摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. TRANSACTIONS O F THE FARADAY SOCIETY Founded in 1903 to promote the study of Sciences lying between Chemistry, Physics and Biology Volume 61, 1965 Pages 1-1292 THE FARADAY SOCIETY LONDON@ The Faraday Society and Contributors, 1965 PRINTED IN GREAT BRITAIN AT THE UNIVERSITY PRESS ABERDEEN

ISSN:0014-7672    

DOI:10.1039/TF96561FP001

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. TRANSACTfONS OF THE FARADAY SOCIETY Founded in 1903 to promote the study of Sciences lying between Chemistry, Physics and Biology Volume 61, 1965 Pages I 293-2868 THE FARADAY SOCIETY LONDON@ The Faraday Society and Contributors, 1965 PRINTED IN GREAT BRITAIN AT THE UNIVERSITY PRESS ABERDEm

ISSN:0014-7672    

DOI:10.1039/TF96561FP003

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Vibrational Spectrum of Metaborate Trimer and Polymer Ions, and of Metaborate Fluoride Mixtures BY A. MITCHELL Dept. of Metallurgy, University of Sheffield Received 29th June, 1964 A novel technique of dissolving a polymer oxide in liquid KBr in order to simplify structural analysis is used to examine the structure of polymer metaborate ions, and fluoride+ metaborate mixtures. The results are compared with existing frequency and structure data. Vibrational spectra of inetaborate ions and metaboric acid have been exainined,l,6 and frequency assignations have been made for the metaborate monomer and trimer,ll 6 but the vitreous metaborates, and vitreous B2O3 have not been analyzed in this way.The ‘‘ boron anomaly ” has been studied using X-ray radial distribution techniques,7 in an attempt to define the co-ordination structure around boron in these glasses. Conflicting views on the relative proportion of 3- and 4- co-ordina- tion have been published.7~ 8 The structure of metaborates (also phosphate and silicate) mixtures with fluorides is of interest in this connection. Although alkali chlorides are not decomposed by these liquid oxides at high temperatures, they are virtually in- soluble. The alkali fluorides, on the other hand, dissolve extensively in liquid oxides, Work on the vibrational spectra of such melts has been reported,g as has work on the viscosity and evaporation products.10 Frequency assignations for the molecule (FB0)3 have been made,ll although the physical properties of this compound make its existence most unlikely at temperatures of around 1000°K.Since the added fluoride considerably lowers the viscosity of the liquid oxide, it has been assumed 10 that the fluoride ion breaks down the liquid ring structure by forming substitutional compounds at the same co-ordination number as the oxide. The object of the series of experiments reported here was to examine polymer metaborate ions, and systems containing fluoride ions, in the light of the frequency assignations for these systems.11 6 EXPERIMENTAL CHEMICALS : KBr, NaF and NaNO2 were A.R. grade ; B2O3 was analyzed, and found to contain only traces of impurities, comparable to the other reagents used.INFRA-RED INSTRUMENTS ; A Perkin-Elmer Infracord double-beam instrument, with NaCl optics, was used to obtain spectra. SALT PREPARATION ; Since even small amounts of water might have a large effect on the borate structure, through hydrogen bonding, all the materials used were carefully dried, and handled under dry nitrogen. The KBr, NaF and NaN02 were heated at 140°C for several days, ground under nitrogen, and stored in a desiccator. B2O3 was melted, in a platinum 56 VIBRATIONAL SPECTRUM OF METABORATE POLYMER IONS dish, at 900°C in a Kanthal wound furnace, and cast on a thick steel plate. The Na2O+ B203 melts were prepared in the same way, utilizing the reactions: 2N0~+NO+N02+02- B,O,+02-+2€30~, in place of the normal carbonate reaction, co~-+coz+02- B,O, + 0 2 - -+2BO,, since the nitrite decomposition appears to be considerably faster, and has no tendency to retain nitrite ion at high oxide ion concentrations.The borate solids were ground under dry nitrogen. Melts of KBr were prepared using Purox recrystallized alumina crucibles, which do not show any significant reaction in the limes used (about 2 h). These were also poured on to a steel plate and rapidly chilled. DISC PREPARATION; KBr discs were prepared by compression under vacuum in a hy- draulic press. The concentration of powder mixes of borate and KBr was 2 w/o, and this concentration was maintained in the borate+ KBr molten systems. RESULTS The spectra obtained are shown in fig. 1-5. The main frequency assignments are those given by Hisatsune and Suarez,G in which the sharp bands at 1960 cm-1 and 2060cm-1 are due to the linear symmetric BO; monomer, the remainder to polymers of this ion.The D3h fundamental bands of (B02)3 can account for the observed absorption at 1350-1450 em-1, and at 700-750 crn-1 (allowing for some distortion to C2J. The B-0- stretch at 950 cm-1 is observed in the (NaZO + B203) based melts, but not in B203 itself. There remain, however, several features of interest . FIG. 1 .-Vibrational spectrum of (Na2O . NaF)1 . (B203)l quenched from IOOWK (2 w/o in KBr). (i) THE MONOMER BAmS.-The main object of dissolving the borates in liquid KBr, was to break down the glass structure, whilst retaining sufficient co-ordination to indicate what the parent structure had been. The monomer is not observed in the glassy melts, but appears on solution in KBr.(ii) THE FUNDAMENTALS OF (B0;)3.-h the glasses, the bands at 1400 and 1220 cm-1 appear to merge with no intermediate band. This might be expected, since both these are ring stretching modes. However, on dissolution in KBr, theseA . MITCHELL 7 bands are well separated to their calculated positions for D3h, and an intermediate band at 1350 cm-1 appears in the (Na20 + B203), and (Na20 + NaF + BzO3) systems, but not in B203. Similarly, the B-0- stretch at 950 cm-1 is resolved into a band 700 cni ’ rim nOG FIG. 2.Vibrational spectrum of (Na2O)l . (B203)l quenched from 1000°K (2 w/o in KBr). FIG. 3.-Vibrational spectrum of (Na2O)i. (B203)l: 2 w/o in liquid KBr, quenched from 1000°K. t . . . . I , . . , I 40003OOO 2000 1500 ~OOO 8 0 0 700 crn-1 FIG.4.-Vibrational spectrum of (Na20. NaF), . (B203), : 2 w/o in liquid KBr, quenched from 1000°K. at 950 cm-1, and one at 1050 cm-1, in the liquids Na20 + €3203 and NazO + NaF + B203 ; but not significantly in BzO3. The A$ and E” modes at 717 and 734 cm-1 in (BO& are likewise resolved in the KBr solution and not in the glass.8 VIBRATIONAL SPECTRUM OF METABORATE POLYMER IONS 0 (iii) THE €3-F BAND.-The frequency assignments 11 for (]FBO)3 and for BF3 give out-of-phase B-F stretches at 966 and 1454cm-1 respectively. In small amounts, the 966cm-1 band would have been obscured by the 9SOcm-1 band of the (BO& ring. However, in the concentrations used, it should have been observed. I k . . n . I a . . , I FIG. 5.Vibrational spectrum of B203 : 2 w/o in liquid KBr quenched from 1000°K.Similarly, a band at 1454cm-1 ought to have been visible in spite of the 1405 and 1440cm-1 modes of the ( % j 0 ; ) 3 ring. We Conclude, then, that therc is no simple substitution of F- into the boron + oxygen system. Any substitutional structurcs with a fluorine/oxygen ratio lying between (FBO)3 and (BO;)3 would presumably give rise to significant changes in the B-0 freqnencies. We have observed no difference in these frequencies between Na20 + B203 and NazO + NaF--B203 systems. (iv) THE 1350 cm-1, 795 cm-1, 1040 cm-1 BANDS, IN (Na20-B203) (I<&) SYSTEMS.-These bands cannot be assigned to any mode of (BOT)~. There are no fundamentals at these frequencies, and the possible overtone or combination bands would be at much lower intensities.We assign these bands to the tetrahedrally co-ordinated 79 8 B-0 structure. Following assignments 12 for B(OH),, the 1350 cm-1 band is a ring breathing mode corresponding to the 1405-1440cm-1 mode of the D3h borate ion. The bands at 1040 and 795cm-1 would appear 12 to be the in-phase and out-of-phase B-0- stretches respectively. (The normally infra-red inactive A ; mode may become active in the lower symmetry of the solid state.) There is some slight evidence of these in the (B203)(KBr) system, and that they are of intermediate intensity in the (Na2O + NaF+ B203)(KBr) system. They are, however, not identified with any certainty in the glass systems. DISCUSSION KBr SOLUTION TECHNIQUE The object of this method was not to reproduce the pure liquid structures accurately, but was to give some indication of the type of structures which might be found, so easing the interpretation of the broad bands found in the spectra of the pure solids.Hence, we would not suggest that BOY monomers were present in liquid sodium metaborate, but it docs seem likely that in this liquid there is a inixture of 3- and 4- co-ordinate boron. In pure B203 liquid, the amount of 4- co-ordination appears to be small, contrary to the predictions of Grotheim,7 but in agreement with Biscoe.8A . MITCHELL 9 STRUCTURE OF FLUORIDE SOLUTIONS Although the structure of liquid NaF + Na20 + €3203 solution has not specific- ally been studied before, it seems reasonable to compare this system with the phosphate + fluoride 9 and silicate + fluoride systems,l* which have been studied.In these, no direct evidence of P-F or Si-F bonds has been found, although viscosity measurements indicate that the polymer structure is broken by fluoride ions. In order to account for this observation, and for the spectra presented above, we must incorporate F- in the borate structure without producing a B--IF bond. Also, the mechanism must be applicable equally to borates, phosphates and silicates. These three all have at least two co-ordination numbers, and form coniplex oxide ions principally with the lowest of these. It is likely, then, that F- adds to the central atom to increase its co-ordination number, retaining Na-k in close proximity. This would not essentially affect the borate vibration fre- quencies, although the SiO; - fundamentals might be significantly shifted by strain- ing the tetrahedral bonding.If the borate ions rearrange to give a true tetrahedral structure, the bands due to this would be submerged due to the normal proportional of tetrahedral ions. CONCLUSIONS The technique of dissolving a polymer oxide in liquid KBr provides a useful way of simplifying the vibrational spectrum, and thus identifying absorption bands. Applied to B203 and metaborates it shows a close relation to structures determined by conventional techniques. In the borate +fluoride mixtures it has provided evidence that B-F bonds are not formed by substitution in the 13-0 network. The author is indebted to Prof. H. Flood for discussions on the structural inter- pretations presented, to Prof. A. G. Quarrel1 and Prof. G. R. Porter for the pro- vision of laboratory facilities. 1 Parsons, J. Chem. Physics, 1960, 33, 1S60. 2 Parsons and Milberg, J. Amer. Ceram. SOC., 1960, 43, 326. 3 Miller and Wilkins, And. Chem., 1952, 24, 1253. 4 White et al., J. Chem. Physics, 1960, 32, 488. 5 Goubeau and Hummel, Z. physik. Chem., 1959,20, 15. 6 Hisatsune and Suarez, Inorg. Chern., 1964, 3 (3, 168. 7 Grjothein and Krogh-Moe, Det Kong. Norske Videns. Sels. Forhand., 1954, 27 (1 8), 27. 8 Biscoe and Warren, J. Amer. Ceram. SOC., 1938, 21, 287. 9 Williams et al., Trans. Soc. Glass Tech., 1959, 43, 337. 10 Ward et al., Disc. Faruday Soc., 1961, 32, 147. 1 1 Fisher, Lehmann and Shapiro, J. Physic. Chem., 1961 , 65, 11 66. 12 Edwards, Morrison, Ross and Schultz, J. Amer. Chem. Soc., 1955, 77, 266.

ISSN:0014-7672    

DOI:10.1039/TF9656100005

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No.13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Density and Surface Tension of Liquid Xenon and Theory of Corresponding States for the Inert Gases BY A. J. LEADBETTER AND H. E. THOMAS Department of Physical Chemistry, The University, Bristol 8 Received 1st June, 1964 The density of liquid xenon has been measured in the temperature range 162-273"K, under its saturated vapour pressure, with an accuracy of a few parts per thousand. The surface tension has been measured with an accuracy of 1 % in the normal liquid region (triple point 161*4"K, normal b.p. 165.1 OK). These and other condensed state data for Ne, Ar, Kr and Xe, together with data for the dilute gases, have been examined in the light of the quantum mechanical theory of corresponding states.The primary object of this investigation was to search for deviations from accurate corresponding states behaviour which might arise from many-body forces in the condensed state. We conclude that the effect of such forces is smaller than corresponds to a change of a few percent in the parameters of the intermolecular pair potential. The inert gases are of theoretical interest because of their relatively simple inter- atomic forces. However, the detailed form of the intermolecular potential function is still not known with high accuracy.1-3 Less is known about the extent to which the pair interactions are non-additive at high densities (many-body forces), although some degree of non-additivity appears to be necessary to account for the existence of the heavier inert gas solids (Ne, Ar, Kr, Xe) in the cubic, rather than the hexagonal, cl o se-packe d structure .4-6 The molar volume is one of the most fundamental properties and is not known with high accuracy for any of the inert gases over the complete range of existence of the condensed phase, even at the normal vapour pressure.7 The lack of experimental data is particularly serious for the solids.For the liquids, except for xenon, the molar volunies are known accurately over almost the complete liquid range. For xenon, density measurements have been made from 206°K to the critical point (289-7°K) by Patterson et aZ.,s but no data have been reported for the temperature range be- tween the triple point (161-4°K) and 206°K.We therefore undertook density measurements in the normal liquid range (161.4-165~1°K). These results differed by several percent from the values predicted by extrapolating the data of Patterson et al. and we therefore made additional measurements at 189, 230, 248 and 273°K. Measurements of surface tension have been reported for argon 9 over the complete liquid range, and for neon 10 over a more limited temperature range. We have measured the surface tension of xenon in the normal liquid range. The liquid densities, surface tensions and other condensed state data for the heavier inert gases, together with data for the dilute gases, have been examined in the light of the theory of corresponding states in order to see what information could be obtained about the intermolecular forces in these substances.In particular, we have been interested in looking for deviations from corresponding states behmiour which might be due to many-body forces. 10A . J . LEADBETTER A N D H. E . THOMAS 11 EXPERIMENTAL The material used was supplied by the British Oxygen Co. Ltd. as 99.5 % pure, balance krypton, with less than 5 p.p.m. each of oxygen and carbonaceous materials. Mass spectro- metric analysis showed that the sample used contained 0.61 mole % krypton. No attempt was made to purify the sample further. TEMPERATURE CONTROL A N D MEASUREMENT For all the experiments the liquid xenon was thermostatted in a dewar vessel.At 273°K an ice bath was used and at 189°K a well-stirred solid CO2+ acetone bath, which gave tem- peratures constant to about 0-1°K for 10-15 min. For temperatures between 230 and 273°K the evaporator unit of a Rheinische TK1 thermostatic refrigerator was immersed in a well- stirred acetone bath. By this means the temperature could be maintained constant to within 0-1-0.2"K for periods up to about 15 min. Temperatures in the range 189-273°K were measured with a platinum resistance thermometer. In the normal liquid range the refrigerant liquid was CF2C12 (Arcton 12, I.C.P. Ltd.). The temperature was controlled by using a xenon vapour pressure thermometer to activate an electromagnetic valve which controlled the flow of cold air (obtained by evaporating liquid air) through a cooling coil immersed in the refrigerant ; the temperature could be maintained constant to -f0.04"K for long periods.The vapour pressure was measured with a probable error of d10-04 mm Hg using a Precision Tool and Instrunient Co. cathetometer and telescope, and the temperature was derived using the vapour pressure data of Freeman and Halsey.11 In all cases the overall uncertainty in the temperature is estimated to be less than O-l"K. DENSITY The density of liquid xenon was determined by condensing a known mass of gas into a volume-calibrated glass capillary tube. For the experiments in the normal liquid range the mass of xenon was found by measuring the pressure (-400mmHg) and temperature (~300'K) of about 0.015 mole of gas contained in a thermostatted bulb of known volume f- 700 cm3).The second virial coefficients of Whalley, Lupien and Schneider 12 were used in computing the mass of gas from the PVT data. The xenon was then condensed into the capillary tube at liquid-air temperatures and the capillary isolated by means of a tap. The residual pressure in the bulb (<Om05 mm Hg) was measured, and a correction applied for the amount of gas not condensed. For the experiments at higher temperatures the mass of xenon (approximately 1 g) was determined by direct weighing. The gas was condensed at liquid-air temperatures into a capillary tube of known weight and the capillary then sealed off in an oxygen-gas flame. In order to obtain the mass of xenon present as liquid at any temperature the mass of vapour present was calculated from the measured vapour volume and the vapour density data of Patterson et nE.8 The amount of xenon present in the vapour phase was never more than 2.5 % of the total, so that the uncertainty introduced by errors in the vapour density data probably amounts to less than 0.1 %, even in the most unfavourable case.The height of the liquid meniscus was measured relative to a reference mark on the capil- lary tube. For the low temperature measurements the capillary tube had a bore of 2.6 mm, while for the measurements at higher temperatures (p> 1 atm) a 2 mm bore tube was used. 'The volumes of the tubes were calibrated by weighing measured mercury threads. Correc- tions were made for the meniscus volumes of both mercury and xenon, assuming menisci of spherical section.As the meniscus volumes were never more than 0.3 % of the total, no significant errors were introduced by this correction. A further correction was applied to take account of the effect of temperature on the volume of the capillary tube. The effect of pressure on the volume of the tube was negligible. We estimate that the total probable error in the mass of liquid is about 0.1 %, and in the volume about 0.05 %. SURFACE TENSION The surface tension was measured by the method of capillary rise using three capillaries, as described by Stansfield.9 The method involves the measurement of the relative heights of12 CORRESPONDING STATES FOR THE INERT GASES liquid in three interconnected capillaries of different bore. The capillaries were of Veridia precision tubing with nominal bores 0.2, 0.4 and 2.0 mm.They were initially cleaned with benzene, methyl alcohol and distilled water and their bores then determined to an accuracy of f0.1 % by measuring the length (-20 cm) of mercury threads of known mass, using a travelling microscope accurate to &0.01 mm. Corrections were made for the shape of the meniscus. By measuring the length of short mercury threads (- 3 cm) at various positions along the tubes it was verified that the bores were constant over the 20 cm lengths to 10.1 %. After calibration, a 6cm length was cut from each tube, cleaned as before and the three joined in parallel. This cell was connected to the gas-handling system by a wide-bore capillary tube. The xenon was condensed directly into the capillaries at the required temperature, the capillaries isolated from the rest of the system and readings obtained of the meniscus heights at a series of temperatures.The differences in height between the meniscus in the widest bore tube and those in the two narrow bore tubes were approximately 12 mm and 6 mm and these differences were measured with a probable error of *0.04 mm. RESULTS DENSITY The final results for the density of pure liquid xenon are given in table 1 ; they include a correction which takes account of the presence of 0.6 mole % krypton in the xenon sample. In calculating this correction the krypton content of the actual specimen isolated in the capillary tube was taken to be 0.6 mole % also. This was so to a good approximation because the specimen was always initially condensed into the capillary tube at liquid-air temperatures, and measurements of the residual pressure obtained under these conditions showed that nearly all the krypton was TABLE 1.-THE DENSITY OF LIQUID XENON T("K) p(g cm-3) T(OW P k cm-3) 161.9 161.9 1 62.1 162-2 162.3 162.7 162-8 162.8 1629 163.2 163.6 2.980 2.978 2.977 2.978 2,978 2-97 1 2.972 2.974 2.972 2.969 2.965 163.7 163.9 164-1 189.0 189.1 189-4 229-5 230.3 247-9 273.2 2.966 2-963 2.960 2.772 2.771 2-772 2.453 2.447 2.264 1.912 present in solid solution.The correction to the liquid density was then calculated using the known density and vapour pressure of krypton,7 the measured liquid and vapour volumes and assuming the solutions to be ideal. For the results above the critical temperature of krypton the " vapour pressure " used in this calculation was obtained by extrapolating the experimental data from lower temperatures as suggested by Hildebrand and Scott13 ; the partial molar volume of the dissolved krypton was assumed to be equal to its critical volume.A further correction was applied to the high temperature results to take account of the small compression (<0-2 %) of the xenon due to the excess pressure of undissolved krypton. The total magnitude of the krypton correction amounted to approximately 0-2 % in the results for T<200°K and 0.5, 0.4 and 0.2 % respectively at 230, 248 and 273°K. We estimate that for T<20OoK the tabulated results are accurate to about +0.1 % while at higher tempera-A .J . LEADBETTER AND H. E . THOMAS 13 tures the uncertainty may be two or three times greater as a result of uncertainties in the krypton correction. The present results for the density are consistently 4-5 % lower than those of Patter- son et al. It is significant that the critical density found by these workers, using a rectilinear diameters treatment of their data, is 5 % higher than that found in recent investigations. 14- 16 By using the heat of fusion 17 and the value of dp/dTfor the melting curve at the triple point,l8J9 together with our data for the density of the liquid, we obtain a value of 3.419 g cm-3 for the density of the solid at the triple point. This is about 0.5 % lower than the value (3.437 g cm-3) obtained by linear extrapolation of the lattice parameter results of Eatweli and Smith20 from 120°K to the triple point.This result is satisfactory since we should expect the volume of the solid to increase with temperature at more than a linear rate as the melting point is approached. SURFACE TENSION The surface tension was derived from the measured difference in height Ah between the lowest points of the menisci in any two tubes, using the standard formula It was assumed that the contact angle between the liquid and glass is zero. bi is the radius of curvature at the lowest point of the meniscus ; it was obtained from the known radius of the capillary tube by successive approximations, using Sugden's tables.21 The remaining symbols have their usual meaning. Sufficiently accurate values of pv were obtained assuming the vapour to be a perfect gas.Results were obtained with two independent sets of capillaries. If the subscripts 1, 2 and 3 represent the capil- laries in each set in order of increasing bore, then all the results involving tube 2 of the first set were found to be unsatisfactory and were discarded. This showed up as a lack of internal consistency between the y~ calculated from the height differences Aijh; in particular, 713 and y12 differed by 3 %. As the mean deviation of these TABLE TH THE SURFACE TENSION OF LIQUID XENON T (OK) 161.96 161.99 1 62.4 1 162.49 162.68 163.05 163.33 163.45 163.94 163.96 164.24 162.oO 164.58 y (dynes cm-1) 18.7 18.7 18.6 18.7 18.6 18.6 18-5 18.5 18.4 18-3 18.2 18.9 18.4 measurements from the smooth curve was respectively 0.3 and 0.8 % the difference is significant.Measurements were therefore made at extreme ends of the temperature range using the second set of capillary tubes with which internally consistent results had been obtained for nitrous oxide.22" These results were internally consistent to * We are grateful to Mr. D. J. Taylor for carrying out these measurements.14 CORRESPONDING STATES FOR THE INERT GASES withm 0.5 % and agreed with 713 from the first set within about 1 %. An explanation of these results is that tube 2 of the first set was unclean, resulting in a non-zero contact angle. The final results (713) are given in table 2. The last two entries arc the mean values obtained with the second set of capillaries. We estimate the accuracy as about +,1 %. In this case the effect of the krypton impurity should be very small since it was possible to condense the xenon directly as liquid, in equilibrium with a large vapour volume, before isolating the capillaries. The amount of krypton dissolved in the liquid xenon probably amounts to less than 0.1 mole %.DISCUSSION The densities of neon,23 argon 24 and krypton 25 have been measured by Matluas et al. The argon results have been confirmed by Von Itterbeek and Verbeke 26 over a limited temperaturc range. We thus know the densities of four inert gas liquids with a probable accuracy of a few parts in a thousand over the complete liquid region. We now examine these, and other results, using the theory of corresponding states. A classical system obeys 27 the law of corresponding states if its molecules interact with a pairwise additive potential of the form$(r) = &f(r/o), where E is a characteristic energy, o a characteristic length and f a universal function.For the condensed phases, quantum effects may be taken into account by introducing 28 the quantum parameter A = h/(m~)*, and the reduced equation of state may then be written as p* = p"(T*,V*,A*), where No" & Although the magnitude of the quantum contribution cannot be calculated without the use of a model for the condensed phase, it can be expressed generally as a power szries in A*. Hence, provided that the only source of deviations from correspond- ing states behaviour is the quantum efTects, then a property such as the molar volume should show a smooth vuiation with A*.The deviations from classical behaviour, in the limit of low A*, should be proportional to A*2, except in the vicinity of 0°K where they will be proportional to A*, due to the dominance of the zero-point energy. If many-body forces are important, we should expect the above simple dependence of the various properties on A* to break down. Hence, the most direct way of carry- ing out the investigation would be to use reducing parameters determined from dilute gas data, which depend only on two-body interactions, to construct plots of the various reduced condensed state properties against A* or A*2 (cf. De Boer 28). For this purpose we need only accurate relative values of the reducing parameters for the various inert gases. However, the determination even of accurate relativc values of e and oisiiot easy, andinorder todistinguishclearly the effects of errorsin the parameters, we adopt the following procedure.We first determine sets of reducing parameters from a variety of dilute gas properties. Secondly, we derive sets of effective para- meters which give accurate corresponding states behaviour (including quantum effects) when used to reduce various condensed state properties. These effective parameters will also be influenced by many-body effects, if these are sufficiently large. Finally, we compare the relative values of the two groups of reducing parameters, and any significant differences will give a direct indication of the importance of many- body effects.A . J . LEADBETTER A N D H. E. THOMAS 15 DILUTE GAS PARAMETERS Kihara 1 has suggested a set of reducing parameters viz., the Boyle temperature TB and the Boyle volume VB, defined as follows : B(TB) = 0; VB = (TdB/dT)T = TB, where B(T) is the second virial coefficient.These parameters have the advantage of being experimental quantities which depend strictly on two-body interactions, and it may readily be shown that E is proportional to TB and a3 to VB. The Boyle properties of the heavier inert gases have been derived by Munn,3 and the results are included in table 3. Using these parameters the second virial coefficients obey the law of corres- ponding states within experimental uncertainty. The uncertainty of these parameters is unlikely to be less than about 2 %. The critical constants are often used as reducing parameters, and this involves the assumption that E is proportional to TC and 0 3 to VC.However, quantum effects, particularly for neon, are not negligible at the critical point, and many-body forces may be important at the critical density. Nevertheless, for argon, krypton and xenon both the second virial coefficients 29 and the viscosities 30 correspond within experimental error over a wide temperature range when reduced in this way, and we therefore include the critical parameters in our comparison (table 3). Dilute gas data are often interpreted in terms of the parameters of the Lennard- Jones 6 : 12 potential. Although this is only a fair approximation to the real potential, the relative values of the parameters will be accurate, provided they are determined for all the substances in a self-consistent manner.Parameters have been obtained by Schneider and co-workers 319 32 for all of the gases, by Michels et al. for argon 33 and xenon,34 and Beattie et al. for krypton 35 and xenon.36 The values are given in table 3. Comparison of the virial coefficient data 37 suggests that the main cause of the discrepancies lies in the fitting procedures used in deriving the parameters, rather than in the original data. This, in turn, reflects the relative insensitivity of the second virial coefficient to the shape of the intermolecular potential. However, since Schneider and co-workers have investigated all four gases we give in table 3 relative values of the parameters calculated from their results, and we estimate that these values are uncertain by at least 1-2 %.Hirschfelder, Curtiss and Bird 38 have obtained 6 : 12 parameters from an analysis of gas viscosity data. The Elk valucs are probably less reliable than those derived from the virial coefficients. Furthermore, the para- meters for krypton, and to a lesser extent xenon, are based on limited experimental data. The various dilute gas reducing parameters, and their values relative to argon, are compared in table 3. This comparison suggests that the relative values of the two- body parameters are not known to better than about 2 %. CONDENSED STATE PARAMETERS A set of effective 6 : 12 parameters for the heavier inert gases has been derived by Boato and Casanova 39 essentially from liquid state data, and is given in table 4. Their parameters give reasonably accurate corresponding states behaviour for properties at O'K, the triple point and the critical point.The molar volumes of the liquids reduced with these parameters are shown in fig. 1 plotted against A* at three reduced temperatures. The new data for xenon clearly do not fall on the smooth curve formed by the reduced volumes of the other substances, and the discrepancies suggest that the U-value for xenon is 0.7 % too low. The sur- face tension data support this conclusion, as shown in fig. 2, where the reduced surface16 CORRESPONDING STATES FOR THE INERT GASES M 8 w cl 2 * S*S * w w w b b b z m vl U .3 1 * a !i a 2A . J . LEADBETTER AND H. E. THOMAS 17 tensions of neon, argon and xenon are shown plotted against A* ; unfortunately, there are no data for krypton.Since measurements have been made for neon and xenon only over limited temperature ranges it is possible to make such a plot only at one reduced temperature. For the above reasons, and also because the reduced surface tensions are less accurate, and proportional to a2 rather than 03, they can be given less weight than the molar volume data. However, if the value of CT is increased by 0.7 % as suggested by the molar volumes, the deviations of y* from classical behaviour are proportional to A*z within experimental error. Examination, in the above manner, 2. 2.' V' I. I. / ,/ //" T*= 1.15 / Kr Ar NC 0.1 0 2 0 3 0.4 0 5 0-6 I I I I A* FIG. I.-A plot of V* against A* for Ne, Ar, Kr, and Xe at various values of T*. 0, reducing parameters of Boato and Casanova ;39 0 , modified u for Xe (see text).of other a-sensitive reduced data given by Boato and Casanova support our conclusion about the a-value for xenon. The 0°K molar volumes of the solids (with the inclusion of the results of Sears and Klug40 for xenon) suggest that CT is 0.5 % low, and the critical pressures indicate a value too low by 1.3 %. We therefore suggest that the value of CJ for xenon should be increased from 3.97 to 4-00 A, which is probably inside the experimental error with which the parameters were determined. The &-sensitive plots of Boato and Casanova are generally smooth, and appear to have the correct limiting dependence on A*, so we conclude that with the above minor modification to the a-value of xenon, the effective parameters of Boato and Casanova give corres- ponding states behaviour for condensed state properties accurate in general to better than 1 %.Another set of 6 : 12 parameters has been determined in a self-consistent manner from solid state data by Hortor, and Leech,41 and are also given in table 4. The18 CORRESPONDING STATES FOR THE INERT GASES agreement of the solid and liquid state parameters is always within the combined experimental uncertainty, and except for the &-values of neon is within about 1 %. A careful investigation of the corresponding states behaviour of gaseous argon and xenon has been made by Levelt.42 She derived parameter ratios which are required to give accurate correspondence of the properties of the gases at high densities.In table 4 we compare these ratios with the relative values of the other parameters, also expressed as ratios relative to argon. The agreement is good, the relative values of the molecular parameters obtained from dense gas, liquid and solid state data are the same to within about 1 %, except for the &-values of neon which still agree, however, within experimental error. 0 . 7 1 xe Ar I I 1 I---. - p p _ l l I 0 1 0 . 2 0 3 0 4 0.5 0 . 6 A' FIG. 2.-A plot of y* against A* for Ne, Ar and Xe at T* = 0.71. 0, reducing parameters of Boato and Casanova39 ; e, modified G for Xe. COMPARISON OF CONDENSED STATE AND DILUTE GAS PARAMETERS We now compare the relative values of the reducing parameters which give accurate corresponding states behaviour for condensed state and for two-body gas data.The appropriate values are contained in tables 3 and 4. In no case is there a difference between the two sets of values which appreciably exceeds the probable uncertainty in the data, and the differences appear to be random. This shows that any deviations from corresponding states behaviour due to many-body forces are less than would be obtained by a change of a few percent in the parameters of the inter- molecu!ar potential. Since theory predicts that the relative magnitude of many- body effects should increase considerably from neon to xenon,4-6 it seems likely that the absolute magnitude of such effects in these substances also amounts to less than corresponds to a change of a few percent in the potential parameters. The significance of our conclusions may be illustrated by considering the static lattice energy.To a first approximation, this is directly related to E, so that the many- body contribution to the lattice energy probably does not amount to more than about 3 or 4 o/o, even for xenon. On the other hand, theoretical estimates 435 suggest that this contribution increases from about 1 % for neon to 10-20 % for xenon. The estimates thus appear to be too high by at least a factor of two. We are grateful to Professor D. H. Everett for his encouragement. One of us (H. E. T.) acknowledges receipt of a D.S.I.R. maintenance grant.A . J . LEADBETTER AND H. E. THOMAS 19 1 Kihara, Revs. Mod. Physics, 1953, 25, 831. 2 Guggenheim and McGlashan, Proc. Roy. SOC. A , 1960, 255,456. 3 Munn, J.Chern. Physics, 1964, 40, 1439. 4 Axilrod, J. Chem. Physics, 1951, 19, 719. 5 Jansen and McGinnies, PhyJic. Rev., 1956, 104, 961. 6 Jansen, Physics Lerters, 1963, 4, 91, 95. 7 Hollis-Hallet, Argon, Helium and the Rare Gases, ed. Cook (Interscience, 1961), chap. IX. 8 Patterson, Cripps and Whytlaw-Gray, Proc. Roy. Soc. A, 1912, 86, 579. 9 Stansfield, Proc. Physic. SOC., 1958, 72, 854. 10 Van Urk, Keesom and Nijhoff, Comm. Physics Lab. University of Leiden, 1928, 182b. 1 1 Freeman and Halsey, J. Physic. Chem., 1956, 60, 1 1 19. 12 Whalley, Lupien and Schneider, Can. J. Chem., 1953, 31, 722. 13 Hildebrand and Scott, Solubility of Non-Electrolytes, 3rd ed. (Rheinhold, 1950), chap. XV. 14 Schneider and Habgood, J. Chem. Physics, 1953, 21,2080. 15 Habgood and Schneider, Can. J. Chem., 1954,32,98 ; 32, 164. 16 Julien, Thesis, (Massachusetts Institute of Technology, 1955). 17 Clusius and Riccoboni, Z. physik. Chem., B, 1938, 38, 81. 18 Clusius and Weigand, Z. physik. Chem., B, 1940, 46, 1. 19 Stryland, Mastoor and Crawford, Cart. J. Physics, 1960, 38, 1546. 20 Eatwell and Smith, Phil. Mag., 1961, 6, 461. 21 Sugden, J. Chem. SOC., 1921, 119, 1483. 22 Leadbetter, Taylor and Vincent, Can. J. Chew., in press. 23 Mathias, Crommelin and Onnes, Comm. Physics Lab. Univ. Leiden, 1923, 162b. 24 Mathias, Onnes and Crommelin, Comm. Physics Lab. Univ. Leiden, 1912, 131a. 25 Mathias, Crommelin and Meihuizen, Comm. Physics Lab. Uniu. Leiden, 1937, 248b; Physica, 26 Van Itterbeek and Verbeke, Physica, 1960, 26, 931. 27 Pitzer, J. Chem. Physics, 1939, 7, 583. 28 De Boer, Physica, 1948, 14, 139, 149, 520. 29 McGlashan and Potter, Proc. Roy. SOC. A., 1962, 267, 478. 30 Whalley, Can. J. Chem., 1954, 32, 485. 31 Nicholson and Schneider, Can. J. Chem., 1955, 33, 589. 32 Whalley and Schneider, J. Chem. Physics, 1955,23, 1644. 33 Michels, Wijker and Wijker, Physica, 1949, 15, 627. 34 Michels, Wassenaar and Louwerse, Physica, 1954, 20, 99. 35 Beattie, Barriault and Brierley, J . Chem. Physics, 1952, 20, 1615. 36 Beattie, Brierley and Barriault, J. Chem. Physics, 1951, 19, 1222. 37 Beattie, Argon, Helium and the Rare Gases, ed. Cook (Interscience, 1961), chap. VIlI. 38 Hirschfelder, Curtiss and Bird, Molecular Theory of Gases and Liquids (Wiley, 1954). 39 Boato and Casanova, Physica, 1961, 27, 571. 40 Sears and Hug, J, Chem. Physics, 1962, 37, 3002. 41 Horton and Leech, Proc. Physic. SOC., 1963, 82, 816. 42 Levelt, Physica, 1960, 26, 361. 1937,4, 1200.

ISSN:0014-7672    

DOI:10.1039/TF9656100010

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No.13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Dilatometric Measurements of Apparent Molar Volumes of Dilute Aqueous Electrolytes BY LOREN G. HEPLER," JEAN M. STOKES? AND R. H. STOKES? Received 25th May, 1964 A simple magnetically-operated dilatometer is described, in which it is possible to determine the volume-change on mixing a relatively concentrated electrolyte solution with up to several hundred times its volume of water. An accuracy of -1 x 10-4 ml can be obtained with a total volume of 300ml. The apparent molar volumes at infinite dilution of NaOH, (CH&NBr, K3Fe(CN)6 and &Fe(CN)6 are determined and the large effects of electrostriction in the last two are discussed.Accurate knowledge of the apparent molar volumes of electrolytes at low con- centrations is of fundamental interest in connection with the pressure-dependence of equilibria in solution 1 and the understanding of ion-solvent interactions.2 For theoretical purposes the most useful quantity is the apparent molar volume at infinite dilution #f, since this is determined by the intrinsic size of the ion and the ion-solvent interactions only. Since the apparent molar volume increases roughly linearly with the square root of the concentration, data at low concentrations (ionic strengths down to 0.01 or less) are necessary for accurate extrapolation. At such concentrations the density of the solution differs so little from that of the pure solvent that density measurements must have an accuracy of about & 1 x 10-7 g ink1 in order to give reasonable precision in the apparent molar volume.Direct pyknometry at this level presents serious difficulties both in reproducibility of weighings and in constancy of isotopic composition/ of the solvent. The differential magnetic float method of Lamb and Lee 3 9 -1. has yielded excellent results, but appears from the infrequency of its use to be a difficult technique. Dilatometers have also been used, but the usual designs do not appear to be well suited to work at high final dilutions.5-7 The dilatometer described here is extremely simple in design, construction and operation, and yields an accuracy of a few hundredths of 1 ml in 4 v at concentrations as low as 0.002 M.It was developed from an instrument used by one of us (L. G. H.) for determination of the volume change on dissolution of solids. THEORY OF THE DILATOMETRIC METHOD The definition of the apparent molar volume is where Y = total volume of solution ; Vy = molar volume of pure solvent ; n1, n2 = numbers of moles of solvent and solute respectively in the volume Y of solution. At concentrations above a few tenths molar, density determinations (to & 1 x 10-5 g ml-1) in a standard Ostwald pyknometer on solutions of known concentration suffice to give #v with useful accuracy, but at a few thousandths molar the presence of n2 in the denominator of (1) results in a magnification of the uncertainty by a factor of the * U.S.National Science Foundation Visiting Research Fellow from Carnegie Institute of Techno- logy, Pittsburgh, U.S.A. t Department of Physical and Inorganic Chemistry, University of New England, Armidale, N.S.W., Australia. 20L . G . HEPLER, J . M. STOKES AND R. H. STOKES 21 order of 100. However, consider now an experiment in which a small volume v of a relatively concentrated solution is mixed isothermally with a large volume v' (of the order of 100 v) of pure solvent. Denote the value of #v for the concentrated solution by @Lit ; this quantity can be determined by direct pyknometry with the necessary accuracy. Let Av be the expansion on mixing, and V the final volume : V = v+v'+Av. (2) Let 4lna1 be the value of #v in the solution after mixing.Then manipulation of (1) and (2) leads to the useful exact result Thus if#git is known with an accuracy of 0.01 ml mole-1, and (Av/n2) can be measured with similar accuracy, 4ka1 in the dilute solution after mixing is obtained within +Om02 ml mole-1. The dilatometer used here makes possible the determination of Av/na with the required accuracy, without demanding any unattainable precision in absolute volume measurements. EXPERIMENTAL THE DILATOMETER Fig. 1 shows the instrument in its assembled form before mixing the solution; the inset shows in more detail the construction of the capsule which contains the concentrated solution. The lid of this capsule is a plano-convex lens shaped piece of glass of the same diameter as the outside of the capsule tube (17.5 mm) ; its plane surface and that of the open end of the capsule are lapped flat with fine emery. Cemented on to the convex side of the lid is a loop of platinum wire, the ends of which extend 1 inm beyond the edge of the lid and are slightly bent so as to retain the wire clips which hold the lid in place.These clips are made of nichrome wire work-hardened by stretching to the point of fracture. Attached to the platinum loop is a piece of nichrome wire carrying a piece of soft iron encased in polythene. The length of,this wire is adjusted so that the piece of iron either hangs clear of the bottom of the flask, or rests against the flask in an off-centre position so as not to foul the magnetic stirrer. The magnetic stirrer is a commercial type 2-4 cm in length, also encased in polythene. The capillary tube is of 1 mm precision bore tubing, calibrated before assembly by measuring the length of mercury threads of known weight.It is marked with fine reference lines about every 2 cm of its length. The method of use is as follows : a supply of conductivity-water is outgassed on the filter pump, along with the magnetic stirrer and the soft iron rod. Outgassing is necessary to prevent the formation of air bubbles during the run, but need not be complete. The flask is filled to the top- of the neck with this water and checked for absence of air-bubbles trapped on the walls, and the stirrer is inserted. The clean and dry capsule is clamped vertically upside-down by the B24 stopper to which it is attached.Its flat ground rim is lightly greased with stopcock grease. The outgassed concentrated solution (of which the density and composition are known) is pipetted into the capsule so that the meniscus bulges above the greased rim. The flat ground surface of the lid is then slid across into position, leaving the capsule completely full. The spring clips of nichrome wire are attached to hold the lid in place, and the soft iron bar is hooked in to the platinum loop. The assembly is rinsed free of external solute, the B 24 stopper is lightly greased with stopcock-grease and the stopper and assembled capsule are lowered slowly into position, care being taken that no air-bubbles are entrained. At this stage a final inspection for bubbles on the outside or inside of the capsule is facilitated by the magnifying action of the surrounding water in the flask.The rubber-faced holding clamp, shaped to fit the neck of the flask, is attached and the springs are fitted to hold the stopper in place. The stopper is then pressed home with small rotary oscillatory movements, during which excess grease is squeezed out ; in the find position the glass surfaces should be on the point of binding. The temperature of the room22 APPARENT MOLAR VOLUMES in which the assembly is done should be only a degree or two below that of the thermostat so that leakage out of the capsule during temperature equilibration will be minimized. The assembly is clamped in the thermostat and the capillary is adjusted to vertical by means of the ball-joint. The magnetic stirrer drive (a rotating bar magnet 5-7 cm long) is positioned near the bottom or side of the flask and set rotating at about 200 rev/min. After about an hour the overflow from the capillary is mopped off and the level in the capillary is adjusted to a few cm below the top by means of a hypodermic needle.Cathetometer read- ings of the meniscus and one of the reference marks on the capillary are taken at 5-10 min intervals. Provided the stopper is properly seated they should reach constancy within about 0.05 m i within 2 h of placing the flask in the thermostat. For the flasks used, 0.05 mm movement in a 1 mm capillary corresponds to a change of the order of 1 in 107 in volume. --. - ~ ~ - _ _ _ _ _ FIG. 1.-The dilatometer. Inset : detail of solution capsule. For such a change to have significance the temperature must be constant to better than O~OOl", and the external pressure to 1-2 mm Hg.(A temperature change of 0.001" causes a relative volume change of 2 . 8 ~ 10-7, and a barometric pressure charge of 1 mm causes a relative volume change of 6 x 10-8. The barometric effect is thus significant only in change- able weather.) The temperature control was found to be adequate in the large thermostat used for our isopiestic studies; this is a 550-litre water-bath stirred at two places by a 1/3 h.p. motor, and controlled by a mercury-toluene regulator in which the toluene is contained in several metres of 8 mm copper tubing wound into a helix. The variation shown on a calorimeter-thermometer divided to 0.01 " is less than 0.001 ".When a proportioning-head is fitted to the regulator the cycle time is about 20 sec. When a satisfactory constancy of reading is attained the magnetic stirrer drive is swung aside and a large powerful permanent magnet (of the type used with magnetron tubes) is brought up to the side of the flask. Its field seizes the soft iron bar, and suitable movements of the magnet drag the lid off the solution capsule. This operation is thus done without inL. G . HEPLER, J . M. STOKES AND R. H. STOKES 23 any way disturbing the position of the flask or its stopper, the instrument remaining in position in the thermostat throughout. Themagneticstirrer driveis then replaced and stirring is resumed, with an initial period of a few minutes' more rapid stirring to ensure thorough mixing.The near-vertical position of the solution capsule ensures that the solution drains out into the bulk because of its higher density. Meniscus and reference-mark readings are taken at intervals of a few minutes as soon as mixing is complete. Any small temperature changes arising from heat of mixing are dissi- pated within 15 min, and the readings thereafter are constant within 0-05 mm when a flask of 300 m1 volume is used. CORRECTION FOR CHANGE OF HYDROSTATIC HEAD.-&CaUSe the Capillary tube iS Vertical, the hydrostatic pressure on the liquid in the flask is greater when the meniscus is higher, so that the volume change calculated directly from the observed meniscus drop is not the true value for constant pressure. This effect arises partly from the compressibility of water and partly from the volume-expansion of the flask due to the head of water in the capillary.It was measured by setting up the apparatus full of water, applying known heads of positive or negative air pressure from a water-manometer, and measuring the meniscus shift. The shift was linear with applied pressure ; expressed as the percentage increase in the effective cross- section of capillary it varied from 0.48 % for a 300 ml apparatus to 1-69 % for one of 1 1 0 0 ml. The capsule volume and the total volume in the assembled apparatus are determined by weighing water. Capsule volumes ranged from 2.5 to 14 ml, and total volumes from 300 to 1100 ml. The capsule volume needs to be known accurately since this determines n2 ; it was found to be reproducible within 0.001 ml.The total volume needs to be determined only within, say, 0.1 %, since it does not appear in eqn. (3), and is required only in order to know at what concentration the value of 4Znal applies. As a check on the validity of the method, some tests were made with potassium chloride, the final concentrations ranging from 0.008 to 0.05 M. The apparent molar volumes lay within 0.03 ml mole-1 of a smooth curve drawn through the data of Geffcken and Price 4 which were obtained by the magnetic float method. Blank runs with water in the capsule gave A v e 1 x 10-4 ml. MATERIALS TETRA-METHYL AMMONIUM BROMIDE was prepared by two recrystallizations of commercial material from conductance-water, followed by duplicate gravimetric analyses (0.02 %) of a stock solution as AgBr.SODIUM HYDROXIDE was prepared from electrolytic sodium amalgam by the method of Marsh and Stokes 8 and analyzed by weight-titration and conductimetry of the resulting sodium chloride as described by Stokes.9 The composition errof is estimated as less than 0.02 %. A.R. POTASSIUM FERRICYAMDE was recrystallized from conductance water and dried to constant weight in a desiccator and then at 95". POTASSIUM FERROCYANIDE was twice recrystallized from the A.R. salt and made into a stock solution which was analyzed by measuring its conductance and interpolating the concentration from a suitable d.eviation- function prepared from the data of Jones and Stauffcr.10 RESULTS The densities of the concentrated solutions used were determined in two 50-ml Ostwald pyknometers. Immediately after each pair of density measurements the pyknometers were calibrated with conductance water ; appropriate vacuum- corrections were applied. The duplicate densities agreed to * 1 x 10-5 g ml-1.Since the sodium hydroxide solutions were made up and stored under argon, the pyknometers in this case were calibrated with argon-saturated water, which was found to have a density exceeding that of the air-saturated conductance water by 1.9 x 10-5 g ml-1. Table 1 gives the densities and apparent molar volumes of the concentrated solutions. With potassium ferrocyanide, checks with the data of Jones and Stauffcr 10 agreed within 0-1 ml in 4v. In the range above 0.05 M the density24 APPARENT MOLAR VOLUMES data reported by these workers appear to be accurate to about 2 x 10-5 g ml-1, although quoted to 1 x 10-6.Accordingly it was not necessary to determine the densities of solutions 7-1 1. Table 2 gives the essential information about the dilato- meter experiments. For determining $r, the data were plotted against J. as in fig. 2-4. TABLE 1 .-DENSITIES AND APPARENT MOLAR VOLUMES OF CONCENTRATED SOLUTIONS solution clmole 1-1 dt5 +Urn1 mole-* 0.8451 0.27357 0.6090 0.3022 1.2129 0.23939 0.4978 0.1903 0.1987 0,04649 0.03 949 0.16742 0-10078 1.833011 1.009075 1 e020990 1.008994 1-17322 1.03880 - 1 -03717 1 -02149 - 2.536 - 3.89 115.12 114.94 163.42 156.40 (1 3 7-6) (1 30.0) (1 30.3) (1 23.1) 129.21 126.33 (1 22.2) Values in parentheses are interpolated from the data of Jones and Stauffer and the present work.The density of water at 25°C was taken as 0.997070 g rn1-l. TABLE 2.-DILATOMETRIC DATA FOR APPARENT MOLAR VOLIJMES AT LOW CONCENTRATIONS V - 'final +final solution moles - AV mole 1.-1 ml mole-1 in capsule solute (n2) ml 0.00729 1 0.009851 0.005429 0403 189 0*001757 0.001 757 0.007099 06003687 0.003566 0.007102 0402790 0.00 1402 0.000848 0.00287 1 0.00221 9 0.001 276 0.001098 O*OOO40 1 0-001 145 0.000509 0.000299 0.000254 0.000254 0-01 687 0.02323 0.01 370 0,00377 0*00210 0.00221 0.00476 0.00252 0.00264 0.08293 0.01761 0.00978 0.0061 2 0.0573 0.0289 0.01 85 0.0 1 60 0.00404 0.0 197 0.00380 0.00297 0.00558 0.00276 0,02445 0-01765 0.01 110 0.0057 14 0.003 145 0.001 573 0.02394 0.01 290 0.01 202 0-02399 0.009412 0.004725 0.02865 0.009537 0-007274 0.004253 0.003646 0.001346 0*001022 O-OoO4 56 0.000267 0.000227 0-000227 - 4.87 - 4.89 - 5.06 - 5.08 - 5.09 -5.15 1 14.45 1 14-44 114.38 151.74 150.09 149.32 149.1 8 1 17.62 1 16-98 115-8 115.4 113-0 113.1 1 12.0 110.3 11 1.3 110.4L .G. HEPLER, J. M. STOKES AND R . H. STOKES 25 The measurements on potassium ferrocyanide had to be carried to extreme dilutions because of the curvature of the q5v against 4. graph. At the lowest con- centration, (0.000227 M) duplicate measurements gave two values of Av differing by I I I I I 1 , I 0 . 2 0'4 0.6 0.8 1.0 z / C FIG. 2.-Apparent molar volunles of 1 : 1 electrolytes at 25" in water. 0 pyknometer; 0 dilatometer ' 2 FIG. 3.-Apparent molar volume of potassium ferricyanide in water at 25". 0 pyknometer; 0 dilatometer; K3Fe(CN)6; 4 l = 147.8 ml mole-1 2 x 10-4 ml.At this concentration the resulting difference in duplicate 4 v values is 0.9 ml mole-1, whereas at 0.01 M it would be only 0.02 ml mole-1. The lowest point shown in fig. 4 is an average for the three most dilute solutions given in table 2.26 APPARENT MOLAR VOLUMES DISCUSSION The theoretical limiting slope (d4v/d 4;) for the apparent molar volume, which involves the isothermal pressure-derivatives of the dielectric constant and the molar volume of water, has been recalculated by Redlich 11 as 1-86[(ml mole-1) (mole-+ 1+.)] for 1 : 1 electrolytes. The corresponding values for 3 : 1 and 4 : 1 electrolytes are re- spectively 26-4 and 58.8. These slopes are shown as broken lines in fig. 2-4. The 1 0. I 0.2 0.3 0.4 0 - 5 I f vc FIG.4.-Apparent molar volume of potassium ferrocyanide in water at 25". 0 pyknometer; 0 dilatometer; x Jones and Stauffer pyknometer curves for sodium hydroxide and tetra-methyl-ammonium bromide approach the theoretical limiting slope from above and below respectively. This is consistent with the behaviour of the activity coefficient, (CH&NBr showing clear evidence of ion- association while sodium hydroxide is probably fully dissociated at those con- centrations. The limiting values 4; at zero concentration are given in table 3 for the four solutes studied. For purposes of theoretical discussion, it is desirable to separate these values into separate cationic and anionic values, but this requires some extra- thermodynamic assumption to fix the value for one chosen ionic species, e.g., H+.Various values have been proposed, e.g., &!(H+)/ml mole-1 Fajans and Johnson 12 - 0.2 Mukerjee 13 - 4.5 Stokes and Robinson 14 - 7.2 Couture and Laidler 15 - 6.0 Eucken 16 - 2.4 Until better agreement exists, it seems best to adopt the " conventional " value of Owen and Brinkley,l7 @(H+) = 0 ; this is not far from the estimates of ref. (12) andL. G. HEPLER, J . M. STOKES A N D R . H . STOKES 27 (16). Using this conventional reference-point, combination of our results with those for various 1 : 1 electrolytes tabulated by Harned and Owen 18 leads to the ionic values given in table 3. TABLE 3.-LIMITING APPARENT MOLAR VOLUMES IN WATER AT 25" IN Ill1 AND IONIC VALUES BASED ON +r(H+) = 0 NaOH - 5-25 ; OH- - 3.79 ; K3Fe(CN)6 147.8 ; Fe(CN) 2 - 12iS6 ; &Fe(CN)6 110 h0.5 ; Fe(CN)%- 75.(CH3)4NBr 114.25 (CH3)4N+ 89-36 ; SODIUM HYDROXIDE Our value of 4; = - 5-25 ml mole-1 is more negative than the estimate of - 4.6 ml at 25" made by Bodansky and Kauzmann 7 from dilatometric studies at 30" and higher concentrations, but confirms their conclusion that the value of - 7.5 ml mole-1 extrapolated from Akerlof's 19 measurements above 0.5 M is too low. The curvature evident in fig. 2 makes it clear how the long-standing error in this important quantity arose. Combining our value with those 18 for HC1 and NaCl we find for the neutral- ization-process at infinite dilution : H+ + OH-+ H20, A4: = - 2 1-86 ml mole-1. TETRAMETHYL AMMONIUM I O N Wyckoff 20 gives details of the crystal structure of N(CH&Cl, N(CH3)4Br, and N(CH3)4I.A11 are tetragonal, the lattice dimensions (N-N distances in A) being a0 =:bo CO NCH3)4C1 7.78 5.53 "CH314Br 7.76 5.53 N(CH3)d 7.96 5.75 The virtual identity of the dimensions of the chloride and bromide crystals suggests that they are fixed by cation-cation contacts. A model of the crystal was made up from Catalin atomic models, and it was found that if the methyl groups on each cation were rotated into the positions giving maximum overlap of the hydrogens of adjacent methyl groups on the same nitrogen, the N-N internuclear distances for cation-cation contact were a0 = bo = 7.75A and co = 5.53& as given by Wyckoff for the chloride and bromide salts. Furthermore the " holes " left in this cation struc- ture were just large enough to accommodate chloride or bromide ions of radii 1-81 or 1.95 A but not iodide ions of 2.16 A radius.Heat capacity measurements 21 on solid (CH&NCl show a &transition at 185"K, which could possibly arise from the onset of methyl rotation. For the iodide, an anomalous " bump " in the heat capacity at about 275"K, was attributed 22 to a trace of water in the salt. On plotting the unsmoothed heat capacity measurements we find a marked similarity in shape between this " bump " and the 1-transition in the chloride, and we suggest that the iodide does in fact show a 2-transition also. If this interpretation is correct, however, the absence of a A-transition in the bromide is unexpected. The halide ions occupy vertically staggered positions in the holes in the cation structure ; the vertical distances of chloride ions from the plane of the nitrogen atoms are alternately 5.53 x 0.35 = 1.94 A and 5.53 x 0.65 = 3.59 A.The shortest N-C1 in t e rnuclear distance is accordingly [(7.78/2)2+ 1-942]* = 4-35 A.28 APPARENT MOLAR VOLUMES Subtracting from this the Pauling chloride ion crystal radius of 1.81 A we obtain for the “ radius ” of the N(CH3): ion, as seen by the chloride ion, 2.54 A. Similar calculations for the bromide and iodide salts lead 2.44 and 2-41 8, respectively; the apparent decrease is probably connected with the greater polarizibility of the larger anions rather than an actual change in the dimensions of the cation. The model shows that the halide ions are practically in contact with carbon atoms of the cation, so that the distance of 2-54 A can be regarded as a minimum “ radius ” when the methyl groups are in free rotation.The maximum “ radius ”, with free rotation of the methyl groups, is one-half the distance between adjacent cations, provided these are in contact as appears to be the case in the chloride and bromide. This distance is and 5.5312 = 2.77 A in the c-direction, so that we may take a maximum radius of 2-76 A. On each cation there are 4 positions giving the minimum radius and 6 giving the maximum; the weighted mean radius is therefore 2.67 A. Since the heat of solution is small, we assume that the aqueous ion also has an effective radius of 2-67A. This is supported by the viscosity data of Huckel and Schaaf 23 which give an Einstein radius of 2.65 A.Hepler,24 using the present basis #(H+) = 0, concluded that the apparent molar volumes of z-valent monatomic ions could be represented by 4: = Ar3-Bz2/r, where for cations A = 5.3 ml mole-1 A-3, B = 4.7 ml mole-1 A, and for anions A = 4.6 ml mole-1 A-3, B = 19 ml mole-1 A. Here the first term represents the intrinsic volume of the ion, (greater than the sphere-in-continuum value of 2.523 ml mole-1A-3 because of inefficient packing), and the second represents the effect of electrostriction. Using for OH- the ‘‘ radius ” of a water molecule, 1.40 A, Hepler’s equation gives - 1.0 in1 mole-1 for c/Y(OH-) ; and for NMez using the value r = 2.67 A arrived at above it gives 4: = 99 ml mole-1. The latter is 10 ml mole-1 larger than the value in table 3, but this discrepancy could be removed by chanigng the “ radius ” from 2.67 to 2-58 A.7-77/(2 4’2) = 2.75 A in the ab plane, FERRI- AND FERROCYANIDE IONS With the ferri- and ferrocyanide ions the wide departure from spherical shape makes the quantitative treatment of the volume difficult. A scale model of the hypo- thetical ion Fe(CW)z +, based on dimensions given 25 for its methyl-derivative Fe(CNCH&+, shows that this ion is a decidedly spiky-looking object, and its effective size is considerably less than that of the circumscribing sphere (radius 4.23 A). Owing to the presence of an additional 5 or 6 electrons, the Fe(CN); - and Fe(CN);- ions would be larger than the hypothetical Fe(CN)i+ ion. Even so, the effective size of ferri- and ferrocyanide ions should still be less than that of a sphere of 4.23A radius.. If we assume that the intrinsic volumes of Fe(CN):- and Fe(CN)Z- are the same, table 3 leads us to the conclusion that the additional electrostriction caused by an increase in negative charge from - 3 to - 4 produces a decrease of 46 ml mole-1 in 4:. According to Hepler’s equation for anions, the change in electrostriction volume should be Setting (4) equal to 46 ml mole-1 leads to Y = 2.9 A for the radius effective in electro- striction, which is a value of reasonable magnitude. 19(42/r- 321r) ml mole-1 A. (4)L . G . HEPLER, J . M. STOKES AND R. H . STOKES 29 One conclusion that can be drawn with some confidence is that the decrease in volume for an additional negative charge (- 3 to - 4) is at least twice as large as the 20 ml mole-1 (independent of radius) proposed by Couture and Laidler.15 Fig.4 shows that for K4Fe(CN)6 the curve for +v against ,/c%es above the theoreti- cal limiting slope at concentrations below 0.01 M, in spite of the evidence from con- ductance data 26 that appreciable ion-pairing niust be present. It seems probable that the ion-pair is an intimate one, a K+ ion being inside the solvation sheath, so that the ion-pair KFe(CN) 2 - causes electrostriction similar to that around Fe(CN) 2 -. Thus, as ion-pairing increases with concentration, the apparent volume rises more sharply than the theoretical slope because of the decrease in electrostriction. At high concentrations the first stage of ion-association is nearly complete, and the slope approaches that for a 3 : 1 electrolyte. One of us (L. G. H.) is indebted to the U.S. National Science Foundation for a Visiting Fellowship during the tenure of which this work was done. We also thank Miss B. J. Levien for check analyses and densities of the N(CH3)4Br solutions, and h4r. L. A. Dunn for the preparation and analysis of the sodium hydroxide solution. 1 Hamann, Physico-Chemical Eflects of Pressure (Butterworths, London, 1957). 2 Stokes and Robinson, Trans. Fizraday Soc., 1957,53, 301. 3 Lamb and Lee, J. Amer. Chem. SOC., 1913, 35, 1666. 4 Gdcken and Price, 2. physik. Chem. 426,1934, 81. 5 Kruis, 2. physik. Chem. B., 1936, 34, 1. 6 Wirth, Eundstrom and Johnson, J. Physic. Chem., 1963, 67,2339. 7 Bodansky and Kaumann, J. Physic. Chem., 1962,66,177. 8 Marsh and Stokes, Austral. J. Chm., 1964,17, 740. 9 Stokes, J. Physic. Chem., 1961, 65, 1242. 10 Jones and Stariffer, J. Anzer. Chem. SOC., 1936, 58, 2558. 11 Rediich, J. Physic. Chem., 1963,67,496. 12 Fajam and Johnson, J. Amer. Chem. Sm., 1942,64, 668. 13 Mukerjee, J. Physic. Chem., 1961, 65, 740. 14 Stokes and Robinson, Trans. Farday Sac., 1957, 53, 301. 15 Couture and Laidler, Can. J. Chem., 1956, 34, 1209. 16 Eucken, 2. Elektrochem., 1948,51, 6. 17 Owen and Brinkley, Cltem. Rea, 1929, 29, 461. 18 Hai-nd and Owen, The Physical Chemistry ofElectrolytic Solutions, (Reinhold, N.Y.), 3rd edn., 19 Akerlof and Teare, J. Amer. Chem. Soc., 1938, 60, 1226, 20 Wyckoff, Crystal Structures (Interscience, New York), voi. I, table 111-9 and fig. 111, 6a, 6b. 21 Chang and Westrurn, J. Chem. Physics, 1962, 36,2420. 22 Coulter, Piizer and Latimer, J, Am-. Chem. Sw., 1940,62,2845. 23 Hiickel and Schaaf, 2. physik. Ckem., 1959,21, 326. 24Hepler, J. Physic. Chem., 1957, 61, 1426. 25 Interatomic Distances. Spec. publ. no. 11, (The Chemical Society, London, 1958). 26 James, Trans. Fiiraday SOC., 1949,45, 855. 1958, p . 361.

ISSN:0014-7672    

DOI:10.1039/TF9656100020

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Thermodynamic Treatment of Binary Compound Freezing Point Curves Formula Determination of Non-Electrolyte Clathrate Hydrates BY D. N. GLEW Exploratory Research Laboratory, Dow Chemical of Canada, Limited, Sarnia, Ontario, Canada Received 9th April 1964 A general treatment of the thermodynamics of solid binary compound formation from real solu- tions is given.Simple equilibrium equations are developed which quantitatively represent and reproduce binary compound freezing point measurements within limits of experimental error. A new numerical method of analysis of binary compound freezing point measurements permits quantitative evaluation of the compound formula and its confidence limits. Application to the published freezing point measurements of aqueous trimethylamine and diethylamine solutions has shown the existence of the following non-electrolyte clathrate hydrates : (CH3)3N. 10H20, (C2Hs)zNH. 6.6iH2O and (C2H5)2m. 8 .10H20. The probable structures of these hydrates are discussed in relation to the known gas hydrate and clathrate hydrate structures.The water structures of the gas hydrate clathrates 1-3 and of the structurally rclated tri-alkyl sulphonium and tetra-alkyl ammonium salt clathrate hydrates, 4-6 considered together strongly indicate that non-electrolyte hydrates containing more than six water molecules per non-electrolyte molecule will also be of the clathrate type with water lattices similar to the gas hydrates. It was therefore of interest to character- ize a group of aliphatic amine hydrates with high water contents for which extensive freezing point measurements were available.738 In order to obtain the hydrate stoichio- metries as reliably as possible only those freezing curves furnishmg congruent points were examined since these would be free from ambiguities in phase interpretation. The problem was to determine from aqueous freezing point curves the values of n for the hydrate formula M .nHzO, in which M is a non-electrolyte hydrate former and n takes large and not necessarily simple integral values. For these hydrates, furnish- ing skew freezing curves, the usual technique of inspection to locate the maxima leads to uncertainties of unknown magnitude for the congruent liquid compositions and to undefined errors in n. Thus, general quantitative methods are needed for fitting continuous branches of binary compound freezing point curves and to determine the compound formula and its crystallization thermodynamic functions, where the accuracy of the freezing measurements is properly transmitted to define the confidence limits of these derived functions. BINARY COMPOUND FREEZING POINT EQUILIBRIUM A similar problem of providing thermodynamic equations for the freezing curves of compounds of optical antipodes from ideal binary solutions has been treated else- where.99 10 However, we derive from first principles the general equilibrium equations for hydrate crystallization from aqueous solution, simultaneously introducing the system variables and the crystallization thermodynamic functions.30D. N. GLEW 31 Consider an equilibrium system at unit pressure at absolute temperature T con- sisting of components M and H20 and inert diluents. A gas phase and a solid hydrate phase of formula M . nH20 with chemical potential pi; coexist with a single liquid phase in which H20 and M have the respective chemical potentials p! = pyl+ RTIn xl y l and pi = pi1 +RT In x2y2, x1 and x2 being the independently variable mole fractions and y1 and y2 the activity coefficients.Under these equilibrium condi- tions the Gibbs free energy change for freezing solid M . nH20 from the liquid phase is AG(Z+s) = pyi -pi - np: = 0, so that the expression AG"(l-+s) = p;: -pi'-np:' = AH"(I4s)- TAS"(l+s) (2) defines the standard thermodynamic functions for solid hydrate formation from the pure separate liquids at T i n terms of the equilibrium liquid H20 and M solution activities xlyl and x2y2. Alternately eqn. (2) may be considered as defining the functional dependence of the freezing temperature I' on the H20 and M solution activities in terms of the constants, AH"(Z-+s) the crystallization standard enthalpy change, AS"(Z+s) the standard entropy change and iz the hydrate formula number. Here AH"(l-+s) and AS"(Z+s) are assumed to be temperature invariant ; over long temperature ranges it may be necessary to include in eqn.(2) further term in the crystallization standard heat capacity change AC'(Z+s). = RT In x2y2 + nRT 111 x,y, DETERMINATION OF COMPOUND FORMULA A N D THERMODYNAMIC FUNCTIONS The general solution of eqn. (2) for the three unknown constants n, AH"(Z+s) and A\S"(Z-+s) requires a minimum of three independent freezing point determinations and the corresponding three pairs of solution activity coefficients. When more freezing points and activity coefficients are available, the three constants and their limits of error can be determined by substituting the data into eqn.(2) and applying the method of least squares to the resulting set of simultaneous equations. The hydrates of structural interest freeze from binary solutions for which neither the water nor the hydrate former activity coefficients are known, so that other methods must be used to determine n. Here x1 +x2 = 1 and eqn. (2) yields the relationship AH"(l-+s)- TAS"(Z+s) = R T In (1-x,)y2+ nRT In xlyl, ( 3 ) in which Tis uniquely defmed by the single variable x1. Consider a series of freezing determinations ordered in mole fraction, for which freezing temperature Tj corresponds to a solution water activity x l j y l j and to a com- ponent M activity (1 - xlj)y2,, while the adjacent freezing temperature T k correspoiids to water and M activities xlkylk and (1 -x,k)y2k and so on.In order to solvc for n, the adjacent pairs of freezing determinations such as Ti and T k , T k and TZ are taken in eqn. (3) to give a series of difference equations of the type Ajk In (€ -xl) - Ajk In x1 A H o ( l + s ) - P In y2+nAjk In y1 AjkllT AjJT + R A j k l / T - -n- containing only two unknown constants and in which Ajkln (1 -XI) = In (1 - x l j / 1 - X I E ) , Ajic: In 72 = In Ajkl/T = l/q- l/Tk, and so on. Provided that x1 is near the congruent composition, the Gibbs-Duhem condition for binary solution d In 7 2 + [xl/(l -XI)] d In y1 = 0 makes the activity coefficient difference within the32 BINARY COMPOUND FREEZING POINT CURVES square bracket of eqn. (4) small, so that n can be evaluated ignoring the activity coefficients.The series of difference equations in T and XI, taken over all adjacent pairs, are treated by the method of least squares to determine n and its standard error. Only adjacent determinations are considered to minimize the effect of neglect of the activity coefficients, while the application of eqn. (4) automatically gives greater weight in the definition of n to those measurements nearer to the congruent composi- tion, as is both experimentally and theoretically desirable. When the hydrate stoichiometry has been established, n is substituted into eqn. (3) rearranged in the form ( 5 ) AH"(E+s) 1 AS"(l-+s) - - ~ In (1 - - x I j ) + n I n xIj+[In yZj+n In ylj] = R Tj R Y from which AH"(Z-+s) and AS"(Z+s) are determined by the method of least squares from the variation of the left-hand side with respect to 1/T taken over all j freezing- point determinations.Here with no activity coefficients eqn. (5) is used in the reduced form as a correlating equation log (1 -xlj)+n log x,j = A/Tj+B, (6) in which A and B are empirical constants defining the T-xl locus of the hydrate freezing point curves. APPLICATION TO TRIMETHYLAMINE A N D DIETHYLAMINE HYDRATES A search for aqueous freezing-point measurements indicating hydrates with pos- sible relationship to the clathrate hydrates 1-6 revealed a paucity of significant modern data. A study is presented here using the extensive and reliable older works of Piclcering 7 and of Somerville 8 on the aqueous systems of trimethylamine and of diethylamine which freeze congruently to form hydrates containing between 6 and 10 water molecules per amine molecule.Results for the numerical analysis of these hydrate freezing point measurements are presented in table 1. The first two columns show the hydrate-former species and the hydrate water: hydrate-former molecular ratio ncalc. with its 95 % confidence interval, obtained from statistical analysis of the simultaneous difference eqn. (4). TABLE 1 data "talc. - A B ?C) source n hydrate former 10.22 +0*34 f0.37 P3 (CH313N (CH313N (CH313N 10.03 f0.12 10.0. 2314 6.8313 &0.01 s5 (C2H5)2NH 6.80 f0.39 6-66 2519 8.1595 f0-15 P5 9-91 f0.38 ::::} 2314 6'8526 { ~ 0 . 4 0 s1 !:;:} 2780 9.0870 {$:A: S P3 (CZH512NH 8.12f0.45 (C2H5)2NH 8*10f0*12 The third column contains the probably correct value for n, assessed from ncaic.and the probable relationship of the hydrate with the clathrate hydrate structures. 1-6 The fourth and fifth columns record the best values of A and B to be used with n to calculate the hydrate freezing curve with eqn. (6), while in the sixth column st is the standard deviation of a single freezing temperature determination about that freezing curve. The final reference column indicates the source of the experimental data analyzed ; for trimethylamine, e.g., P3 refers to Pickering's 7 series 3 experiments and S1 and S5 are Somerville's 8 run 1 and run 5 experiments.D. N. GLEW 33 TRIMETHYLAMINE HYDRATE (CH3)3N. 10H20 The analysis contained in the first two rows of table 1 for trimethylamine hydrate is illustrated in fig. 1-3. Fig. 1 shows the use of eqn.(4) neglecting the activity co- efficients to determine ncalc. as the negative gradient of the variation of Ajk log (1 - XI)/ Ajkl/T with Ajk log xl/Ajkl/T. The points in the upper left quadrant of fig. 1 derive from the amine-rich branch of the freezing curve, in the lower right quadrant from the water-rich branch. Those points farthest from the origin in both quadrants derive from solutions with concentrations nearest to the congruent composition. I I I I - 1 0 1 2 Ajk log XllAjkl/TX 10-3, OK FIG. 1 .-Trimethylamhe hydrate formula determination. 9, Pickering, series 3 ; 0, Somerville, run 1 . That the amine-rich points and the water-rich points are both accurately colinear with the best straight line representing all points indicates sensible cancellation of the square bracketed activity coefficient differences in eqn.(4), even for the extreme amine- and water-rich regions. Fig. 2 shows the straight line defined by eqn. (6) with the values of n, A and B given in table 1. The high concentration of points at the upper left of the line arises from freezing measurements nearly uniformly spaced in XI on each side of the congru- ent composition where dT/dxl is small : this weights eqn. (6) to give a better fit with small errors near to the congruent point with increasing and larger errors at composi- tions farther removed from that point. In the vicinity of the congruent point the P3 and S 1 measurements have standard errors on single freezing temperature determina- tions of +O-20 and +0.19"C respectively, whereas over the range of the whole freezing 234 BINARY COMPOUND FREEZING POINT CURVES I / T X 105, I/OK FIG.2.-Trimethylamine hydrate (CH3)3N. lOH20 plot of eqn. (6). 0, Pickering, series 3 ; 0, Somervillc, run 1 . 0 10 20 30 mole % trimethylamine FIG. 3.-Trimethylamine hydrate (CH3)3N . 10H20 freezing point curve. a, Pickering, series 3 ; 0, Somerville, run 1.D . N. CLEW 35 curve these errors are increased to k0.37 and &O.4O0C as shown in table 1. The absence of two separate branches in fig. 2 for freezing measurements in the amine- rich and water-rich solutions at lower temperatures indicates solution activity co- efficients not greatly different from unity. Fig. 3 provides a direct comparison of the calculated freezing curve according to eqn. (6) and the freezing point measurements from wbich the curve was derived.It has been suggested 11 that the crystal structure of (CH3)3N. 10H20 is that of the missing orthorhombic gas hydrate of formula M . 10H20 predicted by Jeffrey,4 which hydrate has a water lattice structurally similar to that of the tetra-iso-amyl ammonium fluoride hydrate. In the gas hydrate, the unit cell 4 containing 80 water molecules would be stabilized by eight triinethylamine molecules occupying the four tetrakiadecahedral and the four pentakiadecahedral sites. DIETHYLAMINE HYDRATES (C2Hs)NH. (6.6iH20) AND (C2H&NH. (8.10&0) The freezing determinations for aqueous solutions containing 6-30 mole % diethylamine are illustrated in fig. 4, together with their two representative curves \ x\ I I I I I 10 20 30 mole % diethylamine FIG.4.-Diethylaniine hydrates (C2H5)T\iH. (6,66H2O) and (C2Hs)lNH . (8 . 10HzQ) freezing point curves. i: , Pickering, series 5 ; 8, Pickering, series 3 ; 0, Somerville. calculated from eqn. (6). The standard errors 0x1 single frzezing temperature deter- minations of +0-15, k0.12 and +0*08"C for the P5, P3 and S measurements respec- tively provide a realistic measure of the accuracy. The upper dashed curve for the hydrate stable in the presence of solutions with more than 10 mole % diethylamine has been calculated from the sixteen P5 data in the region where no confusion can arise between the two curves. The left-hand extrapolated branch of the dashed curve passes with zero error through the single datum of Somerville at 6.53 mole%36 BINARY COMPOUND FREEZING POINT CURVES which deviates from the full line curve by 4.6 standard errors.The full line curve has been calculated for the P3 and S measurements taken together as a single set, after analyzing each separately for ncalc. using eqn. (4). The lower melting meta- stable hydrate was successfully seeded far into the concentration domain of the stable hydrate. It has been suggested 11 that the stable diethylamine hydrate characterized as (CzH&NH. 6 . 80H20 is structurally similar to the tri-n-butyl sulphonium fluoride hydrate 5 (n-C4H9)3SF. 20H20, in which one tri-n-butyl sulphonium fluoride unit is replaced by three diethylamine molecules of equivalent volume : this would lead to a diethylamine hydrate formula of (C2Hs)zNH.(6.6kH2O) in which the water lattice is structurally related to that of the M . 7 . 6kH20 family of gas hydrates.192 Formerly, the lower melting diethylamine hydrate (C2H&NH. (8 . 10H20) was taken to indicate a possible new group of clathrate octahydrates.lll 12 Recently Jeffrey 13 has suggested that this diethylamine hydrate may be structurally related to the tetragonal group of clathrate hydrates 6 and to the tetragonal bromine hydrate Br2 . 8 . 60H20.3 This appears probable since the required unit cell formula for the diethylamine hydrate, 20(C2H&NH. 162H20, is almost identical with that for the tetra-n-butyl ammonium fluoride hydrate,6 5(n-C4H9)4NF . 1 64H20, where 20 diethylamine molecules in the larger cavities replace five tetra-n-butyl ammonium fluoride units of equivalent volume and where the two water lattices are the same, apart from those two additional water molecules 6 in the ammonium salt hydrate lattice arising from charge distortions. 1 Pauling and Marsh, Proc. Nut. Acad. Sci., 1952, 38, 112. 2 von Stackelberg and Miiller, 2. Elektrochem., 1954, 58, 25. 3 Allen and Jeffrey, J. Chem. Physics, 1963, 38, 2304. 4 Feil and Jeffrey, J. Chem. Physics, 1961, 36, 1863. 5 Jeffrey and McMullan, J. Chem. Physics, 1962, 37, 223 1. 6 McMullan, Bonamico and Jeffrey, J. Chem. Physics, 1963, 39, 3295. 5 Pickering, Trans. Chem. Soc., 1893, 63, I, 141. 8 Somerville, J. Physic. Chem., 1931, 35, 2412. 9 Prigogine and Defay, Chemical Thermodynamics, trans. Everett (Longmans, Green, London, 10 Mauser, Ber., 1957, 90, 307. 11 Glew, Nature, 1964, 201, 922. 12 Glew, Int. Union Pure and Appl. Chem., Symp. Thermodynamics and Thermochemistry, 13 Jeffrey, private communication. 1954), p. 374. Lund, 1963, 4, 1.

ISSN:0014-7672    

DOI:10.1039/TF9656100030

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No.13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Thermoelectric Powers and Entropies of the Hydrogen Ion BY W.BRECK, G. CADENHEAD AND M. HAMMERLI Dept. of Chemistry, Queen’s University, Kingston, Ontario, Canada Received 7th February, 1964 Initial and final (steady-state) thermoelectric powers have been determined for the strong acids HCl, H2S04, HClO4 and HNO3 at a series of concentrations by the use of quinhydrone electrodes at a mean temperature of 25°C. From these values have been determined entropies of transport and transported entropies as well as their concentration dependence. By extrapolation the standard transported entropy of the hydrogen ion has been determined as 5-1 cal/mole deg. Support for the results has been found in other data. Owing to the scarcity of adequate electrode systems and to other experimental difficulties, few measurements of thermal diffusion potentials have been made in electrolytic thermocells throughout the development and attainment of the Soret steady state. The present purpose is to report the results of such measurements in solutions of the common strong acids by the use of quinhydrone electrodes.Values of the initial thermoelectric powers have been reported in a previous paper.1 Small differences were found in these values for different strong acids at comparable concentrations, a result which was attributed to the predominance of the properties of the hydrogen ion over those of the various anions. The con- centration dependence of the initial thermoelectric powers is mainly in agreement with theoretical relations included in those given below.THEORETICAL RELATIONS Agar’s 2 treatment of thermal diffusion is employed because it provides for the inclusion of non-electrolytes in the relations. He writes a general expression for an electrode reaction in the form where 3, are stoichiometric coefficients required for a one electron change, A, are the various ionic and molecular species in solution, and Ap substances which may exist in other phases (usually metal in the electrodes). For substances present which do not take part in the electrode reaction the R are taken as zero. The general expression for the e.m.f. of a thermocell consisting of two such electrodes is given by n FdE = FdE, + c(jZj - mj)(Dpj + S;dTj. (2) 0 Here I; is the faraday, E is the e.m.f. in the general case, Em the e.m.f.at the Soret steady state; mj is the Washburn number which for the ions present is taken as tJzj and for neutral species as zero; D is an operator which signifies a change in chemical potential p owing to change in composition at constant temperature ; and S: is the entropy of transport of the species j . At the Soret steady state, n - - FdE, = -(zAjSj+zArSr+ S,)dT, 0 r (3) 3738 ENTROPIES OF THE HYDROGEN ION where 3 is the transported entropy of the particular species, being the sum of the partial molar entropy and the entropy of transport of the species, i.e., - si = sj+s; for ionic and molecular species in solution and (4) for the electrons condition, before - - se = se+s*, ( 5 ) in the metallic leads which are not isothermal. any changes in composition have occurred, Dpj = 0, and For the initial n FdEo = FdE, +C(Aj-oj)S;dT.( 6 ) 0 The corresponding thermoelectric powers, E, = dE,/dT, and E~ = dE,/dT, are given respectively by n 0 F E ~ = F & ~ + C ( ~ ~ - ~ ~ ) S ; . For a thermocell employing quinhydrone electrodes in an electrolyte of, say, HCl, the electrode reaction is where +Q-+H2Q+H++e = 0, (9) 1Q = 3, AH2Q = -+, AH+ = 1, -&J- = 0, Cnrsr = 0. r Substituting these values, along with into eqn. (7) and (8) there is obtained O H + = tH+/ZH+, WCl- = fCl-/ZCl-, CC)Q = mHzQ = 0, fH+ = l-tCI-9 - - - - A - _ - F E , = - i ( S Q - S H z Q ) - S H + - S e , (10) and the difference, F(&g--E,) = ~ ( S ~ - ~ ~ , Q ) + fcl-S&l. (12) The concentration dependence of the transported entropy of an ionic species, sf = Si+S: is determined partly by that of the partial molar entropy and partly by that of the entropy of transport.These can be written respectively as Si = Sp-R In rni+Si, (13) s; = s;o+s,*', (14) where S; is the standard value of the partial molar entropy and S;*" the entropy of transport at infinite dilution; S/ and S:' are comprehensive, non-ideal terms which should vanish on extrapolation to infinite dilution. Combining (13) and (14) and putting sf = S;+ST', - - - = g - R I n mi+$. (15)W. BRECK, G. CADENHEAD A N D M . HAMMERLI 39 Eqn. (10) and (11) can iiow be rewritten: - - - - - - - - F&,--R 111 mH+ = -~(~Q-sHz~)-s=-s~+-s~+, (16) - - - FcO-R In mH+ = -3(SQ-S~2p)-Se-S;;+-S;i+ +tcl-(S:&+S&), (17) with their difference as in eqn.(12). The concentration dependence terms for Q and HzQ are not shown as it is presumed that their concentrations are constant (saturated at a definite temperature) in the various concentrations of acid. On extrapolation to infinite dilution of acid, eqn. (16), (17) and (12) become : - - - - - - - - EE: = -+(SQ-SH2Q)-Se-Si+, (1 8) F'E; = -3(SQ-SH,Q)-Se-Si+ + t&-Si&, (19) (20) - - - - F(&: - &:) = $(s: - S:2~) -k tEp- s,*,.,. && and E ~ O are the standard thermoelectric powers whose evaluation is indicated above by plotting Fgm - R In m H + and FEO- R In mH+ respectively against some suitable function of mH+, say, ~ G H + , or ,/&~+/(1+,/&+) ; the quantity s", is small and its evaluation has been described by Agar 3 and Tyrrell4; the term $(SQ-SH,Q) can be obtained from the temperature coefficient of e.m.f. of the appropriate isothermal cell as given in the results of this paper; the value of S& has been reported by Agar 3 from Soret measurements by a conductance method ; and t&- is at hand from ionic conductance data at infinite dilution.With this knowledge, one pro- cedure would concern solving eqn. (19) for s&+ ; the advantage in doing so is that this value is independent of any thermal diffusion of Q and H2Q which does not appear in eqn. (19). The qu_antity +(S;--S&) can then be found from eqn. (20) or eqn. (18), as can ~ ( ~ Q - S H ~ Q ) . It is expected that *(S;-S&) is small. In most cases (but not for H+) the transported entropy consists mainly of the partial molar entropy and the contribution by the entropy of transport is relatively minor. This is presumably the case for Q and HzQ where furthermore, these molecules are much alike as judged by molecular weights, structures, third-law entropies 5 (respect- ively 38.9 and 33.5 cal/mole deg.) and the term involves only half the difference.Returning to eqn. (10) and (11), once +(S6-SGla) and ~ ( S Q - ~ H ~ Q ) are known these can be solved for &I+ and S& (or S* for the other acids as appropriate) at the various finite concentrations. Finally, the equation which expresses the e.m.f. of the thermocell as a function of time, Et, for the thermal diffusion of a single substance has been given as 6 E , - E , = (Eo-E,)(8/n2) (l]n2) exp (-n2t/O), (21) 0 = h2/n2D. (22) n= 1,3,5.. .where 8 is a characteristic time, sometimes defined as In this relation h is the length of the diffusion path (or usually the height of the cell) and D an effective diffusion coefficient applicable at the mean temperature and concentration to the particular diffusing substance. Except at very short times, only the first term of the series in (21) need be considered, so that E , - E , = (Eo-E,)(8/n2) exp (-t/8), (t>8/3); (23) (24) log (E, - E,) = log ( E , - E,) + log ( 8 1 ~ 2 ) - tp.3038.40 ENTROPIES OF THE HYDROGEN ION EXPERIMENTAL THE CELL The thermocell (fig. 1) consisted of a polystyrene ring 1 cm thick cemented between two matched, fine gold, electrode discs. Each electrode was provided with a radial hole for the ion of the hot junction of a calibrated, copper-constantan thermocouple ; the two cold - I crn K thermocell FIG.1 .-A, electrodes ; B, polystyrene ring ; C , axle ; D, paddle ; E, axle retainer ; F, teflon bushings; G, grease seal; H, thermocouple holes; I, filling hole; J, propeller ; K, brass screws. junctions were kept at the same temperature by insertion in thin glass tubes into a small mercury bath in a vacuum flask containing crushed ice and water. A small screw on each electrode served as an electrical contact for applying the e m f . of the cell to a Tinsley potentiometer. The polystyrene ring was fitted with a mechanical stirrer consisting of a plati- num axle on which was mounted an impeller of fibre-glass screen and a plexiglass propeller to drive it with air. A teflon bushing was used to allow rotation of the axle without leaking, but this was backed up by a seal of silicone grease in a recess on the outside of the ring.A filling hole to accommodate a syringe needle was drilled through the ring and bevelled on the inside to permit the escape of the last bubble of air on filling. The flat cell design helped to minimize con- vection and at the same time keep the duration of the experiment within reasonable bounds (about 9 h). Additional stability to convection was achieved by applying the temperature gradient vertically to the cell with the upper electrode hot so that the densest solution was at the bottom. Stability to convection was also aided during an experiment by the migration of solute to the cold end of the cell. TEMPERATURE CONTROL A similar apparatus for controlling the tem- perature difference between the electrodes has been described previously.7 Its main features were as follows.The lower, cold electrode was in thermal contact with a large block of aluminium which served as a thermal anchor; its temperature was controlled by a system consisting of a thermistor, Sargent Thermonitor, and infra-red lamp as heater. The aluminium block was cooled by water circulating at constant head. The temperature of the upper, hot electrode was kept at a fixed interval of about 10°C above that of the lower by a system of two thermistors connected to complemen- tary arms of another Thermonitor bridge with a second infra-red lamp as heater. The resistance settings of the third and fourth arms of the bridge determined the temperature difference applied to the cell.The aim was thus to achieve a reliably fixed temperature with accurate temperature diference centred at 25°C rather than two accurately fixed tempera- tures, and to achieve this without incurring disturbing electrical contact with the cell. ConsiderabIe improvement in temperature control was gained by thermostatting the cooling water before it entered the aluminium block and by the introduction of two 250-W constant-voltage transformers between the a.c. mains and the input to the two Sargent Themonitors. With the above improvements the upper heater operated on a cycle of aboutW. BRECK, G . CADENHEAD AND M. HAMMERLI 41 0.3 sec with continuous proportional heating and a constancy of temperature difference within 0.01"C or better, being beyond the sensitivity of the thermocouple measurements.The lower temperature (and also the mean) was constant to within 0.05"C over a period of hours. By running ice-cold water through the coils in the thermostat ahead of the alumi- nium block the apparatus could be operated through the summer. PROCEDURE All solutions were made up using distilled, deionized water. Quinhydrone was added in quantity such that the solutions were saturated at a temperature below the working temperature. Oxygen was then removed from the solutions by suction and sweeping out with nitrogen gas which had previously passed through a scrubber containing chromous chloride solution. The cell was finally filled with the appropriate solution by means of a syringe after several rinsings with the same solution.Care was taken to eliminate any bubbles since these had been found to ruin the experiment. The cell was usually left over- night to equilibrate and its e.m.f. measured after at least 6 h in an isothermal condition. Isothermal e.m.f.'s exceeding 50 pV were not tolerated ; in such a case the cell was refilled. The cell was placed in position and the temperature control system, which required a warm-up period of 2 h, set in operation. A small jet of air was used to spin the impeller alternately in each direction to destroy concentration gradients existing in the solution. By this procedure it was hoped to simulate the instantaneous establishment of a temperature gradient in a solution homogeneous as to concentration.The stirring was stopped after 10 sec and this point in time was taken as zero for the run. At appropriate time intervals the e.m.f. of the cell and the temperature difference between electrodes were measured until the value of the e.m.f. became virtually constant. At the end of each run the cell was allowed to return to an isothermal condition, and the isothermal e.m.f. checked. RESULTS The values Et of the e.m.f. measured with time at a mean temperature of 25°C are shown in fig. 2 for 0.10 m HC104 as an example. The value Em at the steady state can be readily estimated. The evaluation of the e.m.f. EO at the initial condition is more difficult and as in previous work 6 was determined by a plot of log (Et-Em) against time according to eqn. (24) and shown in fig.3 for the same solution of HC104. The lack of linearity at very early times has been observed before in studies of both thermal and isothermal diffusion; it arises from neglect of higher terms in the thermal diffusion eqn. (21) and possibly from adjustment of temperature distribution. The time dependence of the e.m.f. is more complex than indicated above since, in general, the thermal diffusion of Q and HzQ is involved as well as that of the acid so that the equation should have the form, E, - E , = A exp (- t&) + B exp (- t/OJ + C exp (- t/O,). However, the thermal diffusion of Q and HzQ vanishes at the initial state ; further- more, the thermal diffusion of the acid should be more rapid and hence pre- dominate in the early stages. For these reasons the above extrapolation for Eo is justified and confirmation of this conclusion is afforded by comparing such Eo values (per degree) with those of other work, obtained from measurements in a " static " cell 1 9 8 wherein no appreciable thermal diffusion occurs in the time of the experiment.Values of EO and Em are converted into the respective thermoelectric powers, EO and by dividing by the appropriate temperature difference. These latter are plotted against the logarithm of molality in H f in fig. 4 for the various strong acids in accordance with eqn. (16) and (17). A straight line has been drawn on the plot42 ENTROPIES OF THE HYDROGEN ION at the theoretical slope of 2.303 R/F indicating that the concentration dependence of both EO and E, is, in the main, that predicted by the theoretical expressions for 5- 6- t in min FIG.2.-Time plot (0.10 m HClO4). t in min FIG. 3.-Log plot (0.10 m HC104). all acids studied. In order to obtain objective extrapolations on the basis of this common trend it was decided to fit lines of type y = a+bx+ cx2 to the above data by the method of least squares. These results are entered in table 1 includingW. BRECK, G. CADENHEAD AND M. HAMMERLI 43 standard deviations Q which are notably small in relation to EO and E, individually but not to the difference EO-E,. For the purpose of examining the non-ideal behaviour more critically, values of FEO- R In ?nH+ and FE, - R In mH+ have been calculated, included in table 1 and plotted against the function &&+/(l+ &a+) in fig. 5a.As expected from eqn. (18) the trend of the curves for the final values of the various acids is to con- verge at infinite dilution on a common value of FE& taken as -6.50 cal/mole deg. - 500- I a Q 400- C .- 8 w" I .;. 300- 2GO- 100- 700 J I 6 00 A 0 B A , I I / / ,/' 0 I I I I I 0.0 - 0.5 -1.0 - 1.5 - 2 . 0 h 3 0 mH+ 0, HCI ; A , H ~ S O ~ ; m, H C ~ O ~ ; EI, HNO~ FIG. 4.-Plot of &&, against log m~ + . On the other hand, the curves for the initial values seek no such common value of FE; since according to eqn. (19) they differ because of the term in t 0 S * O . The value of FE; for HCl is taken as -4.50 cal/mole deg. The temperature coefficient of e.m.f. of the cell at 25"C, H2 I H+ I Q . H2Q, has been measured by Harned and Wright 9 as -736.06 pV/deg. which corresponds to an entropy change of - 33.96 cal/mole deg.for the cell reaction, H2 + Q = H2Q. Taking Sg2 at 25"C, 1 atm as 31-2110, +(SQ-&,Q) is t(33.96-31-21) or 1.38 ca!/mole deg. 3, has been given 3 as -0-045 cal/mole deg. and S s 1 10.89 cal/mole deg. (from Agar's value 3 of QZc, 3245 cal/mole) ; f&- is calculated from ionic conductances at infinite dilution as 0.179. The above values can now be inserted and eqn. (19) solved to obtain &+ = 5.12 cal/mole deg. The use of this value along with FEZ = -6.50 cal/mole deg. allows the solution of either eqn. (20) or (18) for t(S6 - S;,,), yielding 0-05 cal/mole deg. and ~ ( S Q - &,Q) = 1.43 cal/mole deg.acid HCl HC104 HNO3 H2S04 *H+ 1-00 0.50 0.10 0.05 0.0 1 1-00 0-50 0.10 0.05 0.01 1-00 0.50 0.10 0.05 0.01 1.00 0-50 0.10 0.05 0.01 ---EO*Q bV/des.) 244f3 311 f 3 452 1 3 508 f 3 625 f 3 241 f 4 308 f 4 457 f 4 517 f 4 649 1 4 254 f 5 318 f 5 457 f5 512 f 5 632 f5 308 f 2 364 f:! 492 f 2 546 &2 669 f 2 TABLE 1 .-THERMOELECTRIC PROPERTIES AT 25°C -Em f a Wldeg.) 358 f 4 412 f 4 535 f 4 587 f 4 704 f 4 330 f 3 406 f 3 559 f 3 614 f 3 718 f 3 375 f 3 432 f 3 551 f 3 598 f 3 696 f 3 411 f 3 471 f 3 596 f 3 643 f 3 734 zt3 (pV/deg.) 114 102 83 79 79 89 98 102 97 69 122 114 95 86 64 102 107 104 97 65 5-63 5.79 5-86 5.77 5.27 5.56 5.73 5-97 5.98 5.82 5-86 5.96 5.97 5.86 5-43 7.1 1 7-02 6.78 6-65 6.28 8-26 8.12 7-77 7.59 7-09 7.61 7.99 8.33 8.21 7.41 8.65 8-59 8-14 7.85 6.91 9.4 8 9.49 9.18 8-88 7.78 0.1 59 0.1 62 0.1 686 0.1708 0.1 749 0.142 0-145 0.151 0-152 0.1 56 0.134 0.142 0-156 0.160 0.165 0.192 0.1 85 0.181 0.181 0.185 ref.13 13 13 13 13 calc. calc. calc. calc. calc. calc. calc. 15 15 15 14 14 14 14 14 S* s,+ cal/mole deg. cal/mole deg. 16.1 14.2 11.0 10.3 10.1 14.1 15.2 15.2 14.4 9.9 20.6 18.2 13.7 12-1 8.7 12.0 13.1 13.0 12.1 7.8 6.9 8-1 11.0 12.2 14.9 6.2 8.0 11.5 12.8 15-2 7.3 8.6 11.3 12.4 14.7 8.1 9.5 12.4 13.5 15.6W. BRECK, G. CADENHEAD A N D M. HAMMERLI 45 In fig. 5b are plotted. on the same scale as in fig. 5a the data of various workers for the electrolyte HCl with silver chloride electrodes, as presented by Agar 11 but converted to FQ+R In mcl- in cal/mole deg. The E ~ O value extrapolated by Tyrrell -8 -7 - I 1 X X I SgJ Ea - x /-- - 4 I I I I 0.1 0!2 0.3 0.4 0 . 5 0 .6 dGl-/U + l / G l - ) FIG. 5.--(a) A plot of the quantities FQ-R In nqq+ and Fco0 --R In m ~ + in entropy units against the function d G ~ + / ( l + l / i ~ + ) . (b) A plot of the quantity F~~+RInrncl- in entropy units (a) 0, HCl ; A, H2S04 ; B, HC104 ; El, HN03. (b) x , HCI using Ag/AgCl electrodes ; data from ref. 11. against the function ~ & ~ - / ( l + 2/mc1-) (see ref. 11). and Colledge 12 gives F E O = -3.34 cal/mole deg. The equation corresponding to (19) for this system is Taking S& = 10.21,10 SLc, = 22.97 cal/mole deg. ; t&+ = 0.821 ; and se,S& as above, $,- = 18.41 cal/mole deg. By inspection of eqn. (17) it is to be expected that the slopes of the curves for the initial values in fig. 5a and 5b would differ in sense for cation- and anion-reversible electrodes.The entropies of transport per equivalent, S*, for the various electrolytes have been calculated from the known quantities in equations corresponding to (12). The results are entered in table 1 along with values of the transport numbers t2 of the amom used.13 15 Where experimental data were not available (e.g., HC10446 ENTROPIES OF THE HYDROGEN ION at all m and HN03 at 1.00 and 0.50 m) the transport numbers were calculated by an equation given by Robinson and Stokes.13 The quantity +(S6 - S;,Q> is taken as 0.05 cal/mole deg. and the values of E O - E , from table 1. The transported entropies sH+ for the acids at finite concentrations can be cal- culated from eqn. (10) by inserting appropriate values of f ' ~ ~ and putting $(SQ - &,Q) = 1.43 ; 3, = -0.05 cal/inole deg. Values obtained are on the right of table 1.The quantities, SH+ + R In mH+, might also be calculated and plotted against a function of mH+ for extrapolation to obtain sfi+ ; however, the plot essentially follows that already given for FE, - R In mH+ in fig. 5a, with the values converging on a common value of sg+ of about 5-1 cal/mole deg. An overall or effective value of the characteristic time 8 can be estimated for each of the various runs from the log plot (e.g., fig. 3) and a corresponding effective diffusion calculated by means of eqn. (22) as shown in table 2. The diffusion co- efficients for HCl (as the sole solute) at 25°C for most of the concentrations 13 are included for comparison. The cell height h is 1.0106 em.TABLE 2.-EFFECTIVE DIFFUSION COEFFICIENTS FOR HC1 RUNS ( C d / S e C ) m in HC1 8 (sec) 105 Defective lOs&ci 1-00 8760 1-18 3.43 0.50 7560 1.37 3.1 8 0.10 4860 2 1 3 3-05 0.05 2940 3.52 3-07 Any such simple treatment is not applicable since the diffusion process is complex, involving the separation of Q and H2Q as well as HCI. Only for the solution 0.05 m is the effective diffusion coefficient of the expected magnitude for the dif- fusion of the HCI alone; at higher concentrations of HCI the process is slower than expected on such a basis. This would be the case if at high concentrations of HCI the separation of Q and H2Q were to an appreciable extent postponed. In any case the value of s&+ derived is independent of any thermal diffusion of Q and H2Q.DISCUSSION TRANSPORTED ENTROPIES $&+ has been evaluated in the results as 5.12 cal/mole deg. This value may be compared with that given by Agar 3 (4~82)~ by Khoroshin and Temkin 8 (5.2) and by Haase, Hoch and Schonert 16 (5.6). Another gauge of the reasonability of the above value is available through the evaluation of 3;;- for comparison with the value of 18.41 cal/rnole deg. derived in the results from the data of Tyrrell and Colledge.12 Latimer 10 gives Sscl as 13.16 cal/mole deg., and since S$& is taken as 10.89, s&-., becomes 24.05 cal/mole deg., and g&-, 18.93 cal/mole deg. Thus the results for HC1 using quinhydrone electrodes are in fair agreement with those obtained from silver chloride electrodes. The non-ideal part of the concentration dependence of S,+ can be best indicated by a plot of &+ + R In mH+, or what is almost equivalent, a plot of I;E,-R In mH+ as in fig.5a. Plots of this type have been employed mainly in the study of initial thermoelectric powers for solutions of salts where the change in transported entropy consists mainly of the partial molar contribution and the entropy of transport is relatively small. The concentration dependence of the transported entropy ac- cordingly follows closely the mass action (Rlnm) dependence of the partial molarW. BRECK, G . CADENHEAD AND M. HAMMERLI 47 entropy. For the acids under study, however, the transported entropies are relatively small and the entropies of transport relatively large; it is not surprising that such plots do not yield horizontal straight lines.Attempts have also been made to predict the non-ideal part of the transported entropy by a Debye-Huckel cal- culation of the terms in the mass action expression involving the single-ion activity coefficient. Since this calculation requires the usual assumption about single-ion activities and applies strictly only to the partial molar contribution and takes no account of the behaviour with concentration of the entropy of transport, its application here was considered ineffective. It has been stated elsewhere that values of E, should be independent of the identity of the gegenion. From the plot in fig. 5a it appears that this is true at infinite dilution but not accurately so at higher concentrations, especially where the entropies of transport are relatively large.ENTROPIES OF TRANSPORT The entropies of transport in table 1 are not particularly precise. A standard deviation in EO-E, of 5 ,uV/deg., for example, corresponds to about 0.7 cal/mole deg. in the entropy of transport. This lack of precision can be attributed, at least in part, to the presence of small, isothermal e.m.f. observed with these electrodes. Such isothermal values were not allowed to exceed 50 pV, but with a difference in temperature between electrodes of 10°C, this could affect the calculation by 5 pV/deg. Nevertheless, the entropy of transport obtained for HCl at 0.01 m is 10.1 cal/mole deg. as compared with the value of Snowdon and Turner 17 of 10*3cal/moledeg. At lower concentrations than studied here the values for HC1 should rise in more predictable fashion as discussed by Agar; 3 at higher concentrations the values rise again and pass through a maximum according to Tanner 18 and Chipman19 at about 1 m which is in accord with this work.Their results are not comparable on an absolute basis. All of the acids appear to exhibit minima at low concentra- tions and maxima at high; this behaviour would appear to be conferred by the hydrogen ion, the common factor. With regard to the values for H2S04, the second dissociation of this acid is incomplete. The e.m.f. method of measuring entropies of transport as used here suffers in precision in depending on a small difference in quantities measured over a large interval of time. To be precise the electrode system must behave reproducibly to within a few pV; the quinhydrone system hardly qualifies.The values cal- culated are also sensitive to the transport numbers used. On the other hand, theoretical quantities are measured directly without translation of empirical data through the behaviour of activity coefficients. All the methods available, how- ever, are more complementary than competitive, the e.m.f. method overlapping the conductance method at low concentrations and optical methods at high con- centrations, as exemplified by CdSQ4,179 209 21 where agreement among all the data is excellent. The concentration range used for the acids here is not dilute enough for extrapolation to infinite dilution; this is better done from conductance data. SINGLE-ION ENTROPIES The transported entropy of a single ion is experimentally determinable on an absolute basis.Entropies of transport and partial molar entropies of single ions, however, can be found absolutely only on the provision of additional information or assumptions.48 ENTROPIES OF THE HYDROGEN ION (a) On the basis that S&+ = -5-5 cal/mole deg. In order to match for cations and anions the correlation between entropies and viscosity B-coefficients, Gurney 22 assigned the value - 5.5 cal/mole deg. to Sfi+ which is close to the value -5.4 of Lee and Tai.23 If Sfi+ is taken as -5-5, and s&+ is experimentally 5.1, then Si: becomes 10.6 cal/mole deg. (b) On the basis that Szf- = 0. The contribution by the chloride ion to the entropy of transport in dilute chloride solutions is judged to be small.According to the above assumption, plus - the information that S& = 10.9 cal/mole deg.,3 S;l;% = 10.9, and since S&+ is 5.1 by experiment, S&+ = -5.8 cal/mole deg. The main difficulty here concerns the extrapolation of S&l to infinite dilution. Khoroshin and Temkin 8 quote 9-7 and de Bethune 24 10.5 cal/mole deg. for SP,, ; using these values SA+ becomes respectively - 4.6, - 5.4 cal/mole deg., representing as good agreement with the result in (a) as there is among the values themselves and indicating that the chloride contribution is small. (c) On the basis that S & - ~ O ~ ~ ~ = 0. The concept of additivity of ionic entropies of transport at 0.01 m has consider- able support (see, e.g., ref. (17)-agreement within 1 % for predicted and measured values).For HCl at 0.01 m, the value of S* determined here is 10.1 cal/mole deg. (compared with Snowdon and Turner's value of 10.3). If S&-co,l is taken as zero, Sz+(.ol) is 10.1 cal/mole deg., and since gH+ = 14.9 (table l), SH+col) becomes 4.8 cal/mole deg. The extrapolation to infinite dilution is now on a better basis since for the concentration dependence of the partial molar entropy of an ion i can be written : and Ss+ = 4.8 -9.15 -0.12 == -4-5 cal/mole deg. (or using Snowdon and Turner's value of S;*IatOl) = 10-3, SH+ = -4.7 cal/mole deg.). The assumption involved in the calculation of the single-ion activity coefficient by the Debye-Huckel limiting law is not serious as the non-ideal term amounts to only 0.12 cal/mole deg. It is possible to check independently the reasonableness of the above result for Sg+ through the CdS 3 4 system which is well documented. Breck and Agar 20 have determined &d2+ by direct measurement of E, at 0.005 m (which corresponds to C1- at 0.01 m for purposes of additivity) as - 8.96 cal/mole deg.and Q* for CdS04 as 2300cal/mole, in agreement with Snowdon and Turner's value (2408 at a slightly higher temperature). On the basis that Q&-Coll = 0, Sagert and Breck 7 give QZoi-c005) as 830 cal/g ion as compared with Agar and Turner's value 25 of 865. At 25°C then, Q&+coo5) is 1470 cal/g ion and S&2+(.005) 4-93 cal/mole deg. It follows that SCd2+(.005) = - 13.89 cal/mole deg., and by use of eqn. (27), S&+ = - 13.89 - 10.53 - 1-02 = -24.44 cal/mole deg. Latimer 10 reports - 14.6 cal/mole deg.as the conventional (Ss+ = 0), standard entropy of Cd2+, which implies that for the reaction at 25"C, Cd2++H2 (g) = Cd (s)+2H+, AS" = -4.3 cal/mole deg. (since S& = 31.21, S& = 12.3 cal/mole deg. and SA+ is conventionally zero). On the present basis, however, with S&-coll = 0, ,y&+ = -24.44, and S&, S& as above, 2S&+ = -4.3-12.3-24.44+31-21 = -9.8, and S;+ = -4-9cal/mole deg., representing good agreement with the results above ( - 4.5, - 4.7) consideringW. BRECK, G. CADENHEAD AND M. HAMMERLI 49 the diverse sources of data (although agreement is independent of values selected for S& and S&, or for S&-). Another approach is available through experimental data for the thallous ion 6 which are not so well substantiated. A calculation similar to that above leads to the same result. Irrespective of the datum used to separate ionic values, the results for hydrogen ion have been shown to be consistent with those from other measurements. The values obtained for hydrogen ion, along with assumptions employed, are summarized in table 3. TABLE 3.-ENTROPIES OF THE HYDROGEN ION IN Cd/mOk deg. at 25°C z;+ si?I+ @+ assumption 5.1 - 5.5 10.6 s;+ = .- 5.5 5.1 - 5.8 10.9 $19- = 0 (S$+ = 10.9) 5-1 - 4 5 9.6 S&-(.Ol, = 0 ( q $ + ( . O l ) = 10.1) We gratefully acknowledge the support of the National Research Council of Canada in this work in the form of grants, and that of the Polymer Corporation of Canada in the form of a Polymer Teaching Fellowship (held by M. Hammerli). 1 Breck, Trans. Faraday SOC., 1963, 59, 729. 2 Agar, Thermal Diffusion in Electrolyte Solutions, chap. 13, appendix, in Hamer (ed.) The 3 Agar, Thermogalvanic Cells, in Advances in Electrochemistry and Electrochemical Engineering, 4 Tyrrell, Diflusion and Heat Flow in Liquids (Butterworths, London, 1961). 5 Prigogine and Defay, Chemical Thermodynamics (Longmans Green, New York, 1954). 6 Agar and Breck, Trans. Faraday Soc., 1957, 53, 167. 7 Sagert and Breck, Trans. Faruduy SOC., 1961, 57, 436. 8 Khoroshin and Temkin, Zhur. Fiz. Khim., 1952,26,500. 9 Harned and Wright, J. Amer. Chem. SOC., 1933, 55,4849. 10 Latimer, Oxidation Potentials (Prentice-Hall, N. J., 2nd ed., 1952). 11 Agar, Rev. Pure Appl. Chem., 1958, 8, 23. 12 Tyrrell and Colledge, Trans. Faraday SOC., 1954, 50, 1056. 13 Robinson and Stokes, Electrolyte Solutions (Butterworths, London, 1955). 14 Hamer, J. Amer. Chem. Soc., 1935,57, 662. 15 Stonehill, J. Chem. SOC., 1943, 647. 16 Haase, Hoch and Schonert, 2. physik. Chem., 1961,27,421. 17 Snowdon and Turner, Trans. Fmuduy Soc., 1960,56, 1409. 18 Tanner, Trans. Faraday Soc., 1927,23, 75. 19 Chipman, J. Amer. Chem. SOC., 1926,48: 2577. 20 Breck and Agar, Trans. FaradQy SOC., 1957,53, 179. 21 Longsworth, chap. 12 in Hamer (ed.) The Structure of Electroi'yte Solutions (Wiley, New 22 Gurney, Ionic Processes in Solution (McGraw-Hill, New York, 1953). 23 Lee and Tai, see Conway and Backris, Modern Aspects of Electrochemistry, chap. 2 (Butter- 24 de Bethune, J. Electrochem. SOC., 1960, 107, 829. 25 Agar and Turner, Proc. Roy. SOC. A, 1960, 255, 307. Structure of Electrolyte Solutions (Wiley, New York, 1959). vol. 3, Electrochemistry (Interscience, New York, 1963). York, 1959). worths, London, 1954).

ISSN:0014-7672    

DOI:10.1039/TF9656100037

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. System U03 +U308: dissociation pressure of Y-UO~ BY E. H. P.CORDFUNKE AND P. ALING Reactor Centrum Nederland, Petten, The Netherlands Received 22nd June, 1964 The oxygen pressure of the system pUO3fU308 has been measured as a function of tem- perature. The results can be expressed as log p o l (mm) = (-12338/T)+16-192. AH2980~ = -293.5 kcal/mole. The heat of formation of pUO3 derived from the measurements, is A tentative phase diagram for the system UO3SU3O8 is suggested. The phase relationships in the system U03+U308 are comphated and un- certain. Oxygen pressures have only been measured for amorphous UO3 by Biltz and Muller.1 However, Boulle and DominC-Berg& 2 show that amorphous U03 decomposes via an intermediate phase (UO2.9) to U3O8. This has been confirmed by Hoekstra and Siegel,3 who also showed that the 5 crystalline modifications of U03 (a . .. E ) all decompose directly to U308, The few thermodynamic data avail- able on these systems do not permit the calculation of the areas of stability of the crystalline phases of UO3. This paper presents direct dissociation pressure measurements of y-U03, the stable phase at ordinary oxygen pressures. Together with recent data, a tentative diagram for the region UO3 + U3O8 has been derived. EXPERIMENTAL y-U03 was prepared by thermal decomposition of uranyl nitrate hexahydrate in air at 500°C. The hydrate was heated slowly and then kept at this temperature for several weeks in order to improve its crystallinity. The purity was checked both by chemical analysis (ignition to U3O8) and by X-ray diffraction. TI he static oxygen pressure measurements were carried out with an apparatus consisting of a closed horizontal quartz tube, connected with a closed mercury manometer.The tube was heated by means of a furnace with a zone of constant temperature (f0.5"C) over a length of about 6cm. The temperature was measured with a calibrated Pt/Pt-10 % Rh thermocouple and a sensitive mV-meter. 4 The hot junction of the thermocouple was placed just above the boat with y-UO3. Before the measurements the apparatus was thoroughly evacuated, after which the furnace was heated to 4OO0C, moisture, air and other residual gases being pumped off. The temperature was then fixed at the desired value. Constant pressures were reached only after periods of 3-5 weeks at constant temperature, possibly due to a slow diffusion of the uranium atoms as in U02.5 The pressure was assumed to be constant when the value did not change over at least a week. True equili- brium pressures were measured ; this was checked by pumping off at constant temperature. In agreement with Boulld and Domind-Berges 6 we found the dissociation of U03 to be a reversible reaction. The re-oxidation of U3O8, however, is even much slower than the decomposition and depends to a large extent on the degree of sintering of the U3O8 particles, which occurs at relatively low temperatures. 5051 E . H . P. CORDFUNKE A N D P. ALING RESULTS The oxygen pressure of the three-phase equilibrium y-UO3 + U303 + O2 has been determined as a function of temperature. The results, compiled from three different samples of y-UO3, are collected in table 1.The oxygen pressures listed in table 1 have been plotted as log PO, (mm) against 1/T in fig. 1. The resulting 0 1.1 1.2 1.3 1 0 3 1 ~ FIG. 1.-Logarithm of the oxygen pressure as a function of the reciprocal temperature ("K). stra'ght line has been calculated by the method of least squares, assuming that the errors lie entirely in the pressure measurements. We thus obtain log po,(mm) = (-12338i:210)/T+16.192f0.270 Froin the slope, the enthalpy change for the reaction : was found to be AH830 = +9.41 t-0.15 kcal/mole. Using the high-temperature heat-capacity equations for y-U03 (Moore and Kelley 7), oxygen 8 and UO2.67 (= +U308),9 the enthalpy change at room temperature TABLE 1 .-DISSOCIATION PKESSURE OF y-UO3 temp. ("C) 512 525 530 535 539 544 549 558 576 577 600 pressure (mm) 3.0 5.2 6.4 9.2 10.8 12.4 14.0 21.9 45.8 45.4 119.2 Error in temperatures f0*5"C, in the pressures 10.1 mm .I-UO,(S)-+UO, , G ~ ( s ) + 0.165 O,(g)52 SYSTEM U03+u30g was calculated, according to r T AH298 = AHT- J AC,dT 298 to be AH298 = +8.66 kcal/mole.With the value of the heat of formation of U02.67 recommended by Westrum and Grsnvold : 9 AH298 = -284.8 kcal/mole, the heat of formation of y-U03 is AH298 = -293.5 kcal/mole. The error in this value consists of a contribution to the reaction enthalpy (k0.2 kcal/mole) and that of the heat of formation of u02.67(+0-8 kcal/mole), the total error thus being 1.0 kcal/mole. This heat of formation of y-U03 is in good agreement with the value (AH298 = -293.0 kcal/mole) estimated by Rand and Kubaschewski .lo The entropy change for the reaction y'uo3-+uo2.67 at room temperature was calculated from the entropy change at the mean temperature of the measurements (AS& = 10.15 cal/mole deg.) and the C,-values to be AS& = 10.34 cal/mole deg.Using the entropies of oxygen (49.02 cal/mole deg.) and of U O Z . ~ ~ (22.51 cal/mole deg.) the entropy of y-U03 at room temperature was S2O9* = 20.34 cal/mole deg. This value is consistent with the value derived from low-temperature C,-measure- ments by Jones, Gordon and Long,ll S& = 23-57 cal/mole deg. The latter value has to be preferred. The good agreement, however, is a check of accuracy of the oxygen pressure measurements. Using the specific heat data for a-U, derived by Rand and Kubaschewski,lo C, = 2-61 +&95 x 10-3T+ 1.17 x IO5Te2, and the values for oxygen and y-U03 previously mentioned, the heat and free energy of formation of y-UO3 are found.The results are listed in table 2 and may thus provide a correction on the figures given by Coughlin.12 TABLE 2.-HEAT AND FREE ENERGY OF FORMATION OF Y-uo3 T W ) AH (cal/mole) AGO (cal/mole) 298.16 - 293,500 - 275,000 400 - 293,200 - 267,900 500 - 292,850 - 260,850 600 - 292,500 - 253,700 700 - 292,250 - 246,500 800 - 292,000 - 239,200 900 - 291,900 -231,900 Entropy of y-U03 : Sig8 =23.57 callmole deg. The free energies listed in table 2 can be represented by the equation AG;= - 296,500 + 71W. DISCUSSION y-UO3 is one of the 5 known crystalline modifications of UO3.3 With the ex- ception of 6-UO3, all forms have been prepared by oxidation of U308 at high oxygen pressures. The exact phase relationships, however, are not clear and cannot be cal- culated due to the absence of thermodynamic data.Combining all data available,39 13 including high-pressure data by Vidavskii 14 and our present data, a tentative phase diagram is suggested in fig. 2. The results indicate that y-UO3 is the stable UO3- phase at oxygen pressures below 10 atm at all temperatures.E . H . P . CORDFUNKE A N D P . ALING 53 As is well-known 3 9 15 the U03-phases can all be obtained at ordinary oxygen pressures. The formation of the metastable phases is influenced by a number of factors such as the structure of the starting material, the heating velocity and' heating time. This is illustrated by the formation of either p-UO3 or y-U03 in the ignition 250 200- - I 0 0 ; w o , I 0 op 0 rh Sheft et i g$@ Hoekstro and Siegc 0 Vidavski e 4 present auth e 400 500 600 700 80C temp.("C) FIG. 2.-The phase diagram u03+u308. of uranyl nitrate in air at 500°C. p-U03 is only formed when the heating to 500°C is carried out very rapidly. Prolonged heating at this temperature (several weeks) causes recrystallization to y-U03, as was found by us when attempting to measure the dissociation pressure of p-UO3. The recrystallization of cr-UO3 to y-UO3 was reported earlier.16 1 Biltz and Muller, 2. anorg. Chem., 1927, 163, 257. 2 Boull6 and Domin&Berg&s, Compt. rend., 1948, 227, 1365. 3 Roekstra and Siegel, J. Inorg. Nucl. Chem., 1961, 18, 154. 4 Meyer and Oosterom, Rec. trav. chim., 1960, 79, 622. 5 McNamara, Thesis (London, 1963). 6jBou116 and DominBBerg&s, Compt. rend., 1949, 228, 72. 7 Moore and Kelley, J. Amer. Chem. Soc., 1947, 69, 2105. 8 Kelley, Bull. US. Bur. Mines, 476 (U.S. Govt. Printing Office, 1949). 9 Westrum and Grsnvold, J. Physics Chem. Solids, 1962, 23, 39. 10 Rand and Kubaschewski, The Thermochemical Properties of Uranium Compounds (Oliver 11 Jones, Gordon and Long, J. Chem. Physics, 1952,20, 695. 12 Couglin, Bull. U.S. Bur. Mines, 542 (U.S. Govt. Printing Office, 1954). 13 Sheft, Fried and Davidson, J. Amer. Chem. Soc., 1950, 72, 2172. 14 Vidavskii, Labut, Kovba and Ippolitova, Dokl. Akad. Nauk. S.S.S.R., 1964, 154, 1371. 15Cordfunke, J. Inorg. Nucl. Chem., 1961, 23, 285. 16 Cordfunke and Aling, Rec. truv. chim., 1963, 82,257. and Boyd, 1963).

ISSN:0014-7672    

DOI:10.1039/TF9656100050

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No.13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Structural and Thermodynamic Aspects of Phosphate Glasses BY T.R. MEADOWCROFT" AND F. D. RICHARDSON Nuffield Research Group in Extraction Metallurgy, Imperial College, London Received 22nd April, 1964 A study has been made of the distribution of phosphate chains obtained in phosphate glasses by quenching melts with compositions corresponding approximately to the mean anions P3O 3.0 and P4O 9 5. The cations present were Na+, Lif, Ca2f and Zn2f singly, and Na++ Li+, Ca2+ + LI+, Ca2++Zn2+, Na++Zn2+ in pairs. The glasses were dissolved in water and the distributions deter- mined chromatographically ; the validity of the techniques were checked by measurements on crystal- line phosphates. The distributions obtained were always narrower than the ideal Flory distributions, the width increasing from Na+ to Zn2+ in the above order.The divergence from the Flory distributions can be expressed in terms of the phosphate ion equilibrium products, i.e., [N(Pn+103n+4)-n-3N(Pn-103,-2)-n-1 I/CN2(Pn03n+1)-n-21 for the equilibria For the Flory distributions these products are equal to unity for all values of n. For the melts investigated and for any one cation these products do not change significantly with composition : they are substantially less than unity at small values of n and rise to the limiting value of unity as n increases from 2 to 5. The deviations from unity are least for zinc glasses and greatest for sodium. They can reasonably be attributed to endothermic enthalpy changes accompanying the above reaction. In the glasses containing two cations, the logarithms of the equilibrium products are a linear function of the cation composition, except where there is a big difference between the limiting binary values.2(Pr~03n+l)-"-~ = (Pn+1%1+4)-*-~ + (Pn-103n-2)-n-1 Metal oxides form ionic compounds with phosphorus pentoxide and these have a close resemblance to those they form with silica. The anionic groups consist primarily of chains with the general formula (Pn03n+1)-n-2, which are analogous to the silicate ions (Sin0Sn+l)-2"-2. In both cases the anions get longer or bigger, as the proportion of metal oxide in the phosphate or silicate becomes less. Like the silicates, many of the phosphates can be obtained as glasses, merely by quenching the melts sufficiently fast, and thereafter the glasses are stable at room temperature. The phosphate glasses and the corresponding crystals can be dissolved in water (either simply or in the presence of agents to complex the cations), without the lengths of phosphate chains being altered.The resulting solutions can then be analyzed chromatographically and the proportions of different chains thereby determined. The structures of a number of alkali metal phosphate glasses have been determined by Westman and Gartaganis 1 and others in this way. The structures of these phosphate glasses, and the factors which determine them, are of interest to the glass technologist, the polymer chemist and to the metallurgist, who uses slags which consist predominantly of silicates, and mixtures of silicates and phosphates. Unfortunately no way has yet been found of taking such silicates into solution without simultaneously changing their chain struc- tures.The structures of silicate glasses have been studied only by X-ray diffraction * present address : Dep t. of Metallurgy, Massachusetts Institute of Technology, Cambridge, Mass. 54T. R . MEADOWCROFT AND F . D . RICHARDSON 55 and by optical, viscosity and conductivity measurements. None of these methods yield as precise or as unequivocal information concerning the distributions of chains as the chromatographic studies. Consequently, measurements have been made of the distributions that occur in the glassy phosphates of lithium, sodium, calcium and zinc and in mixtures containing pairs of these cations. The techniques have been checked against certain crystalline phosphates. The distributions may be considered in terms of their deviations from the ideal Flory distributions and viewed in conjunction with the thermo- chemical data on crystalline and glassy phosphates? EXPERIMENTAL GENERAL PROCEDURE The materials used have been described previously.2 The mixtures were melted in open platinum crucibles in air at the desired temperature and were then quenched quickly to glass by being poured out and pressed between two flat aluminium blocks.The glasses were then ground to fine powders and examined under polarized light to determine whether any crystallization had occurred. Any glass containing crystalline material was discarded. A 100 rng sample of glass was then dissolved in 5 in1 of neutral solvent at 15°C. The sodium and lithium phosphates were dissolved in distilled water; zinc and calcium phosphates were dissolved in an aqueous 5 % ethylenediamine tetra-acetate solution which had been neutralized with ammonia.3 A 20-50 pl sample was then painted near one end of a tapered strip of filter paper and the chromatogram was developed at 4°C for 16 h, in an airtight battery jar. The developer was the mixture of trichloroacetic acid, ammonia, acetone and distilled water, suggested by Bernhart and Chess 4 after J.P. Ebel. The paper strips were dried at 110°C for 10 min to convert all phosphate to ortho ; they were sprayed with a fine mist of ammonium molybdate (1 g molybdate, 5 ml 72 % HC104 and 1 ml conc. HC1 in 100 ml aqueous solution), dried at 50°C and exposed to long-wave ultraviolet light. This last step converted the phosphate to the blue ammonium phospho- molybdate complex, and so rendered visible the separate bands on the paper.The chro- matogramwas then cut up, and the separated sections analyzed for phosphorus by the method of Lucenda-Conde and Prat,S modified for chromatographic work by Sniith.6 With this technique it was possible to separate from one another, anions ranging from ortho- phosphate to septaphosphate. There was insufficient movement to permit separation of longer chains, so these were grouped together and referred to as hypoly. In preliminary tests with the two-dimensional chromatographic technique of Westman et aZ.,7 it was established that less than 1 % of the phosphorus was present in ring structures. QUENCHING OF THE GLASSES In order to maintain the phosphates as glasses they had to be quenched rapidly between the aluminium blocks.The normal time for the glass to reach about 30°C was about 2 sec, so the rate of passage through the glass temperatures was some 3-400 deg./sec. Normally the sodium, lithium and zinc glasses and their mixtures, were quenched from 1000°C, and mixtures containing calcium phosphates from 1400°C. To discover whether the tempera- ture of heating, the heating time and the quenching rate had any effect on the glasses, melts of composition Na20+P205, 7/5 and (NazO+ZnO)+P205, 6/4, were heated at 850, lo00 and 1200°C for times ranging from 10 min to 16 h and quenched in times ranging from 2 to 150 sec. Melts of composition CaO+P205, 6/4 were quenched from 1400 and 1500°C and a number of glasses were studied after storing in a desiccator for periods up to 3 months.Refractive indices were also measured. RESULTS The results of the chromatographic analyses of the phosphate glasses are shown in table 1. The figure under each component is the % weight of the totalmetal oxides Na2O Liz0 CaO ZnO Flory Na20 Li20 G O ZnO Flory Na20 + Li20 311 Y Y 1/1 Y Y 1 /3 Y Y 311 Y Y 111 Y Y 113 Y Y 111 Y Y 1 /3 Y Y 311 >> 111 7 ) 113 Li2O+CaO 311 TABLE 1 .-RESULTS OF THE CHROMATOGRAPHIC ANALYSES OF PHOSPHATE GLASSES- PERCENT OF TOTAL PHOSPHORUS IN EACH FORM ortho 0.00 0.00 2-87 6.53 11.15 0.00 0.00 1-88 3.10 6.26 0.00 0.00 0.00 0.00 0.00 0.00 0.17 0.89 2.43 0.9 1 0.81 0.98 PYro 22.69 31-40 30-71 22.63 14.87 5.96 12-92 15.62 15.04 9.39 24.73 26.01 29.05 8.55 10.63 11.16 31.36 30.12 30.40 13.56 15.03 14.94 tri 49-36 40.35 30.02 20-97 14.86 28-76 26-26 20-26 16.52 10.57 47.93 46.2 1 42.65 28-41 29.32 27-37 37.50 34.00 32-1 5 23.43 23-15 21.73 tetra 21.48 19-67 17.56 15.57 13-21 26.98 20.52 16.97 14-64 10.55 21.07 20.76 18.80 26-38 23-67 21-25 19.30 18-24 17.82 18-87 17.76 17-69 penta 5-48 6.21 9-77 12.10 11.04 16.90 14.15 13.43 11.66 9.90 5.50 5-90 7.08 15-72 14.56 14-73 7.35 8-00 9.06 14.35 12.97 13.35 hexa 0.93 2.32 4.65 7.58 8.82 9-58 8.83 8.37 8-93 8-91 0.94 1-25 2.45 8.76 8.38 9-22 3.07 4.54 4.32 9.29 8-73 8.68 hepta 0.00 0.00 2.35 5.98 6.84 5-52 5.95 6.36 8.34 7.80 0.00 0.00 0.00 5.24 5.34 6.09 1.1 1 2.49 2.00 6.36 6.3 1 6.29 0.00 0.00 2.07 8-64 19-20 6.3 1 11-37 17.11 21.77 35.61 0.00 0.00 0.00 6.94 8.09 10.11 0.34 1 -72 1.82 13-23 15-24 16-34 no.of chains per 100 P atoms 34.22 35.70 35.92 34-22 33-33 25.69 26.75 27.39 26.98 25.00 34.87 34.94 35.27 26-46 26.98 26.49 35-25 34-95 35.82 26-87 26.96 26.77CaO/ZnO Y ¶ Y Y Y7 9 7 7 7 Na20/ZnO Y Y 7 9 9 Y Y Y 614 7 7 I 9 3.43 28.75 26.68 17.06 10.48 5-94 4-26 27-10 25.37 16.58 10.46 6.44 5.68 25.82 23.30 16-00 10.92 7.12 2.3 1 15.84 18-43 15.83 13.10 8-94 2.32 15.98 18.44 16-27 12.86 8-59 2-81 14.56 17-49 14.89 11-74 8.93 0.32 28.52 32.96 20.28 9.57 4.18 1.13 31.02 29.25 17.43 9.89 4.98 1 *49 30.23 30.28 18.63 9.89 4-69 0.65 14.59 21-59 18.73 13-24 9.48 1.15 15.40 19.81 16.76 12.86 8.94 1.39 15.01 20-32 17.72 12.80 9.23 * hypoly gives phosphorus in all chains containing more than 7 P atoms. 3-5 1 4.0 1 4-68 6.87 6.46 6.59 2.3 1 2.64 2-48 6.92 7.30 7-35 TABLE 3 .-COMPARISON OF RESULTS FOR SODIUM PHOSPHATES NazO/PzOs source ortho pyro tri tetra penta hexa 614 Westman and Crowther 0.0 5.6 28.0 29.0 17.4 9.4 7 7 Westman and Gartaganis 0.0 6.65 28.25 27.43 16-87 9.41 77 this study 0.0 5.96 28.76 26.98 16-90 9.58 715 Westman and Crowther 0-0 5.7 19.0 24.4 17.3 13.1 7 7 Westman and Gartaganis 0.0 3.20 16.05 19-93 16-26 12.53 9 9 this study 0.0 3.19 15.45 19.59 17.47 12.43 4-15 5-78 6.48 18.68 19-08 22-99 1-86 3.60 2-3 1 14-80 17.78 16.18 hepta 5.8 5.70 5-52 9-7 9.35 9.07 35.01 34-79 35.12 1 27.29; 27.36 4 26-72 ?j 34.34 U 33-79 E 9 0 < 34.73 26.5 1 c! w w 26.53 0 26-86 cl 4.7 F1 5.67 0 6.3 1 z 10-8 22.69 22.8958 PHOSPHATE GLASSES phosphorus present in that form.At least six chromatograms were run on each of two separate melts made for each composition.The standard deviations and the standard error were calculated for each component at each composition and these are listed in table 2 ; the error of each mean result has been taken as k0.5 wt. % of total phosphorus. The reproducibility at the 5/3 composition was slightly worse than at the 6/4. Also the reproducibility in the results for the pyro, tri and hypoly structures was rather less than for the others. TABLE 2.-ERRORS IN CHROMATOGRAPHY FOR ALL MIXTURES-Wf . % OF PHOSPHORUS (MO or MzO)/PzOs = 6/4 (MO or M20)/P205 - 5/3 component standard deviation standard error standard deviation standard error ortho PYro tri tetra pent a hexa hepta hYP0lY 0.30-0.7 1 0.40-1 -40 0.40-1 *20 0.47- 1 -00 0.26-0.67 0.23-0.70 0.52-0.84 0.71 -1 -45 0.19-O.28 0.18-0.54 0.18-0*52 0.19-0.42 0.1 1-0.27 0.10-0.28 0.21 -0.34 0.44 -0.65 0.25-1 -05 0.80- 1 *78 0.39-1 -29 0.26-1 020 0*45-1.00 0.28-0.6 1 0.45-0.88 0.40-1 -46 0.1 2-0.43 0.33-0.73 0.16-0.53 0.1 1-0.48 0.18-0.41 0.1 2-0.25 0*18-0*36 0.18-0*60 DISCUSSION SOURCES OF ERROR The results for the sodium glasses are compared in table 3 with those obtained by Westman et al.: 1, 7 agreement lies well within the stated error limits. The main uncertainty in the results lies in the possible hydrolysis of the phosphates to give anions that are smaller than those which occurred in the glass. A typical hydrolysis in which an end is cut off a phosphate chain to give an extra ortho- phosphate ion may be written as The P-0-P links in rings and long chains, hydrolyze relatively slowly,S-lO but the hydrolysis of branching chains proceeds rapidly at the branch points.The glasses had to be dissolved at room temperature in order to get satisfactory rates of solution. This took about 20min but thereafter the solutions were kept and manipulated at 4°C. Tests were made on the hydrolysis of phosphate ions in aqueous solutions at various temperatures, and in the chromatographic solution at 4°C. These showed that in 20min at 15°C and during the whole chromatographic separation at 4"C, no significant hydrolysis can take place homogeneously in the aqueous phase. But some breakdown by reaction (1) may occur during the dissolution step, for in chromatograms from crystalline tripoly-sodium phosphates, and the pyrophosphates of sodium, lithium and calcium 0.6rt0-4 % of the total phosphorus was found as orthophosphate.This was presumably not present in the original crystals. The chromatograms for the glasses never showed less than 0.6 % ortho-phosphorus although more was often found; 0-60 % phosphorus was therefore subtracted from the ortho-phosphate phosphorus and the other percentages were multiplied by the factor 100/99.4 to give the results listed in table 1. It is evident that every ortho- phosphate ion produced during dissolution, is accompanied by another phosphate ion containing one phosphorus atom less than it held originally. If all the P - 4 - P links are liable to hydrolysis, the proportion of phosphorus found in each anionT.R. MEADOWCROFT AND F. D. RICHARDSON 59 should be increased by the hydrolysis of the longer anions and decreased by its own hydrolysis. The two effects tend to cancel, and it is not worthwhile correcting for the hydrolysis in a more refined manner. If hydrolysis of all P-0-P links in the glasses proceeds at the same speed as in the pyro- and tri-poly crystals studied,* one may calculate the extent to which any particular distribution in glass may be changed by chain breaking during dis- solution. An example is given in table 4 for a glass which approximates to 2 calcium phosphate of 6/4 ratio. After deducting 0.5 % phosphorus from the ortho observed after hydrolysis, the distribution after dissolution is little different from that for the original glass, and the values of Kn are not changed beyond the error limits.In addition, the distribution calculated after hydrolysis shows less than 1 % more chains per 100 phosphorus atoms than was present in the original glass. TABLE 4.-cALCULATED EFFECTS OF HYDROLYSIS ON THE DISTRIBUTION OF CHAINS; ii = 3.66: NUMBER OF PHOSPHORUS ATOMS = 100 no. of P atoms no. of chains in chain before dissolution 1 2.00 2 7.80 3 6.70 4 4.20 5 2.60 6 1.60 7 0.99 8 0.61 9 0.38 lo+ 0.50 no. of chains after dissolution 2.51 corr to 2-00 8-06 6.77 4.21 2.58 1-58 0.96 0.59 0.36 0.46 K. origmal - 0.22 0.73 1.00 1-00 1.00 1-00 1 moo 1.00 Kn final - 0.21 0.74 0.99 1.00 1.00 1-00 1.00 1 -00 % change in K - -5 + 2 - 1 0 0 0 0 0 27.38 27.57 In table 1, the number of anions found per 100 atoms of phosphorus should have been 25 or 33 plus approximately 1 %, if the glasses had had the compositions intended, and if there had been no hydrolysis apart from that already considered.This is because the formation of a distribution of anions which may be represented by the following equation, does not affect the number of anions present per unit of phosphorus. The mean chain length is always n where (n+2)/n is the mo!ar ratio of metal oxide to phosphorus pentoxide : Even after the correction for orthophosphate, however, the number of anions found is greater than expected, though the excess is in no case greater than 8 %. These extra anions might have come from hydrolysis of branching chains,ll but branches do not exist in significant concentrations in melts more basic than the meta- phosphates.12 The excess anions could also have bcen caused by the presence of small amounts of water in the melts, by consistent errors in the starting materials, or by eva- poration of P205 during melting.The amount of water required to account for the extra anions is at most 0.29 % by weight and usually much less ; the compositional errors in the starting materials or the vaporization losses which would give corresponding effects, are also small. It is extremely difficult to make phosphate melts completely free from dissolved moisture, and also to avoid small vaporization losses and small errors * It is probable that hydrolysis of the ends of chains to give ortho is faster than the hydrolysis of other P-0-P links and that the hydrolysis of pyro is slower than tripoly or tetrapoly.Even if this is so, the corrections are still negligible.60 PHOSPHATE GLASSES in the compositions of the starting materials. The distributions observed have therefore been allocated to compositions richer in metal and/or moisture by 0.004- 0-010 mole fraction than those originally intended. (The distributions observed may, as explained later (see fig. 13a), be calculated from the values of K1, K2, K3, etc., provided the observed values of the mean chain length Z are taken as, e.g., 3.75, instead of 4.0, and 2-80 instead of 3.0, for Li20+P205, etc. If the values of n estimated from the starting materials are accepted, the distributions calculated from K are substantially different from those observed. If hydrolysis were seriously upsetting the Kvalues, it is unlikely that such good agreement would be obtained when the observed values of i are used.Such calculations show that the distributions are reasonably sensitive to the values of Kn, that the mean values of Kn (over all compositions) lead to distributions at each composition that agree within the error limits with those observed.) The distributions actually measured might be characteristic of the aqueous phase or the dissolution process, rather than the original glass. It is most im- probable, when the end product of hydrolysis is the ortho ion, that an intermediate equilibrium distribution of ions could be set up in the aqueous phase with the same mean chain length as in the glass. This would necessitate the improbable occurrence of equal amounts of chain breaking and chain making for all the mixtures studied.In addition, apart from the very small amounts of ortho and pyro produced by hydrolysis, only one length of chain is observed when the crystalline pyro- and tripoly-phosphates are dissolved. Certainly no longer chains are found. The dissolving glasses should behave in much the same way as dissolving crystals, so that serious errors arising from dissolution may be discounted. - EFFECT OF COOLING RATE The times and the temperatures at which glasses were held in the molten state, the rates of cooling and the times they were kept at room temperature before dis- solution, had no effect on the distributions obtained. They also had no effect on the refractive indices of the glasses, which were measured to an accuracy of +0.0003 in all cases.Preliminary measurements made by Cripps Clark 13 show that the glass temperatures of these phosphates (which in most cases lie some 20" below the crystallization temperatures) vary markedly with the cations present, but little with the mole fraction of phosphorus pentoxide. The values ( -t IOOC) are as follows : K20 + P205, 250°C ; NaaO, 270°C ; Li20, 315°C ; CaO, 550°C ; ZnO+ P205, 400°C. For the ternary glasses, the glass temperatures are intermediate between those of the cor- responding binaries but the first 25 mole % of the binary with the lower glass tem- peratures has more effect on lowering the glass temperature than the remaining 75 %. As indicated earlier, it was necessary to cool the phosphates quickly in order to preserve them as glasses, but it was possible to vary the rate of cooling in the region of the glass temperature about a hundredfold. One might expect, on the basis of Ritland's 14 analysis of the effect of cooling rate on the density of a borosilicate glass, that the fictive temperatures would vary by some 50" or so.The constancy of the refractive indices suggests that they varied less than this, and may therefore be put equal to the glass temperatures without much error. A difference of 50" would not affect the distributions beyond the limits of error (see fig. 3b). COMPARISON WITH THE FLORY DISTRIBUTION In all cases, the observed distributions are narrower and more peaked than the Flory distributions,lsf 16 which are given in table 1 for both 5/3 and 614 compositions.T.R . MEADOWCROFT AND F. D. RICHARDSON 61 But with both mixtures the distributions approach the Flory type as one passes from Na, through Li and Ca, to Zn. The distributions may be considered in terms of the equilibrium products for reac- tions of the type represented by eqn. (2). For the Florydistributionandamelt in which the mean phosphate chain contains fi phosphorus atoms, the mole fraction of (Pn03n+1)-”-2 is given by the equation, From this, K , = [ N(P, - 1 0 3 , - 2) - - IN(P, + 1 O,, + 4) - - 3]/ [N2( P, 0 3” + 1) - - ’1 = 1. (4) Values of Kn are shown in table 5, together with those derived from the results of Westman et aZ.19 79 8 for Li, Na, K and H, and of Jameson 17 for H. The results obtained by Murthy and Westman18 for rubidium glasses are not shown.The Kn values derived from their results are very scattered and lack the consistency of the values for the other alkaliphosphates. This scatter may be attributedto the diffi- culty of working with these highly hygroscopic materials. The results for potassium phosphates which are less hygroscopic than those of rubidium but more than those of sodium, are also somewhat scattered. The accuracy of the Kn values is about _+lo %, when the equilibrium involves the dominant anions, i.e., when n approaches 2, and probably near &30 % when n and 5 differ markedly. Within these limits the values of most of the equilibrium products are independent of Z. But where the products are much less than unity, and notably for Kl and K2 for hydrogen, the values increase, as E increases.This trend may, however, be caused by hydrolysis, which would tend to raise K1 and K2, and to have its greatest effects when the proportions of the short chains in the glasses are small. The values of the equilibrium products for each cation approach unity as one passes from K2 to K6. In addition, the values of K1, K2, K3 and K4 approach unity more closely as the cation becomes smaller, e.g., Na+ to Hf, Ca2f to Znz+. Because of this approach of Kn to unity as n increases and the fact that for the H20+P205 glasses, Kn is so close to unity, once n exceeds 2,” the Flory model can usefully be applied to these glasses. Because the equilibrium products, with the possible exception of K1 and K2, are nearly independent of Z, for the purpose of estimating configurational entropies of mixing, the anions may be permuted with one another irrespective of their lengths, except possibly for ortho and oxygen.Therefore one may attribute the extent to which the values of Kn differ from unity, to endothermic enthalpy changes associated with reaction (2) above, and estimate the entropies of the mixtures in the Flory manner. The entropy of heterogeneity A& is taken as -RZN(Pn03n+l)lnN(Pn03n+l). Each value of AHn is then equal to - RTln Kn, T being taken as the glass temperature. The results are listed in table 6. From the values of AH, and A&, one may calculate the thermodynamic properties of the heterogeneous glasses relative to hypothetical glasses bf single chain length equal to E. These quantities, indicated by the subscript h, are shown for glasses with the formulae M3P4013, or M6P4013 in fig. 1 .The five points on each curve going from right to left, are for the Fhry distribution and the distributions which would be obtained (and which have to be calculated) for Zn, Ca, Li and Na when * Jameson’s results show K7 to K14 which are not listed in table 5, also effectively constant and equal to unity.TABLE 5.--VALUES OF EQUILIBRIUM PRODUCTS FOR VARIOUS BINARY GLASSES cation Li ri 3.1, 3.0 3.6 4-1, 4.0 4.6 5.1 5.6 6-1 7.1 means 4 *47, -43 -48 *46, 4 3 -44 *52 -50 -52 -52 -48 K4 -90, -69 994 093, -94 1.13 -87 a92 1 moo -88 a93 K5 1.07, 1-23 1.06 1.01, -94 a87 1.09 1 -05 *95 1-16 1.04 K6 1 -07 094 1.04, 1.11 098 1.00 -98 1-01 -87 1.00 Na 3.0 3.5 4.0 4.5 5.0 6.0 7.0 9-0 means negligible Y Y 9 ) 9 9 *24, -22 -24 ~26, -22 a26 -28, .29 -3 1 64, ~ 6 2 -68 -67, -7 1 *7 1 *70, -75 *65 -61 -52 -66 1.37, *69 094 -95, -94 -96 -99, *8 3 997 1.10 - -97 1 -03 1-12, 1-04 1.10 -99 1.04 -92 - 1 *03 9 9 9 9 9 9 K 3.5 4.0 5.0 6-0 7.0 9.0 means negligible 9 9 9 9 9 9 9 9 9 9 - -56 a22 -24 -32 -35 -50 *265 -94 a62 -58 *60 .80 -52 -68 .87 1.12 -86 87 -8 1 1.1 1 -94 -86 -52 -96 -98 -87 -85 -82 Zn 3 4 means -36 -30 -33 -90 -9 1 09 1 1.12 0.95 1 -04 -84 1-00 0.92 1.30 1-25 1 *28Ca H H 3 -12 4 a21 means -17 1.12 1.34 1.56 1.9 2.20 2.6 2.94 3.6 4.00 5.1 7.8 9-1 means 0.2 1 0.20 0.29 0.36 0.47 0-3 1 0-26 0.34 0.36 0.49 0.77 0.92 0-42 K1 0.83 0.002 0.86 0.004 1 -00 0.005 1 -09 0.006 1 -42 0.006 1 *46 0.010 means 0.006 -67 *73 -70 - - -75 1 *07 1 -04 1.21 1-44 1.56 1.15 1 -05 1.1 1 0-99 1.00 1-12 1.01 1.01 1.01 0.89 0.82 0.86 1 009 1 -25 1-17 - 1.28 0.99 0.99 0.99 0.92 0.90 0.83 0.78 0.70 0.92 0.93 1 -08 0.85 1 *04 1 *01 1 -05 0.98 0.9 1 1 *03 1 -09 1 -00 - 0.98 1 025 0.92 1.01 0.62 1-04 1 -07 1 -06 0.96 0.99 The results for K and the left-hand figures for Li, Na and H are those of Westman et a/.The right-hand figures fofH are:those of Janieson. The remainder are the authors.64 PHOSPHATE GLASSES E is precisely 4.00. In order to represent the distributions by single parameters only, they have been described in terms of the mole fractions of the anion which has the mean chain length, i.e., N(P4013)6-. The wider the distribution, the smaller is this mole fraction and the greater are the entropy and the endothermic heat of heterogeneity. The free energies of formation show minima at correct distributions. 1000 600 s a 6oo 400 200 1000 5 2000 I 3000 mole fraction of mean anion FIG. 1.-The entropies, in cal deg.-1, and heats and free energies, in cal, of forming distributions of phosphate anions from one mole of the single anion P40: 5, from the authors' results : Na 270"C, Li 315"C, Ca 550°C and Zn 400°C.The heats of formation of the observed distributions are all less than 450 cal/mole of ions, and even the maximum value of A S is only 4.3 cal mole-1 deg.-l. When a crystalline phosphate such as M6P4OI3 melts, the entropy may be considered as TABLE 6.-ENTHALPY CHANGES ASSOCIATED WITH DISTRIBUTION FORMING REACTIONS AH,,, cal K Na Li H Ca Zn react ion 2PO4 = P2O7+0 - - - 3000 - - 2P2O7 = PO4+P3010 - >lo000 SO00 500 2900 1500 2p3010 = P207+P4013 1400 1400 840 0 580 130 2p4013 = p301O+p5016 400 440 80 0 0 0 2p5016 P4013+p6019 30 30 0 0 0 0T .R . MEADOWCROFT A N D F. D . RICHARDSON 65 arising from fusion to produce a melt consisting of the mean anion only (perhaps 5 cal deg.-1 per mole of anions) and a further 4 cal mole-1 deg.-1 or so for formation of the distribution. The detailed ionic structure of tri- and tetra-polyphosphate glasses has not yet been established. But the type of structure can be inferred from the work of Biscoe et aZ.19 and Brady 20 on the X-ray diffraction of calcium and sodium meta- phosphate glasses and the crystal structures of sodium tripoly phosphate.21 The co-ordination number for the cations appears to be six in the tripolyphosphate crystal but may be as low as two in the metaphosphate glass.It is not known to what extent the zig-zag P-0-P chains niay be twisted in the glasses. Thus one 0 10 2 0 30 =? 2 5 * 40 d 1 50 60 70 80 mole % P205 25 50 75 I I I FIG. 2.-The heats of formation of crystalline phosphates 0 and glasses 0 in kcal/mole oxide (MO+P205) at 35°C obtained by solution calorimetry (2). Broken line : extrapolated heats for single chain glasses, which cannot be retained at room temperature. cannot calculate how the internal energy would change if a single chain glass, consisting of tri- or tetra- poly anions only, were to form the distributions actually observed. The distribution of charge must be less uniform in the heterogeneous glass, because there is a concentration of ionic charges about the ends of chains.One may thus reasonably expect AH, to be endothermic and also to change con- sistently with cation size for a fixed cation charge. This is suggested by the fact that the crystals consist of one type of chain only, and that the separation of a glass into two parts, one with a shorter mean chain length and one with a longer, is endothermic according to fig. 2. 366 PHOSPHATE GLASSES The larger distributions. of the glasses or free energy HEATS OF FORMATION OF THE MELTS the cation, the greater are the values of AH, and the narrower the The larger the cation the more negative are the heats of formation from metal oxide and phosphorus pentoxide.2 Thus a deep heat curve is to be associated with a narrow distribution and vice versa.This type of relation has been contended on general grounds for silicate melts,22 but this is the only case in which the relationship has been definitely proved. From the values of Kn and AH,, it is possible to calculate the heats of formation of the hypothetical single chain glasses. One starts from the knowledge that for the meta- and 6/4 glasses and for compositions in between, the differences between the heats of formation of the single chain glasses and the values established for the heterogeneous glasses are negligibly small, i.e., less than 90 cal (per mole MO+ P2O5) in all cases. The heat of forming two single chain glasses with n equal to 1 and 7 from one with n equal to 4, is given by the sum of AH2+2AH3+3AH4+ 2AH5+ AH6.Thus the heat of formation, from the component oxides, of the single chain glass for which n is equal to unity (mole % P2O5 equal to 25.0) may be derived by combining this sum with the established heats of formation for the glasses for which n is equal to 4 and 7. The heats of formation for phosphate crystals and for glasses from meta- to tri-poly have been established at 35°C by solution calorimetry.2 The values are plotted in fig. 2 and the curves for the glasses have-been extended beyond the measured points by the type of calculation just described. The differences be- tween the heats of formation of the single chain glasses and the crystals are the heats of fusion at the glass temperatures. These values may be considerably less than the heats of fusion at the melting points, because the heat capacities of glasses are greater than those of the corresponding crystals, between the melting points and the glass temperatures.* The differences between the curves extrapolated for the glasses and the crystal curves are reasonable and lend support to the interpretation of the Kn values in terms of enthalpy effects.If, e.g., there were no such heat effects the transformation of glassy calcium orthophosphate to crystal would be endothermic instead of exothermic. DISTRIBUTIONS AT OTHER MEAN CHAIN LENGTHS AND HIGHER TEMPERATURES For this calculation it is first necessary to derive a relationship between the mean chain length 5 and the ratio of the numbers of anions for which n is equal to any pair of consecutive numbers.The ratio N(P3010)5-/N(P4013)6- is a con- venient one to use. For any value of this ratio, the values of Kn from K1 to K12 determine the value of i. The relation between n and N(P3010)5-/N(P4013)6- is shown in fig. 3(a) for CaO+P205 at 820°K for the measured Kn values, and at 1800°K for Kn values t derived from these on the assumption that log Kn (1800°K) = The two distributions when n is equal to 2.0 may then be calculated from the ratio N(P3010)5-/N(P4013)6- derived from fig. 3(a). The results are shown in fig. 3(b). In this case and in all others, the distribution becomes narrower as Z becomes smaller, because the values of Kn decrease as n decreases. It is almost certainly this narrower distribution and the consequent scarcity of long chains, which makes *The enthalpy change required to form the heterogeneous glass from the single chain glass is rather small as fig.1 shows. -f K1 was taken as negligible at both temperatures. log Kn (820°K) x 82011 800. AHh for Q(Ca~P207) would be about 260 cal. from fig. 3b.T. R . MEADOWCROFT AND F. D. RICHARDSON 67 no. of phosphorus atoms per chain (b) FIG. 3 . 4 4 Relationship between n and nP3/nP4 for CaO$-P2O5 melts, A at 820°K and B at 1800°K. (b) The distributions calculated for CaO+P2O5 glasses for which fi is equal to 2 at 820 and 1800°K.68 PHOSPHATE GLASSES crystallization of these melts so easy that they cannot be retained as glasses even with very fast rates of cooling. If this analysis is correct, the sodium distribution at 2000°C should lie between the distributions for calcium and zinc shown in table 1.DISTRIBUTIONS AT VERY HIGH TEMPERATURES At temperatures of 2000"K, and values of AHn equal to 3000, 1000 and 500 cal the values of Kn would be 0.47, 0.78 and 0.88. At such temperatures therefore the melts will mainly differ from one another in the equilibrium, 2po:- = p,o;- + 02-, ( 5 ) 2p20;- = Poi- +p,o:;. (6) 2si044- = ~i,0,6-+ 02-, (7) 2~i,0$- = Si,O;, + SiO:-. (8) 2( iSi-0') = (iSi-0-Si i) + 02-. and to a lesser extent in Similar considerations probably apply to silicate melts for which the appropriate reactions would be Eqn. (7) is analogous to that already proposed 22 for representing the oxygen ion equilibrium in silicate melts. (10) There is insufficient evidence to indicate whether the equilibrium products for reactions ( 5 ) and (6) remain constant over any substantial range of Z.If they were to do so, even over the range where h exceeds 3, it might be possible to calculate metal oxide activities over a wide range of compositions from a measurement made at one. GLASSES CONTAINING TWO CATIONS The distributions observed for glasses containing two cations are intermediate between those for the separate single cation glasses. The effects of the two cations on the values of K2, K3 and K4 are shown in fig. 4(a), (b) and (c). When the charges on the two cations differ from one another, as for Na+Zn, the cation fraction is equal to nNa+/(nNa++2nZn2+). Most of the values for K2 cannot be accurate to better than a factor of 2 or 3, on account of the small amounts of ortho present (particularly in the Na+Zn and Li+Ca mixtures) and the deductions that have to be made for ortho produced by hydrolysis during dissolution; for fig.4(a), only the results for the 5/3 mixtures have been plotted, because there should be more ortho present in these glasses than in the 6/4. The values of K3 and K4 are more reliable than those of K2, and there is good consistency between the 5/3 and 6/4 results in fig. 4(b) and (c). The glass tem- perature of a glass containing two cations in substantial proportions, is intermediate between the glass temperatures for the corresponding single cation glasses.13 If the lines in fig. 4(b) are drawn for glasses at the same equilibrium temperatures, then the K3 values must be adjusted accordingly.For the pair Na+Li, T, varies between 540 and 590°K ; for the extreme case of Ca+Li, Tg varies between 590 and 820°K. The corrections for these effects amount to less than k0.06 on log Kz and in most cases lie well within the error limits. If the distributions of the different cations were random, then the enthalpy changes, which give rise to the K values, might vary linearly with cation fraction, so that log K would vary linearly also. This appears to be the case for log K3 andT . R . MEADOWCROFT AND F . D. RTCHARDSON 69 -2.f -2.2 4.8 % 3 -1.4 c.( -1.c Li .l\ / I I / cation fraction (a> A - L1 1 1 1 I I 25 50 75 cation fraction FIG. 4.-Equilibrium products in glasses with two cations present, shown as a function of cation fraction, e.g., nNa+/(nNa++ZnZn*+), etc., for 5/3 and 6/4 glasses ; (a) log K2, 513 only ; (b) log K3, (4 log K4.70 PHOSPHATE GLASSES log K4 with Na+Li, Li+Ca and Ca+Zn, and for log K2 with Ca+Zn.The pronounced departures from this linear relationship seem to arise when the end values of K are very diEerent, i.e., for K2 and K3 with Na+Zn and for K2 with Li+Ca. In these cases the enthalpies of the glasses would be lowered, if the smaller cations were to associate preferentially with the shorter chains and the larger cations with the longer chains. A similar situation appears to arise with mixtures of Na20 + H20 + P205.23 Their cation fractions of sodium ranged from about 0.25 to 0.75 and Z ranged from 1.1 to about 10. Their results show that KI, K2, K3 and K4 in these mixtures are virtually the same as for the H20+P205 melts, although KI and K2 are both negligibly small for NazO+P205 glasses. The heats of formation of some of these mixed glasses have been measured by solution calorimetry.2 Mixing is exothermic in all cases, presumably on account of polarization of the singly charged oxygens of the phosphate ions in the presence of cations of different charge and size. The effect appears to be greatest for Na+Zn, where these differences of charge and size are greatest and least for Na+Li where the differences are least. The mixtures which exhibit the highest heat of mixing are those with the greatest deviation of log K from linearity. The two effects may be connected, for the preferential association of the smaller cations with the larger chains and vice versa should make a contribution to the heat of mixing. The authors are indebted to the Athlone Fellowships Committee and the National Research Council of Canada for Fellowships to T. R. M. during the time this work was conducted, and to Messrs. Albright and Wilson Ltd., and the British Iron and Steel Research Association for financial assistance for materials and equipment. They are grateful to Dr. John Lumsden for helpful discussions. 1 Westman and Gartaganis, J. Amer. Cernm. SOC., 1957, 40, 293. 2 Meadowcroft and Richardson, Trans. Faraday Soc., 1963,554 1564. 3 Ohashi and Van Wazer, J. Amer. Chem. Soc., 1959, 81, 830. 4 Bernhart and Chess, Anal. Chem., 1959,31, 1026. 5 Lucenda-Conde and Prat, Anal. Chem. Acta, 1957,16,473. 6 Smith, Anal. Chem., 1959, 31, 1023. 7 Westman and Crowther, J . ,lmer. Cer. Soc., 1954, 37, 420. 8 Crowther and Westman, Can. J. Chem., 1954,32,42; 1956,34,969. 9 Pfanstiel and Iler, J. Amer. Chem. SOC., 1952, 74, 6058. 10 Van Wazer and Holst, J. Amer. Chem. SOC., 1950,72, 639, 644. 11 Van Wazer, Phosphorus and Its Compounds, 1958, vol. 1, p. 438. 12 Straws and Treitler, J . Amer. Chem. SOC., 1955, 77, 1473. 13 Cripps Clark, C. J., Nuffield Research Group in Extraction Metallurgy, Imperial College, 14Ritland, J. Amer. Ceram. SOC., 1954, 37, 370. IsFlory, J. Amer. Chem. SOC., 1936, 58, 1877. 16 Flory, J. Amer. Chem. SOC., 1942, 64, 2205. 17 Jameson, J. Chem. Soc., 1959,752. 18 Krishna Murthy and Westman, Inorganic Chemistry, 1962, 1, 712. 19 Biscoe, Pincus, Smith and Warren, J. Amer. Ceram. SOC., 1941,24, 116. 20 Brady, J. Chem. Physics, 1958, 28,48. 21 Davies and Corbridge, Acta Cryst., 1958, 11, 315. 22 Richardson and Fincham, Proc. Roy. Soc. A, 1954,223,40. 23 Westman, Smith and Gartaganis, Can. J. Chem., 1959, 37, 1764. London, private communication.

ISSN:0014-7672    

DOI:10.1039/TF9656100054

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Measurements of Heats of Combustion by Flame Calorimetry Part 3.-Ethylene Oxide, Triinethylene Oxide, Tetrahydrofuran and Tetrahydropy BY A. S. PELL AND G. PILCHER Chemistry Dept., University of Manchester Received 27th July, 1964 The heats of combustion of the following cyclic ethers have been measured in the gaseous state AH,"(ethylene oxide, 9) = -312.15f0.14 kcal mole-1 4H,"(trimethylene oxide, g) = -467*85+0.14 kcal mole -1 AHc(tetrahydrofuran, g) = -605.44&0-16 kcal mole-1 AH;(tetrahydropyran, 9) = - 758.44 10.23 kcal mole-1 at 25°C and 1 atm pressure in a flame calorimeter : These results were used to derive the heats of formation of each of the cyclic ethers.By application of the Allen bond energy scheme the strain energies in these ethers have been calculated and com- pared with the strain energies in other small ring compounds. In parts 1 1 and 2 2 the heats of combustion of some simple aliphatic ethers were measured and the derived heats of formation discussed in terms of the Allen bond energy scheme.3 This paper reports the heats of combustion of cyclic ethers of ring size 3 to 6 atoms and by application of the same bond energy scheme the strain energies may be calculated.The heats of combustion of liquid tetrahydrofuran and tetrahydropyran have been reported by Springall et al.4 and by Skuratov et a1.59 6 but the results were not in agreement. By flame calorimetry the heat of combustion in the gaseous state at 1 atm is measured directly and the completeness of the combusion reaction established by quantitative analysis of the products, carbon dioxide and water. The results reported here are in excellent agreement with those of Skuratov et al. EXPERIMENTAL PURIFICATION AND PURITY OF THE COMPOUNDS ETHYLENE oxrm.-Ethylene oxide (B.D.H.) was fractionally distilled using a 3-ft 1-in. diam. vacuum jacketed column (column A) packed with stainless steel wire (Knitmesh Multi- fil).Examination of the centre fraction by n.m.r. spectroscopy showed no impurities other than water. TRIMETHYLENE oXIDE.-Trimethylene oxide (Kodak) was purified by gas chromatography using a 4-cm diam. 3-m column of " Chromosorb " with a methylsilicone oil as stationary phase. The purity measured using a melting point calorimeter 7 was 99.90 f0-02 mole %. TETRAHYDROFURAN.-A commercial sample was fractionally distilled using a 1 -in. diam. 5-ft column packed with Knitmesh Multifil. The centre fraction was refractionated from lithium aluminium hydride and the purity of the final sample determined as 999410.02 mole %. TETRAHmR0PYRAN.-Tetrahydropyran (Light and co.) was fractionally distilled using column A.The purity of the centre fraction was found to be 99.98f0.01 mole %. This compound has a small heat of fusion so that calorimetric determination of purity could be 7172 FLAME CALORIMETRY vitiated by solid-solution formation. Separate tests using gas chromatography and n.m.r. spectroscopy failed to show the presence of the most probable impurity, dihydropyran. APPARATUS A N D PROCEDURE The same apparatus and procedure as described in part 1 have been used. Ethylene oxide was dried before reaching the calorimeter by passing the gas through barium oxide. To achieve complete combustion it was necessary to premix with argon to raise the flame to the top of the jet to avoid deposition of carbon. Samples of the other ethers were distilled from calcium hydride before each experiment.In each case the ether was introduced by saturating a stream of argon, at 0°C for trimethylene oxide, at room temperature for the other ethers. For these compounds, stable combustion conditions were found without premixing with oxygen before reaching the flame. DETERMINATION OF THE IGNITION ENERGY The ignition energy was determined as described in part 1, from expefiments in which the flame was allowed to burn for only 60 sec, so that the heat of combustion is determined from that part of the normal experiment when the flame is in a steady state. The mean ignition energies were : ethylene oxide 5.20 f 1.10 cal trime t h ylene oxide 6.62 f 1.24 cal tetrahydrofuran 8.57 i 1.20 cal tetrahydropyran 5.91 11-10 cal These ignition energies are close to the sparking energy (5.80 f0.05 cal) indicating that deviations from the steady state on ignition and extinction of the flame were small.DETERMINATION OF THE AMOUNT OF REACTION A N D COMPLETENESS OF COMBUSTION The number of moles of compound used in each experiment was determined from the mass of carbon dioxide produced taking 44-00995 as the molecular weight of carbon dioxide. The stoichiometric ratio Y is defined by mass C02lmass HzO(obs.) mass C02/mass H20 (expected) The excess of water observed in the ignition energy experiments was subtracted from the total mass of water collected in normal experiments before calculating the stoichiometric ratio. The mean values of Y, with standard deviations, were : r = ethylene oxide 1~00001+0*00022 trime th ylene oxide 1 -00027 f 0*00009 tetrahydro furan 1 -00024 f O.OoO54 tetrahy dropyran 1.00007 f0*00008 The closeness of these ratios to unity demonstrates the completeness of the combustion reaction.From tests on the product gases, the amount of carbon monoxide has always been less than 0.002 % of the amount of carbon dioxide formed. RESULTS UNITS.-A~~ energy quantities are given in calories defined by 1 cal = 4- 1840 abs. joules. The atomic weights used are those based on C12 = 12: C = 12.01115, 0 = 15.9994, H = 1.00797.8 CALIBRATION The apparatus was calibrated by burning hydrogen in oxygen. This was accepted as a standard reaction for flame calorimetry by the formal Commission on Thermo-A . S. PELL AND G . PILCHER 73 chemistry of the International Union 9 from data given by Rossini.10 For the cali- bration reaction the value given by Rossini 11 is based on a molecular weight of water of 18.016.The details of procedure and calculation of the energy equivalent were given in part 1. A closely similar calorimeter system was used here and the standard energy equivalent found from 8 experiments was Es = 371 32.86 2.89 cal ohm-1. H2(d + 402(9) = H20(1) - AH(H20) at 25°C = 285,828+40 J mole-1 HEATS OF COMBUSTION The heat of the combustion reaction occurring in the calorimeter at the mean temperature Tc is given by The details of the combustion experiments are given in tables 1, 2, 3 and 4. The symbols used are the same as in parts 1 and 2. Auxiliary quantities and units are the same. To calculate qg the following additional heat capacities, in cal deg.-1 mole-1 AH^ = ( n x ~ O ~ ) - ~ [ ( E , + E = ) A R , - ~ , - ~ , - ~ ~ ~ .TABLE 1 .-COMBUSTION OF ETHYLENE OXIDE Ec -AH, G3i (cal ohm-1) (kcal mole-1) ether ARC - 4s expt* no* (molex 10-3) (ohm) (cat) 1 3 8.4207 0-3 19484 7.68 11 8.35 6-00 311.97 2 38.3653 0.318769 11.92 130.18 5.89 312.15 3 38.1852 0.3 17023 10.85 133.01 5.8 1 31 1.97 4 38.2703 0.317957 8-93 136.19 5-82 312.21 E, = 371 32.86 cal ohm-1 ; qi = 5-20 cal ; Tc = 26~53°C ; AH, mean value = - 3 12.08 kcal mole-1 ; standard deviation of the mean = f0.06 kcal mole-1. TABLE 2.-COMBUSTION OF TRIMETHYLENE OXIDE Ec -AH, & (cal ohm-1) (kcal mole-1) ether ARC - 48 expt* no. (molex 10-3) (ohm) (Call 1 24.6215 0.306737 9.78 126.71 5.61 467.95 2 25.2944 0.3 14944 10.48 129.02 5.77 467.67 3 25.2559 0.3 14354 9-99 1 3 7.42 5.69 467.83 4 25,3262 0,315219 10.07 135.49 5-72 467.73 E, = 3713286 cal ohm-1 ; qi = 6.62 cal ; T, = 26.52"C ; AH, mean value - -467.80 kcal mole-1 ; standard deviation of the mean = &0.06 kcal mole-1.TABLE 3.-cOMBUSTION OF TETRAHYDROFURAN E.2 -AHc d>" (cal ohm-1) (kcal mole-') ether ARC - 48 expt* no. (mole x 10-3) (Ohm) (call 1 19.6740 0.317163 10.54 126.58 6.10 605.25 2 19.7373 0.318328 12.32 121.36 6.10 605.32 2 19.6821 0.3 17502 12.56 120.02 6.09 605-41 4 19.7036 0-3 17878 10.44 1 20.7 3 6.11 605.38 5 19.6634 0.3 17240 11.62 122.44 6.09 605.56 E, = 37132.86 cal ohm-1 ; qf = 8.57 cal ; T, = 2652°C ; AH, mean value = -60538 kcal mole-1 ; standard deviation of the mean = h0.05 kcal mole-1.74 FLAME CALORIMETRY TABLE 4.-cOMBUSTION OF TETRAHYDROPYRAN Ec -AH, rM4", (cal ohm-]) (kcal mole-1) ether ARC - 4s expt* no* (molex 10-3) (Ohm) (call 1 15.5387 0.3 12872 11.30 160.87 5.66 758.48 2 15-5807 0-3 13843 9.34 157.67 5.71 758-42 3 15.7137 0,316301 13-52 161.00 5.74 758-29 4 15-6855 0.3 15808 11-17 160.36 5.73 758.30 Es = 37132.86 cal ohm-1 ; qi = 5-91 cal; Tc = 26~52°C; AH, mean value = -758.37 kcal mole-1 ; standard deviation of the mean = &Om05 kcal mole-1.were used : ethylene oxide = 11-45,13 trimethylene oxide = 14.03,14 tetrahydrofuran = 18-08,22 tetrahydropyran = 25.3 (est.). The combustion reactions (to which AH, refer), at temperature T, and 1 atm pressure were : C2H40(g) + 4*5Ar(g) + 702(g) = [2C02 +4.5Ar + 4502](g) + 2H20(E) [C3H60 + 7Ar](g) + 9-502(g) = [3CO2 + 7Ar + 5*502](g) + 3H20(1) [C5H100 + 2OAr](g) + 1502(g) = [KO2 + 20Ar + 802](g) + 5H20(1) To obtain the standard heat of combustion AH: from AH, it is necessary to allow for the change in heat content of each gas from its actual pressure to the thermo- dynamic standard state and to correct AH: from Tc to 25°C.The corrections to the ideal gaseous state were based on the following values (in cal mole-1) for Hreal- Hideal, at 26.5"C and 1 atm : ethylene oxide -39.56, trimethylene oxide - 65-66, tetra- hydrofuran - 85-24, tetrahydropyran - 11 1-10, Hreal- Hideal was calculated using the Berthelot equation of state and the critical constants: ethylene oxide, pc = 71 atm, Tc = 468OK15; tetrahydrofuran, Pc = 51.2 atni, Tc = 541OK.16 The values for the other ethers were calculated from estimated critical constants.16 For the CO2 + 0 2 mixtures the equation of Rossini and Fransden 17 was used.Values of AH,(obs), AH",T,) and AHZ(25"C) are collected in table 5, together with derived AH> values : the following standard heats of formation were used : AH;(C02, g) = - 94.052 kcal mole-1, and AH;i(H,O, E ) = - 68.31 5 kcal mole-1,12 where the values given in ref. (12) have been amended to comply with the atomic weights used here. The errors quoted in table 5 are twice the standard deviation of the mean including the uncertainties in calibration and measurement.18 [C~HSO + 9k](g) + 1302(g) = [4co2 + 9Ar -I- 7*502](g) + 4H20(1) TABLE 5.-SUMMARY OF COMBUSTION RESULTS -AHc(obs) -A Hg(Tc) -AHS(25"C) AH? kcal mole-1 kcal mole-] kcal mole-1 kcal mole-] compound ethylene oxide 3 12.08 312.11 312*15&-0*14 - 12.58 rt0.15 trimethylene oxide 467.80 467.79 467.85 f0-14 - 19-25 f0.15 tetrahydro furan 605.38 605-37 605.44 f0.16 -44.03 f0.17 tetrahydropyran 758.37 758.35 75844 f0-23 - 53.50 f0.24 DISCUSSION COMPARISON WITH PREVIOUS INVESTIGATIONS ETHYLENE oxIDE.-The measurement by Moureau and Dode 19 was on the liquid and has been converted to the gaseous state using AH,,, = 5.96 +O-Ol kcal mole-1.20 Crog and Hunt 21 measured AH",(g) with a flame calorimeter but gave no experimen- tal details.A.S . PELL A N D G . PILCHER 75 - AHg(g) kcal mole-' Moureau and Dode, 1937 308.2 f0.3 Crog and Hunt, 1942 312.55 f0.22 this investigation 312-15 rf0-14 TETRAHYDROFURAN.-PreViOUS measurements on the liquid have been converted to the gaseous state using AH,,, = 7-65 kcal mole-1.22 Skuratov's value has been corrected from 20 to 25°C using Cp (tetrahydrofuran, I ) = 29-56 cal deg.-1 mole-1.22 -AH:&) kcal mole-1 Cass et al., 1958 4 Skuratov et al., 1957 5 this investigation 606.4 f0.5 605-4 f0.2 605.44 f 0.16 TETRAHYDROPYRAN.-PreViOUS measurements on the liquid have been converted to the gaseous state using AHvap = 8.35 0.20 kcal mole-1.4 Skuratov's values have been corrected from 20 to 25°C using Cp (tetrahydropyran, I ) = 37-4 cal deg.-1 mole-1 (es t .) .- AH,O(g) kcal mole-1 Skuratov et al., 1957 5 758.3 f0-3 Skuratov and Kozina, 1958 6 758.63 &to-25 Cass et al., 1958 4 761.2 f l . 6 Snelson and Skinner, 1961 759.31 f0.60 this investigation 758.44 f0.23 Our measurements agree with those of Skuratov to within the limits of experi- mental error.For tetrahydropyran we were especially concerned with establishing the purity of our sample. Furthermore the analysis ratio is close to unity providing further evidence of high purity. Cass et al. did not establish the purities of the samples they examined and for tetrahydropyran the amount of C02 they collected was greater than expected. For this compound Snelson and Skinner made three combustions on a pure sample using glass ampoules, and large corrections for carbon deposits were necessary. STRAIN ENERGY IN SMALL CYCLIC COMPOUNDS The Allen bond energy scheme applied to the heats of atomization of simple - U cyclic molecules (CH&X, gives the equation n H"(CH,),X = 2nBcH + ( n - + 2Bcx + (n - 2)rccc + 2rccx + - [ S ] U where the B's are the effective bond energy terms and the T's the bond interaction terms, e.g. rccx is for the interaction C-C-X.[ S ] is the destabilizing term which we call strain energy. The heat of atomization is calculated from the heat of formation of the gaseous molecule by n The following parameters used here are taken from those given by Skinner and Pilcher :24 the heats of formation of gaseous atoms in kcal g atom-1, C 170.9, H 52.10,76 FLAME CALORIMETRY 0 59-56, S 65-65, N 113.0: and the effective bond energy terms and interaction parameters in kcal mole-1, BCH 99.29, Bcc 78.84, Bco 78.15, Bcs 65.19, BCN 64.73, Additional to the heats of formation of cyclic ethers determined above, there are reliable values for small cycloalkanes, cyclothialkanes and cyclic imines. Except for cyclopropane, the measurements have been made by bomb calorimetry and the values must be converted to the gaseous state.The following values have been selected from the literature as being the most reliable and precise ; for cyclopentane and cyclohexane there are other measurements agreeing within the limits of error quoted. The heat of formation for the gaseous molecule is given in kcal mole-1, the first ref. is to AH: and the second to AHvaB. Cyclopropane 12-73f0-14,25 cyclobutane 6.44+0-13,269 27 cyclopentane - 18.45 & 0.19,2*9 29 cyclohexane -29.42 & 0~22,289 29 thiacyclopropane 19.68 f 0.3 1,301 31 thiacyclobutane 14.64+0-22,329 33 thiacyclopentane - 7-93 4 0-28,34 thiacyclohexane - 15-07 0.25,35 ethyleneimine 30.06 & 0.30,369 37 pyrrolidine - 0.81 & 020,389 39 piperidine - 1 1.66 & 0.58.40 From these heats of formation the strain energies are calculated as described above and are given in table 6.TABLE 6 BNH 93-45, rccc 2.58, rcco 5-66, rccs 3-30, TCCN 4-10, rcoc 6-00, rcsc 2-97, rCNC 5.10. ring sue compound no. O f atoms alkane ether sulphide imine 3 27.43 27.28 19.78 26.87 4 26.04 25.5 1 19.64 5 6.05 5.63 1 *97 5.80 6 - 0.02 1.16 - 0.27 -0.15 Several aspects shown by the data in table 6 are noteworthy. (a) The strain energy in 4-membered rings is only slightly less than in 3-membered rings. Some theoretical descriptions of cyclopropane and cyclobutane, in terms of “ bent bonds ” have been made 41 but theoretical quantitative investigations have not yet been made.(b) The strain energy in cycloalkanes, cyclic ethers and cyclic imines for 3, 4 and 5 membered rings are closely similar whereas it is much less in cyclic sulphicies. This may be expected if we consider the typical average bond lengths ; C-C 1.54 A, C-0 1.43 A, C-N 1.47 A, C-S 1-81 A.42 The large drop in strain energy for thiacyclopentane suggests that the source of strain in 5-membered rings may not be due solely to repulsions between eclipsed hydrogen atoms. (c) The only 6-membered ring to exhibit strain energy is tetrahydropyran, of 1.16 kcal mole-1. From the heat of formation of 1,4-dioxan given by Snelson and Skinner, AH/”(g) = - 75.95 & 0.40 kcal mole-1 23 and using the parameters given above, a strain of 3.77 kcal mole-1 is calculated for this molecule.This is consistent with strain in tetrahydropyran. We can offer no explanation of the source of these strain energies except that they occur where there are bonds of high polarity within the ring. Any satisfactory explanation would also have to account for the results of Skuratov et aZ.43 on di-n-butylformal and cyclic formals from whence by the above procedure we calculate a strain energy in 1,3-dioxan of -0.18 kcal mole-1, i.e. effec- tively zero. The authors express thanks to Prof. G. Gee, F.R.S., and Dr. H. A. Skinner for their interest and encouragement. One of us, A. S. P., also acknowledges a D.S.I.R. studentship.A. S . PELL AND G. PILCHER 77 1 Pilcher, Skinner, Pell and Pope, Trans.Faraday SOC., 1963, 59, 316. 2 Pilcher, Pell and Coleman, Trans. Faraday SOC., 1964, 60, 499. 3 Allen, J. Chem. Physics, 1959, 31, 1039. 4 Cass, Fletcher, Mortimer, Springall and White, J. Chem. SOC., 1958, 1406. 5 Skuratov, Strepikheev and Kozina, Doklady Akad. Nuuk S.S.S. R., 1957, 117, 452. 6 Skuratov and Kozina, Doklady Akad. Nauk S.S.S.R., 1958, 122, 109. 7 Brooks and Pilcher, J. Chem. SOC., 1959, 1535. 8 Compt. rend. XXI Conference (I.U.P.A.C.) (Butterworths, London, 1962), p. 284. 9 1st Report Standing Comm. Thermochemistry (Int. Union of Chemistry, Paris, 1934) ; Appendix 10 Rossini, J. Res. Nat. Bur. Stand., 1931, 6, 1 ; 1931, 7, 329. 11 Rossini, Experimental Thermochemistry, vol. I, chap. 4 (Interscience, New York, 1956). 12 Selected Values of Chemical Tl~ermodynamic Properties, circ.500 (Nat. Bur. Stand., Washington, 13 Sundaram, 2. physik. Chem. (Frankfurt), 1963, 36, 376. 14 Ziircher and Giinthard, Helu. chiin. Acta., 1957, 40, 89. 15 Lynn and Kobe, Chem. Reu., 1953, 52, 181. 16 Kobe, Ravicz and Vohra, J. Chem. Eng. Data, 1956, 1, 50. 17 Rossini and Fransden, J. Res. Nat. Bur. Stand., 1932, 9, 733. 18 Rossini and Deming, J. Wash. Acad. Sci., 1939,29,416. 19 Moureau and Dode, Bull. SOC. Chem. (France), 1937, 4, 637. 20 Giaque and Gordon, J. Amer. Chem. Sac., 1949,71, 2176. 21 Crog and Hunt, J. Physic. Chem., 1942, 9, 1162. 22 U.S. Bureau of Mines, Bartlesville, Oklahoma, unpublished data, personal communication 23 Snelson and Skinner, Trans. Faraday SOC., 1961, 57, 2125. 24 Skinner and Pilcher, Quart. Rev., 1963, 17, 264. 25 Knowlton and Rossini, J. Res. Nat. Bur. Stand., 1949, 43, 113. 26 Kaarsmaker and Coops, Rec. Trav. Chim., 1952, 71, 261. 27 Rathjens and Gwinn, J. Amer. Clzem. Soc., 1953, 75, 5629. 28 Johnson, Prosen and Rossini, J. Res. Nat. Bur. Stand., 1946, 36, 463. 29 Osborne and Ginnings, J. Res. Nat. Bur. Stand., 1947, 39,453. 30 Sunner, Acta Chem. Scand., 1963, 17, 728. 31 Guthrie, Scott and Waddington, J. Amer. Chern. SOC., 1952, 74, 2795. 32 Hubbard, Katz and Waddington, J. Physic. Chem., 1954, 58, 142. 33 Scott, Finke, Hubbard, McCullough, Katz, Gross, Messerly, Pennington and Waddington, 34 Davies and Sunner, Acta Chem. Scand., 1962, 16, 1870. 35 McCullough, Finke, Hubbard, Good, Pennington, Messerly and Waddington, J. Amer. Chern. 36 Nelson and Jessup, J. Res. Nat. Bur. Stand., 1952, 48, 206. 37 Burg and Good, J. Inorg. Nucl. Chem., 1956, 2, 237. 38 McCullough, Douslin, Hubbard, Todd, Messerly, Hossenlopp, Frow, Dawson and Waddington, 39 Hildebrand, Sinke, McDonald, Kramer and Stull, J. Chem. Physics, 1959, 31, 650. 40 Bedford, Beezer and Mortimer, J. Chem. Sac., 1963, 2039. 41 Coulson and Goodwin, J. Chem. SOC., 1962, 2851. 42Interatomic Distances, ed. Sutton (Chem. SOC., Spec. Pub.), no. 11, 1958. 43 Skuratov, Steprikheev, Shtekher and Volokina, Doklady Akad. Nauk. S.S.S. R., 1957, 117 (Paris, 1936). D.C., 1952). from H. L. Finke. J. Amer. Chem. SOC., 1953, 75, 2797. SOC., 1954, 76, 2661. J. Amer. Chem. SOC., 1959, 81, 5884. 263.

ISSN:0014-7672    

DOI:10.1039/TF9656100071

出版商:RSC    

年代:1965

数据来源: RSC