K) of the effects of various added reagents upon the concentration of CIO radicals generated by the reaction, Cl + OClO+2CIO. Ultraviolet absorption spectrophotometry at the 12,O band head of the A2II--X2II system near 277.2 nm was used to measure directly the concentration of C10 radicals. The absorption cross section of ClO was taken from previous Except for CO and N20, all the remaining reagents invcstigated (H,, CH4, C2H4, C2H2, NH,) are known to react with C12P+ atoms at appreciable rates, even at 298 IS.' C12P+ atoms, which are formed during second order decay of C10 + ClO,,M .A . A . CLYNE A N D R . T . WATSON 2255 were therefore removed with Br, (or HBr), which rapidly react with C1 atoms to generate Br atoms. Abstraction of H by a Br atom is endoenergetic and therefore very slow at temperatures <700 K.16 If not removed in this way, Cl atoms initiate chain reactions capable of removing both ClO radicals and reactant RH, e.g., for H2,5 C1+ H2+HCl+H, H+ClO+HCl+O or Cl+OH, etc. In the absence of C1 atoms, no significant effect of any of the added reagents upon C10 concentration could be observed.Consideration of the added reagent concen- tration and the reaction times involved led to the upper limits for the C10 + RH rate constants given in table 1. TABLE RATE CONSTANTS ( k ) FOR ELEMENTARY REACTIONS OF c10 x2n RADlCALS reactant T / K reference k/cm3 molecule-1 s-1 0 3P NO BrO a0 298 298 298 298 298 587 587 670 273-710 670 670 670 670 3 this work 18 2, 5, 14 15 2,5 this work this work this work 5 this work this work this work this work (5.3k0.8)~ lo-" (1.7k0.2)~ 10-l' (1.3k0.3)~ (2.4+ 0.4) x 10-14 2 , s ; 4.4 x 10-14 1 4 g 5 x 10-15 G ~ X 10-15 < 7 x < 1 x 10-15 <5x 10-l6 g 4 x 10-15 < 1 x 1 0 4 5 < 1 x G 1 x 10-15 (1.3k0.1)~ exp[(-ll50f50 K ) / T ] Approximately 50 % of the BrO + C10 reaction gives Br + OClO, and the remainder gives inert products (BrCI + 02).DISCUSSION REACTIVITY OF c10 x2n RADICALS Table 1, which contains most of the direct data for the rates of elementary reactions of C10 radicals, shows three distinct groups of reactions : (i) reactions of C10 with non-singlet states (0 3P, NOX211, BrOX211), which have a collisional efficiency of around 0.1 at 298 K ; (ii) the reaction C10 + C10, which shows significant activation energy (9.4 kJ mol-I 15), and a collision efficiency of about at 298 K ; (iii) re- actions of C10 with singlet molecules (e.g., 03, CO, CH4), which are undetectably slow at temperatures up to 670 K, mostly with collision efficiencies < Direct abstraction of an atom from substrate molecules (e.g., H2, 0,) by C10 radicals, which was formerly suggested from indirect evidence,19 is now seen to be extremely inefficient.The reactivity formerly ascribed to ClO radicals in chlorine-oxygen systems l 9 is believed to be explained by the reactivity of those Cl atoms generated in the ClO+ClO decay reaction. The rapidity of the reactions of C10 with 0 3P atoms [k298 = (5.3 *0.8) x lo-" cm3 molecule-' s-' 3], and with NO [k298 = (1.7k0.2) x 10-1 ' cm3 molecule-1 s-'1, confirm the validity of the titration methods which have been employed to measure absolute ClO con~entrations,~*l~ and hence, the absorption cross section of C10 in the ultra-violet. or2256 REACTIONS OF THE c10 x2n RADICAL THE ROLE O F c1 ATOMS AND OF c10 RADICALS I N ATMOSPHERIC CHEMISTRY The NO-NO2 cycle is believed to be closely involved in determining the present level of O3 in the earth's atmosphere.20 This cycle is based on the following major elementary reactions (8) and (9) : NO+03+N02+02; kG9* = 1.8 x 10-14 cm3 molecule-'^-^,^^*^^ O+N02+NO+02 ; kgg8 = 9.5 x ks k s cm3 m ~ l e c u l e - ~ .~ ~ ~ ~ ~ These reactions together cause catalytic removal of stratospheric O3 by nitric oxide.20 At stratospheric temperatures (200-250 K), our results 3, l 3 show that the rate constant for reaction of C10 with 0 is six times as great as that for reaction of NO2 with 0 [see table 2(a)].29 The following C1 atom cycle, in some circumstances, may therefore be more efficient than the NO-NO2 cycle in its catalytic removal of O3 * ; Cl + O3 -+ ClO + 02, c10 + o-+c1+ 0,.This mechanism,6* consumption of O3 and of 0. as for the NO-N02 (NO,) mechanism, leads overall, to the TABLE 2(a).-(i) ELEMENTARY REACTIONS OF MAJOR IMPORTANCE IN THE c10, CYCLE altitude/ km temperature/K reaction J , k i c12 + hv-2C1 kz CI+ o3+c1o+ o2 0 + CIO+CI + 0 2 k4 CI + CHA+CH3 + HCl k5 0 + HCI-tHO + CI k6 HO + HCl+H20 + CI k7 NO + CIWN02 + C1 k3 C1+ C1+ M-412 + M species units 10-3 s 10-11 cn13 10-11 10-11 10-14 10-17 10-13 10-31 cm6 conc./ cm-3 1018 1012 106 1012 109 109 15 25 35 217 223 234 2 2 2 1.7 1.7 1.7 1.8 1.8 1.8 5.3 5.3 5.3 1.7 2.1 3.1 5.5 7.3 11.6 4.4 4.6 4.9 3.7 3.3 2.7 (ii) CONCENTRATIONS 21 4.3 0.84 0.17 1.2 4.4 2.4 1 . 4 ~ 105 1 . 9 ~ 107 3 . 2 ~ 108 0.5 0.89 3.1 7.1 1.3 0.17 1.4 1.4 1.1 0.63 2.5 1.2 45 264 2 1.7 1.8 5.3 7.2 34.7 5.8 1.8 0.041 0.29 9.6 0.02 0.30 0.014 5.3 x 109 references & comments calculated using ref.(22) this work ; assumes E, = 0 this work ; assumes E, = 0 ref. (3) ; assumes E, = 0 calculated from ref. (23) ref. (26) ref. (27) ref. (28) At most altitudes, the first reaction for converting C1 atoms to an (inert) even- electron chlorine-containing species is the abstraction of H from CH4,* k4 C1+ CH,+CH3 + HCI. However, at stratospheric concentrations, HC1 reacts with OH to regenerate C1, 1; 6 OH + HCI+H,O + C1. (HCl may be photolyzed in the atmospheric spectral window (175-210 nm), which lies between the intense Hartley bands of 0, and the Schumann-Runge bands of 0,.hi. A . A . CLYNE AND R. f'. WATSObf 2257 However, the rate of photolysis of HC1 is generally less than the rate of its reaction with OH.) Chain terminations either involving the C10, cycle alone, or with species involved in the NO, cycle, generally lead to molecules which are readily dissociated photolytically between 300 and 350 nm, e.g.Our value for k , , C10+NO+C1+N02, [reaction (l)], confirms that under some calculated stratospheric conditions, reaction (1) is faster than the reaction C10 + O+Cl+ 02.* This conclusion shows that there is likely to be interaction between the C10, and NO, cycles, and all the relevant rate constants should be employed in order to calculate O3 concentration profiles. The role of the C10, cycle in depleting atmospheric ozone, with particular re- ference to interaction of the C10, and NO, cycles, is considered further using simple models.Concentrations of 03, 0 3P, NO, NO2 etc. [table 2(a)] are those determined from Chang's computational model. The steady-state concentrations of major chlorine species (HCl, ClO, Cl) are calculated on the assumption that the total C10, mole fraction at any altitude (15-45 km) is The rate constants for the C10, reactions of major importance are listed in table 2(a). Steady state concentrations are given by eqn (11) and (111), C1+ NO + M-ClNO + M, Cl+ NO2 + M-ClNO, + M. [~~Ol/[ClI = kz[O3l/(k,"Ol +kJCOl) (11) [HCII/[C1I = ~ ~ [ C H ~ I / ( ~ J [ O I f bCOHI)* (111) The values for these ratios, [ClO]/[Cl] and [HCl]/[Cl], as a function of altitude, are given in table 2(b). Mechanisms (A) and (B) are considered for ozone depletion in the C10, cycle k2 k3 C1+O,-,C10+0,, 0+c10+c1+02, (A) net O + 0 3 - d 0 2 .k2 ki NO + C10 +NO2 + CI, ks 0 +NO,+NO + 0 2 C1 +03 - 4 1 0 +02, (B) net 0 +o, +202 The efficiency of these mechanisms may be directly compared with that of the NO, cycle (C), for which many column density computations have been performed : k9 ks (C) NO+03 4N02+02, 0 +NO,+NO + 0 2 net 0 +03 +202 The data of table 2(b) show that, except at 45 km, reaction (1) is always more rapid than reaction (3), so that the dominant fate of C10 is reaction with NO to form NO2. This discussion assumes that neither OClO nor ClOO is important in the stratosphere ; both these species, if formed, would probably be readily photolyzed. Turning now to the efficiency of each mechanism (A), (B), (C) for ozone depletion, this efficiency is kinetically controlled by the slowest elementary reaction rate within2258 REACTIONS OF THE c10 x2n RADICAL the mechanism in question.The high calculated stratospheric NO concentration and the rapidity now reported for reaction (l), lead to the result that at 25 km and below, reaction (8), O+NO,-+NO+O,, is rate controlling in both mechanisms (B) and TABLE 2(b).-CALCULATED STEADY STATE CONCENTRATIONS AND RELATIVE REACTION RATES IN THE c10, CYCLE 15 altitude/ km 25 35 45 comments 0 . 5 2 ~ 106 9.2 x 102 17.3 x 10-4 4.3 x 109 7.9 x 103 7.4x 106 54.7 17.61 x 104 8.1 x 102 I 7.4 x 104 concentration ratios 0.63 x 105 3.3 x 103 1.7 x 102 5.3 x 10-2 0.36 10.5x 10-2 3.3 x 103 1 . 2 ~ 103 18.2 concentrationS cm-3 8.4 x 10s 1 . 4 ~ 108 3.8 x lo7 4.4 x 107 6.0 x 107 4.4 x 106 13.1 x 103 4 .3 ~ 104 2 . 2 ~ 105 rates of reaction/molecule cm-3 s-I 4.4X lo4 10.2X 105 1 2 . 4 ~ 105 mechanismA 10.5~ 105 1 1 . 5 ~ 105 2.2 X lo4 mechanism B 4.4 x 105 3.5 x 106 6.8 x 105 mechanisms B, C 1 0 . 3 ~ 105 1 8 . 6 ~ lo5 1 1 . 5 ~ 105 mechanisms A, B (C) [table 2(6)]. The effects of added C10, are highly dependent on concentrations of active chlorine species. The C10, acts as an addition to the NO, pool, and does not contribute via (B) to the depletion of ozone until the rate of reaction k,[NO][ClO] is comparable to the rate of reaction k,[NO][03]. At altitudes above about 25 km, the relative contributions of cycles (A) and (B) to O3 destruction are very dependent on the concentration level of ClO,. However, within the more likely limits of that level, the pure C10, cycle (A) is expected to be more effective than the mixed CI0,-NO, cycle (B), for the destruction of stratospheric ozone.Finally, we note that C10, chemistry is strongly dependent on the concentrations of NO and of OH in the stratosphere; these are probably no better known than within factors of 2 and 3, respectively. We thank the S.R.C., the Ministry of Defence and the Central Research Fund Committee of London University for support of this research. We are grateful to F. S. Rowland, D. Garvin, R. S. Stolarski and R. J. Cicerone, for preprints of their articles. The contribution of R. F. Walker to aspects of the experimental work is gratefully acknowledged. Part 1, M. A. A. Clyne and R. T. Watson, J.C.S. Faruday Z, 1974, 70, 1109.M. A. A. Clyne, D. J. McKenney and R. T. Watson, J.C.S. Furaday I, 1975, in press. P. P. Bemand, M. A. A. Clyne and R. T. Watson, J.C.S. Faruduy I, 1973, 69, 1356. W. D. McGrath and R. G. W. Norrish, Proc. Roy. SOC. A , 1960, 254, 317. M. A. A. Clyne and J. A. Coxon, Proc. Roy. SOC. A, 1968,303, 207. R. S. Stolarski and R. J. Cicerone, Canad. J. Chein., 1974, 52, 1610. D. Garvin, C.I.A.P. Monograph No. 5.7.5. Chlorine and the Chlorine Oxides (Nat. Bur. Stand., Washington D.C., 1973). M. J. Molina and F. S. Rowland, Nature, 1974, 249, 810; see also M. A. A. Clyne, Nature, 1974, 249, 796. S. Chapman, Mem. Roy. Meteorol. SOC., 1930, 3, 130. M. A. A. Clyne and J. A. Coxon, Trans. Faruday Soc., 1966,62, 1175. lo H. S. Johnston and G. Whitten, Pure Appl. Geoplzys., 1973, 106-108, 1468.l 2 J. A. Coxon, Ph.D. Thesis, (University of East Anglia, 1967). l3 P. P. Bemand, M. A. A. Clyne and R. T. Watson, J.C.S. Faruduy ZI, 1974,70, 564. l 4 N. Basco and S. K. Dogra, Proc. Roy. SOC. A, 1971, 323, 1. l 5 M. A. A. Clyne and I. F. White, Traits. Faruduy Soc., 1971, 67, 2068. l 6 G. C. Fettis and J. H. Knox, Progr. Reaction Kinetics, 1964, 2, 1. l 7 M. A. A. Clyne and H. W. Cruse, J.C.S. Faruduy ZI, 1972, 68, 1377.M. A . A . CLYNE AND R. T . WATSON 2259 l 8 M. A. A. Clyne and R. T. Watson, to be published. l9 see, for example, T. Iredale and T. G. Edwards, J. Amer. Chern. SOC., 1937,59, 761 ; R. G. W. 2o H. S. Johnston, Science, 1971, 173, 517; P. J. Crutzen, J. Geophys. Res., 1971, 30,7311. 21 J. S. Chang, Lawrence Livermore Calculations.The set of column densities given is for a one-dimensional diffusion model with the sun at 45". 2 2 D. J. Seery and D. Britton, J. Phys. Chem., 1964, 68, 226. 23 M. A. A. Clyne and R. F. Walker, J.C.S. Faraday I, 1973, 69, 1547. 24 H. S. Johnston and H. J. Crosby, J. Chem. Phys., 1954,22,689; L. F. Phillips and H. I. Schiff, J. Chem. Phys., 1962, 36, 1509; M. A. A. Clyne, B. A. Thrush and R. P. Wayne, Trans. Faraday SOC., 1964,60,359; P. P. Bemand, M. A, A. Clyne and R. T. Watson, J.C.S. Faraday II, 1974, 70, 564. Norrish and G. H. J. Neville, J. Chem. SOC., 1934, 1864. 2 5 D. D. Davis, J. T. Herron and R. E. Huie, J. Chem. Phys., 1973, 58, 530. 26 V. P. Balakhnin, V. I. Egarov and E. I. Intezorova, Kinetics and Catalysis, 1971, 12, 299. " F. Kaufman, to be published; G.A. Takacs and G. P. Glass, J. Phys. Chem., 1973,77,1948. 28 M. A. A. Clyne and D. H. Stedman, Trans. Faraday SOC., 1968, 64, 2698. 29 As discussed in ref. 3, k3 is assumed to have a zero temperature coefficient. Kinetic Studies of Diatomic Free Radicals using Mass Spectrometry Part 2.-Rapid Bimolecular Reactions involving the C10 X211 Radical BY MICHAEL A. A. CLYNE‘:: AND ROBERT T. WATSON? Department of Chemistry, Queen Mary College, Mile End Road, London El 4NS Received 18th April, 1974 The kinetics of rapid bimolecular reactions involving C10, X2rI, v = 0, radicals at 298 K have been studied mass spectrometrically using molecular beam sampling from a discharge-flow system. The following rate constants (298 K, cm3 m~lecule-~ s-I) are reported : ClO+NO+Cl+NOz; kl = (1.70+0.22)~ (1) CI2P+ + 03-tC10 + 0 2 ; k2 = (1.85 0.36) x lo-’ I .(2) C10 radicals were found to be unreactive towards a range of singlet ground state molecules, up to 670 K. The reactions (1) and (2) are important rate-determining steps in the proposed C10, cycle for depletion of ozone in the stratosphere. The implications for this C10, cycle of recent measurements of rate constants involving C1, C10 and OCIO, are discussed. k i k2 The detection and determination of ground state C10 radicals using mass spectrometry, with collision-free sampling from a discharge-flow system, has been des- cribed previous1y.l This technique has been used to study the kinetics and mechan- isms of the second order decay reaction, C10 + C10-+products.2 The high sensitivity of the mass spectrometric method used has been exploited in order to measure the rate constants for a number of rapid bimolecular reactions of chlorine dioxide, OC10, with free atoms3 ; a concentration equal to 5 x 10s ~ m - ~ of OClO could be measured with signal/noise of unity.The similarly high sensitivity for measurements of 03, and of C10 radicals, in a discharge-flow system, has now been used to measure the rate constants for the rapid bimolecular reactions (1) and (2), k i k2 C1Q+NO-+C1+NQ2 ; AU19, = -39 kJ mol-I Cl2P3+ O3+C1O + O2 ; AU,”,, = - 163 kJ mol-I . (1) (2) Reaction (1) has been used as a titration reaction for the determination of absolute C10 radical concentration^,^* l 1 whilst reaction (2) has sometimes been utilized as a source of C10 radicals for kinetic studies.4* Recently, reactions (1) and (2), as well as other rapid bimolecular reactions in- volving C10 and C1, have been proposed as major steps in the C10, cycle.6* This cycle, it is suggested, depletes stratospheric ozone in atmospheres polluted by chlorine containing compounds, such as CFCl, (freons) originating from the earth’s surface, and HC1 from aerospace vehicle exhaust gases.6.The present work now provides P present address : Department of Chemistry and Lawrence Radiation Laboratory, University of California, Berkeley, California, U.S.A. 2250M. A . A . C L Y N E A N D R. T. W A T S O N 225 1 direct measurements of k , and kZ, which may be used to compute ambient concen- trations of active species in the C10, cycle.The similar NO, cycle for depletion of ozone was proposed originally in order to remedy the inadequacy of the Chapman mechanism for the production and destruction of ozone in the stratosphere, which failed to quantitatively account for the observed vertical ozone column concen- trations.' O EXPERIMENTAL The experimental system consisted of a glass discharge-flow apparatus, in which ClO radicals or Cl atoms were generated and then reacted, linked via a two-stage sampling system, to the ion source of a 90" mass spectr0meter.l An all-metal vacuum line, with careful attention to minimizing residual gases, was employed for pumping the mass spectro- meter ion source,' since the minimum detectable concentration of any species was determined in practice by the background ion current at the relevant mass peak.The details of the entire system,' and of the experimental procedures employed for studies of CI atoms and CIO radical^,^*^ have been described previously. RESULTS h i RATE OF THE REACTION NO+ClO-+NO,+Cl The measurements of the rate constant at 298 K for the reaction of NO with C10, k l , were carried out at low initial C10 concentrations, 12.0 x 10" >,[CIO]o 2 1.4 x lo1, ~ m - ~ , where second order decay of C10 was negligible,2- ClO+ClO--, products. C10 radicals were generated by addition of small concentrations of OClO to an excess (- 1 00-fold excess) of C12P+ atoms upstream of the NO + C10 reaction zone, Cl+OCl0-+2C10; k298 = (5.9k0.9) x lo-'' cm3 molecule-' s - ' . ~ For the kinetic measurements of reaction (l), NO + C10-+N02 + C1, pseudo first- order conditions were used, with [NO],~[C10],, and the rate of attenuation of C10 was measured mass spectrometrically2 using m/e 51 (35C10+) : k i + d In ([ClO],/[ClO]) = k,[NO],t.(1) NO was added at a series of reaction times (2-55 ms) to the ClO radical stream, and the various values of [ClO] remaining at the mass spectrometer inlet were measured. A wide range of initial concentrations of ClO and of NO was used (23.0 x 10I2 3 [NO], 2 1.2 x 10I2 ~ m - ~ ) , giving initial stoichiometries [NO],/[ClO], from 4 to 65, with a median value of 20. Fig. 1 shows typical data for the decay of CIO in the presence of NO; good fit to first-order kinetic behaviour for [ClO] was obtained up to the highest decays observed (a factor of lo3). The lower limit of C10 concentration which could be detected (signal-to-noise of unity) was 1.5 x lo9 ~ r n - ~ , an improvement by a factor of E lo4 over detection by ultra-violet absorption spectrophotometry.Fig. 2 shows that values of -d In [ClO]/dt were directly proportional to [NO],, verifying that the rate of removal of C10 is first-order in [NO]. The mean value obtained for kl from least mean squares analysis of the nineteen independent data (fig. 2) was (1.7, k0.2,) x lo-', cm3 molecule-' s-l at 298 K. Previous work by Clyne and Coxon 5 9 l 1 showed that reaction (I), between NO and C10, was rapid compared with the ClO+ClO decay reaction. Reaction (I) has been used as a flow system titration to determine 5 9 l1 absolute concentrations of C10 by detection of the null point at which the C10 absorption spectrum was just removed by addition of NO, [ClO] = [NO].However, apart from the lower limit2252 REACTIONS OF THE c l o x2n RADICAL k f g 8 > 3 x 10-1 cm3 molecule-l s-l reported by Coxon,12 no determination of kl appears to have been made. The present result, ktg8 = (1.70+o.21) x cm3 molecule-l s-l, confirms the rapidity of reaction (1) and the validity of its use as a titration foithe measurement of ClO concentrations. It also enables the mechanism of the NO + OClO reaction to be satisfactorily reinter~reted.~ 25- 2.0 - 1 u 1.51 p time /ms FIG. 1 .-Kinetics of the NO + C10 reaction at 298 K. First order decay plots of [ClO] in the presence of various excess concentrations ~ r n - ~ ) of NO as follows: A, 2.8; 0, 6.2; M, 9.9; V, 23.2.kz RATE OF THE REACTION Cl+03+C10+02 Low concentrations of C12P+, [Cl], = 3.2 to 1 3 . 6 ~ 10l2 crn-,, flowing from the discharge-bypass,2 were reacted with 0, (diluted with 0,) at still lower concentrations (range of [O& : 3.4 to 12.4 x loll cm-,). (The decay of [Cl] through the reaction zone (<50 ms, 120 Nm-2 total pressure) was found to be less than 5 %, based on measurements of O3 consumption under different conditions (much higher [O,]) where the C1+ 0, reaction was > 99 % complete in <2 ms. ] For the kinetic measurements, pseudo first-order conditions were used with [Cl],~[O,],, and +d In ([O,],/[O,])/dt was measured from the rate of attenuation of the 0; (m/e 48) ion current : +d In ([03]o/[03])/dt = k2[ClJot.Absolute values forM. A. A . CLYNE AND R . T. WATSON 2253 [Cll0 were determined by measurement of the O3 consumption when an excess of O3 was added to the C1 atoms, [Cl], = [O,] consumed. The concentration of C1 was inadequate to generate sufficiently high concentrations of ClO for the second-order [NO]o/10’2 molecule ~ r n - ~ first-order rate constant, -d In [ClO]/dt, with [Nolo. FIG. 2.-Kinetics of the NO + C10 reaction at 298 K. Summary plot, showing variation of pseudo decay of this radical to be appreciable on the time scale used. ion current in terms of [O,] for this purpose was carried out, as described previously,l by partial conversion of O3 to NO2 by the NO+O, reaction, The calibration of 0; NO+ 03+NOz + 0 2 , time/ms FIG. 3.-Kinetics of the ClfO3 reaction at 298 K.Typical first-order decay plots of [03] in the presence of excess [Cl]. Initial concentrations (10l2 as follows: A, [Cl], = 4.00, [o& = 0.36; 0, [CI]o = 6.65, [O& = 0.70; 0, [CIIo = 10.2, [03]0 = 0.70; 0, [Cllo = 13.6; [ 0 3 ] 0 = 1.0.2254 REACTIONS OF THE c10 x2n RADICAL and then by equating [0,] reacted to the [NO,] produced in this reaction. The measurement of [Cl], was thus obtained indirectly from a calibration of NO; ion current in terms of [NO,]. The indirect nature of the measurement of [Cl], suggests that the present determination of k , may possess a greater random error than that of k,, and this possibility is reflected in the wider limits of error estimated for k 2 . 200- ,- I, a" P - c 100- . n . - . rn I W / OO 5 10 15 [Cl],/lO" atom ~ m - ~ dt with [Cll0.FIG. 4.-Kinetics of the C1+03 reaction at 298 K. Summary plot, showing variation of -d In [03]/ Fig. 3 shows typical results for the variation of log,, ([O,],/[O,]) with time, whilst the summary plot (fig. 4) shows the variation of all the 12 results for the pseudo first-order rate constant - d In [03]/dt, with [Cl],. The results of 12 independent determinations gave a value for k2 of (1 .85 & 0.36) x 10-l' cm3 molecule-l s-I at 298 K. No previous determinations of k , appear to have been reported, other than a lower limit, kZg8 >. 7 x 10W3 cm3 molecule-I s-l, by Clyne and Coxon.S REACTIONS OF C1O WITH H2, CH4, C2H4, C2H2, NH3, CO AND N2O Measurements were made (at d670 K) of the effects of various added reagents upon the concentration of CIO radicals generated by the reaction, Cl + OClO+2CIO.Ultraviolet absorption spectrophotometry at the 12,O band head of the A2II--X2II system near 277.2 nm was used to measure directly the concentration of C10 radicals. The absorption cross section of ClO was taken from previous Except for CO and N20, all the remaining reagents invcstigated (H,, CH4, C2H4, C2H2, NH,) are known to react with C12P+ atoms at appreciable rates, even at 298 IS.' C12P+ atoms, which are formed during second order decay of C10 + ClO,,M . A . A . CLYNE A N D R . T . WATSON 2255 were therefore removed with Br, (or HBr), which rapidly react with C1 atoms to generate Br atoms. Abstraction of H by a Br atom is endoenergetic and therefore very slow at temperatures <700 K.16 If not removed in this way, Cl atoms initiate chain reactions capable of removing both ClO radicals and reactant RH, e.g., for H2,5 C1+ H2+HCl+H, H+ClO+HCl+O or Cl+OH, etc.In the absence of C1 atoms, no significant effect of any of the added reagents upon C10 concentration could be observed. Consideration of the added reagent concen- tration and the reaction times involved led to the upper limits for the C10 + RH rate constants given in table 1. TABLE RATE CONSTANTS ( k ) FOR ELEMENTARY REACTIONS OF c10 x2n RADlCALS reactant T / K reference k/cm3 molecule-1 s-1 0 3P NO BrO a0 298 298 298 298 298 587 587 670 273-710 670 670 670 670 3 this work 18 2, 5, 14 15 2,5 this work this work this work 5 this work this work this work this work (5.3k0.8)~ lo-" (1.7k0.2)~ 10-l' (1.3k0.3)~ (2.4+ 0.4) x 10-14 2 , s ; 4.4 x 10-14 1 4 g 5 x 10-15 G ~ X 10-15 < 7 x < 1 x 10-15 <5x 10-l6 g 4 x 10-15 < 1 x 1 0 4 5 < 1 x G 1 x 10-15 (1.3k0.1)~ exp[(-ll50f50 K ) / T ] Approximately 50 % of the BrO + C10 reaction gives Br + OClO, and the remainder gives inert products (BrCI + 02).DISCUSSION REACTIVITY OF c10 x2n RADICALS Table 1, which contains most of the direct data for the rates of elementary reactions of C10 radicals, shows three distinct groups of reactions : (i) reactions of C10 with non-singlet states (0 3P, NOX211, BrOX211), which have a collisional efficiency of around 0.1 at 298 K ; (ii) the reaction C10 + C10, which shows significant activation energy (9.4 kJ mol-I 15), and a collision efficiency of about at 298 K ; (iii) re- actions of C10 with singlet molecules (e.g., 03, CO, CH4), which are undetectably slow at temperatures up to 670 K, mostly with collision efficiencies < Direct abstraction of an atom from substrate molecules (e.g., H2, 0,) by C10 radicals, which was formerly suggested from indirect evidence,19 is now seen to be extremely inefficient.The reactivity formerly ascribed to ClO radicals in chlorine-oxygen systems l 9 is believed to be explained by the reactivity of those Cl atoms generated in the ClO+ClO decay reaction. The rapidity of the reactions of C10 with 0 3P atoms [k298 = (5.3 *0.8) x lo-" cm3 molecule-' s-' 3], and with NO [k298 = (1.7k0.2) x 10-1 ' cm3 molecule-1 s-'1, confirm the validity of the titration methods which have been employed to measure absolute ClO con~entrations,~*l~ and hence, the absorption cross section of C10 in the ultra-violet.or2256 REACTIONS OF THE c10 x2n RADICAL THE ROLE O F c1 ATOMS AND OF c10 RADICALS I N ATMOSPHERIC CHEMISTRY The NO-NO2 cycle is believed to be closely involved in determining the present level of O3 in the earth's atmosphere.20 This cycle is based on the following major elementary reactions (8) and (9) : NO+03+N02+02; kG9* = 1.8 x 10-14 cm3 molecule-'^-^,^^*^^ O+N02+NO+02 ; kgg8 = 9.5 x ks k s cm3 m ~ l e c u l e - ~ . ~ ~ ~ ~ ~ These reactions together cause catalytic removal of stratospheric O3 by nitric oxide.20 At stratospheric temperatures (200-250 K), our results 3, l 3 show that the rate constant for reaction of C10 with 0 is six times as great as that for reaction of NO2 with 0 [see table 2(a)].29 The following C1 atom cycle, in some circumstances, may therefore be more efficient than the NO-NO2 cycle in its catalytic removal of O3 * ; Cl + O3 -+ ClO + 02, c10 + o-+c1+ 0,.This mechanism,6* consumption of O3 and of 0. as for the NO-N02 (NO,) mechanism, leads overall, to the TABLE 2(a).-(i) ELEMENTARY REACTIONS OF MAJOR IMPORTANCE IN THE c10, CYCLE altitude/ km temperature/K reaction J , k i c12 + hv-2C1 kz CI+ o3+c1o+ o2 0 + CIO+CI + 0 2 k4 CI + CHA+CH3 + HCl k5 0 + HCI-tHO + CI k6 HO + HCl+H20 + CI k7 NO + CIWN02 + C1 k3 C1+ C1+ M-412 + M species units 10-3 s 10-11 cn13 10-11 10-11 10-14 10-17 10-13 10-31 cm6 conc./ cm-3 1018 1012 106 1012 109 109 15 25 35 217 223 234 2 2 2 1.7 1.7 1.7 1.8 1.8 1.8 5.3 5.3 5.3 1.7 2.1 3.1 5.5 7.3 11.6 4.4 4.6 4.9 3.7 3.3 2.7 (ii) CONCENTRATIONS 21 4.3 0.84 0.17 1.2 4.4 2.4 1 .4 ~ 105 1 . 9 ~ 107 3 . 2 ~ 108 0.5 0.89 3.1 7.1 1.3 0.17 1.4 1.4 1.1 0.63 2.5 1.2 45 264 2 1.7 1.8 5.3 7.2 34.7 5.8 1.8 0.041 0.29 9.6 0.02 0.30 0.014 5.3 x 109 references & comments calculated using ref. (22) this work ; assumes E, = 0 this work ; assumes E, = 0 ref. (3) ; assumes E, = 0 calculated from ref. (23) ref. (26) ref. (27) ref. (28) At most altitudes, the first reaction for converting C1 atoms to an (inert) even- electron chlorine-containing species is the abstraction of H from CH4,* k4 C1+ CH,+CH3 + HCI. However, at stratospheric concentrations, HC1 reacts with OH to regenerate C1, 1; 6 OH + HCI+H,O + C1. (HCl may be photolyzed in the atmospheric spectral window (175-210 nm), which lies between the intense Hartley bands of 0, and the Schumann-Runge bands of 0,.hi.A . A . CLYNE AND R. f'. WATSObf 2257 However, the rate of photolysis of HC1 is generally less than the rate of its reaction with OH.) Chain terminations either involving the C10, cycle alone, or with species involved in the NO, cycle, generally lead to molecules which are readily dissociated photolytically between 300 and 350 nm, e.g. Our value for k , , C10+NO+C1+N02, [reaction (l)], confirms that under some calculated stratospheric conditions, reaction (1) is faster than the reaction C10 + O+Cl+ 02.* This conclusion shows that there is likely to be interaction between the C10, and NO, cycles, and all the relevant rate constants should be employed in order to calculate O3 concentration profiles.The role of the C10, cycle in depleting atmospheric ozone, with particular re- ference to interaction of the C10, and NO, cycles, is considered further using simple models. Concentrations of 03, 0 3P, NO, NO2 etc. [table 2(a)] are those determined from Chang's computational model. The steady-state concentrations of major chlorine species (HCl, ClO, Cl) are calculated on the assumption that the total C10, mole fraction at any altitude (15-45 km) is The rate constants for the C10, reactions of major importance are listed in table 2(a). Steady state concentrations are given by eqn (11) and (111), C1+ NO + M-ClNO + M, Cl+ NO2 + M-ClNO, + M. [~~Ol/[ClI = kz[O3l/(k,"Ol +kJCOl) (11) [HCII/[C1I = ~ ~ [ C H ~ I / ( ~ J [ O I f bCOHI)* (111) The values for these ratios, [ClO]/[Cl] and [HCl]/[Cl], as a function of altitude, are given in table 2(b).Mechanisms (A) and (B) are considered for ozone depletion in the C10, cycle k2 k3 C1+O,-,C10+0,, 0+c10+c1+02, (A) net O + 0 3 - d 0 2 . k2 ki NO + C10 +NO2 + CI, ks 0 +NO,+NO + 0 2 C1 +03 - 4 1 0 +02, (B) net 0 +o, +202 The efficiency of these mechanisms may be directly compared with that of the NO, cycle (C), for which many column density computations have been performed : k9 ks (C) NO+03 4N02+02, 0 +NO,+NO + 0 2 net 0 +03 +202 The data of table 2(b) show that, except at 45 km, reaction (1) is always more rapid than reaction (3), so that the dominant fate of C10 is reaction with NO to form NO2. This discussion assumes that neither OClO nor ClOO is important in the stratosphere ; both these species, if formed, would probably be readily photolyzed.Turning now to the efficiency of each mechanism (A), (B), (C) for ozone depletion, this efficiency is kinetically controlled by the slowest elementary reaction rate within2258 REACTIONS OF THE c10 x2n RADICAL the mechanism in question. The high calculated stratospheric NO concentration and the rapidity now reported for reaction (l), lead to the result that at 25 km and below, reaction (8), O+NO,-+NO+O,, is rate controlling in both mechanisms (B) and TABLE 2(b).-CALCULATED STEADY STATE CONCENTRATIONS AND RELATIVE REACTION RATES IN THE c10, CYCLE 15 altitude/ km 25 35 45 comments 0 . 5 2 ~ 106 9.2 x 102 17.3 x 10-4 4.3 x 109 7.9 x 103 7.4x 106 54.7 17.61 x 104 8.1 x 102 I 7.4 x 104 concentration ratios 0.63 x 105 3.3 x 103 1.7 x 102 5.3 x 10-2 0.36 10.5x 10-2 3.3 x 103 1 .2 ~ 103 18.2 concentrationS cm-3 8.4 x 10s 1 . 4 ~ 108 3.8 x lo7 4.4 x 107 6.0 x 107 4.4 x 106 13.1 x 103 4 . 3 ~ 104 2 . 2 ~ 105 rates of reaction/molecule cm-3 s-I 4.4X lo4 10.2X 105 1 2 . 4 ~ 105 mechanismA 10.5~ 105 1 1 . 5 ~ 105 2.2 X lo4 mechanism B 4.4 x 105 3.5 x 106 6.8 x 105 mechanisms B, C 1 0 . 3 ~ 105 1 8 . 6 ~ lo5 1 1 . 5 ~ 105 mechanisms A, B (C) [table 2(6)]. The effects of added C10, are highly dependent on concentrations of active chlorine species. The C10, acts as an addition to the NO, pool, and does not contribute via (B) to the depletion of ozone until the rate of reaction k,[NO][ClO] is comparable to the rate of reaction k,[NO][03]. At altitudes above about 25 km, the relative contributions of cycles (A) and (B) to O3 destruction are very dependent on the concentration level of ClO,. However, within the more likely limits of that level, the pure C10, cycle (A) is expected to be more effective than the mixed CI0,-NO, cycle (B), for the destruction of stratospheric ozone.Finally, we note that C10, chemistry is strongly dependent on the concentrations of NO and of OH in the stratosphere; these are probably no better known than within factors of 2 and 3, respectively. We thank the S.R.C., the Ministry of Defence and the Central Research Fund Committee of London University for support of this research. We are grateful to F. S. Rowland, D. Garvin, R.S. Stolarski and R. J. Cicerone, for preprints of their articles. The contribution of R. F. Walker to aspects of the experimental work is gratefully acknowledged. Part 1, M. A. A. Clyne and R. T. Watson, J.C.S. Faruday Z, 1974, 70, 1109. M. A. A. Clyne, D. J. McKenney and R. T. Watson, J.C.S. Furaday I, 1975, in press. P. P. Bemand, M. A. A. Clyne and R. T. Watson, J.C.S. Faruduy I, 1973, 69, 1356. W. D. McGrath and R. G. W. Norrish, Proc. Roy. SOC. A , 1960, 254, 317. M. A. A. Clyne and J. A. Coxon, Proc. Roy. SOC. A, 1968,303, 207. R. S. Stolarski and R. J. Cicerone, Canad. J. Chein., 1974, 52, 1610. D. Garvin, C.I.A.P. Monograph No. 5.7.5. Chlorine and the Chlorine Oxides (Nat. Bur. Stand., Washington D.C., 1973). M. J. Molina and F. S. Rowland, Nature, 1974, 249, 810; see also M. A. A. Clyne, Nature, 1974, 249, 796. S. Chapman, Mem. Roy. Meteorol. SOC., 1930, 3, 130. M. A. A. Clyne and J. A. Coxon, Trans. Faruday Soc., 1966,62, 1175. lo H. S. Johnston and G. Whitten, Pure Appl. Geoplzys., 1973, 106-108, 1468. l 2 J. A. Coxon, Ph.D. Thesis, (University of East Anglia, 1967). l3 P. P. Bemand, M. A. A. Clyne and R. T. Watson, J.C.S. Faruduy ZI, 1974,70, 564. l 4 N. Basco and S. K. Dogra, Proc. Roy. SOC. A, 1971, 323, 1. l 5 M. A. A. Clyne and I. F. White, Traits. Faruduy Soc., 1971, 67, 2068. l 6 G. C. Fettis and J. H. Knox, Progr. Reaction Kinetics, 1964, 2, 1. l 7 M. A. A. Clyne and H. W. Cruse, J.C.S. Faruduy ZI, 1972, 68, 1377.M. A . A . CLYNE AND R. T . WATSON 2259 l 8 M. A. A. Clyne and R. T. Watson, to be published. l9 see, for example, T. Iredale and T. G. Edwards, J. Amer. Chern. SOC., 1937,59, 761 ; R. G. W. 2o H. S. Johnston, Science, 1971, 173, 517; P. J. Crutzen, J. Geophys. Res., 1971, 30,7311. 21 J. S. Chang, Lawrence Livermore Calculations. The set of column densities given is for a one-dimensional diffusion model with the sun at 45". 2 2 D. J. Seery and D. Britton, J. Phys. Chem., 1964, 68, 226. 23 M. A. A. Clyne and R. F. Walker, J.C.S. Faraday I, 1973, 69, 1547. 24 H. S. Johnston and H. J. Crosby, J. Chem. Phys., 1954,22,689; L. F. Phillips and H. I. Schiff, J. Chem. Phys., 1962, 36, 1509; M. A. A. Clyne, B. A. Thrush and R. P. Wayne, Trans. Faraday SOC., 1964,60,359; P. P. Bemand, M. A, A. Clyne and R. T. Watson, J.C.S. Faraday II, 1974, 70, 564. Norrish and G. H. J. Neville, J. Chem. SOC., 1934, 1864. 2 5 D. D. Davis, J. T. Herron and R. E. Huie, J. Chem. Phys., 1973, 58, 530. 26 V. P. Balakhnin, V. I. Egarov and E. I. Intezorova, Kinetics and Catalysis, 1971, 12, 299. " F. Kaufman, to be published; G. A. Takacs and G. P. Glass, J. Phys. Chem., 1973,77,1948. 28 M. A. A. Clyne and D. H. Stedman, Trans. Faraday SOC., 1968, 64, 2698. 29 As discussed in ref. 3, k3 is assumed to have a zero temperature coefficient.

ISSN:0300-9599    

DOI:10.1039/F19747002250

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Kinetics of the Reaction of the Nickel(I1) Ion with Pyridine- 2-azo-p-dimethylaniline in t-Butanol+ Water Mixtures BY EDWARD F. CALDIN' AND PETER GODFREY University Chemical Laboratory, Canterbury, Kent Received 24th April, 1974 Rate constants and activation parameters have been determined for the reaction of the nickef(I1) ion with pyridine-2-azo-p-dimethylaniline, in a series of t-butanol +water mixtures with mole fractions from 0 to 0.4 t-butanol. The rate constant at 25°C varies little with composition, but the enthalpy and entropy of activation both vary considerably, with compensation; they show maxima and minima, which are discussed in relation to theories of solvent structure, In earlier work, rate constants and activation parameters for the ligand-sub- stitution reactions of the nickel(I1) ion with bipyridyl in methanol + water,I methanol + acetonitrile,2 and t-butanol + water mixtures have been reported.The reaction may be represented by ( S = solvent, L = ligand) : ki kb Nisi -i- + L + NiS5L2+ + S. (1) The rate constant at 25°C varies little with solvent composition, but the enthalpy and entropy of activation vary considerably, with a large degree of compensation. In the alcohol + water mixtures, both AH * and A S * show a minimum in the water-rich com- position range. This may be interpreted in terms of the view, for which there is much e~idence,~ that the structure of water is strengthened by addition of a little alcohol, but is eventually broken down as more alcohol is added. It would be expected that for the reaction in t-butanol+ water mixtures the minima in AH * and A S * would be more pronounced than in methanol + water mixtures, and would be found at a lower mole fraction of alcoh01.~ We have therefore measured the rate of the reaction of the nickel(I1) ion with pyridine-2-azo-p-dimethylaniline (PADA) in t-butanol + water mixtures.EXPERIMENTAL MATERIALS Nickel perchlorate hexahydrate and pyridine-2-azo-g-dimethylaniline (Sigma) were used without further purification. Water was triply distilled. t-Butanol was refluxed with sodium for 6-8 h and distilled through a long fractionating column, under nitrogen ; b.p. 82 _+ 0.5"C. SOLUTIONS Solvent mixtures were made up by weight. Nickel(I1) solutions were standardised by adding standard ethylenediaminetetra-acetic acid solution and back-titrating with ZnS04 solution.In the reaction mixtures the ratio of metal ion to PADA was not less than 25. KINETIC MEASUREMENTS These were made in the stopped-flow apparatus described by Davies.6 The reaction was usually monitored at 575 nm; the observed rate constant was independent of the wavelength 2260E . F . CALDIN AND P . GODFREY 226 1 used. The oscilloscope trace was photographed on 35-mm film, and the first-order rate constant determined by the method of Crooks, Tregloan and Zetter.' Each trace was replicated about 6 times. At each solvent composition, experiments were done at 5 con- centrations, and at 4 temperatures 10 K apart. TREATMENT OF RESULTS RATE CONSTANTS The observed rate constant k is related to k, and k , in eqn (I), when the nickel ion is in large excess, by : A plot of k against [Ni2+] is linear, with slope k, and intercept k,.The plots derived from experimental data were good straight lines. The results were fitted to eqn (2) by a weighted least-squares procedure with the aid of a computer program, which assigned to each experimental value of k a weight inversely proportional to the square of the standard deviation of the mean of the six replicated values, and produced " best " values of k, and k, with their standard deviations. Values of k calculated from these values of kf and kb usually agreed with the observed value within 1-2%. k = k, + kf[Ni2+]. (2) ARRHENIUS PARAMETERS These were determined from the rate constants k, and kb by a similar computer program; each point was given a weight inversely proportional to the square of the standard deviation.We are indebted to Dr. D. J. Loose for these computer programs. RESULTS The individual first-order rate constants are too numerous to list; over 1000 were determined. In table 1 we record, for each solvent composition at each temperature, the range of concentrations used and the values of k, and kb determined as described above. The derived activation parameters are shown in table 2. Values of kf and kb calculated from these activation parameters are shown in table 1 for comparison with the experimental values. 'rABLE l.-OBSERVED RATE CONSTANTS k AND DERIVED RATE CONSTANTS kf AND kb FOR THE REACTION OF THE NICKEL(I1) ION WITH PADA IN AQUEOUS f-BUTANOL MIXTURES mol % t -but an01 0.0 1.5 temp./"(= 15.02 25.02 35.06 45.04 15.02 25.02 35.06 45.04 104[Ni2+]/ mol dn1-3 0.5-5 .O 0.5-5.0 0.5-5.0 0.5-5.0 1.2-6.5 I .2-6.5 1.2-6.5 1.2-6.5 k/s-1 0.05 -0.26 0.15-0.35 0.30-1.24 0.91-2.5 0.11 -0.44 0.26-1 .O 0.68-2.3 1.56-4.2 1 k1/dm3 nol-1 s-1 kr(ca1c.) 467 426 k 14 897 910 + 6 2082 1858 -t 30 3600 3608 110 63 5 65 1 1 6 1385 1380 - f 5 3054 2790 & 34 5230 5378 - + 33 kb1S-l 0.0262 +0.0006 0.1002 5 0.006 0.21 1 - 4- 0.03 0.709 k 0.05 0.0352 * 0.001 0.loo & 0.005 0.304 2 0.02 0.918 & 0.04 kb(ca1c.) 0.0267 0.086 0.256 0.631 0.0333 0.108 0.328 0.9182262 mol "/, t-butanol 2.5 5.0 6.5 7.5 10.0 15.0 20.0 Nilr + PADA IN AQUEOUS t-BUTANOL TABLE 1 .--continued 104[Ni2+]/ in01 dm-3 1.2-6.5 1.2-6.5 1.2-6.5 1.2-6.5 0.75-5.0 0.75-5.0 0.75-5.0 0.75-5.0 1.25-6.6 1.25-6.6 1.25-6.6 1.25-6.6 1.25-6.4 1.25-6.4 1.25-6.4 1.25-6.4 1.25-8.0 1.25-8.0 1.25-8.0 1.25-8.0 1.25-6.6 1.25-6.6 1.25-6.6 1.25-6.6 1.25-6.4 2.5-6.4 k / S - ' 0.09-0.26 0.23-0.65 0.55-1.53 1.25-3.01 0.05-0.1 6 0.15-0.38 0.40-0.92 1.21-2.0 0.07-0.17 0.17-0.35 0.64-0.96 1.37-2.04 0.07-0.1 6 0.21-0.38 0.55-1.02 1.61-2.20 0.07-0.17 0.1 9-0.41 0.56-1.08 1.55-2.45 0.06-0.14 0.24-0.43 0.7-1.0 1.7-2.6 0.09-0.13 0.29-0.42 krldrn3 mol- 1 s - 1 48 1 - +5 91 6 1 9 1912 +9 3405 - + 23 248 +1 524 +1 1220 + 30 1861 +7 190 1 2 340 +2 606 j= 10 1255 - + 6 201 - t l 423 +2 736 +7 1500 + 10 135 318 +1 761 + 12 1332 +s 1 44 +3 456 + 14 877 - +2 1 602 26 86.6 & 0.3 259 + I li r (calc.) 476 965 1873 3470 253 519 1016 1902 181 358 679 1262 202.5 41 1 801 1488 139 31 6 683 1432 158 3 82 873 1886 86.8 257 /ib/s-' 0.056 +0.0015 0.125 + 0.005 0.310 & 0.01 0.829 - + 0.008 0.029 +O.ool 0.128 + 0.007 0.29 + 0.05 1.07 & 0.02 0.048 + 0.002 0.125 + 0.002 0.56 & 0.23 1.21 - + 0.02 0.0435 +0.001 0.163 - + 0.01 0.44 + 0.05 1.47 - + 0.04 0.061 & 0.01 0.153 k0.004 0.47 - + 0.01 1.37 + 0.02 0.039 + 0.00 1 0.129 0.003 0.636 + 0.01 6 1.54 & 0.05 0.075 + 0.007 0.213 & 0.01 A b(calC.) 0.045 0.128 0.336 0.829 0.033 0.113 0.36 1.07 0.03 8 0.130 0.41 1.21 0.0435 0.152 0.49 1.47 0.052 0.165 0.49 1.365 0.060 0.195 0.586 1.64 0.067 0.21 7E .F. CALDIN AND P . GODFREY 2263 TABLE 1 .-continued 25.0 30.0 35.0 40.0 35.06 45.04 15.02 25.02 35.06 45 .Os 15.02 25.02 35.06 45.04 25.02 35.06 45.04 50.01 15.02 25.02 35.01 45.01 2.5-6.4 1.25-6.4 1.25-6.4 1.25-5.0 1.25-6.4 1.25-6.4 1.25-6.6 1.25-6.6 1.25-6.6 1.25-6.6 1.25-6.4 1.25-6.4 1.25-6.4 2.5-6.4 1.25-6.4 1.25-6.4 1.25-6.4 1.25-6.4 0.83-1.13 2.02-2.74 0.18-0.25 0.3 1-0.43 0.91-1.23 2.3-3.1 0.08-0.12 0.30-0.48 0.89-1.21 2.15-2.74 0.35-0.56 0.91 -1.47 2.82-3.64 3.86-5.97 0.12-0.24 0.40-0.70 1 .lo-1.71 2.68-4.44 736 - +8 1500 k 30 136 - +1 330 & 23 626 & 19 1554 +7 156 - +2 333 + 5 604 + 16 1121 - + 16 + l 1086 1 39 1639 1 3 1976 & 33 -tl +6 2028 + 43 3402 - + 32 398.2 220.3 590.5 712 1840 I36 229 617 1554 159 320 617 1137 398.6 828 1636 2259 220.8 593.4 1495 3555 0.656 k 0.05 1.84 * 0.01 0.162 & 0.0005 0.271 k0.005 0.829 k 0.001 2.081 -t 0.003 0.070 - + 0.01 1 0.02 0.82 - + 0.08 2.00 - + 0.08 0.302 0.003 0.77 $0.16 2.58 - f 0.65 2.58 $ 0.55 0.097 & 0.01 5 0.32 0.04 0.956 + 0.02 2.25 - + 0.09 0.253 0.656 1.84 0.182 0.306 0.828 2.096 0.105 0.300 0.806 0.024 0.302 0.78 1 1.893 2.833 0.139 0.375 0.955 2.280 4 solutions at each temperature; concentration of PADA in final solution = 2.5 x mol dm-3.Errors are standard deviations. k = observed first-order rate constant; kf = forward rate constant from slope of plot of k against nickel(I1) concentration; kb = backward rate constant from intercept of plot of k against nickel(I1) concentration; k*-(calc.) = value of kf calculated from Arrhenius para- meters given in table 2; kb (calc.) = value of kb calculated from Arrhenius parameters given in table 2. Fig. 1 shows the values of AH: plotted against solvent composition, expressed as mol per cent of t-butanol.Fig. 2 shows the values of AH$ in the water-rich t- butanol mixtures, compared with values reported for the analogous reaction of N" with bipyridyl in aqueous mixtures of various alcohols. The results in water are in reasonable agreement with those of Cobb and Hague,8 who used solutions with an ionic strength of 0.3 (NaNO,) and found rate constants kf = (1.35 f 0.11)103 dm3 mol-' s-' and k , = 0.1 s-l at 25"C, with AH$ = 13.6 & 1.1 kcal mol-l, AS! = 1 4 2 cal K-* mol-I and AH: = 16 kcal mol-'.P TABLE 2.-ACTIVATION PARAMETERS FOR THE REACTION OF THE NICKEL(I1) ION WITH PADA IN AQUEOUS T-BUTANOL MIXTURES 1.5 2.5 5.0 6.5 7.5 10.0 15.0 20.0 25.0 30.0 35.0 40.0 mol % t-butanol 0.0 A.Gf/kcal mol-l 13.365 AH:/kcal mot1 12.36 { k0.36 ASj/cal K-l mol-1 {I Z AGt/kcal mol-l 18.83, AH;/kcal mo1-1 19.29 { 0.49 As$/cai K-1 mol-1 {z 2 12.120 12.21 f0.39 - 3.2 1.3 18.698 19.52 & 0.41 + 2.5 & 1.4 13.331 1 1.45 & 0.34 - 6.4 f 1.1 17.22 f 0.83 f 2.8 18.578 - 2.9 13.698 11.64 f 0.27 -7.1 k 0.9 18.673 20.54 & 0.80 + 6.0 & 2.6 13.916 11.05 0.45 - 9.8 1.5 18.592 20.40 k0.57 + 5.8 f 1.9 13.834 11.51 5 0.34 - 8.0 f 1.1 1 8.4g9 20.75 k 0.29 + 7.3 - + 1.0 13.990 13.42 f 0.42 -2.1 f 1.4 18.451 19.29 -t 0.74 + 2.6 - + 2.4 13.878 14.4 f 1.2 + 1.7 &- 3.9 18.352 19.44 & 2.50 + 3.4 - + 8.3 14.112 17.93 - + 0.40 + 12.6 f 1.3 1 8.2S9 19.53 fO.19 + 3.9 - +0.6 14.180 17.45 - + 0.26 + 10.7 f 0.9 18.086 17.53 - + 0.32 - 2.1 - + 1.1 13.983 11.35 - 9.0 * 1.0 17.39 f 0.83 2.8 0.30 1 8.098 - 2.6 1 cal = 4.184 J.Errors are standard deviations. Values of K, AG:, AGi, and AGO at 25°C. 13.853 12.70 - + 0.24 -t 0.8 16.68 k 0.78 - 4.9 - + 2.6 - 4.0 18.094 13.618 16.3 & 0.64 + 8.8 k2.1 17.969 16.39 - + 0.05 - 5.5 k2.1 z + C. c( L1 2 0 rmol % t-butanol FIG. 1.-Plot of AH! against mol t-butanol. mol % alcohol FIG. 2.-Plots of AH:, relative to the value for water, against mol % alcohol, for reactions of NcII) with (A) PADA in t-butanol (this work); (B) bipyridyl in t-butanol;3 (C) bipyridyl in ethanoli3 (D) bipyridyl in methanol.'2266 Nil1+ PADA I N AQUEOUS t-BUTANOL DISCUSSiON COMPARISON BETWEEN ALCOHOLS In the water-rich range, it would be expected, by analogy with the results on solvolysis and heats of solution,' that the minima in AH! and AS: would be more pronounced for aqueous t-butanol than for other aqueous alcohols, and would be found at a lower mole fraction of alcohol.Our results show that this is so (fig. 2), as in the work of Chattopadhyay and Coetzee3 with bipyridyl. The effect is evidently related to the breaking down of the water structure by the alcoh01.~ At higher alcohol concentrations, while the value of AG f varies monotonically with solvent composition and its overall change is only about 1 kcal mol-I, the values of AH{ and AS! show variations of about 6 kcal mol-l, with a maximum at about 20 mol% and a second minimum at about 30 mol % t-butanol (fig. 1). The increase in AH; between 5 and 20 11101% t-butanol is presumably related to the progressive breakdown of the water structure. The subsequent fall between 20 and 30%, and the rise between 30 and 40%, may be due to entry of the alcohol into the first coordination shell of the nickel(I1) ion, as well as to further changes in the solvent structure.(A minimum at about 30% alcohol has also been reported for the solvolysis of t-butyl chloride in methanol + water mixtures. g, COMPARISON BETWEEN PADA AND BIPYRIDYL I N AQUEOUS t-BUTANOL In the water-rich region, our results are parallel to those obtained by Chatto- padhyay and Coetzee with bipyridyl; the changes in AH: and ASH relative to the values in water are fairly similar (fig. 2), and the minima occur at roughly the same solvent composition. Since both ligands are bidentate and flexible, and are not strongly bound to water, this is not unexpected.At higher alcohol concentrations, the results with the two ligands diverge; PADA shows a much higher maximum, and the subsequent fall by over 6 kcal mol-1 to a second minimum is not paralleled by bipyridyl. The difference, according to such a model as that of Bennetto and Caldin,lo reflects different effects of the two ligands on the local solvent structure. We thank Professor Coetzee for communication of results before publication, and Dr. H. P. Bennetto for helpful discussions. ' H. P. Bennetto and E. F. Caldin, J. Chem, Soc. A, 1971, 2207; J. Solution Chem., 1973, 2, 217. H. P. Bennetto, J. Chem. Soc. A, 1971, 2211. P. K. Chattopadyay and J. F. Coetzee, Inorg. Chem., 1973, 12, 113. F. Franks and D. J. G. Ives, Quart. Rev., 1966, 20, 1 . e g., E. M. Arnett and D.R. McKelvey, Rep. Progr. Chem., 1965, 26, 185; Hydrogen-bonded Solvent Systems, ed. A. K . Covington and P. Jones (Taylor and Francis, London, 1968): M. C. R. Symons and M. J. Blandamer, p. 211; J. €3. Hyne, p. 99; D. N. Clew, H. D. Mak and N. S. Rath, p. 195; E. Tommila, A. Koivisto, J . P. Lyyra, K. Antell, and S. Heimo. A m . Acad. Sci. Fenn, A (11), 1952, no. 47. G. Davies, Inorg. Chem., 1971, 10, 1155. J. E. Crooks, P. A Tregloan and M. S. Zetter, .I. Phys. E, 1970, 3, 73. R. Huq, J.C.S. Faraday I, 1973, 69, 1195. * M. A. Cobb and D. N. Hague, J.C.S. Faruduy I, 1972, 68,932. l o H. P. Bennetto and E. F. Caldin, J Chem Soc. A, 1971, 2198. Kinetics of the Reaction of the Nickel(I1) Ion with Pyridine- 2-azo-p-dimethylaniline in t-Butanol+ Water Mixtures BY EDWARD F.CALDIN' AND PETER GODFREY University Chemical Laboratory, Canterbury, Kent Received 24th April, 1974 Rate constants and activation parameters have been determined for the reaction of the nickef(I1) ion with pyridine-2-azo-p-dimethylaniline, in a series of t-butanol +water mixtures with mole fractions from 0 to 0.4 t-butanol. The rate constant at 25°C varies little with composition, but the enthalpy and entropy of activation both vary considerably, with compensation; they show maxima and minima, which are discussed in relation to theories of solvent structure, In earlier work, rate constants and activation parameters for the ligand-sub- stitution reactions of the nickel(I1) ion with bipyridyl in methanol + water,I methanol + acetonitrile,2 and t-butanol + water mixtures have been reported. The reaction may be represented by ( S = solvent, L = ligand) : ki kb Nisi -i- + L + NiS5L2+ + S.(1) The rate constant at 25°C varies little with solvent composition, but the enthalpy and entropy of activation vary considerably, with a large degree of compensation. In the alcohol + water mixtures, both AH * and A S * show a minimum in the water-rich com- position range. This may be interpreted in terms of the view, for which there is much e~idence,~ that the structure of water is strengthened by addition of a little alcohol, but is eventually broken down as more alcohol is added. It would be expected that for the reaction in t-butanol+ water mixtures the minima in AH * and A S * would be more pronounced than in methanol + water mixtures, and would be found at a lower mole fraction of alcoh01.~ We have therefore measured the rate of the reaction of the nickel(I1) ion with pyridine-2-azo-p-dimethylaniline (PADA) in t-butanol + water mixtures.EXPERIMENTAL MATERIALS Nickel perchlorate hexahydrate and pyridine-2-azo-g-dimethylaniline (Sigma) were used without further purification. Water was triply distilled. t-Butanol was refluxed with sodium for 6-8 h and distilled through a long fractionating column, under nitrogen ; b.p. 82 _+ 0.5"C. SOLUTIONS Solvent mixtures were made up by weight. Nickel(I1) solutions were standardised by adding standard ethylenediaminetetra-acetic acid solution and back-titrating with ZnS04 solution. In the reaction mixtures the ratio of metal ion to PADA was not less than 25.KINETIC MEASUREMENTS These were made in the stopped-flow apparatus described by Davies.6 The reaction was usually monitored at 575 nm; the observed rate constant was independent of the wavelength 2260E . F . CALDIN AND P . GODFREY 226 1 used. The oscilloscope trace was photographed on 35-mm film, and the first-order rate constant determined by the method of Crooks, Tregloan and Zetter.' Each trace was replicated about 6 times. At each solvent composition, experiments were done at 5 con- centrations, and at 4 temperatures 10 K apart. TREATMENT OF RESULTS RATE CONSTANTS The observed rate constant k is related to k, and k , in eqn (I), when the nickel ion is in large excess, by : A plot of k against [Ni2+] is linear, with slope k, and intercept k,.The plots derived from experimental data were good straight lines. The results were fitted to eqn (2) by a weighted least-squares procedure with the aid of a computer program, which assigned to each experimental value of k a weight inversely proportional to the square of the standard deviation of the mean of the six replicated values, and produced " best " values of k, and k, with their standard deviations. Values of k calculated from these values of kf and kb usually agreed with the observed value within 1-2%. k = k, + kf[Ni2+]. (2) ARRHENIUS PARAMETERS These were determined from the rate constants k, and kb by a similar computer program; each point was given a weight inversely proportional to the square of the standard deviation. We are indebted to Dr.D. J. Loose for these computer programs. RESULTS The individual first-order rate constants are too numerous to list; over 1000 were determined. In table 1 we record, for each solvent composition at each temperature, the range of concentrations used and the values of k, and kb determined as described above. The derived activation parameters are shown in table 2. Values of kf and kb calculated from these activation parameters are shown in table 1 for comparison with the experimental values. 'rABLE l.-OBSERVED RATE CONSTANTS k AND DERIVED RATE CONSTANTS kf AND kb FOR THE REACTION OF THE NICKEL(I1) ION WITH PADA IN AQUEOUS f-BUTANOL MIXTURES mol % t -but an01 0.0 1.5 temp./"(= 15.02 25.02 35.06 45.04 15.02 25.02 35.06 45.04 104[Ni2+]/ mol dn1-3 0.5-5 .O 0.5-5.0 0.5-5.0 0.5-5.0 1.2-6.5 I .2-6.5 1.2-6.5 1.2-6.5 k/s-1 0.05 -0.26 0.15-0.35 0.30-1.24 0.91-2.5 0.11 -0.44 0.26-1 .O 0.68-2.3 1.56-4.2 1 k1/dm3 nol-1 s-1 kr(ca1c.) 467 426 k 14 897 910 + 6 2082 1858 -t 30 3600 3608 110 63 5 65 1 1 6 1385 1380 - f 5 3054 2790 & 34 5230 5378 - + 33 kb1S-l 0.0262 +0.0006 0.1002 5 0.006 0.21 1 - 4- 0.03 0.709 k 0.05 0.0352 * 0.001 0.loo & 0.005 0.304 2 0.02 0.918 & 0.04 kb(ca1c.) 0.0267 0.086 0.256 0.631 0.0333 0.108 0.328 0.9182262 mol "/, t-butanol 2.5 5.0 6.5 7.5 10.0 15.0 20.0 Nilr + PADA IN AQUEOUS t-BUTANOL TABLE 1 .--continued 104[Ni2+]/ in01 dm-3 1.2-6.5 1.2-6.5 1.2-6.5 1.2-6.5 0.75-5.0 0.75-5.0 0.75-5.0 0.75-5.0 1.25-6.6 1.25-6.6 1.25-6.6 1.25-6.6 1.25-6.4 1.25-6.4 1.25-6.4 1.25-6.4 1.25-8.0 1.25-8.0 1.25-8.0 1.25-8.0 1.25-6.6 1.25-6.6 1.25-6.6 1.25-6.6 1.25-6.4 2.5-6.4 k / S - ' 0.09-0.26 0.23-0.65 0.55-1.53 1.25-3.01 0.05-0.1 6 0.15-0.38 0.40-0.92 1.21-2.0 0.07-0.17 0.17-0.35 0.64-0.96 1.37-2.04 0.07-0.1 6 0.21-0.38 0.55-1.02 1.61-2.20 0.07-0.17 0.1 9-0.41 0.56-1.08 1.55-2.45 0.06-0.14 0.24-0.43 0.7-1.0 1.7-2.6 0.09-0.13 0.29-0.42 krldrn3 mol- 1 s - 1 48 1 - +5 91 6 1 9 1912 +9 3405 - + 23 248 +1 524 +1 1220 + 30 1861 +7 190 1 2 340 +2 606 j= 10 1255 - + 6 201 - t l 423 +2 736 +7 1500 + 10 135 318 +1 761 + 12 1332 +s 1 44 +3 456 + 14 877 - +2 1 602 26 86.6 & 0.3 259 + I li r (calc.) 476 965 1873 3470 253 519 1016 1902 181 358 679 1262 202.5 41 1 801 1488 139 31 6 683 1432 158 3 82 873 1886 86.8 257 /ib/s-' 0.056 +0.0015 0.125 + 0.005 0.310 & 0.01 0.829 - + 0.008 0.029 +O.ool 0.128 + 0.007 0.29 + 0.05 1.07 & 0.02 0.048 + 0.002 0.125 + 0.002 0.56 & 0.23 1.21 - + 0.02 0.0435 +0.001 0.163 - + 0.01 0.44 + 0.05 1.47 - + 0.04 0.061 & 0.01 0.153 k0.004 0.47 - + 0.01 1.37 + 0.02 0.039 + 0.00 1 0.129 0.003 0.636 + 0.01 6 1.54 & 0.05 0.075 + 0.007 0.213 & 0.01 A b(calC.) 0.045 0.128 0.336 0.829 0.033 0.113 0.36 1.07 0.03 8 0.130 0.41 1.21 0.0435 0.152 0.49 1.47 0.052 0.165 0.49 1.365 0.060 0.195 0.586 1.64 0.067 0.21 7E .F. CALDIN AND P . GODFREY 2263 TABLE 1 .-continued 25.0 30.0 35.0 40.0 35.06 45.04 15.02 25.02 35.06 45 .Os 15.02 25.02 35.06 45.04 25.02 35.06 45.04 50.01 15.02 25.02 35.01 45.01 2.5-6.4 1.25-6.4 1.25-6.4 1.25-5.0 1.25-6.4 1.25-6.4 1.25-6.6 1.25-6.6 1.25-6.6 1.25-6.6 1.25-6.4 1.25-6.4 1.25-6.4 2.5-6.4 1.25-6.4 1.25-6.4 1.25-6.4 1.25-6.4 0.83-1.13 2.02-2.74 0.18-0.25 0.3 1-0.43 0.91-1.23 2.3-3.1 0.08-0.12 0.30-0.48 0.89-1.21 2.15-2.74 0.35-0.56 0.91 -1.47 2.82-3.64 3.86-5.97 0.12-0.24 0.40-0.70 1 .lo-1.71 2.68-4.44 736 - +8 1500 k 30 136 - +1 330 & 23 626 & 19 1554 +7 156 - +2 333 + 5 604 + 16 1121 - + 16 + l 1086 1 39 1639 1 3 1976 & 33 -tl +6 2028 + 43 3402 - + 32 398.2 220.3 590.5 712 1840 I36 229 617 1554 159 320 617 1137 398.6 828 1636 2259 220.8 593.4 1495 3555 0.656 k 0.05 1.84 * 0.01 0.162 & 0.0005 0.271 k0.005 0.829 k 0.001 2.081 -t 0.003 0.070 - + 0.01 1 0.02 0.82 - + 0.08 2.00 - + 0.08 0.302 0.003 0.77 $0.16 2.58 - f 0.65 2.58 $ 0.55 0.097 & 0.01 5 0.32 0.04 0.956 + 0.02 2.25 - + 0.09 0.253 0.656 1.84 0.182 0.306 0.828 2.096 0.105 0.300 0.806 0.024 0.302 0.78 1 1.893 2.833 0.139 0.375 0.955 2.280 4 solutions at each temperature; concentration of PADA in final solution = 2.5 x mol dm-3.Errors are standard deviations. k = observed first-order rate constant; kf = forward rate constant from slope of plot of k against nickel(I1) concentration; kb = backward rate constant from intercept of plot of k against nickel(I1) concentration; k*-(calc.) = value of kf calculated from Arrhenius para- meters given in table 2; kb (calc.) = value of kb calculated from Arrhenius parameters given in table 2. Fig. 1 shows the values of AH: plotted against solvent composition, expressed as mol per cent of t-butanol. Fig. 2 shows the values of AH$ in the water-rich t- butanol mixtures, compared with values reported for the analogous reaction of N" with bipyridyl in aqueous mixtures of various alcohols. The results in water are in reasonable agreement with those of Cobb and Hague,8 who used solutions with an ionic strength of 0.3 (NaNO,) and found rate constants kf = (1.35 f 0.11)103 dm3 mol-' s-' and k , = 0.1 s-l at 25"C, with AH$ = 13.6 & 1.1 kcal mol-l, AS! = 1 4 2 cal K-* mol-I and AH: = 16 kcal mol-'.P TABLE 2.-ACTIVATION PARAMETERS FOR THE REACTION OF THE NICKEL(I1) ION WITH PADA IN AQUEOUS T-BUTANOL MIXTURES 1.5 2.5 5.0 6.5 7.5 10.0 15.0 20.0 25.0 30.0 35.0 40.0 mol % t-butanol 0.0 A.Gf/kcal mol-l 13.365 AH:/kcal mot1 12.36 { k0.36 ASj/cal K-l mol-1 {I Z AGt/kcal mol-l 18.83, AH;/kcal mo1-1 19.29 { 0.49 As$/cai K-1 mol-1 {z 2 12.120 12.21 f0.39 - 3.2 1.3 18.698 19.52 & 0.41 + 2.5 & 1.4 13.331 1 1.45 & 0.34 - 6.4 f 1.1 17.22 f 0.83 f 2.8 18.578 - 2.9 13.698 11.64 f 0.27 -7.1 k 0.9 18.673 20.54 & 0.80 + 6.0 & 2.6 13.916 11.05 0.45 - 9.8 1.5 18.592 20.40 k0.57 + 5.8 f 1.9 13.834 11.51 5 0.34 - 8.0 f 1.1 1 8.4g9 20.75 k 0.29 + 7.3 - + 1.0 13.990 13.42 f 0.42 -2.1 f 1.4 18.451 19.29 -t 0.74 + 2.6 - + 2.4 13.878 14.4 f 1.2 + 1.7 &- 3.9 18.352 19.44 & 2.50 + 3.4 - + 8.3 14.112 17.93 - + 0.40 + 12.6 f 1.3 1 8.2S9 19.53 fO.19 + 3.9 - +0.6 14.180 17.45 - + 0.26 + 10.7 f 0.9 18.086 17.53 - + 0.32 - 2.1 - + 1.1 13.983 11.35 - 9.0 * 1.0 17.39 f 0.83 2.8 0.30 1 8.098 - 2.6 1 cal = 4.184 J.Errors are standard deviations. Values of K, AG:, AGi, and AGO at 25°C. 13.853 12.70 - + 0.24 -t 0.8 16.68 k 0.78 - 4.9 - + 2.6 - 4.0 18.094 13.618 16.3 & 0.64 + 8.8 k2.1 17.969 16.39 - + 0.05 - 5.5 k2.1 z + C. c( L1 2 0 rmol % t-butanol FIG.1.-Plot of AH! against mol t-butanol. mol % alcohol FIG. 2.-Plots of AH:, relative to the value for water, against mol % alcohol, for reactions of NcII) with (A) PADA in t-butanol (this work); (B) bipyridyl in t-butanol;3 (C) bipyridyl in ethanoli3 (D) bipyridyl in methanol.'2266 Nil1+ PADA I N AQUEOUS t-BUTANOL DISCUSSiON COMPARISON BETWEEN ALCOHOLS In the water-rich range, it would be expected, by analogy with the results on solvolysis and heats of solution,' that the minima in AH! and AS: would be more pronounced for aqueous t-butanol than for other aqueous alcohols, and would be found at a lower mole fraction of alcohol.Our results show that this is so (fig. 2), as in the work of Chattopadhyay and Coetzee3 with bipyridyl. The effect is evidently related to the breaking down of the water structure by the alcoh01.~ At higher alcohol concentrations, while the value of AG f varies monotonically with solvent composition and its overall change is only about 1 kcal mol-I, the values of AH{ and AS! show variations of about 6 kcal mol-l, with a maximum at about 20 mol% and a second minimum at about 30 mol % t-butanol (fig. 1). The increase in AH; between 5 and 20 11101% t-butanol is presumably related to the progressive breakdown of the water structure. The subsequent fall between 20 and 30%, and the rise between 30 and 40%, may be due to entry of the alcohol into the first coordination shell of the nickel(I1) ion, as well as to further changes in the solvent structure.(A minimum at about 30% alcohol has also been reported for the solvolysis of t-butyl chloride in methanol + water mixtures. g, COMPARISON BETWEEN PADA AND BIPYRIDYL I N AQUEOUS t-BUTANOL In the water-rich region, our results are parallel to those obtained by Chatto- padhyay and Coetzee with bipyridyl; the changes in AH: and ASH relative to the values in water are fairly similar (fig. 2), and the minima occur at roughly the same solvent composition. Since both ligands are bidentate and flexible, and are not strongly bound to water, this is not unexpected. At higher alcohol concentrations, the results with the two ligands diverge; PADA shows a much higher maximum, and the subsequent fall by over 6 kcal mol-1 to a second minimum is not paralleled by bipyridyl. The difference, according to such a model as that of Bennetto and Caldin,lo reflects different effects of the two ligands on the local solvent structure. We thank Professor Coetzee for communication of results before publication, and Dr. H. P. Bennetto for helpful discussions. ' H. P. Bennetto and E. F. Caldin, J. Chem, Soc. A, 1971, 2207; J. Solution Chem., 1973, 2, 217. H. P. Bennetto, J. Chem. Soc. A, 1971, 2211. P. K. Chattopadyay and J. F. Coetzee, Inorg. Chem., 1973, 12, 113. F. Franks and D. J. G. Ives, Quart. Rev., 1966, 20, 1 . e g., E. M. Arnett and D. R. McKelvey, Rep. Progr. Chem., 1965, 26, 185; Hydrogen-bonded Solvent Systems, ed. A. K . Covington and P. Jones (Taylor and Francis, London, 1968): M. C. R. Symons and M. J. Blandamer, p. 211; J. €3. Hyne, p. 99; D. N. Clew, H. D. Mak and N. S. Rath, p. 195; E. Tommila, A. Koivisto, J . P. Lyyra, K. Antell, and S. Heimo. A m . Acad. Sci. Fenn, A (11), 1952, no. 47. G. Davies, Inorg. Chem., 1971, 10, 1155. J. E. Crooks, P. A Tregloan and M. S. Zetter, .I. Phys. E, 1970, 3, 73. R. Huq, J.C.S. Faraday I, 1973, 69, 1195. * M. A. Cobb and D. N. Hague, J.C.S. Faruduy I, 1972, 68,932. l o H. P. Bennetto and E. F. Caldin, J Chem Soc. A, 1971, 2198.

ISSN:0300-9599    

DOI:10.1039/F19747002260

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Modified Entrainment Method for Measuring Vapour Pressures and Heterogeneous Equilibrium Constants Part 1 .-Theory, and Validation of the Method using Water and Lead BY DAVID BATTAT, MARC M. FAKTOR,* TAN GARRETT AND RODNEY H. MOSS Post Office Research Station, Dollis Hill, London NW2 7DT Received 27th March, 1974 A method of evaluating vapour pressures and equilibrium constants for heterogeneous reactions is proposed. It replaces the usually indeterminate contribution of gaseous transport in the conven- tional entrainment method by a calculable amount. The method was successfully applied at around room temperature to the evaporation of water, and to the vaporisation of lead in the temperature range 900-1050°C. 1 . INTRODUCTION The thermodynamics of heterogeneous equilibria provides the corner-stone for many branches of physical and chemical science, for example, materials preparation, corrosion and combustion.For reacting systems the enthalpy and entropy changes for the reactions which are involved have in the past been measured by various meth- ods. Vapour pressures and dissociation pressures have been measured by calorimetry, manometry, effusion, torsion-effusion, mass-spectrometry, entrainment, and other methods,l* and a similar variety of techniques is available for determining the equilibrium constants for chemical reactions. For vapour-solid and vapour-liquid reactions, entrainment has long been a popular method. We present a method which is a modification of the normal entrainment method. Before doing so, we briefly appraise the normal method.A stream of reactive gas is passed over the solid or liquid maintained at a given temperature and the amount of product formed in a given time is found from the loss of weight of the solid or liquid, or by condensing or dissolving the products out of the gas stream and determining them by standard analytical techniques. While this method is both simple and flexible, it suffers from the disadvantage that the effect of jlowing the reactants at a finite rate must somehow be accounted for or eliminated. If the gas-flow is very fast, the vapour is not fully equilibrated with the condensed phase, whereas if the flow is very slow, products may travel away from the zone in which equilibrium is being established at a significant rate by diffusion.Furthermore, unmixing of the gas by thermal diffusion becomes a serious source of error, particu- larly if the gas mixture contains hydr~gen.~ Traditionally, extrapolation to zero flow rate has been used, but this results in error for the reasons given above. By constrict- ing the flow channel either side of the equilibrium zone containing the condensed phase the effect of diffusion at low flow rates can be reduced. If the apparent partial pressure of the product is plotted as a function of flow rate, there may be a range of flow rates in which the apparent partial pressure does not alter greatly, and this I ' plateau " value is often taken as representing the true partial pre~sure.~ In well- designed apparatus this assumption may be justifiable, but because equilibrium is established only at the surface of the condensed phase, there must always be some 22672268 MODIFIED ENTRAINMENT METHOD diffusion of reactants towards the surface and of products away from the surface.The region in which diffusion operates is usually illldefined. This diffusion can be made less limiting by causing turbulent mixing of the gas in the reaction zone, or by flowing the gas stream fast to reduce the boundary layer over the solid or liquid. Inevitably there is some composition change in the gas in a direction normal to the surface of the condensed phase, and this is an eventual limitation of the method. When a " plateau " in the plot of apparent partial pressure against flow rate is not found, the true partial pressure is in doubt. Tn the new method described in this paper, we have come to terms with the un- avoidable diffusion effect by confining its region of action to a long, narrow channel of known geometry (typically 2 cm long, 1 mm diameter).One end of the channel is connected to a bulb or reservoir containing the condensed phase under study, and the other end is directed into the stream of reactive gas. The reservoir and channel are suspended from a recording microbalance, so that the loss of weight can be measured continuously. By making the gas flow resistance of the channel high, we can ensure that the rate at which the sample substance loses weight is limited by gas transport kinetics in the channel, the effects of which can be calculated accurately. As a good approximation, we assume that the vapour has a uniform composition in the reservoir above the condensed phase, so that the partial pressure variations are confined to the channel.It would not be difficult to relax this assumption. When the vapour leaves the open end of the channel, it is rapidly diluted and swept away in the fast stream of gas. This paper presents the simple theory of the method, showing how the enthalpy and entropy changes for the reaction, evaporation, or dissociative sublimation may be found from the rate at which the sample loses weight. We also give the results of calibration and test experiments performed on evaporating water and lead. These results are in excellent agreement with the other values reported in the literature. By varying the dimensions of the channel so as to decrease its resistance to gas flow, and by decreasing the surface area of the condensed phase, the chemical reaction or evaporation process at the surface can be made to limit the rate at which weight is lost.Here we have an analogy with a Knudsen effusion experiment, performed with larger and larger orifices, until Langmuir evaporation conditions are approached. Our method, then, may be used to study both equilibria and chemical kinetics for heterogeneous reactions. 2. THEORY OF WEIGHT LOSS 2.1 MODEL SYSTEM USED We describe the channel through which the vapour in the bulb communicates with the stream of reactive gas by a simple one-dimensional model (see fig. 1). At the point x = 0, we assume that the vapour composition is the same as that over the surface of the condensed phase, and at x = Z, we assume that the composition of the vapour in the channel has become identical with that in the external gas stream.The first assumption is reasonable if the bulb diameter is large compared with the channel diameter. The second assumption is investigated in detail in section 2.5, and is a very good approximation under the conditions of flow used. 2.2 SIMPLE THEORETICAL DESCRIPTION We consider first the evaporation of a single species A in a stream of inert gas 2. Because of the increase in molar volume when species A evaporates, a " wind " or Stefan flow is generated in the ~hannel,~ vbich sweeps both species upwards. TheD. BATTAT, M. M. FAKTOR, I . GARRETT AND R . H . MOSS 2269 partial pressure gradient of A, and the corresponding gradient of Z, cause diffusion fluxes which must result in zero nett flow of species 2.We can thus write the flow equations in the form 6, : (1) dp.4 - bk JA = RT-RT dx - KC where D is the binary diffusion coefficient, U is the “ wind ” or Stefan velocity, W is the measured rate of weight loss, MA is the molecular weight of species A, and C the cross-sectional area of the channel. In writing the diffusion fluxes in terms of dpA/dx, instead of d(pA/P)/dx, we are assuming that the total pressure is essentially constant all along the channel. Although some pressure gradient is necessary to maintain the Stefan flow, this gradient is negligible unless the channel is very narrow.6 V gas stream I condensed phase FIG. 1.-Reaction bottle. FIG.2.-Streamline pattern in vicinity of channel exit. Addition of eqn (1) and (2) causes the diffusion terms to cancel out, and we ob- tain : J A = UP/RT (3) where P is the total pressure. We now substitute eqn (3) in eqn (1) to eliminate U, and integrate from x = 0 to x = 1. At x = I, pA is zero (see section 2.5), and at x = 0, pA is the saturated vapour pressure of species A, pi. Thus : p i = P[I -e-g] (4) where (4) to obtain : = JARTl/DP = WRTl/DPM,C is the “ transport function ”. If the rate of weight loss is not large, we may approximate the exponential in eqn p i % wRTl/DMAc. ( 5 ) If measurements of weight loss are carried out over a fairly restricted temperature range, it may be acceptable to assume that T/D is a constant, in which case a plot of2270 MODIFIED ENTRAINMENT METHOD R In ri/ against 1/T has a slope of -AH, and an intercept at 1/T = 0 of AS,- R ln(RTI/DM,C), since R In p i = -AH,/T+AS, where AH, and AS, are the enthalpy and entropy changes of evaporation of substance A.However, it is preferable to carry out measurements of weight loss over as wide a temperature range as possible, for which reason it is necessary to correct for the temperature dependence of the diffusion coefficient. Over a range of temperature, the expression holds,8 where Do is the value of D at a reference temperature To and 1 atm pressure, and s lies usually between 0.5 and I, frequently near 0.8 (but see section 3 for a case where s z 1.5 for water in nitrogen). Eqn ( 5 ) now becomes (still for small w> p i z WRPIT~'S/DoTSMAC. (7) A plot of R In( WIT") against l / T again has a slope of - AHv, and an intercept at 1 /T = 0 of AS, - R ln(lRPT~+s/DD,MAC).We thus have a method for establishing the enthalpy and entropy changes of evaporation or sublimation which gives results that can be made independent of the rate at which the external stream of gas flows. Because of uncertainties about diffusion coefficients and their variation with temper- ature, AH, and ASv are subject to small errors, which will be discussed in section 2.4. In section 4 we present the results of two calibration experiments, which show the accuracy that can quite easily be achieved. Next we consider a heterogeneous reaction of a fairly simple but general type : where M is the condensed phase, assumed to be a single component, and X could be a halogen or, with the necessary changes in stoichiometric coefficients, oxygen or sulphur, for example.The equilibrium constant for reaction (8) may be expressed as : M(s)+HX(g)+MX(g)+W, (g) (8) wherephx, etc. are the equilibrium vapour pressures which we assume exist at x = 0. Since reaction (8) involves an increase in the number of vapour phase molecules, there will again be a " wind '' in the channel. The flow equations are : D d - RT RT dx U J - --(pHX + 2p,J - _1 +PHX + 2 P d = O Here we assume an average value for D. We discuss this point in the next section. As there are no sources or sinks for hydrogen or X inside the channel or the bulb (neglecting absorption in the condensed phase), the fluxes of these species are zero. Again, addition of the flow equations eliminates the diffusion terms, and yields : JM = 2UP/RT. ( 1 3)D .BATTAT, M . M . FAKTOR, I . GARRETT AND R . H . MOSS 2271 We again eliminate U from eqn (10) using eqn (13), and integrate from x = 0 to x = 1. At the exit of the channel, pkIX(I)-O (see section 2.5), so that : phX = 2 ~ t i - e - 9 where now j = JMRTf/2DP = WRTLJ2DPMMC. By similar integration, we also find : pGx = ( p z k + 2 ~ ) e - t - 2~ p i 2 = ( p ~ ~ ~ - ~ ) e - ~ + ~ . Note that the sum of the partial pressures is constant and equal to the tota1 pressure in the system. Measurement of the rate of weight loss allows us to calculate the equilibrium partial pressures, p& etc., and hence arrive at the equilibrium constant using eqn (9). Alternatively, we may formulate the equilibrium constant from eqn (14)-( 16) and hence derive a relation between Kp and ri/.Let us define the fraction of reactive species in the free stream as : p,'lLiP = E . (17) We consider various approximate expressions for the equilibrium constant Kp in terms of the transport function 5, and reactive species fraction E , which arise when < < 1, i.e. small rate of weight loss. This situation occurs if either E is small (there is little reactant in the system) or if the equilibrium of reaction (8) is well to the left (K, < 1). We treat each case separately. CASE (1) -4 I, c - 1 .-Eqn (14)-(16) become : p& = 2Pj p;;x = P(E-&<-225) p& = P(l--E+EC). 'Thus or In this case, a plot of R In wagainst l/Tyields AHr and ASr, directly from the slope and the intercept.K , w 2P5(pgy/pgk. (18) CASE (2) E 4 1, then &x ;y" 2P5 pi>; w P(c-25) p i 2 % P(1-E). (Note that since pLX > 0, 5 cannot be greater than ~ / 2 . ) For this case we find : In this case, LZ plot of R In iy against I / T does not yield AH, and AS, directly. It is necessary to calculate KI, at each temperature from eqn (19). is near c/2, the reaction has gone essentially to completion, K,, is very large and the experiment will not be revealing. However, if2272 MODIFIED ENTRAINMENT METHOD and a plot of R In w against 1/T yields AHr and AS, directly, as in case (1). 2.3 MULTICOMPONENT DIFFUSION The treatment of multicomponent diffusion is lengthy,8 and we will not apply it to this problem. However, it frequently happens that one species is present in consider- able excess.It is then permissible to consider the diffusion of each minority species in the majority species as an independent binary diffusion system. For a ternary system, this approximation can be justified rigorously. We ignore diffusion of one minority species into another, because the collisions which give rise to these diffusion phenomena are rare. The flow equations can now be re-written in the form :' where DMX and DH, are the binary diffusion coefficients of MX and HX in hydrogen, and the relations between the J values for each species result from the conditions : J H = J H x + 2 J H 2 = 0 Jx = JHx+JMx = 0 as before. By summing eqn (21)-(23), the diffusion fluxes cancel out, and eqn (13) is obtained again.Eliminating U and integrating from x = 0 to x = I yields : = 2 ~ [ 1 - e - 5 ~ ] pix = [p& + 2 ~ l e - r ~ ~ - 2~ where JMRTl JMRT1 and tHX = - CMX = GP ~DHxP ' For hydrogen, we simply subtract the minority partial pressures from the total pres- sure : Eqn (24)-(26) may be used to calculate the equilibrium partial pressures from the measured rate of weight loss. Since the flow eqn (21)-(23) hold for a mixture with one majority species only, p& is a small fraction of the total pressure P (E < 1). Furthermore, the transport functions tHX and tMX cannot be greater than 4 2 and (&X/&X)(&/2) respectively. Hence we can usefully simplify the expression for the partial pressures and for Kp : Pi2 = p - Pbx- PGx* (26) P&X 2p<MX pix % p#fc-22p~HX Pi2 = P~~--pc25,x-25,xl.D.BATTAT, M. M. FAKTOR, I . GARRETT AND R . H . MOSS 2273 Hence If, in addition, 5 Q E , then Kp = 25MX/E. In practice, we found eqn (28) was applicable to our calibration experiments, de- scribed in section 3. 2.4 ERRORS I N ENTHALPY AND ENTROPY CHANGES We will not consider errors in measurement of temperature and partial pressures in the external stream of gas. Also we assume that the dimensions of the channel and the total pressure are known well. Our concern here is with the effect of errors in the diffusion coefficient Do and the index of its temperature variation s on the experimental values of enthalpy and entropy changes. The parameter Do appears only in the expression for the entropy, and then only as a logarithm.An uncertainty of a factor of two in the diffusion coefficient contributes an error of 6 J mol-l K-l. While the value of Do may not be known accurately, it may be estimated from critical-point data,lo* l 1 by comparison with pairs of similar gases for which Do is known,12* l3 or from empirical curves such as that of Shep- herd. The index s affects both A H and AS. We can find the error 6(AH) introduced by an error S(s) : Hence 6(AH) = - RT 6(s). Thus an error of 0.1 in s at 1 2 0 0 K produces an error of 1 kJ mol-I in AH. The index s is, of course, not known for species for which the diffusion coefficient has not been measured as a function of temperature. This includes the products of many high-temperature reactions. For most pairs of gases, s is in the range 0.5-1.' How- ever, anomalous values of s for some combinations of gases are known, e.g.M 1.5 for H20+N2, as calculated from the experimental data of Schwertz and Similarly we find the error &AS) caused by an error S(s) in the index s, and one calculates &AS) = - R6(s)[l+ In(T/To)]. Thus an error of 0.1 in s introduces an error in A S of 1 J mol-1 K-l at 320 K and 2 J mol-', K-I at 1200 K, if To = 273 K. 2.5 HYDRODYNAMICS OF THE FLOW AT THE CHANNEL EXIT We have assumed so far that at x = 2, i.e. at the exit of the channel, the gas becomes rapidly diluted and swept away by the external stream. Let us examine the flow pattern near the channel exit. The vapour leaving the channel spills out into a region of length AZ, and on reaching the bounding streamline, its concentration has 1-722274 MODIFIED ENTRAINMENT METHOD been reduced effectively to zero.We take A1 as being the distance from the exit of the tube to the stagnation point (fig. 2). According to potential flow theory,16 the flow in the stagnation region may be constructed by superposition of the uniform flow of the external stream at velocity V, and the flow issuing from the channel. The flow from the channel may be approxi- mated by a point source, from which the flow falls off as l/r2 in accordance with the conservation of matter. l 6 For this flow, the velocity u(x) a distance x from the source is given by : 2nx2u(x) = UC = WRT/PM where U is the Stefan velocity in the channel. At the stagnation point, x = A1 and u(x) = V, hence A2 = (WRT/2nVPM)t. (29) On substituting ( l + A l ) for 1 in the expression for < (the transport function), we obtain v as a function of PV from eqn (4) : W3RT/2nPM V = [CyJ7T,)I { :}-T' (30) In 1-- +ZW ~- We have investigated the dependence of the rate of weight loss due to simple evapor- ation, as a function of the velocity V of the external stream and of the length I of the channel.The substance evaporating was water, in a stream of nitrogen (this system has also been investigated experimentally for calibration and testing the method, see section 3). The left-hand limit, for zero V, corresponds to the entire volume of the apparatus reaching the saturated vapour pressure p i , where i@ becomes zero. As V increases, A1 decreases and ri/ increases, until a limit is approached asymptotically. Having a rough idea of the Solutions to this equation are presented in fig.3. 'I U - 0' I I I I -__I I d3 ICY2 Id ' I 10 I o-2 V/cm s-' FIG. 3.-Effect of external stream velocity on rate of weight loss. (A) I = 0.1 cm ; (B) I = 0.25 cm ; tC) I = 0.5 cm ; (D) I = 1 cm. T = 40°C, P = 1 atm, channel diam. = 2 mm.D . BATTAT, M . 111. FAKTOR, I . GARRETT A N D R . H . MOSS 2275 maximum value of Wto be expected (say within a factor of lo), it is a simple matter to calculate the necessary velocity for the external stream to make AZ 4 1. For our apparatus, we calculate a maximum value of AZ of around 0.1 mm at the speed V = 1 cm s-l. 3.1 APPARATUS The reaction bottle, shown in fig. 4(i), was suspended on a silica fibre from a Cahn RH electrobalance, and hung inside a furnace tube which could be heated with a small furnace to temperatures in the range 300- 1 lOO"C, or with a water jacket (condenser) in the range 0-55°C. Two gas inlets are provided 3.EXPERIMENTAL The apparatus is illustrated scheinatically in fig. 4. r- I ! I 1 2 0 m m i 1.0 I*' [r 0.9 L 0 gas Inlet s i l i c a fibre t o ma no meter s t o p p e r B 5 ground silica joint silica bottle sail1 p I e gas inlet jet tube f dmacc silica flbre silicone oil bubbler to vacuum system (ii) FIG. 4.-(i) Reaction bottle ; (ii) experimental system. 0 0 0 0 0 ot-z2ro 0.5 0.4 I I I 1 I - _ L . - - - . . - - L ~ 0 5 0 I00 153 200 2 5 0 3 0 0 flow rate/cm3 miti-' FIG. L-Effect of flow rate on rate of evaporation. T = 44.4'C, P = 1 atni, H,O/N, t e2276 MODIFIED ENTRAINMENT METHOD 0 -101 I I I I I 3.1 3.2 3.3 3.4 3.5 1000 K/T FIG.6.-Evaporation of water in nitrogen. 0, ref. (17); +, ref. (18); 0, this work. near the top of the apparatus : the lower one will pass reactive gases into the furnace tube in future experiments, the upper one, directly into the balance chamber, serves to keep the chamber free of reactive gases. The temperature of the gas stream was measured with a Pt/Pt-13 % Rh thermocouple on the outside of the furnace tube for high temperatures, and an alcohol-in-glass thermometer positioned with its bulb immediately below the reaction bottle for the lower temperature work. Gas flow rates were measured using Meterate flow meters. TABLE 1 .-CALIBRATION DATA (4 (b) T/OC *W/mg h-' T/OC W/mg h-I water in nitrogen lead in hydrogen 9.5 0.0936 892 0.208 14.55 0.135 902 0.259 19.5 0.19 902 0.217 19.5 0.2092 925 0.354 24.6 0.2747 930 0.358 29.9 0.39 958 0.526 34.75 0.5175 961 0.548 39.7 0.74 979 0.794 40.5 0.675 979 0.804 44.5 0.955 1009 1.201 49.7 1.219 1028 1.510 1028 1.582D.BATTAT, M. M. FAKTOR, I . GARRETT AND R . H . MOSS 2277 3.2 FLOW VISUALISATION EXPERIMENTS Preliminary experiments demonstrated the need for controlling the gas flow near the exit of the neck of the bottle (channel). The flow pattern was made visible by passing ammonia and hydrogen chloride through the furnace tube so that they mixed at the top of the furnace tube and reacted to form a smoke. At the flow rates used (about 100 cm3 min-l), no steady flow pattern developed in the wide (20 mm) furnace tube.The main flow was down one side of the tube, but this pattern changed erratically with temperature and flow rate. To direct the flow and increase the linear velocity by a factor of 10 a constriction or jet tube was introduced, which resulted in a steady flow around the reaction bottle. 3.3 DEPENDENCE OF WEIGHT LOSS ON FLOW RATE The theoretical basis for the dependence of the rate of weight loss on the velocity of the external stream of gas was given in section 2.5. We find that, with the jet tube fitted, the rate of weight loss of a reaction bottle containing water is independent of the rate of flow of nitro- gen in the furnace tube over the entire range of flows under our control (1-350 cm3 min-l), corresponding to linear velocities of 0.6 to 200 mm s-l).The results are shown in fig. 5. - ic - I I -1; n a P E Y . $ 4 Q -1: - I d - I ! I I I 5 8.0 8.5 9.0 104 KIT FIG. 7.-Evaporation of lead in hydrogen. 4. RESULTS 4.1 EVAPORATION OF WATER The experi- mental results are given in table l(a) as rate of weight loss at various temperatures. We have converted these weight loss rates to partial pressures of water, using eqn (4), and taking the diffusion coefficient for water in nitrogen from Schwertz and Brow. The sample material was deionized, double quartz-distilled water.2278 MODIFIED ENTRAINMENT METHOD Fig. 6 shows a plot of our experimental values for R ln(p3,0/atm) against l/T, with literature values ' ' 9 for comparison. From our plot we calculate the following second-law values for AH," and AS: (at our mean operating temperature of 30°C) as 43.6 kJ mol-1 (10.4 kcal mol-') and 116.7 J mol-1 K-l (27.9 e.u.) respectively.4.2 EVAPORATION OF LEAD The sample material was lead granules (AnalaR; Hopkins and Williams Ltd.). The experimental rates of weight loss at various temperatures are given in table I@). These results have been converted to partial pressures using eqn (4). The diffusion coefficient of lead in hydrogen was estimated from Shepherd's curve I4 to be 0.16 cm2 s-I, and we have taken s to be 0.8 as discussed in section 2.4. Our values for R ln(p&/atm) are plotted against 1/T in fig. 7, and from this plot we calculate the second-law values of AH," and AS: (at our mean operating temperature of 960°C) as 180 kJ mol-' (43.0 kcal mol-I) and 94.7 J mol-l K-I (22.6 e.u.) respectively.5. DISCUSSION Our value for AH: for water is in excellent agreement with the literature value of For the evaporation of lead, we find the following values for AH," in the literature : 43.6 kJ mol-l, but our value for AS," is too high by 0.8 J mol-1 K-1 (0.2 e.u.). AHt/kcal rno1-I 29QK 46.36 46.615 46.47 47.06 46.80 45.8k0.7 AH,O/kcal mol-1 1235 K ref. 43.36 (181.2 kJ mol-I) 19 43.615 (182.3 kJ mol-I) 20 43.47 (181.7 kJ mol-l) 21 44.06 (184.2 kJ mol-I) . 21 43.8 (183.1 kJ mol-l) 22 42.810.7 (178.91 3 kJ mol-l) 1 this work 43.0 (180 kJ mol-l) The value of AS; at 1235 K, calculated from the data of Stull and Sinke,22 is 91.1 J mol-1 K-l, in good agreement with the data recommended as reliable by Nesmeyanov, and 3.6 J mol-1 K-I below our value.The effect of errors in the diffusion coefficient and in its temperature dependence have been discussed in section 2.4. Other errors arise in the measurement of ri/: T, C and 1. The dimensions of the channel, C and Z, were measured with a travelling microscope. Small systematic errors originate from the channel being slightly oval in section and the ends not being quite perpendicular to the axis. Measurement of l@ introduces very small systematic errors from inaccuracies of the balance, and larger random errors, which may be as large as 5 %. One serious source of systematic error at the high temperature is in the measurement of temperature. The cold gas entering the furnace is accelerated in the jet tube, so that we would not have been surprised to find indications that our temperature measurements were too high.This would have resulted in a low value for the entropy of evaporation, whereas we find too high a value. Our analysis in section 2 is based on a one-dimensional model, wherein the flux J is uniform over the entire cross-section C of the channel. Obviously, this is not so, Stefan's velocity U will have a parabolic distribution due to viscosity forces, and the more realistic problem is one of axi-symmetric (diffusion) flow in two dimensions. For small rates of evaporation, the variations of the flow quantities in the channel are small and we would expect the mean flow described by the one-dimensional model to yield a good approximation.D. BATTAT, M . M . FAKTOR, I . GARRETT AND R. H . MOSS 2279 In view of the systematic and random errors which are involved, we consider our results for water to be in excellent agreement with the literature values.For lead, we will discuss the possible errors from two points of view. Looking at our experiment as a calibration of the method, we find that by choosing Do = 0.168 cm2 s-l, and s = 0.64 for the diffusion of lead in hydrogen, and taking the measured temperatures to be 1 % too low, we bring our results into line with those recommended by Stull and Sinke. Alternatively, looking at the experiment as a measurement of AHv and AS,, for lead, and assessing the likely errors to be 10 % in Do, 25 % in s, and possibly as large as 2 % in T, we calculate uncertainties in our values for AHv and AS,, of & 8 kJ mol-1 in AH,, and f5 J mol-1 K-1 in AS,,.It would be possible to eliminate many of the sources of error, but we are interested here in assessing the method for measuring equilibrium constants for reactions which are far less well characterised than the vaporisation of lead. The results of one such investigation are reported in the next paper. 6. CONCLUSIONS The modification of the entrainment method, described in this paper, has been discussed theoretically on the basis of a one-dimensional model, and tested on the evaporation of water and of lead. The results obtained are in good agreement with literature values, and demonstrate that the method is reliable. While little effort was made to refine the apparatus, and various sources of random and systematic errors certainly exist, the accuracy obtained is adequate for our present purpose.With some sophistication of the technique, the precision could be improved considerably. Acknowledgement is made to the Director of Research of the Post Office for permission to publish this paper. A. N. Nesmeyanov, Vapour Pressure of the Elements (Infosearch, 1963). 0. Kubaschewski, E. L1. Evans and C. B. Alcock, Metallurgical Thermochemistry (Pergamon, New York, 1967). M. M. Faktor and J. I. Carasso, J. Electrochem. Soc., 1965, 112, 817. J. L. Margrave, Characterisation of High Temperature Vapours (Wiley, New York, 1967). D. A. Frank-Kamenetskii, Diflusion and Heat Transjer in Chemical Kinetics (Plenum, New York, 1969). M. M. Faktor, R. Heckingbottom and I. Garrett, J. Chem. Soc. A , 1970, 2657. ’ M. M. Faktor, R.Heckingbottom and I. Garrett, J . Chem. SOC. A , 1971, 1. * S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge, 1960). D. Battat, to be published. C. R. Wilke, Chem. Eng. Progr., 1950,46,95. l o H. Fujita, Kagaku Kikai, 1951, 15, 234. l 2 International Critical Tables, 1929, 5, 62. l 3 Handbook of Heat Transjer, ed. W. M. Rohsenow and 3. P. Hartnett (McGraw-Hill, New l4 W. H. Shepherd, J. Electrochem. SOC., 1965, 112,988. l 5 F. A. Schwertz and J. E. Brow, J. Chem. Phys., 1951, 19, 640. A. M. Kuethe and J. D. Schetzer, Foundations ofAerodynamics (Wiley, New York, 1950). l 7 G. W. C. Kaye and T. H. Laby, Physical and Chemical Constants (Longman, London, 1959). l 8 D. Ambrose and I. J. Lawrenson, J. Chem. Thermodynamics, 1972, 4, 755.2o J. Fischer, Festsch. Tech. Hochschule, 1935, 172. 2 1 P. Gross, C. S. Campbell, P. J. C. Kent and D. L. Levi, Disc. Faraday Soc., 1948, 4, 206. *’ D. R. Stull and G. C. Sinke, Thermodynamic Properties of the Elements (Amer. Chem. SOC., York, 1973). A. C. Egerton, Proc. Roy. SOC. A, 1923, 103, 469. Washington, 1956). Modified Entrainment Method for Measuring Vapour Pressures and Heterogeneous Equilibrium Constants Part 1 .-Theory, and Validation of the Method using Water and Lead BY DAVID BATTAT, MARC M. FAKTOR,* TAN GARRETT AND RODNEY H. MOSS Post Office Research Station, Dollis Hill, London NW2 7DT Received 27th March, 1974 A method of evaluating vapour pressures and equilibrium constants for heterogeneous reactions is proposed. It replaces the usually indeterminate contribution of gaseous transport in the conven- tional entrainment method by a calculable amount.The method was successfully applied at around room temperature to the evaporation of water, and to the vaporisation of lead in the temperature range 900-1050°C. 1 . INTRODUCTION The thermodynamics of heterogeneous equilibria provides the corner-stone for many branches of physical and chemical science, for example, materials preparation, corrosion and combustion. For reacting systems the enthalpy and entropy changes for the reactions which are involved have in the past been measured by various meth- ods. Vapour pressures and dissociation pressures have been measured by calorimetry, manometry, effusion, torsion-effusion, mass-spectrometry, entrainment, and other methods,l* and a similar variety of techniques is available for determining the equilibrium constants for chemical reactions.For vapour-solid and vapour-liquid reactions, entrainment has long been a popular method. We present a method which is a modification of the normal entrainment method. Before doing so, we briefly appraise the normal method. A stream of reactive gas is passed over the solid or liquid maintained at a given temperature and the amount of product formed in a given time is found from the loss of weight of the solid or liquid, or by condensing or dissolving the products out of the gas stream and determining them by standard analytical techniques. While this method is both simple and flexible, it suffers from the disadvantage that the effect of jlowing the reactants at a finite rate must somehow be accounted for or eliminated.If the gas-flow is very fast, the vapour is not fully equilibrated with the condensed phase, whereas if the flow is very slow, products may travel away from the zone in which equilibrium is being established at a significant rate by diffusion. Furthermore, unmixing of the gas by thermal diffusion becomes a serious source of error, particu- larly if the gas mixture contains hydr~gen.~ Traditionally, extrapolation to zero flow rate has been used, but this results in error for the reasons given above. By constrict- ing the flow channel either side of the equilibrium zone containing the condensed phase the effect of diffusion at low flow rates can be reduced. If the apparent partial pressure of the product is plotted as a function of flow rate, there may be a range of flow rates in which the apparent partial pressure does not alter greatly, and this I ' plateau " value is often taken as representing the true partial pre~sure.~ In well- designed apparatus this assumption may be justifiable, but because equilibrium is established only at the surface of the condensed phase, there must always be some 22672268 MODIFIED ENTRAINMENT METHOD diffusion of reactants towards the surface and of products away from the surface.The region in which diffusion operates is usually illldefined. This diffusion can be made less limiting by causing turbulent mixing of the gas in the reaction zone, or by flowing the gas stream fast to reduce the boundary layer over the solid or liquid.Inevitably there is some composition change in the gas in a direction normal to the surface of the condensed phase, and this is an eventual limitation of the method. When a " plateau " in the plot of apparent partial pressure against flow rate is not found, the true partial pressure is in doubt. Tn the new method described in this paper, we have come to terms with the un- avoidable diffusion effect by confining its region of action to a long, narrow channel of known geometry (typically 2 cm long, 1 mm diameter). One end of the channel is connected to a bulb or reservoir containing the condensed phase under study, and the other end is directed into the stream of reactive gas. The reservoir and channel are suspended from a recording microbalance, so that the loss of weight can be measured continuously.By making the gas flow resistance of the channel high, we can ensure that the rate at which the sample substance loses weight is limited by gas transport kinetics in the channel, the effects of which can be calculated accurately. As a good approximation, we assume that the vapour has a uniform composition in the reservoir above the condensed phase, so that the partial pressure variations are confined to the channel. It would not be difficult to relax this assumption. When the vapour leaves the open end of the channel, it is rapidly diluted and swept away in the fast stream of gas. This paper presents the simple theory of the method, showing how the enthalpy and entropy changes for the reaction, evaporation, or dissociative sublimation may be found from the rate at which the sample loses weight.We also give the results of calibration and test experiments performed on evaporating water and lead. These results are in excellent agreement with the other values reported in the literature. By varying the dimensions of the channel so as to decrease its resistance to gas flow, and by decreasing the surface area of the condensed phase, the chemical reaction or evaporation process at the surface can be made to limit the rate at which weight is lost. Here we have an analogy with a Knudsen effusion experiment, performed with larger and larger orifices, until Langmuir evaporation conditions are approached. Our method, then, may be used to study both equilibria and chemical kinetics for heterogeneous reactions.2. THEORY OF WEIGHT LOSS 2.1 MODEL SYSTEM USED We describe the channel through which the vapour in the bulb communicates with the stream of reactive gas by a simple one-dimensional model (see fig. 1). At the point x = 0, we assume that the vapour composition is the same as that over the surface of the condensed phase, and at x = Z, we assume that the composition of the vapour in the channel has become identical with that in the external gas stream. The first assumption is reasonable if the bulb diameter is large compared with the channel diameter. The second assumption is investigated in detail in section 2.5, and is a very good approximation under the conditions of flow used. 2.2 SIMPLE THEORETICAL DESCRIPTION We consider first the evaporation of a single species A in a stream of inert gas 2.Because of the increase in molar volume when species A evaporates, a " wind " or Stefan flow is generated in the ~hannel,~ vbich sweeps both species upwards. TheD. BATTAT, M. M. FAKTOR, I . GARRETT AND R . H . MOSS 2269 partial pressure gradient of A, and the corresponding gradient of Z, cause diffusion fluxes which must result in zero nett flow of species 2. We can thus write the flow equations in the form 6, : (1) dp.4 - bk JA = RT-RT dx - KC where D is the binary diffusion coefficient, U is the “ wind ” or Stefan velocity, W is the measured rate of weight loss, MA is the molecular weight of species A, and C the cross-sectional area of the channel. In writing the diffusion fluxes in terms of dpA/dx, instead of d(pA/P)/dx, we are assuming that the total pressure is essentially constant all along the channel.Although some pressure gradient is necessary to maintain the Stefan flow, this gradient is negligible unless the channel is very narrow.6 V gas stream I condensed phase FIG. 1.-Reaction bottle. FIG. 2.-Streamline pattern in vicinity of channel exit. Addition of eqn (1) and (2) causes the diffusion terms to cancel out, and we ob- tain : J A = UP/RT (3) where P is the total pressure. We now substitute eqn (3) in eqn (1) to eliminate U, and integrate from x = 0 to x = 1. At x = I, pA is zero (see section 2.5), and at x = 0, pA is the saturated vapour pressure of species A, pi. Thus : p i = P[I -e-g] (4) where (4) to obtain : = JARTl/DP = WRTl/DPM,C is the “ transport function ”.If the rate of weight loss is not large, we may approximate the exponential in eqn p i % wRTl/DMAc. ( 5 ) If measurements of weight loss are carried out over a fairly restricted temperature range, it may be acceptable to assume that T/D is a constant, in which case a plot of2270 MODIFIED ENTRAINMENT METHOD R In ri/ against 1/T has a slope of -AH, and an intercept at 1/T = 0 of AS,- R ln(RTI/DM,C), since R In p i = -AH,/T+AS, where AH, and AS, are the enthalpy and entropy changes of evaporation of substance A. However, it is preferable to carry out measurements of weight loss over as wide a temperature range as possible, for which reason it is necessary to correct for the temperature dependence of the diffusion coefficient. Over a range of temperature, the expression holds,8 where Do is the value of D at a reference temperature To and 1 atm pressure, and s lies usually between 0.5 and I, frequently near 0.8 (but see section 3 for a case where s z 1.5 for water in nitrogen).Eqn ( 5 ) now becomes (still for small w> p i z WRPIT~'S/DoTSMAC. (7) A plot of R In( WIT") against l / T again has a slope of - AHv, and an intercept at 1 /T = 0 of AS, - R ln(lRPT~+s/DD,MAC). We thus have a method for establishing the enthalpy and entropy changes of evaporation or sublimation which gives results that can be made independent of the rate at which the external stream of gas flows. Because of uncertainties about diffusion coefficients and their variation with temper- ature, AH, and ASv are subject to small errors, which will be discussed in section 2.4.In section 4 we present the results of two calibration experiments, which show the accuracy that can quite easily be achieved. Next we consider a heterogeneous reaction of a fairly simple but general type : where M is the condensed phase, assumed to be a single component, and X could be a halogen or, with the necessary changes in stoichiometric coefficients, oxygen or sulphur, for example. The equilibrium constant for reaction (8) may be expressed as : M(s)+HX(g)+MX(g)+W, (g) (8) wherephx, etc. are the equilibrium vapour pressures which we assume exist at x = 0. Since reaction (8) involves an increase in the number of vapour phase molecules, there will again be a " wind '' in the channel.The flow equations are : D d - RT RT dx U J - --(pHX + 2p,J - _1 +PHX + 2 P d = O Here we assume an average value for D. We discuss this point in the next section. As there are no sources or sinks for hydrogen or X inside the channel or the bulb (neglecting absorption in the condensed phase), the fluxes of these species are zero. Again, addition of the flow equations eliminates the diffusion terms, and yields : JM = 2UP/RT. ( 1 3)D . BATTAT, M . M . FAKTOR, I . GARRETT AND R . H . MOSS 2271 We again eliminate U from eqn (10) using eqn (13), and integrate from x = 0 to x = 1. At the exit of the channel, pkIX(I)-O (see section 2.5), so that : phX = 2 ~ t i - e - 9 where now j = JMRTf/2DP = WRTLJ2DPMMC. By similar integration, we also find : pGx = ( p z k + 2 ~ ) e - t - 2~ p i 2 = ( p ~ ~ ~ - ~ ) e - ~ + ~ .Note that the sum of the partial pressures is constant and equal to the tota1 pressure in the system. Measurement of the rate of weight loss allows us to calculate the equilibrium partial pressures, p& etc., and hence arrive at the equilibrium constant using eqn (9). Alternatively, we may formulate the equilibrium constant from eqn (14)-( 16) and hence derive a relation between Kp and ri/. Let us define the fraction of reactive species in the free stream as : p,'lLiP = E . (17) We consider various approximate expressions for the equilibrium constant Kp in terms of the transport function 5, and reactive species fraction E , which arise when < < 1, i.e. small rate of weight loss. This situation occurs if either E is small (there is little reactant in the system) or if the equilibrium of reaction (8) is well to the left (K, < 1).We treat each case separately. CASE (1) -4 I, c - 1 .-Eqn (14)-(16) become : p& = 2Pj p;;x = P(E-&<-225) p& = P(l--E+EC). 'Thus or In this case, a plot of R In wagainst l/Tyields AHr and ASr, directly from the slope and the intercept. K , w 2P5(pgy/pgk. (18) CASE (2) E 4 1, then &x ;y" 2P5 pi>; w P(c-25) p i 2 % P(1-E). (Note that since pLX > 0, 5 cannot be greater than ~ / 2 . ) For this case we find : In this case, LZ plot of R In iy against I / T does not yield AH, and AS, directly. It is necessary to calculate KI, at each temperature from eqn (19). is near c/2, the reaction has gone essentially to completion, K,, is very large and the experiment will not be revealing.However, if2272 MODIFIED ENTRAINMENT METHOD and a plot of R In w against 1/T yields AHr and AS, directly, as in case (1). 2.3 MULTICOMPONENT DIFFUSION The treatment of multicomponent diffusion is lengthy,8 and we will not apply it to this problem. However, it frequently happens that one species is present in consider- able excess. It is then permissible to consider the diffusion of each minority species in the majority species as an independent binary diffusion system. For a ternary system, this approximation can be justified rigorously. We ignore diffusion of one minority species into another, because the collisions which give rise to these diffusion phenomena are rare. The flow equations can now be re-written in the form :' where DMX and DH, are the binary diffusion coefficients of MX and HX in hydrogen, and the relations between the J values for each species result from the conditions : J H = J H x + 2 J H 2 = 0 Jx = JHx+JMx = 0 as before.By summing eqn (21)-(23), the diffusion fluxes cancel out, and eqn (13) is obtained again. Eliminating U and integrating from x = 0 to x = I yields : = 2 ~ [ 1 - e - 5 ~ ] pix = [p& + 2 ~ l e - r ~ ~ - 2~ where JMRTl JMRT1 and tHX = - CMX = GP ~DHxP ' For hydrogen, we simply subtract the minority partial pressures from the total pres- sure : Eqn (24)-(26) may be used to calculate the equilibrium partial pressures from the measured rate of weight loss. Since the flow eqn (21)-(23) hold for a mixture with one majority species only, p& is a small fraction of the total pressure P (E < 1).Furthermore, the transport functions tHX and tMX cannot be greater than 4 2 and (&X/&X)(&/2) respectively. Hence we can usefully simplify the expression for the partial pressures and for Kp : Pi2 = p - Pbx- PGx* (26) P&X 2p<MX pix % p#fc-22p~HX Pi2 = P~~--pc25,x-25,xl.D. BATTAT, M. M. FAKTOR, I . GARRETT AND R . H . MOSS 2273 Hence If, in addition, 5 Q E , then Kp = 25MX/E. In practice, we found eqn (28) was applicable to our calibration experiments, de- scribed in section 3. 2.4 ERRORS I N ENTHALPY AND ENTROPY CHANGES We will not consider errors in measurement of temperature and partial pressures in the external stream of gas. Also we assume that the dimensions of the channel and the total pressure are known well.Our concern here is with the effect of errors in the diffusion coefficient Do and the index of its temperature variation s on the experimental values of enthalpy and entropy changes. The parameter Do appears only in the expression for the entropy, and then only as a logarithm. An uncertainty of a factor of two in the diffusion coefficient contributes an error of 6 J mol-l K-l. While the value of Do may not be known accurately, it may be estimated from critical-point data,lo* l 1 by comparison with pairs of similar gases for which Do is known,12* l3 or from empirical curves such as that of Shep- herd. The index s affects both A H and AS. We can find the error 6(AH) introduced by an error S(s) : Hence 6(AH) = - RT 6(s).Thus an error of 0.1 in s at 1 2 0 0 K produces an error of 1 kJ mol-I in AH. The index s is, of course, not known for species for which the diffusion coefficient has not been measured as a function of temperature. This includes the products of many high-temperature reactions. For most pairs of gases, s is in the range 0.5-1.' How- ever, anomalous values of s for some combinations of gases are known, e.g. M 1.5 for H20+N2, as calculated from the experimental data of Schwertz and Similarly we find the error &AS) caused by an error S(s) in the index s, and one calculates &AS) = - R6(s)[l+ In(T/To)]. Thus an error of 0.1 in s introduces an error in A S of 1 J mol-1 K-l at 320 K and 2 J mol-', K-I at 1200 K, if To = 273 K. 2.5 HYDRODYNAMICS OF THE FLOW AT THE CHANNEL EXIT We have assumed so far that at x = 2, i.e.at the exit of the channel, the gas becomes rapidly diluted and swept away by the external stream. Let us examine the flow pattern near the channel exit. The vapour leaving the channel spills out into a region of length AZ, and on reaching the bounding streamline, its concentration has 1-722274 MODIFIED ENTRAINMENT METHOD been reduced effectively to zero. We take A1 as being the distance from the exit of the tube to the stagnation point (fig. 2). According to potential flow theory,16 the flow in the stagnation region may be constructed by superposition of the uniform flow of the external stream at velocity V, and the flow issuing from the channel. The flow from the channel may be approxi- mated by a point source, from which the flow falls off as l/r2 in accordance with the conservation of matter.l 6 For this flow, the velocity u(x) a distance x from the source is given by : 2nx2u(x) = UC = WRT/PM where U is the Stefan velocity in the channel. At the stagnation point, x = A1 and u(x) = V, hence A2 = (WRT/2nVPM)t. (29) On substituting ( l + A l ) for 1 in the expression for < (the transport function), we obtain v as a function of PV from eqn (4) : W3RT/2nPM V = [CyJ7T,)I { :}-T' (30) In 1-- +ZW ~- We have investigated the dependence of the rate of weight loss due to simple evapor- ation, as a function of the velocity V of the external stream and of the length I of the channel. The substance evaporating was water, in a stream of nitrogen (this system has also been investigated experimentally for calibration and testing the method, see section 3).The left-hand limit, for zero V, corresponds to the entire volume of the apparatus reaching the saturated vapour pressure p i , where i@ becomes zero. As V increases, A1 decreases and ri/ increases, until a limit is approached asymptotically. Having a rough idea of the Solutions to this equation are presented in fig. 3. 'I U - 0' I I I I -__I I d3 ICY2 Id ' I 10 I o-2 V/cm s-' FIG. 3.-Effect of external stream velocity on rate of weight loss. (A) I = 0.1 cm ; (B) I = 0.25 cm ; tC) I = 0.5 cm ; (D) I = 1 cm. T = 40°C, P = 1 atm, channel diam. = 2 mm.D . BATTAT, M . 111. FAKTOR, I . GARRETT A N D R . H . MOSS 2275 maximum value of Wto be expected (say within a factor of lo), it is a simple matter to calculate the necessary velocity for the external stream to make AZ 4 1.For our apparatus, we calculate a maximum value of AZ of around 0.1 mm at the speed V = 1 cm s-l. 3.1 APPARATUS The reaction bottle, shown in fig. 4(i), was suspended on a silica fibre from a Cahn RH electrobalance, and hung inside a furnace tube which could be heated with a small furnace to temperatures in the range 300- 1 lOO"C, or with a water jacket (condenser) in the range 0-55°C. Two gas inlets are provided 3. EXPERIMENTAL The apparatus is illustrated scheinatically in fig. 4. r- I ! I 1 2 0 m m i 1.0 I*' [r 0.9 L 0 gas Inlet s i l i c a fibre t o ma no meter s t o p p e r B 5 ground silica joint silica bottle sail1 p I e gas inlet jet tube f dmacc silica flbre silicone oil bubbler to vacuum system (ii) FIG.4.-(i) Reaction bottle ; (ii) experimental system. 0 0 0 0 0 ot-z2ro 0.5 0.4 I I I 1 I - _ L . - - - . . - - L ~ 0 5 0 I00 153 200 2 5 0 3 0 0 flow rate/cm3 miti-' FIG. L-Effect of flow rate on rate of evaporation. T = 44.4'C, P = 1 atni, H,O/N, t e2276 MODIFIED ENTRAINMENT METHOD 0 -101 I I I I I 3.1 3.2 3.3 3.4 3.5 1000 K/T FIG. 6.-Evaporation of water in nitrogen. 0, ref. (17); +, ref. (18); 0, this work. near the top of the apparatus : the lower one will pass reactive gases into the furnace tube in future experiments, the upper one, directly into the balance chamber, serves to keep the chamber free of reactive gases. The temperature of the gas stream was measured with a Pt/Pt-13 % Rh thermocouple on the outside of the furnace tube for high temperatures, and an alcohol-in-glass thermometer positioned with its bulb immediately below the reaction bottle for the lower temperature work.Gas flow rates were measured using Meterate flow meters. TABLE 1 .-CALIBRATION DATA (4 (b) T/OC *W/mg h-' T/OC W/mg h-I water in nitrogen lead in hydrogen 9.5 0.0936 892 0.208 14.55 0.135 902 0.259 19.5 0.19 902 0.217 19.5 0.2092 925 0.354 24.6 0.2747 930 0.358 29.9 0.39 958 0.526 34.75 0.5175 961 0.548 39.7 0.74 979 0.794 40.5 0.675 979 0.804 44.5 0.955 1009 1.201 49.7 1.219 1028 1.510 1028 1.582D. BATTAT, M. M. FAKTOR, I . GARRETT AND R . H . MOSS 2277 3.2 FLOW VISUALISATION EXPERIMENTS Preliminary experiments demonstrated the need for controlling the gas flow near the exit of the neck of the bottle (channel).The flow pattern was made visible by passing ammonia and hydrogen chloride through the furnace tube so that they mixed at the top of the furnace tube and reacted to form a smoke. At the flow rates used (about 100 cm3 min-l), no steady flow pattern developed in the wide (20 mm) furnace tube. The main flow was down one side of the tube, but this pattern changed erratically with temperature and flow rate. To direct the flow and increase the linear velocity by a factor of 10 a constriction or jet tube was introduced, which resulted in a steady flow around the reaction bottle. 3.3 DEPENDENCE OF WEIGHT LOSS ON FLOW RATE The theoretical basis for the dependence of the rate of weight loss on the velocity of the external stream of gas was given in section 2.5.We find that, with the jet tube fitted, the rate of weight loss of a reaction bottle containing water is independent of the rate of flow of nitro- gen in the furnace tube over the entire range of flows under our control (1-350 cm3 min-l), corresponding to linear velocities of 0.6 to 200 mm s-l). The results are shown in fig. 5. - ic - I I -1; n a P E Y . $ 4 Q -1: - I d - I ! I I I 5 8.0 8.5 9.0 104 KIT FIG. 7.-Evaporation of lead in hydrogen. 4. RESULTS 4.1 EVAPORATION OF WATER The experi- mental results are given in table l(a) as rate of weight loss at various temperatures. We have converted these weight loss rates to partial pressures of water, using eqn (4), and taking the diffusion coefficient for water in nitrogen from Schwertz and Brow.The sample material was deionized, double quartz-distilled water.2278 MODIFIED ENTRAINMENT METHOD Fig. 6 shows a plot of our experimental values for R ln(p3,0/atm) against l/T, with literature values ' ' 9 for comparison. From our plot we calculate the following second-law values for AH," and AS: (at our mean operating temperature of 30°C) as 43.6 kJ mol-1 (10.4 kcal mol-') and 116.7 J mol-1 K-l (27.9 e.u.) respectively. 4.2 EVAPORATION OF LEAD The sample material was lead granules (AnalaR; Hopkins and Williams Ltd.). The experimental rates of weight loss at various temperatures are given in table I@). These results have been converted to partial pressures using eqn (4). The diffusion coefficient of lead in hydrogen was estimated from Shepherd's curve I4 to be 0.16 cm2 s-I, and we have taken s to be 0.8 as discussed in section 2.4.Our values for R ln(p&/atm) are plotted against 1/T in fig. 7, and from this plot we calculate the second-law values of AH," and AS: (at our mean operating temperature of 960°C) as 180 kJ mol-' (43.0 kcal mol-I) and 94.7 J mol-l K-I (22.6 e.u.) respectively. 5. DISCUSSION Our value for AH: for water is in excellent agreement with the literature value of For the evaporation of lead, we find the following values for AH," in the literature : 43.6 kJ mol-l, but our value for AS," is too high by 0.8 J mol-1 K-1 (0.2 e.u.). AHt/kcal rno1-I 29QK 46.36 46.615 46.47 47.06 46.80 45.8k0.7 AH,O/kcal mol-1 1235 K ref. 43.36 (181.2 kJ mol-I) 19 43.615 (182.3 kJ mol-I) 20 43.47 (181.7 kJ mol-l) 21 44.06 (184.2 kJ mol-I) .21 43.8 (183.1 kJ mol-l) 22 42.810.7 (178.91 3 kJ mol-l) 1 this work 43.0 (180 kJ mol-l) The value of AS; at 1235 K, calculated from the data of Stull and Sinke,22 is 91.1 J mol-1 K-l, in good agreement with the data recommended as reliable by Nesmeyanov, and 3.6 J mol-1 K-I below our value. The effect of errors in the diffusion coefficient and in its temperature dependence have been discussed in section 2.4. Other errors arise in the measurement of ri/: T, C and 1. The dimensions of the channel, C and Z, were measured with a travelling microscope. Small systematic errors originate from the channel being slightly oval in section and the ends not being quite perpendicular to the axis. Measurement of l@ introduces very small systematic errors from inaccuracies of the balance, and larger random errors, which may be as large as 5 %.One serious source of systematic error at the high temperature is in the measurement of temperature. The cold gas entering the furnace is accelerated in the jet tube, so that we would not have been surprised to find indications that our temperature measurements were too high. This would have resulted in a low value for the entropy of evaporation, whereas we find too high a value. Our analysis in section 2 is based on a one-dimensional model, wherein the flux J is uniform over the entire cross-section C of the channel. Obviously, this is not so, Stefan's velocity U will have a parabolic distribution due to viscosity forces, and the more realistic problem is one of axi-symmetric (diffusion) flow in two dimensions.For small rates of evaporation, the variations of the flow quantities in the channel are small and we would expect the mean flow described by the one-dimensional model to yield a good approximation.D. BATTAT, M . M . FAKTOR, I . GARRETT AND R. H . MOSS 2279 In view of the systematic and random errors which are involved, we consider our results for water to be in excellent agreement with the literature values. For lead, we will discuss the possible errors from two points of view. Looking at our experiment as a calibration of the method, we find that by choosing Do = 0.168 cm2 s-l, and s = 0.64 for the diffusion of lead in hydrogen, and taking the measured temperatures to be 1 % too low, we bring our results into line with those recommended by Stull and Sinke. Alternatively, looking at the experiment as a measurement of AHv and AS,, for lead, and assessing the likely errors to be 10 % in Do, 25 % in s, and possibly as large as 2 % in T, we calculate uncertainties in our values for AHv and AS,, of & 8 kJ mol-1 in AH,, and f5 J mol-1 K-1 in AS,,. It would be possible to eliminate many of the sources of error, but we are interested here in assessing the method for measuring equilibrium constants for reactions which are far less well characterised than the vaporisation of lead. The results of one such investigation are reported in the next paper. 6. CONCLUSIONS The modification of the entrainment method, described in this paper, has been discussed theoretically on the basis of a one-dimensional model, and tested on the evaporation of water and of lead. The results obtained are in good agreement with literature values, and demonstrate that the method is reliable. While little effort was made to refine the apparatus, and various sources of random and systematic errors certainly exist, the accuracy obtained is adequate for our present purpose. With some sophistication of the technique, the precision could be improved considerably. Acknowledgement is made to the Director of Research of the Post Office for permission to publish this paper. A. N. Nesmeyanov, Vapour Pressure of the Elements (Infosearch, 1963). 0. Kubaschewski, E. L1. Evans and C. B. Alcock, Metallurgical Thermochemistry (Pergamon, New York, 1967). M. M. Faktor and J. I. Carasso, J. Electrochem. Soc., 1965, 112, 817. J. L. Margrave, Characterisation of High Temperature Vapours (Wiley, New York, 1967). D. A. Frank-Kamenetskii, Diflusion and Heat Transjer in Chemical Kinetics (Plenum, New York, 1969). M. M. Faktor, R. Heckingbottom and I. Garrett, J. Chem. Soc. A , 1970, 2657. ’ M. M. Faktor, R. Heckingbottom and I. Garrett, J . Chem. SOC. A , 1971, 1. * S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge, 1960). D. Battat, to be published. C. R. Wilke, Chem. Eng. Progr., 1950,46,95. l o H. Fujita, Kagaku Kikai, 1951, 15, 234. l 2 International Critical Tables, 1929, 5, 62. l 3 Handbook of Heat Transjer, ed. W. M. Rohsenow and 3. P. Hartnett (McGraw-Hill, New l4 W. H. Shepherd, J. Electrochem. SOC., 1965, 112,988. l 5 F. A. Schwertz and J. E. Brow, J. Chem. Phys., 1951, 19, 640. A. M. Kuethe and J. D. Schetzer, Foundations ofAerodynamics (Wiley, New York, 1950). l 7 G. W. C. Kaye and T. H. Laby, Physical and Chemical Constants (Longman, London, 1959). l 8 D. Ambrose and I. J. Lawrenson, J. Chem. Thermodynamics, 1972, 4, 755. 2o J. Fischer, Festsch. Tech. Hochschule, 1935, 172. 2 1 P. Gross, C. S. Campbell, P. J. C. Kent and D. L. Levi, Disc. Faraday Soc., 1948, 4, 206. *’ D. R. Stull and G. C. Sinke, Thermodynamic Properties of the Elements (Amer. Chem. SOC., York, 1973). A. C. Egerton, Proc. Roy. SOC. A, 1923, 103, 469. Washington, 1956).

ISSN:0300-9599    

DOI:10.1039/F19747002267

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Modified Entrainment Method for Measuring Vapour Pressures and Heterogeneous Equilibrium Constants Part 2.-Equilibria in the Water/Galliurn System BY DAVID BATTAT, MARC M. FAKTOR," IAN GARRETT AND RODNEY H. Moss Post Office Research Department, Dollis Hill, London NW2 7DT Received 27th March, 1974 The modified entrainment method is applied to the study of a heterogeneous equilibrium : water vapour/liquid gallium, in the temperature range 1200-1400 K. Two gaseous gallium species, GazO and GaOH, were observed. The theory of the modified entrainment method is extended to this more complex case involving two simultaneous reactions. The entropies and enthalpies of formation are : AHsg8/kJ mol-' SZg8/J mol-' K-1 GazO - 90.8 5 8 287 k 6 GaOH - 148+15 248k 12. 1. INTRODUCTION The gallium/water equilibrium at high temperature is of interest for several reasons. Under suitable conditions of temperature and waterhydrogen ratio, volatile gallium species are evolved ' 9 at appreciable partial pressures.The system can therefore be used for chemical vapour transport of gallium compounds, as has been done by several worker^.^'^ Water vapour is an attractive reagent for such a process. It appeared that the gallium/water system was well characterised,l. and would be a useful and interesting reactive system for testing our modified entrainment method described in Part 1. Previous workers 3-5 9 9 have assumed that the volatile gallium species is the sub-oxide, formed by the reaction : (1) The enthalpy of formation of Ga20(g) was reported by Frosch and Thurmond,l and by Cochran and Foster,2 as the result of measurements of the equilibria between gallium and the oxides SiO, and MgO, and Ga,O,.Our work shows that in addition to the suboxide, a volatile mono-hydroxide is formed in the presence of hydrogen : This reaction is important under the conditions that have been used for vapour transport of gallium compounds in water vapour/hydrogen mixtures. 3 - 5 9 79 The equilibrium constant for the reaction : is unity at about 1000 K. This paper describes the application of our method for studying heterogeneous equilibria to the gallium/water vapour system in the temperature range 1200-1400 K, 2Ga(l) + H,O(g)=Ga,O(g) + H2(g). Ga(1) + H,O(g)+GaOH(g) ++H2(g). (2) 2GaOH(g)+Ga20(g) + H,O(g) (3) 2280D. BATTAT, M.M . FAKTOR, I . GARRETT AND R . H . MOSS 2281 and we report second-law and third-law enthalpies and entropies of formation for gallium suboxide and gallium monohydroxide. A third reaction may occur in the system : 2Ga(l) + 3H20(g)-+Ga,0,(s) + 3H&. (4) Gallium sesquioxide forms as a crust on the liquid gallium, and hinders reactions (1) and (2). We designed our experiment so as to avoid formation of the sesquioxide. 2. EXPERIMENTAL In Part 1 of this series we described the method and its application to measurement of vapour pressures. Briefly, a small silica bottle with a long narrow neck of known dimensions is suspended in a furnace from a recording microbalance. The condensed phase sample (gallium in the present instance) is contained in the bottle, and a suitable atmosphere (water vapour/hydrogen mixture) flows round the bottle.The reactant gases enter the bottle via the neck, and the products leave by the same route. Changes in gas composition are confined essentially to the neck of the bottle, and may be accurately described using a simple theory of gas transport.6* The temperature of the bottle is measured with a Pt/Pt-10 % Rh thermocouple, positioned on the outside of the furnace tube level with the reaction bottle. The vapour pressure measurements reported in Part 1 indicate that our temperature measurements were about 1 % too low, and we have corrected the temperatures accordingly. Fig. 1 is a schematic illustration of the apparatus. PJ to vacuum syztem bubbler unit FIG. 1 .-Experimental arrangement. 0, tap ; El, needle valve.The primary hydrogen stream passes through a fine sintered frit bubbler containing de- ionized, double quartz distilled water. The bubbler stands in a thermos flask, and thermo- statted kerosene is passed round it continuously to control its temperature. The coil preced- ing the bubbler allows the hydrogen to reach the temperature of the water. A secondary hydrogen stream enters the system through the balance chamber, thus keeping it free of reactive gases. The hydrogen was purified using a palladium diffuser. The secondary flow was replaced by dry nitrogen for the second experiment, for reasons discussed in section 4. Flow rates were measured with Meterate flow meters, and controlled with needle valves. Successful operation of the balance requires smooth gas flow, which was achieved by using stagnation chambers and capillaries in the equivalent of a capacitor-resistor network (fig.1).2282 MODIFIED ENTRAINMENT METHOD The practical limits of temperature and water vapour/hydrogen ratio that can be used in this experiment are shown in fig. 2, in which an " operating window " is delineated. The upper bound of temperature is set by the furnace elements and by the silica furnace tube. At a given temperature, there is a water vapour/hydrogen ratio at which gallium sesqui-oxide becomes stable, and this ratio is the upper bound for that dimension of the " window ". The lower bounds of the " window " are determined by the sensitivity of the balance to small rates of weight loss. In calculating the bounds in fig.2, we have used literature data for the formation of Ga203 l o and Ga20.'- * L E . 3 L Q. \ \ \ \ IS- \ / ' formation of Ga203 \ \ \ \ \b \ \ \ \ I \ / I I I Oil50 1200 1250 1 3 0 0 TIK FIG. 2.-Bounds of the experimental "window ". (al) ~ H ~ / P = 1, (a2) ~ H ~ / P = 0.5 ; required sensitivity of the balance (bl) 1.0 pg s-', (b2) 0.3 pg s-', (b3) 0.1 pg s-I. 3. RESULTS Two sets of experiments were performed. In the first, experiment (a), a ratio of The rates of loss partial pressures of water vapour to hydrogen of 0.003 25 was used. of weight at the experimental temperatures are given in table 1. A linear least squares fit yields the representation : In ma = -9793.7 K/T+7.094 ( 5 ) with an index of determination of -0.991. In the second experiment, experiment (b), the secondary hydrogen flow was replaced by dry nitrogen.The water vapour partial pressure was 0.001 63 atm, and the hydrogen partial pressure was 0.223 atm. The results of the second experiment are given in table l(b). A least squares fit yields the representation In wT= - 8680.7 K/T+ 5.236 (6) with an index of determination of -0.97.D . BATTAT, M. M . FAKTOR, I . GARRETT AND R . H . MOSS 2283 Throughout the discussion which follows, we use subscripts n and b to distinguish quantities referring to experiments (a) and (b), and subscripts 1 and 2 to distinguish quantities referring to reactions (1) and (2). TABLE 1 .-SAMPLE WEIGHT LOSS AT VARIOUS TEMPERATURES experiment (a) experiment (b) - TI K h-' TI K Wlmg h-' 1186 0.299 1215 0.400 1243 0.464 1268 0.532 1291 0.584 1291 0.636 1303 0.646 1217 0.157 1262 0.181 1292 0.220 1324 0.28 1 4.DISCUSSION 4.1 GENERAL REMARKS To convert the experimental data into equilibrium constants, we apply the theory developed in Part 1.6 In the next subsection, we take the simplest approach and assume that one reaction dominates over the experimental temperature range. We then adduce evidence to show that this assumption is not consistent with all our experimental results. In subsection 4.3, we extend the theory given in Part 1, to cover simultaneous equilibria, and we obtain second law entropies and enthalpies for reactions (1) and (2). The calculation of third law data is described in subsection 4.4, and the two sets of results compared. Our results are compared with previously published results in subsection 4.5.4.2 ONE DOMINANT REACTION weight. We assume that either reaction (1) or reaction (2) accounts for the observed loss of For these reactions, the equilibrium constants are : and Using the analysis in Part 1, and the approximations of Case (2) which are appropriate here ; we can write the equilibrium constants as : and where Y is pH2/P, w 1 in experiment (a) and 0.223 in experiment (b), E = pHIO/P in the gas stream flowing through the furnace, and ti is the transport function of species i, defined by : w RT2 < . = -x- ' 2CMGa PD,(T)'2284 MODIFIED ENTRAINMENT METHOD Di is the binary diffusion coefficient for species i in hydrogen, C and I are the cross- sectional area and the length of the neck of the bottle, MGa is the atomic weight of gallium, P, T, and R are the total pressure, temperature and gas constant.The diffusion coefficients for the minority species in hydrogen were obtained as follows : the diffusivities at 0°C were obtained in terms of the critical temperature and pressure l1 in the case of water, using the relationship proposed by Arnold l 2 and Fujita,13 and in terms of the molecular weights for the volatile gallium species, using Shepherd's l4 empirical curve. The diffusion coefficients at high temperature were then calculated from the equation l 5 : D(T) = D0(T/273 K)'+' where s was taken as 0.833 for the diffusion of water in hydrogen,13 and 0.75 for the other species.15 The values of Do are given in table 2. TABLE 2.-BINARY DIFFUSION COEFFICIENTS AT 0°C species Di,H2/cm2 s-1 Di,Nz/cm2 s-1 DI/crnz s-l H2O 0.686 0.23 1 0.271 0.833 Ga20 0.18 0.0605 0.07 1 1 0.75 GaOH 0.275 0.0925 0.109 0.75 To estimate the effective diffusion coefficients of the minority species in a hydro- gen + nitrogen mixture, we first estimate the diffusion coefficients in nitrogen alone. We assume that the ratio of the diffusion coefficient of species i in hydrogen to that in nitrogen is independent of species i.This assumption holds good for most permanent gases l6 and a large number of organic v a p o ~ r s . ~ ~ We calculate the diffusion coeffi- cient of water in nitrogen, using the critical data l1 and Fujita's equation,13 and hence estimate the diffusion coefficients of the gallium species in nitrogen. The diffusion coefficient Df for species i in a mixture of hydrogen and nitrogen is given by :18 (11) where Y is pHJP in the mixture, and Di,H2 and Di,Nz are the diffusion coefficients of species i in hydrogen and in nitrogen.The values for Di,H2, Di,H2, and Df are given in table 2. It is now possible to calculate the values of the equilibrium constants K1 and K2, using the eqn (9) and (10). As 5 is of the order these approximate formulae are quite adequate. The results are plotted in fig. 3. The corresponding second-law enthalpy and entropy changes for reactions (1) and (2) are given in table 4. If either reaction were dominant over our temperature range, we would expect the values of the equilibrium constant for that reaction yielded by the two experiments to be the same. In table 3, we give the ratio of values of the two equilibrium constants determined from the two experiments. We have used the least-squares fit to the experimental points, as given by eqn (5) and (6), to determine values of the equilibrium constants at several temperatures, because different temperatures were used in the two experiments. The ratios in table 3 depart appreciably from unity, and vary consider- ably with temperature.Although the experimental data from experiment (b) are scattered because the operational " window " is very small, it is clear that neither reaction is dominant over our experimental temperature range. Di,H2/Df = y+(l - Y)(Di,H2/Di,N2) Two other pieces of evidence support this conclusion. (1) We have investigated the composition of the vapour in a capsule loaded with liquid gallium and wet hydrogen and heated to lQoO°C, using a VG Micromass 12 massD. BATTAT, M .M . FAKTOR, I . GARRETT AND R . H. MOSS 2285 spectrometer. Peaks were observed at mass numbers 154, 156, 158 (corresponding to the molecules 69Ga216Q, 69Ga71Ga160, 'lGa,160) and 86 and 88 (corresponding to 69Ga1601H and 71Ga16Q1H), with heights in roughly the ratios expected from the "'I \ '4 3 0 - -0.5- E 5 - 1.0- - Q - 1.5- - 2.0 - - 3.51 I I I 7.5 8.0 8.5 9.0 104 KIT FIG. 3.-Variation of equilibrium constant with temperature assuming a dominant reaction. (A) GaOH : A H = 114 kJ mol-l, A S = 94 J mol-' K-' ; (B) GazO : AH = 93 kJ mol-', A S = 73 J mol-1 K-'. relative abundance of the gallium isotopes. The peaks were only a few times the background in height, however, and we were unable to carry out diagnostic tests (e.g.plotting ionization efficiency curves) that would result in unambiguous identification of the species giving rise to these peaks. TABLE 3 .-EQLJILIBRIUM CONSTANTS DETERMINED FROM THE TWO EXPERIMENTS TIK KI.ctlKLb K2,alK2,b 1200 1.66 0.57 1225 1.63 0.50 1250 1.61 0.43 1275 1.57 0.33 1300 1.52 0.19 (2) We have estimated the enthalpy of formation of GaOH from the dissociation energy of the Ga-OH bond,lg 427f20 kJ rnol-l, and other bond energy data.20* 21 We find it to be 125 20 kJ niol-l, which gives the enthalpy change for reaction (2) as around 116 kJ mol-l at room temperature. The entropy of GaOH (gas) we estimate as 248 & 8 J mol-1 K-' at room temperature (see section 4.4 below), so that the entropy change for reaction (2) at room temperature is around 84 J mol-1 K-l.The free energy change for the reaction is zero at 1300-1400 K, so that we expect the partial2286 MODIFIED ENTRAINMENT METHOD pressure of GaOH to be appreciable in this temperature range. For gallium suboxide, an enthalpy of formation of - 84 kJ mol-' has been reported,'? and we estimate the entropy to be 287+8 J mol-1 K-' (see section 4.4). The enthalpy and entropy changes for the reaction (1) are therefore 159 kJ mol-1 and 151 J mol-I K-I at room temperature, so that the free energy change is zero at 1000-1100 K. In these rough calculations we have ignored the specific heat corrections, but clearly the partial pressures of GaOH and Ga,O are comparable in our experimental temperature range.* 4.3 THEORETiCAL TREATMENT FOR TWO SIMULTANEOUS REACTIONS It is not difficult to show, by extending the treatment given in Part that : where Y, = pH2/P in experiment (b) (= 0.223) and x and y are variables or coordinates which are related to the position of the reaction equilibrium, and are defined by : y = $u, ' HzO/&, FIG. 4.-Reaction domain for the formation of Ga20 and GaOH (Y = 0.25). (i) Locus of K2 = 0, y = 4x/1+3x ; cii) locus of K , = 0, y = x/+-!-x ; (iii) locus of A = 0, y = 3x- 1/2x ; -0-0--, experimental data. * We are indebtFd to a referee for drawing our attention to the following data in the literatute 31 : for GaOH(g), AH,,,, = - 124k 21 kJ mol-', Sig8 = 239k 3 J mol-' K-', and for Ga20, SHt.298 = -86t6 kJ mol-', Sig8 = 284+2 J mol-I K-'.I>.BATTAT, M . M. FAKTOR, I. GARRETT AND R. H. MOSS 2287 where E is againp,,,/P in the gas stream, and and Wb are the measured rates of weight loss in experiments (a) and (b) at one specific temperature. In deriving eqn (12) and (13) we have made the assumptions about the diffusion coefficients which we discussed earlier, and we also take E < 1. Note that if either Kl or K2 is very small, the expression for the other equilibrium constant reduces to eqn (9) or (10). We examine eqn (12) and (13) on a plot of x against y in the range which is physi- cally meaningful, i.e. 0 < x, y , < 1 (fig. 4). Physically acceptable solutions lie between the lines Kl = 0 and K2 = 0, and above the line marked A = 0, A being the denom- inator in eqn (12) and (I 3).1.0 0 - - - 1.0 - - n Y !? - a: -2.0- - 3.0 - -4.0 0.76 0.77 0.78 0.79 0 . 8 0 0.81 0.82 0.83 0.84 0.85 104 KIT FIG. 5.-Variation of equilibrium constant with temperature. (A) GaOH : AH = 55.6 kJ mol-', A S = 41.4 J mol-' K-l, index of determination -0.993 ; (B) Ga20 : AH = 142 kJ mol-', A S = 10.6 J 11101-1 K-', index of determination -0.999. Using the linear representations for In win terms of 1 /T, eqn (5) and (6), we can calculate values of x and y over our experimental temperature range, and plot our experimental results on fig. 4. The values of x and y are subject to uncertainties arising from errors in the experimental values of wand T, and uncertainties in the binary diffusion coefficients of water in hydrogen and in the hydrogen+nitrogen mixture.Calculations using eqn (12) and (13) show that the equilibrium constants are particularly sensitive to experimental errors, and that both random and systematic errors influence the results. The measurements of E and Y are significant sources of errors, but the scatter in Wb (see fit of linear representation) is much more important. Because reactions (1) and (2) are of about equal importance in the short temperature2288 MODIFIED ENTRAINMENT METHOD range studied, the experimental results contain information about Kl and K2 simul- taneously. The requirement that In K should be linear in 1 /T for both reactions im- poses a limit on the range of uncertainties in the experimental data. For instance, an uncertainty in the slopes of Wa(T) and wb(T) greater than 10 % would lead to a nonlinear dependence of one equilibrium constant with temperature.The raw experimental data lead to plots of R In K against 1 /T as shown in fig. 5, but in table 4 we give the ranges for the second law values, which were obtained from considerations of simultaneous linearity of In K against 1 /T. 4.4 THIRD LAW CALCULATIONS We have carried out calculations of the thermodynamic functions of Ga20 and GaOH, using the rigid rotator approximation.22 We took the Ga-0 bond length to be 1.86& and the bond angle to be 143", as reported by Hinchcliffe and O g d e ~ ~ . ~ ~ The product of the moments of inertia is then 4360 x 10-1 g3 cm6. The vibrational frequencies v1 and v3 have been reported 25 as 472 cm-I and 809.4 cm-l. We esti- mated v2 as 137 cm-l using the valence force theory.26 This estimation is subject to an error due to the uncertainty of 5 5" in the Ga-0-Ga bond angle.24 We obtain a room temperature entropy of 287 J mol-1 K-l, a little lower than the value of 318 J mol-1 K-l given by the empirical formula of Dasent 27 for a polyatomic mole- cule.This is acceptable, since the Ga20 molecule has a small moment of inertia about one axis. The results of the calculations are given in table 5 (1). For GaOH, we assumed a linear structure as for NaOH,28 RbOH,28 and CsOH 29 in accordance with Walsh's predi~tion,~~ with a Ga-0 bond length of 1.95 A (0.5 A less than the sum of the covalent radii,23 as in AlOH) 2o and the 0-H bond length as 0.96 A as in H20.20 The rotational constant B is then 0.301. The 0-H stretch frequency v3 was taken as 3600 cm-l as in other hydroxides 2 o s 28* 29 and in water.20 The Ga-0 stretch, vl, and the bending frequency v2 were estimated, on the basis of the weight of the metal atom, to lie part way between those of NaOH and RbOH,28 and we took the values 374 and 316 cm-l. The results of the calculations are given in table 5 (2).We have used these calculated data to obtain third law enthalpy and entropy changes for reactions (1) and (2) and to find the entropy and enthalpy of formation of Ga,O and GaOH, using values of the equilibrium constant for reactions (1) and (2) calculated from our second law results described in the previous section. It makes very little difference which extreme pairs of values of AH and A S one takes for the reactions.The third law results are given in table 4. Free energy functions and entropies for gallium and hydrogen were taken from Stull and Sinke,21 and for water from the JANAP Tables.2o The sources of error in the third-law calculations lie (1) in the parameters used for the calculations and (2) in the values of the equilibrium constants calculated from our second-law results. Uncertainties in the parameters yield an error which we estimate as +6 J mol-1 K-l for Ga20 and 12 J mol-l K-I for GaOH ( + 8 kJ mol-1 and +_ 17 kJ mol-1 in the enthalpies of formation). The errors from the second soIzrce are surprisingly small, since our extreme pairs of values (AH", AS") for the reactions yield very similar equilibrium constants [0.32-0.28 for reaction (l), 0.7-0.9 for reaction (2) at 1250 K].We estimate the errors from this source as +4 kJ mol-l and + 3 J mol-I K-1 in all the enthalpies and entropies. Agreement between the third-law and second-law values (derived from the analysis in section 4.3 for simultaneous reactions) is within the estimated error limits, and is quite good for gallium suboxide.D. BATTAT, M. M. FAKTOR, I . GARRETT AND R . H. MOSS 2289 4.5 COMPARISON WITH LITERATURE VALUES The enthalpy of formation of gallium suboxide has been reported by Frosch and Thurmond as 86.6+ 10 kJ mol-l, and by Cochran and Foster as 82.4f3 kJ mol-l. Our third-law value of 90.8 f 8 kJ mol-l is in good agreement with these data. Cochran and Foster used a value of 291 J mol-1 K-1 for the entropy of gallium suboxide, based on data for the heat capacity of CTeSe and other triatomic molecules of the same molecular weight.The uncertainty in their value is k 8 J mol-1 K-l and it compares well with our value of 287+6 J mo1-1 K-l. TABLE 4.-THERMODYNAMIC DATA FOR REACTIONS (1) AND (2) method dominant reaction 2nd law simultaneous reactions 2nd law third law estimated literature 120 126 117 109 -121 266 -125 273 161 160 59 56 -80 300 -183 221 74 -70 305 -163 239 -1 1 3- 1 3- 1 3- 3- 79 172 165 151 147 94 84 -90.8 28756 -1484 248+12 - +8 17 117+ 20 159 - 84 - 125 + 20 We are not aware of any measurements or calculations of the enthalpy of formation or entropy of gallium hydroxide.* The Ga-OH bond dissociation energy is given as 427 +20 kJ mol-l, from which we deduce an enthalpy of formation of 125+20 kJ mol-l, which is not in conflict with our third-law value of 148 15 kJ mol-l.The Ga-0 bond energy in Ga20 may be calculated from the enthalpies of formation of Ga,O, of sublimation of gallium, and of dissociation of oxygen. We obtain 437$-4 kJ mol-l. This value is very similar to the energy of the Ga-OH bond, as we would expect. 5. CONCLUSIONS The thermodynamic parameters resulting from this work are given in tables 4, 5 (1) and 5 (2). The enthalpies of formation of gallium suboxide measured by previous workers I , and by us agree in the range -82.8 to -96.6 kJ mol-l, lending support to the value reported by Cochran and Foster. For the enthalpy of formation of GaOH, and for the entropies of Ga,O and GaOH, we recommend the third-law results in table 4.Gallium hydroxide is an important volatile product of the reaction between gallium and water vapour + hydrogen mixtures at high temperatures. We believe that this is the first time that thermodynamic data for this species have been reported. * But see footnote on p. 2286.2290 MODIFIED ENTRAINMENT METHOD TABLE 5.-THERMODYNAMIC FUNCTIONS OF (1) GALLIUM SUBOXIDE AND (2) GALLIUM HYDROXIDE TIK 100 204) 273 298 300 400 500 600 700 800 900 lo00 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 100 200 273 298 300 400 500 600 700 800 900 lo00 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 39.773 45.209 48.497 49.423 49.488 52.263 54.002 55.109 55.844 56.352 56.714 56.982 57.184 57.340 57.463 57.562 57.642 57.708 57.763 57.810 57.849 57.883 33.94 44.80 48.45 49.23 49.28 51.22 52.21 52.84 53.35 53.84 54.33 54.83 55.34 55.83 56.31 56.75 57.17 57.56 57.92 53.24 58.54 58.81 (1) GazO 239.375 268.649 283.248 287.536 287.842 302.491 314.355 324.306 332.860 340.352 347.01 1 353.001 358.442 363.424 368.019 372.28 1 376.256 379.978 383.478 386.781 389.908 392.876 (2) GaOH 196.48 223.77 238.34 242.62 242.92 257.40 268.95 278.52 286.71 293.87 300.23 305.98 311.23 316.07 320.56 324.75 328.68 332.38 335.88 339.20 342.36 345.37 (HH-H2*98)/ kJ mol-1 - 8.91 1 - 4.657 - 1.224 O.OO0 0.091 5.190 10.510 15.970 21.520 27.131 32.785 38.471 44.180 49.906 55.646 61.398 67.158 72.926 78.700 84.478 90.261 96.048 - 8.65 - 4.65 - 1.22 0.00 0.09 5.13 10.31 15.56 20.87 26.23 31.64 37.10 42.61 48.17 53.77 59.43 65.12 70.86 76.64 82.44 88.28 94.15 [(Gr - Hi9s)/Tl/ J mol-1 K-1 328.487 291.932 287.730 287.536 287.537 289.5 15 293.334 297.689 302.117 306.438 310.583 314.530 318.279 321.836 325.214 328.426 33 1.483 3 34.399 337.184 339.849 342.402 344.852 282.97 247.01 242.81 242.62 242.62 244.58 248.34 252.59 256.89 261.08 265.08 268.89 272.50 275.93 279.19 282.30 285.26 288.09 290.80 293.40 295.89 298.29D .BATTAT, M . M . FAKTOR, 1. GARRETT AND R . H. MOSS 2291 The ratio a of partial pressures of gallium suboxide to gallium hydroxide is given 0.7- 2 0.6- 0.5- 2 a: 1 cd 0 OA- by : and 86 190 J mol-' RT 64.9 J mol-I K-' R + ~ Kl = exp{ - K2 on the basis of the two-reaction calculations (see fig. 6). The suboxide becomes relatively more important at high temperature, while the reverse condition favours the hydroxide.This conclusion also holds for the vapour products of reactions between 0. o*sl e v 0.2 I I I I I 12co 1250 1 3 0 0 1350 TIK Frc. 6.-Variation of ratio of equilibrium constants with temperature. water + hydrogen mixtures and gallium compounds. It thus seems likely that the vapour species responsible for the chemical vapour transport of gallium arsenide in water+hydrogen mixtures is the hydroxide, not the suboxide as has been assumed previously. 3-5 9 79 This could well account for the appreciable, systematic discrep- ancy between the experimental results of Michelitsch et aL3 and the equilibrium constant for reaction (1). Reaction (3), that is : 2GaOH(g)+Ga20(g) + H,O(g) cannot result in a large change in free energy since on each side of the reaction there are two vapour molecules (i.e.ASo is small), two Ga-0 bonds and two 0-H bonds (i.e. AHo is small). In general, we would expect the same to apply to all metals with a lower valency of one, The corresponding reaction for an element with a lower valency of two, e.g. : results in a decrease in the number of vapour molecules, and hence in entropy, in forming the hydroxide. There would seem to be no compensating enthalpy change. SiO(g) + H,O(g)=Si(OH)*(g)2292 MODIFIED ENTRAINMENT METHOD While our modified entrainment method is capable of yielding accurate thermo- dynamic data for heterogeneous equilibria, the accuracy of our results for this system is low because of the restricted " window '' available in this system. We have demonstrated, however, that the method is applicable to a system in which two reactions of comparable importance are taking place.Acknowledgement is made to the Director of Research of the Post Office for per- mission to publish this paper. C. F. J. Frosch and C. D. Thurmond, J. Phys. Chem., 1962,66, 877. C. N. Cochran and L. M. Foster, J. Electrochem. SOC., 1962, 109, 144. M. Michelitsch, W. Kappallo and G. Hellbardt, J. Electrochem. Soc., 1964, 111, 1248. K. L. Lawley, J. Electrochem. Soc., 1966, 113, 240. C. Lin, L. Chow and K. J. Miller, J. Electrochem. SOC., 1970, 117, 407. ' D. Battat, M. M. Faktor, I. Garrett and R. H. Moss, J.C.S. Faradoy I, 1974, 70, 267. ' P. H. Robinson, R.C.A. Rev., 1963, 24, 574. * G. E. Gottlieb and J. F. Corboy, R.C.A. Rev., 1963, 24, 585. M. M. Faktor, R. Heckingbottom and I. Garrett, J. Chem. SOC. A, 1970, 2657. G. W. C. Kaye and T. H. Laby, Physical and Chemical Constants (Longman, London, 1959). lo A. D. Mah, U S . Bur. Mines Rep. Invest., 1962, no. 5965. I 2 J. H. Arnold, Znd. Eng. Chem., 1930, 22, 1091. l 3 J. Fujita, Kagaku Kikai, 1951, 15, 234. l4 W. H. Shepherd, J. Electrochem. Soc., 1965, 112, 988. l 5 J. Jeans, Kinetic Theory of Gases (Cambridge, 1962). Handbook of Heat Transfir, ed. W. M. Rohsenow and J. P. Hartnett (McGraw-Hill, New York, 1973). l7 Znt. Critical Tables, 1929, 5, 62. l 8 D. Battat, unpublished work. l9 V. I. Vedeneyev, L. V. Gurvich, V. N. Kondrat'yev, V. A. Medvedev and Ye. L. Frankevich, 2o J.A.N.A.F. Thermochemical Tables, NSRDS-NBS 37 (Nat. Bur. Stand., 2nd edn., 1971). 21 D. R. Stull and G. C. Sinke, Thermodynamic Properties ofthe Elements (Amer. Chem. SOC., 22 J. D. Fast, Entropy, (Philips Technical Library, 1962). 23 from a table of Periodic Properties of the Elements, J. Chem. Educ., 1971, 48. 24 A. J. Hinchcliffe and J. S. Odgen, J. Phys. Chem., 1973,77,2537. 25 A. J. Hinchcliffe and J. S. Ogden, J. Phys. Chem., 1971, 75, 3908. 26 G. Herzberg, Molecular Spectra and Molecular Structure, Part I1 (Van Nostrand, New York, 27 W. E. Dasent, Inorganic Energetics (Penguin, London, 1970). 28 N. Acquista and S. Abramowitz, J. Chem. Phys., 1969,51, 2911. 29 N. Acquista, S. Abramowitz and D. R. Lide, J. Chem. Phys., 1968, 49, 780. 30 A. D. Walsh, J. Chem. SOC., 1953, 2288. Bond Energies, Ionization Potentials and Electron Afinities (Arnold, London, 1966). Washington, 1956). 1947). Termicheskie Konstanty Veschestt, (Thermodynamic constants of Substances) (Academy of Science, Moscow, 1971), vol. 5.

ISSN:0300-9599    

DOI:10.1039/F19747002280

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Modified Entrainment Method for Measuring Vapour Pressures and Heterogeneous Equilibrium Constants Part 3.-Measurement of Diffusivity of Hydrogen Chloride in Hydrogen and Extension of the Method to Multicomponent Diffusion at 700-1300 K BY DAVID BATTAT, MARC M. FAKTOR," IAN GARRETT AND RODNEY H. Moss Post Office Research Department, Brook Road, Dollis Hill, London NW2 7DT Received 27th March, 1974 The binary diffusion coefficient of HC1 in H2 may be represented by 0.54(7'/273 K)lSs5 cm2 s-' over the temperature range 700-1300 K. We present a useful second-order approximation to multi- component diffusion, which permits calculation of effective diffusion coefficients in multicomponent gas mixtures. 1. INTRODUCTION Mixtures of hydrogen chloride and hydrogen gases are used in the chemical vapour transport of many semiconductor materials, such as the Group 111-V compounds.* The increasing need for better control over the chemical vapour transport systems used in the electronics industry has led to the construction of a useful theory of vapour transport 3-6 and to the development of a versatile method 7-9 for measuring the chemical thermodynamic and kinetic parameters required to apply the theory. The rate of diffusion of hydrogen chloride in a gas consisting largely of hydrogen, but containing also the products of the transport reaction, is one of the factors which determine the rate of transport6 of the solid material. We used a chemical vapour transport reaction to study the diffusion of hydrogen chloride in such a multi- component gas. We have developed also a useful second-order approximation to the theory of multi-component diffusion, which allows us to obtain the binary diffusion coefficient of hydrogen chloride in hydrogen from experimental transport rates.We are thus able to predict effective diffusion coefficients for multi-component gas mix- tures used in chemical vapour transport. The modified entrainment method described earlier 'p was shown to be useful for measuring equilibrium constants provided they are not extreme (less than about 10). The uncertainties in diffusion coefficients then lead to acceptably small errors. On the other hand, when the equilibrium constant is large, the method becomes suitable f'or investigating gaseous interdiffusion, since the reaction then acts as effective sink f'or the reactant.In this investigation reaction (1) was used : Ga(1iquid) + HCl(gas) +GaCl(gas) + +H,(gas). (1) Existing data suggest that in the temperature range 700-1300 K the enthalpy change for this reaction AHo is + 12 & 8 kJ mol-l, and the entropy change ASo is +65.6+4 J mol-1 K-l. The equilibrium is thus well to the right, and the partial pressure of hydrogen chloride over the gallium is very nearly zero. of gallium, and we conclude that under our experimental conditions their partial pres- sures are negligibly small. 2293 We have considered the possible formation of other gaseous chlorides 9.2294 MODIFIED ENTRAINMENT METHOD 2. EXPERIMENTAL The apparatus has been described in detail elsewhere.' The gallium was 99.9999 %, supplied by Mining and Chemical Products Ltd.The hydrogen was British Oxygen Company electronic grade, and was passed through a palladium diffuser. The hydrogen chloride was Air Products electronic grade, of quoted purity 99.99 %. The flow of hydrogen chloride was controlled by a Drovewood automatic flow controller. Flow rates of hydrogen chloride and of hydrogen were measured with Meterate flow meters. The hydrogen chloride flow meter was calibrated by determining the HCl content of the HCl+H2 gas mixture by titration against NaOH. The temperature was measured with a Pt/Pt-13 % Rh thermocouple running up the centre of the furnace tube to within 3 mm of the sample bottle. The rate of weight loss from the sample bottle, @, was measured as a function of temper- ature, using three ratios E of HCI to H2 in the gas stream : PHCI/P = 0.018, 0.060 and 0.10, where p ~ c l is the partial pressure of HCl and P is the total pressure.3. RESULTS The results from the three runs are given in table 1. E = 0.018 TiK Phimg h- 1290 1.638 1290 1.542 1290 1.542 1239 1.357 1239 1.287 1239 1.386 1184 1.350 1184 1.269 1184 1.255 1136 1.366 1135 1.341 1135 1.233 1082 1.170 1082 1.136 1082 1.140 1036 1.061 1036 1.03 1 1035 1.184 1035 1.241 1035 1.151 984 1.100 984 1.072 984 1.084 935 1.008 935 0.989 888 0.937 888 0.936 TABLE 1 E = 0.060 E = 0.10 Ti K 1271 1271 1271 1225 1225 1225 1183 1183 1183 1129 1129 1129 W/mg h- 3.570 3.449 3.592 3.271 3.438 3.367 3.445 3.28 1 3.319 3.206 3.151 3.104 TIK 1248 1248 1019 1019 832 832 832 779 779 779 786 1274 1274 891 891 891 ~ W/mg h-' 4.976 4.997 4.450 4.406 3.644 3.676 3.704 3.463 3.526 3.512 3.512 5.268 5.250 3.836 3.814 3.884 4.ANALYSIS OF RESULTS Following the lines of argument '9 given previously, we assume that the vapour in the bottle is in equilibrium with the liquid gallium, and that at the outlet from theD. BATTAT, M. M . FAKTOR, I . GARRETT AND R . H . MOSS 2295 neck of the bottle the vapour composition is the same as that in the main stream, i.e., the reaction products are rapidly diluted and swept away. The partial pressures inside the bottle are given by : since pGacl(Z) is taken as zero and cGaCI Q 1 ; PGaCl(O) = [I)GaCl(z) - 2p1 exp( - tGaC1) + 2p 2eGaC1p (2) PHCI(0) = P[& + 21 exp( - tHC1) - 2p p[& - 2511Cll (3) PH2(0) = p-PGaCl(o) -PHC1(0)* (4) In these equations, partial pressures in the bottle are denoted by (0), and ti is the transport function for species i, defined in eqn (5).ti = WRT1/2Di,,PMA. 0 0 loglo(m) FIG. 1 .-Variation of DHCI,H~ with temperature : diffusion coefficients independent of concentration. 0, E = 0.018; 0, E = 0.06; A, E = 0.10. Here R is the gas constant, I is the length and A the cross-sectional area of the neck of the bottle, A4 is the atomic weight of gallium, and Dl,m is the effective diffusion coefficient of species i in the multicomponent gas mixture. The equilibrium constant for reaction (1) can now be expressed as : I n the present experiment, P = 1 atm, so that2296 MODIFIED ENTRAINMENT METHOD We note that if Kp is large, we can neglect DHCl,m/(DGaCl,mKp) in comparison with unity.Now our expression for the diffusion coefficient of the reactant HCl in the gas mixture is simply : In effect we have equated pHC1(0) (over the gallium), to zero. The fractional error in so doing is - l / K p . Using this simple formula, we calculate a value of D for each experimental point. The results are plotted as log,, D against log,, T in fig. 1 . The scatter of points is greatest for the run with E = 0.018, where the rate of loss of weight was very small and is subject to the largest error. The points from each run can be fitted by the well- known expression l6 of the kinetic theory : D = WRTZ/PM&A. D(T) = D0(T/273 K)l+' (9) where Do is a constant (the diffusivity at OOC) and s is around 0.8-0.9. The value of s is the same for each run, within experimental error, but the calculated value of Do increases as E decreases.This is significant. 1. I 1.c 0 . S 0. e ' 0.7 2 M - 0.6 0.5 0.4 0.3 0 FIG. 2.-Variation of DHCI,H~ with temperature : diffusion coefficients dependent on concentration. 0, E = 0.018; 0, E = 0.06; A,E = 0.10. u = 6.5; b = 3.0. In the analysis presented previously, it was assumed that the partial pressures of the minority components (GaCl and HC1 in this case) are so small that the diffusion may be described as two independent binary systems (GaC1 in H, and HCl in H2).D . BATTAT, M. M. FAKTOR, I . GARRETT AND R . H. MOSS 2297 This first-order or very dilute solution approximation becomes increasingly inaccurate as E is made larger. Our experimental range of E is sufficient to introduce an in- accuracy of up to a factor of two.In the Appendix we present a second-order approximation to multi-component diffusion, and we show that the diffusion coefficient &Cl,m ineqn (5) is replaced by the binary coefficient DHCl,H2 divided by a composition- dependent factor yHCl : We may regard the coefficients aHC1 and bHCl as empirical quantities to be obtained from the experiment, or as quantities whose values may be calculated using the theoretical expressions in the Appendix, eqn (A12) and (A13). We have used both approaches, and find adequate agreement. Eqn (8) can now be re-written as : YHCl = + aHCIE+ bHClrHC1. (10) A least-squares fit to our experimental results yields aHc1 = 6.5f 1, bHCl = 3 k 1, DoHCI,H2 = 0.54+0.07 cm2 s-l, s = 0.853L-0.022.5. DISCUSSION There are several sources of experimental error, which are discussed below. The error introduced by ignoring l / K p in comparison with unity is expected to be no greater than 0.3 % at 700 K and 0.1 % at 1300 K. It is much smaller than the experimental error in E , the fractional HCI concentration in the gas stream. I AND A T h e dimensions of the neck of the bottle were measured with a catheto- meter to 1 % or better. We estimate that end effects introduce an error in I of about T AND i@.-The error in T is unlikely to be more than 10 K, and would probably be systematic. The error introduced in D is therefore less than 2 %. The fractional error in l@ increases as l@ decreases, as evidenced by the scatter in experimental results for low E .This scatter is reflected in the standard deviation of k0.022 in s and k0.07 cm2 s-l in D&CI,H2 obtained from the least-squares fit. &.-The principal source of error in E is the uncertainty in reading the flow meters. Although we took precautions to obtain a steady flow, there was a slow drift in flow rate during a run, possibly caused by a change in laboratory temperature. We estimate the uncertainty in E to be + 5 %. aHcl AND bHc,.-These coefficients depend quite sensitively on the ratios of binary diffusion coefficients, in particular, on the ratio &2,HC1/&aCI,Hcl [see eqn (A12)I. Because of the scatter of experimental points, varying aHcl between 5.5 and 7.5, and varying bHcl between 2 and 4, makes very little difference to the standard deviations in s and &Cl,H2 obtained from the least-squares fit.We find, then, that by far the largest source of uncertainty arises from the scatter of experimental points. Our final values for the diffusivity of HCl in H2, and for s, are thus : 1 %. D & - I . H 2 = 0.54k0.07 cm2 s-’ s = 0.85k0.022. We have applied the second-order approximation to rnulticomponent diffusion for E up to 0.1. With the wide disparity in molecular weights and binary diffusivities among the vapour species in our present experiment, it is not clear a priori that the theory is2298 MODIFIED ENTRAINMENT METHOD valid for such large values of c. We observe that there is adequate agreement between empirical and estimated values for aHC, and bHCI, however. Furthermore, we can argue loosely that as E is increased towards unity, the apparent diffusion coefficient of HCl in the gas mixture must approach the binary diffusion coefficient of HC1 in GaCl, which we estimate to be about 0.075 cm2 s-l, using Graham’s law.17 Thus either the apparent diffusion coefficient varies roughly linearly with y, in which case a value of aHC1 = 6 is reasonable, or else some specific chemical interaction between the diffusing species causes a departure from linearity (e.g.short-lived molecular com- plexes). Our experiment suggests that such interactions are insignificant for E < 0.1. 6. CONCLUSION The modified entrainment method which we have developed for investigating heterogeneous equilibria can be used to measure binary diffusion coefficients over a wide range of temperature in reactive gas mixtures.The second-order approximation to multi-component diffusion provides an adequate description for systems containing 90 % of one component, although the first-order approximation is not valid here. In systems not containing highly diffusive gases (H, or He) we expect the approximation to hold for considerably more concentrated mixtures. The empirical approach gives values for a and b, and a value for s which is inde- pendent of composition. It is gratifying to find that the theory predicts values of a and b close to the empirical ones, and confirms that s is independent of E , the fractional HCl concentration in the gas stream. APPENDIX ONE-DIMENSIONAL TERNARY DIFFUSION W I T H ONE MAJORITY COMPONENT In a non-uniform gas, each species i may be thought of as moving with a velocity Ui, which is the average over all molecules of species i, and in general different from the average velocities of all other species.The average velocity of the gas mixture can be defined in terms of the ui values in any way we choose. A common choice l 8 3 l9 is to weight each ui according to the mass fraction ci, to obtain the mass-average velocity : u = c cpi. 1 The diffusion speed ci of species i is then defined as : It follows that the sum of the diffusion fluxes, &cioi, is identically zero. useful tTi = ui -u. (A2) For many chemical problems, the mole-average velocity l 8 defined by eqn (A3) is more u = 1 yiui 1 where yi is the mole fraction of species i in the gas. From eqn (A2) and (A3) we obtain : u = u +c y p i .1 The kinetic theory of gases 1 9 . 2 o gives an expression for bi. tion gradients alone it is : For diffusion due to concentra- ci = -- n C M . 9 . . dY j PYi j l J dx where n is the total mole density, p is the mass density, Mj is the molar weight of speciesj, and gi is the multi-component diffusion coefficient for the flux of species i due to a concentra-D . BATTAT, M . M . FAKTOR, I . GARRETT AND R . H . MOSS 2299 For a ternary mixture, gij is related 2o to the binary coefficient D i j lion gradient in speciesj. by : and gii 5 0. If we take n as constant, we can rewrite eqn (A4), using eqn (AS), as : The total flux of species i is : PCiUi Mi J i = niui = --. We confine our analysis to the case where one component is predominant, i.e.nl, n2 < n3. Using eqn (A2), (A5) and (A7) we can express the flux J1 in terms of the mole-average velocity U and the ternary diffusion coefficients gij as follows : Eqn (A6) can be expanded for nl, n2 << n3, and the resulting approximate expressions sub- stituted in (A9). We retain terms in n,(dnj/dx) (i = 1 , 2 ; j = 1, 2, 3) but ignore higher- order terms. Note that dnj/dx is of the same order as nl, n2, and that n, the total mole concentration, is essentially independent of x . We obtain eqn (A10) for J1 : The corresponding expression for J2 has 2 substituted for 1 throughout. In deriving (AlO), we have neglected all terms which are third order in n l , n2, irrespective of their coefficients. Because of the large ratios of molecular weights in our system, some of these coefficients are not of order unity.We have therefore inspected the third order correction, and find that the only effect is to multiply the last term in (A10) by the quantity : Clearly we may neglect the third-order terms if nl, n2 << n. Eqn (A10) expresses Jl as a sum of three terms. The first is the Stefan flow,18 the second i s binary diffusion of species 1 in the majority species 3, and the third term represents a correction caused by the presence of a significant concentration of species 2. To solve eqn (A10) with the boundary conditions imposed by our experimental conditions [nl(Z)/n = E, n2(Z) = 01, we assume power series solutions of the form : n,(x)ln = .fi(x)c+gi(x)E2, i = 1,2. (A1 1 ) We insert this solution into (A10) and the corresponding equation for J2.The fluxes Ji are related by the stoichiometry of the reaction : We equate terms in like powers of E , and thus determine the functionsf&) and gi(x). We are now able to express each of the mole concentrations ni as a function of x. In particular, we find that for HCl : JGa = - J , = J2 = 2J3. %Icm/n = PHCI(O)/P = ~ - ~ ~ H c l ~ H c ,2300 where MODIFIED ENTRAINMENT METHOD and To estimate the ratios of diffusion coefficients appearing in UHCI and ~ H C I , we have compared the results of two approaches ; Graham’s law,17 and the hard-sphere model ”9 2o of kinetic theory. For Graham’s law, DijlDik = J M k I M j and we obtain aHC1 = 6.75, b ~ c l = 3.92. For the hard-sphere model, where olj is the hard sphere collision diameter.Using the semi-empirical method of Jona and Mandel,2t we obtain LZHC~ = 8.32 and b ~ c l = 5.28. These estimated values of aHCl and b ~ c l are acceptably close to our empirical values, bearing in mind that both HCl and GaCl molecules are polar, so that their dynamics of motion and collision are unlikely to be well described by the above results of the kinetic theory.22 TABLE 2 binary diffusivity Graham’s law hard sphere empirical : this work DiC1,GaCl /cm2 s-’ 0.075 0.061 0.077k 0.024 D&aCl,H* /cm2 S-l 0.32 0.31 0.34rfr0.05 Finally, we have used our empirical values of a ~ c l and hcl and our value for D ’ H ~ , H ~ , to calculate D&Cl,GaCl and DkaCISz from eqn (A12) and (A13). The results are given in table 2, with the corresponding values obtained from Graham’s law and from the hard-sphere model for comparison.The agreement is well within the large error limits which arise from the uncertainties in UHC~ and b ~ c l . The authors thank the Director of Research of the Post Ofice for permission to publish this paper. J. J. Tietjen, R. E. Enstrom and D. Richman, R.C.A. Rev., 1970, 31, 635. H. T. Minden, Solid State Tech., 1973, 31. M. M. Faktor, R. Heckingbottom and 1. Garrett, J. Chem. SUC. A, 1970, 2657. M. M. Faktor, R. Heckingbottom and I. Garrett, J. Chem. Suc. A, 1971, 1. M. M. Faktor and I. Garrett, J. Chem. SOC. A, 1971, 934. M. M. Faktor, I. Garrett and R. H. Moss, J.C.S. Faraday I, 1973, 69, 1915. ’ D. Battat, M. M. Faktor, I. Garrett and R. H. Moss, J.C.S. Faraday I, 1974, 70, 2267.* D. Battat, M. M. Faktor, I. Garrett and R. H. Moss, J.C.S. Faraday I, 1974,70, 2280. D. Battat, M. M. Faktor, I. Garrett and R. H. Moss, J.C.S. Faraduy I, 1974,70, 2302. lo D. J. Kirwan, J. Electrochem. SOC., 1970, 117, 1572. l1 G. F. Day, Heterojunction Device Concepts, Varian Report No. 324-64, Air Force Contract No. AF 33 (615)-1988 (Varian Associates, Palo Alto, California).D. BATTAT, M. M. FAKTOR, I . GARRETT AND R . H . MOSS 2301 l 2 R. Hultgren, R. L. Orr and K. K. Kelley, Supplements to Selected Values of Thermodynamic l 3 J. B. Mullin and D. T. J. Hurle, J. Luminescence, 1973, 7, 176. l4 Yu. Kh. Shaulov and A. M. Mosin, Zhur.fiz. Khim., 1973, 47, 1131. Properties of Metals and Alloys, University of California (up to 1972). 0. Kubaschewski, E. LL. Evans and C.B. Alcock, Metallurgical Thermochemistry (Pergamon, New York, 4th edn., 1967). T. Graham, Phil. Trans. Roy. Soc., 1846, 136, 573. (Plenum, New York, 1969). Cambridge, 1960). l6 J. Jeans, Introduction to the Kinetic Theory of Gases (University Press, Cambridge, 1962). lS D. A. Frank-Kamenetski, Digusion and Heat Transfer in Chemical Kinetics, trans. J . P. Appleton l9 S. Chapman and T. Cowling, The Mathematical Theory of Non-uniform Gases (University Press, 2o W. Dorrance, Viscous Hypersonic Flow (McGraw-Hill, New York, 1962). 21 F. Jona and G. Mandel, J. Chem. Phys., 1963, 38, 346. 22 J. 0. Hirschfelder, C. F. Curtiss and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley London, 1964). Modified Entrainment Method for Measuring Vapour Pressures and Heterogeneous Equilibrium Constants Part 3.-Measurement of Diffusivity of Hydrogen Chloride in Hydrogen and Extension of the Method to Multicomponent Diffusion at 700-1300 K BY DAVID BATTAT, MARC M.FAKTOR," IAN GARRETT AND RODNEY H. Moss Post Office Research Department, Brook Road, Dollis Hill, London NW2 7DT Received 27th March, 1974 The binary diffusion coefficient of HC1 in H2 may be represented by 0.54(7'/273 K)lSs5 cm2 s-' over the temperature range 700-1300 K. We present a useful second-order approximation to multi- component diffusion, which permits calculation of effective diffusion coefficients in multicomponent gas mixtures. 1. INTRODUCTION Mixtures of hydrogen chloride and hydrogen gases are used in the chemical vapour transport of many semiconductor materials, such as the Group 111-V compounds.* The increasing need for better control over the chemical vapour transport systems used in the electronics industry has led to the construction of a useful theory of vapour transport 3-6 and to the development of a versatile method 7-9 for measuring the chemical thermodynamic and kinetic parameters required to apply the theory. The rate of diffusion of hydrogen chloride in a gas consisting largely of hydrogen, but containing also the products of the transport reaction, is one of the factors which determine the rate of transport6 of the solid material. We used a chemical vapour transport reaction to study the diffusion of hydrogen chloride in such a multi- component gas. We have developed also a useful second-order approximation to the theory of multi-component diffusion, which allows us to obtain the binary diffusion coefficient of hydrogen chloride in hydrogen from experimental transport rates.We are thus able to predict effective diffusion coefficients for multi-component gas mix- tures used in chemical vapour transport. The modified entrainment method described earlier 'p was shown to be useful for measuring equilibrium constants provided they are not extreme (less than about 10). The uncertainties in diffusion coefficients then lead to acceptably small errors. On the other hand, when the equilibrium constant is large, the method becomes suitable f'or investigating gaseous interdiffusion, since the reaction then acts as effective sink f'or the reactant. In this investigation reaction (1) was used : Ga(1iquid) + HCl(gas) +GaCl(gas) + +H,(gas).(1) Existing data suggest that in the temperature range 700-1300 K the enthalpy change for this reaction AHo is + 12 & 8 kJ mol-l, and the entropy change ASo is +65.6+4 J mol-1 K-l. The equilibrium is thus well to the right, and the partial pressure of hydrogen chloride over the gallium is very nearly zero. of gallium, and we conclude that under our experimental conditions their partial pres- sures are negligibly small. 2293 We have considered the possible formation of other gaseous chlorides 9.2294 MODIFIED ENTRAINMENT METHOD 2. EXPERIMENTAL The apparatus has been described in detail elsewhere.' The gallium was 99.9999 %, supplied by Mining and Chemical Products Ltd.The hydrogen was British Oxygen Company electronic grade, and was passed through a palladium diffuser. The hydrogen chloride was Air Products electronic grade, of quoted purity 99.99 %. The flow of hydrogen chloride was controlled by a Drovewood automatic flow controller. Flow rates of hydrogen chloride and of hydrogen were measured with Meterate flow meters. The hydrogen chloride flow meter was calibrated by determining the HCl content of the HCl+H2 gas mixture by titration against NaOH. The temperature was measured with a Pt/Pt-13 % Rh thermocouple running up the centre of the furnace tube to within 3 mm of the sample bottle. The rate of weight loss from the sample bottle, @, was measured as a function of temper- ature, using three ratios E of HCI to H2 in the gas stream : PHCI/P = 0.018, 0.060 and 0.10, where p ~ c l is the partial pressure of HCl and P is the total pressure. 3.RESULTS The results from the three runs are given in table 1. E = 0.018 TiK Phimg h- 1290 1.638 1290 1.542 1290 1.542 1239 1.357 1239 1.287 1239 1.386 1184 1.350 1184 1.269 1184 1.255 1136 1.366 1135 1.341 1135 1.233 1082 1.170 1082 1.136 1082 1.140 1036 1.061 1036 1.03 1 1035 1.184 1035 1.241 1035 1.151 984 1.100 984 1.072 984 1.084 935 1.008 935 0.989 888 0.937 888 0.936 TABLE 1 E = 0.060 E = 0.10 Ti K 1271 1271 1271 1225 1225 1225 1183 1183 1183 1129 1129 1129 W/mg h- 3.570 3.449 3.592 3.271 3.438 3.367 3.445 3.28 1 3.319 3.206 3.151 3.104 TIK 1248 1248 1019 1019 832 832 832 779 779 779 786 1274 1274 891 891 891 ~ W/mg h-' 4.976 4.997 4.450 4.406 3.644 3.676 3.704 3.463 3.526 3.512 3.512 5.268 5.250 3.836 3.814 3.884 4.ANALYSIS OF RESULTS Following the lines of argument '9 given previously, we assume that the vapour in the bottle is in equilibrium with the liquid gallium, and that at the outlet from theD. BATTAT, M. M . FAKTOR, I . GARRETT AND R . H . MOSS 2295 neck of the bottle the vapour composition is the same as that in the main stream, i.e., the reaction products are rapidly diluted and swept away. The partial pressures inside the bottle are given by : since pGacl(Z) is taken as zero and cGaCI Q 1 ; PGaCl(O) = [I)GaCl(z) - 2p1 exp( - tGaC1) + 2p 2eGaC1p (2) PHCI(0) = P[& + 21 exp( - tHC1) - 2p p[& - 2511Cll (3) PH2(0) = p-PGaCl(o) -PHC1(0)* (4) In these equations, partial pressures in the bottle are denoted by (0), and ti is the transport function for species i, defined in eqn (5).ti = WRT1/2Di,,PMA. 0 0 loglo(m) FIG. 1 .-Variation of DHCI,H~ with temperature : diffusion coefficients independent of concentration. 0, E = 0.018; 0, E = 0.06; A, E = 0.10. Here R is the gas constant, I is the length and A the cross-sectional area of the neck of the bottle, A4 is the atomic weight of gallium, and Dl,m is the effective diffusion coefficient of species i in the multicomponent gas mixture. The equilibrium constant for reaction (1) can now be expressed as : I n the present experiment, P = 1 atm, so that2296 MODIFIED ENTRAINMENT METHOD We note that if Kp is large, we can neglect DHCl,m/(DGaCl,mKp) in comparison with unity. Now our expression for the diffusion coefficient of the reactant HCl in the gas mixture is simply : In effect we have equated pHC1(0) (over the gallium), to zero.The fractional error in so doing is - l / K p . Using this simple formula, we calculate a value of D for each experimental point. The results are plotted as log,, D against log,, T in fig. 1 . The scatter of points is greatest for the run with E = 0.018, where the rate of loss of weight was very small and is subject to the largest error. The points from each run can be fitted by the well- known expression l6 of the kinetic theory : D = WRTZ/PM&A. D(T) = D0(T/273 K)l+' (9) where Do is a constant (the diffusivity at OOC) and s is around 0.8-0.9. The value of s is the same for each run, within experimental error, but the calculated value of Do increases as E decreases.This is significant. 1. I 1.c 0 . S 0. e ' 0.7 2 M - 0.6 0.5 0.4 0.3 0 FIG. 2.-Variation of DHCI,H~ with temperature : diffusion coefficients dependent on concentration. 0, E = 0.018; 0, E = 0.06; A,E = 0.10. u = 6.5; b = 3.0. In the analysis presented previously, it was assumed that the partial pressures of the minority components (GaCl and HC1 in this case) are so small that the diffusion may be described as two independent binary systems (GaC1 in H, and HCl in H2).D . BATTAT, M. M. FAKTOR, I . GARRETT AND R . H. MOSS 2297 This first-order or very dilute solution approximation becomes increasingly inaccurate as E is made larger. Our experimental range of E is sufficient to introduce an in- accuracy of up to a factor of two.In the Appendix we present a second-order approximation to multi-component diffusion, and we show that the diffusion coefficient &Cl,m ineqn (5) is replaced by the binary coefficient DHCl,H2 divided by a composition- dependent factor yHCl : We may regard the coefficients aHC1 and bHCl as empirical quantities to be obtained from the experiment, or as quantities whose values may be calculated using the theoretical expressions in the Appendix, eqn (A12) and (A13). We have used both approaches, and find adequate agreement. Eqn (8) can now be re-written as : YHCl = + aHCIE+ bHClrHC1. (10) A least-squares fit to our experimental results yields aHc1 = 6.5f 1, bHCl = 3 k 1, DoHCI,H2 = 0.54+0.07 cm2 s-l, s = 0.853L-0.022. 5. DISCUSSION There are several sources of experimental error, which are discussed below.The error introduced by ignoring l / K p in comparison with unity is expected to be no greater than 0.3 % at 700 K and 0.1 % at 1300 K. It is much smaller than the experimental error in E , the fractional HCI concentration in the gas stream. I AND A T h e dimensions of the neck of the bottle were measured with a catheto- meter to 1 % or better. We estimate that end effects introduce an error in I of about T AND i@.-The error in T is unlikely to be more than 10 K, and would probably be systematic. The error introduced in D is therefore less than 2 %. The fractional error in l@ increases as l@ decreases, as evidenced by the scatter in experimental results for low E . This scatter is reflected in the standard deviation of k0.022 in s and k0.07 cm2 s-l in D&CI,H2 obtained from the least-squares fit.&.-The principal source of error in E is the uncertainty in reading the flow meters. Although we took precautions to obtain a steady flow, there was a slow drift in flow rate during a run, possibly caused by a change in laboratory temperature. We estimate the uncertainty in E to be + 5 %. aHcl AND bHc,.-These coefficients depend quite sensitively on the ratios of binary diffusion coefficients, in particular, on the ratio &2,HC1/&aCI,Hcl [see eqn (A12)I. Because of the scatter of experimental points, varying aHcl between 5.5 and 7.5, and varying bHcl between 2 and 4, makes very little difference to the standard deviations in s and &Cl,H2 obtained from the least-squares fit.We find, then, that by far the largest source of uncertainty arises from the scatter of experimental points. Our final values for the diffusivity of HCl in H2, and for s, are thus : 1 %. D & - I . H 2 = 0.54k0.07 cm2 s-’ s = 0.85k0.022. We have applied the second-order approximation to rnulticomponent diffusion for E up to 0.1. With the wide disparity in molecular weights and binary diffusivities among the vapour species in our present experiment, it is not clear a priori that the theory is2298 MODIFIED ENTRAINMENT METHOD valid for such large values of c. We observe that there is adequate agreement between empirical and estimated values for aHC, and bHCI, however. Furthermore, we can argue loosely that as E is increased towards unity, the apparent diffusion coefficient of HCl in the gas mixture must approach the binary diffusion coefficient of HC1 in GaCl, which we estimate to be about 0.075 cm2 s-l, using Graham’s law.17 Thus either the apparent diffusion coefficient varies roughly linearly with y, in which case a value of aHC1 = 6 is reasonable, or else some specific chemical interaction between the diffusing species causes a departure from linearity (e.g.short-lived molecular com- plexes). Our experiment suggests that such interactions are insignificant for E < 0.1. 6. CONCLUSION The modified entrainment method which we have developed for investigating heterogeneous equilibria can be used to measure binary diffusion coefficients over a wide range of temperature in reactive gas mixtures.The second-order approximation to multi-component diffusion provides an adequate description for systems containing 90 % of one component, although the first-order approximation is not valid here. In systems not containing highly diffusive gases (H, or He) we expect the approximation to hold for considerably more concentrated mixtures. The empirical approach gives values for a and b, and a value for s which is inde- pendent of composition. It is gratifying to find that the theory predicts values of a and b close to the empirical ones, and confirms that s is independent of E , the fractional HCl concentration in the gas stream. APPENDIX ONE-DIMENSIONAL TERNARY DIFFUSION W I T H ONE MAJORITY COMPONENT In a non-uniform gas, each species i may be thought of as moving with a velocity Ui, which is the average over all molecules of species i, and in general different from the average velocities of all other species.The average velocity of the gas mixture can be defined in terms of the ui values in any way we choose. A common choice l 8 3 l9 is to weight each ui according to the mass fraction ci, to obtain the mass-average velocity : u = c cpi. 1 The diffusion speed ci of species i is then defined as : It follows that the sum of the diffusion fluxes, &cioi, is identically zero. useful tTi = ui -u. (A2) For many chemical problems, the mole-average velocity l 8 defined by eqn (A3) is more u = 1 yiui 1 where yi is the mole fraction of species i in the gas. From eqn (A2) and (A3) we obtain : u = u +c y p i . 1 The kinetic theory of gases 1 9 .2 o gives an expression for bi. tion gradients alone it is : For diffusion due to concentra- ci = -- n C M . 9 . . dY j PYi j l J dx where n is the total mole density, p is the mass density, Mj is the molar weight of speciesj, and gi is the multi-component diffusion coefficient for the flux of species i due to a concentra-D . BATTAT, M . M . FAKTOR, I . GARRETT AND R . H . MOSS 2299 For a ternary mixture, gij is related 2o to the binary coefficient D i j lion gradient in speciesj. by : and gii 5 0. If we take n as constant, we can rewrite eqn (A4), using eqn (AS), as : The total flux of species i is : PCiUi Mi J i = niui = --. We confine our analysis to the case where one component is predominant, i.e. nl, n2 < n3. Using eqn (A2), (A5) and (A7) we can express the flux J1 in terms of the mole-average velocity U and the ternary diffusion coefficients gij as follows : Eqn (A6) can be expanded for nl, n2 << n3, and the resulting approximate expressions sub- stituted in (A9).We retain terms in n,(dnj/dx) (i = 1 , 2 ; j = 1, 2, 3) but ignore higher- order terms. Note that dnj/dx is of the same order as nl, n2, and that n, the total mole concentration, is essentially independent of x . We obtain eqn (A10) for J1 : The corresponding expression for J2 has 2 substituted for 1 throughout. In deriving (AlO), we have neglected all terms which are third order in n l , n2, irrespective of their coefficients. Because of the large ratios of molecular weights in our system, some of these coefficients are not of order unity.We have therefore inspected the third order correction, and find that the only effect is to multiply the last term in (A10) by the quantity : Clearly we may neglect the third-order terms if nl, n2 << n. Eqn (A10) expresses Jl as a sum of three terms. The first is the Stefan flow,18 the second i s binary diffusion of species 1 in the majority species 3, and the third term represents a correction caused by the presence of a significant concentration of species 2. To solve eqn (A10) with the boundary conditions imposed by our experimental conditions [nl(Z)/n = E, n2(Z) = 01, we assume power series solutions of the form : n,(x)ln = .fi(x)c+gi(x)E2, i = 1,2. (A1 1 ) We insert this solution into (A10) and the corresponding equation for J2.The fluxes Ji are related by the stoichiometry of the reaction : We equate terms in like powers of E , and thus determine the functionsf&) and gi(x). We are now able to express each of the mole concentrations ni as a function of x. In particular, we find that for HCl : JGa = - J , = J2 = 2J3. %Icm/n = PHCI(O)/P = ~ - ~ ~ H c l ~ H c ,2300 where MODIFIED ENTRAINMENT METHOD and To estimate the ratios of diffusion coefficients appearing in UHCI and ~ H C I , we have compared the results of two approaches ; Graham’s law,17 and the hard-sphere model ”9 2o of kinetic theory. For Graham’s law, DijlDik = J M k I M j and we obtain aHC1 = 6.75, b ~ c l = 3.92. For the hard-sphere model, where olj is the hard sphere collision diameter. Using the semi-empirical method of Jona and Mandel,2t we obtain LZHC~ = 8.32 and b ~ c l = 5.28.These estimated values of aHCl and b ~ c l are acceptably close to our empirical values, bearing in mind that both HCl and GaCl molecules are polar, so that their dynamics of motion and collision are unlikely to be well described by the above results of the kinetic theory.22 TABLE 2 binary diffusivity Graham’s law hard sphere empirical : this work DiC1,GaCl /cm2 s-’ 0.075 0.061 0.077k 0.024 D&aCl,H* /cm2 S-l 0.32 0.31 0.34rfr0.05 Finally, we have used our empirical values of a ~ c l and hcl and our value for D ’ H ~ , H ~ , to calculate D&Cl,GaCl and DkaCISz from eqn (A12) and (A13). The results are given in table 2, with the corresponding values obtained from Graham’s law and from the hard-sphere model for comparison. The agreement is well within the large error limits which arise from the uncertainties in UHC~ and b ~ c l . The authors thank the Director of Research of the Post Ofice for permission to publish this paper. J. J. Tietjen, R. E. Enstrom and D. Richman, R.C.A. Rev., 1970, 31, 635. H. T. Minden, Solid State Tech., 1973, 31. M. M. Faktor, R. Heckingbottom and 1. Garrett, J. Chem. SUC. A, 1970, 2657. M. M. Faktor, R. Heckingbottom and I. Garrett, J. Chem. Suc. A, 1971, 1. M. M. Faktor and I. Garrett, J. Chem. SOC. A, 1971, 934. M. M. Faktor, I. Garrett and R. H. Moss, J.C.S. Faraday I, 1973, 69, 1915. ’ D. Battat, M. M. Faktor, I. Garrett and R. H. Moss, J.C.S. Faraday I, 1974, 70, 2267. * D. Battat, M. M. Faktor, I. Garrett and R. H. Moss, J.C.S. Faraday I, 1974,70, 2280. D. Battat, M. M. Faktor, I. Garrett and R. H. Moss, J.C.S. Faraduy I, 1974,70, 2302. lo D. J. Kirwan, J. Electrochem. SOC., 1970, 117, 1572. l1 G. F. Day, Heterojunction Device Concepts, Varian Report No. 324-64, Air Force Contract No. AF 33 (615)-1988 (Varian Associates, Palo Alto, California).D. BATTAT, M. M. FAKTOR, I . 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ISSN:0300-9599    

DOI:10.1039/F19747002293

出版商:RSC    

年代:1974

数据来源: RSC