摘要:

Solvent Participation in Proton Transfer Reactions of Aminesand their Conjugate AcidsBY ERNEST GRUNWALD * AND MICHAEL COCIVERA f-Received 28th January, 1965The principles of the measurement of solvent participation in proton transfer reactions by meansof nuclear magnetic resonance are described briefly. Data for proton transfer reactions are presentedfor the solvents water, methanol, t-butyl alcohol, and acetic acid. Reaction mechanisms are discussed.By means of proton magnetic resonance (p.m.r.) it is possible in favourable casesto measure not only the rate of proton transfer between solute and solvent, but alsothe number of solvent molecules that participate in any given process. In this paperwe shall describe briefly the principles of the method, and then give some results foramines and their conjugate acids in various hydroxylic solvents.MEASUREMENT OF PROTON TRANSFER INVOLVING SOLVENT MOLECULESThe p.m.r.spectrum of a solution of hydrogen compounds in the absence of protonexchange generally consists of a number of resonance lines,l some ascribable to thesolute and others to the solvent. Each resonance line indicates a particular protonsubspecies. For example, in the absence of exchange, water enriched in 0 1 7 wouldshow seven p.m.r. lines $ as a result of spin-spin interaction with the oxygen nucleus.In H2016 and H2Ols the oxygen nuclear spin is zero, and these isotopes produce onep.m.r. line. In H2O17 the oxygen nuclear spin can be either & 1/2, or 3/2, or & 5/2,and this isotope produces six lines.In addition to the seven lines that are producedby water molecules, an aqueous solution would also show lines due to protons inhydrogen-containing solute species.We may describe the scope of the p.m.r. method of measuring proton exchange.It is possible (at least in principle) to measure proton exchange between any pair ofchemical species or subspecies that would give rise to separate p.m.r. lines if therewere no exchange. Thus it is possible (at least in principle) to measure protonexchange between a solvent and a solute, or between different solvent molecules if thesolvent consists of two or more p.m.r. subspecies. For example, in pure H2016 allprotons belong to the same p.m.r. subspecies, and protonexchange cannot be measured.However, if H2017 is added, the number of p.m.r.subspecies increases to seven,and proton exchange between water molecules becomes measurable.The technical aspects of deducing rates from p.m.r. spectra are intricate and cannotbe treated adequately in the brief space of this paper. In the simplest case, that ofexchange between two lines, the lines first broaden, then coalesce, and finally collapseinto a single line as the rate of exchange increases.2 Calculation of the rate of ex-change always involves some kind of comparison between experimental line-shapes* Brandeis University, Waltham, Massachusetts. t Bell Telephone Laboratories, Incorporated, Murray Hill, New Jersey.$ We are assuming that the p.m.r. spectrum is measured at a temperature at which the TI relaxationtime of 0 1 7 is sufficiently long.10106 SOLVENT PARTICIPATIONand theoretically predicted line-shapes.Theoretical line-shapes are solutions of theBloch equations to which appropriate terms have been added to allow for exchange.3-5For exchange involving more than two lines, the required mathematics is tedious(except under conditions where asymptotic solutions apply *) and high-speed com-puters are usually employed.The rate measurements can be accurate only under conditions where the p.m.r.line shapes are sensitive to changes in rate. This requirement greatly restricts thescope of the method, because the rates of exchange, the concentrations of the reactants,and the TI and T2 spin relaxation times of certain nuclei 7 all have to be withinappropriate limits.The method applies especially to relatively fast reactions,because the lifetimes for proton exchange must be less than about 1 sec. When themethod does apply, it provides a very powerful tool for elucidating solvent participa-tion in proton transfer reactions.KINETIC ORDER WITH RESPECT TO THE SOLVENTConsider a reaction in which an acid molecule HA reacts with n solvent moleculesSH such that n + 1 protons are transferred. Let the rate of proton exchange associatedwith this reaction be d[HA]/dt in the acid and d[SH]/dt in the solvent. Then,d[SH]/dt is equal to n times d[dHA]/dt, since n solvent molecules exchange a protonevery time one HA molecule exchanges a proton.Conversely, if we can measure both d[SH]/dt and d[HA]/dt, the ratio is equal to n,which is thereby evaluated.We must show that the measurements apply to the samereaction, at least to the extent of showing that the two rates follow identical rate laws.?In that case, n is also equal to the ratio of the rate constants.If the proton exchange involves several processes in parallel, the rate laws ford[HA]/dt and d[SH]/dt will be sums consisting of several distinct kinetic terms.In that case, it is possible to evaluate the number of solvent molecules participatingin each process by taking the ratio of rate constants for the corresponding kineticterms? For example, in solutions of benzoic acid and sodium benzoate in methanol,the rate law for proton exchange between benzoic acid HBz and methanol at 25" isgiven by eqn.(A), that for OH-proton exchange involving methanol subspecies isgiven by eqn. (B).9rate = 0.71 x 10SIHBz] + 1.52 x 1OS[HBz][B%] (A)(B) I rate = 1-31 x 105[HBz] + 1-21 x 10s[HBz][B~]+ 8.79 x 10''[H+] + 1-85 x 1Of0[Me0-]Eqn. (A) involves two kinetic terms, one first-order in HBz, the other second-order,i.e., first-order each in HB? and BZ. Eqn. (B) involves two similar terms, and alsoan additional term proportional to H+, and one proportional to MeO-. Assumingthat the first order term in HBz in (A) refers to the same process as that in (B), thenumber of solvent (methanol) molecules in that process is (1.31 x 105)/(0-71 x lO5),or 1.85. A similar assumption for the second-order term leads to the conclusionthat the number of methanol molecules in that process is (1.52 x 108)/(1.21 x log),or 0.8.Within experimental error these numbers could be exactly 2 and 1,respectively.* Asymptotic solutions apply, for example, when the relaxation times are large compared to theinverse line separations (life-time broadening), or when they are small compared to the latter (exchange-narrowing).6j. Identity of rate laws is a necessary but not a sufficient condition. For example, CH3NH;reacts with CH3NH2 in aqueous solution by two distinct processes, both of which follow the ratelaw, rate = k[BH+][B], but only one of which involves water molecules.E. GRUNWALD AND M. COCIVERA 107RESULTS FOR AMINES A N D THEIR CONJUGATE ACIDSThe first published report of the use of the p.m.r.method to study the kineticsof proton exchange involved aqueous solutions of methylammonium ion.10 Sincethen, these studies have been extended to a number of amines and a number of hyd-roxylic solvents, covering a wide range of dielectric constant. In solutions of highdielectiic constant, e.g., water and methanol, the major processes in the acidic pHrange are the following.(1) ACID DISSOCIATION OF BH+.kik-1BH+ +ROH+B+ROH;(2) DIRECT PROTON TRANSFER FROM BH' to B.k2BH++B+B+HB+(3) PROTON TRANSFER FROM BH+ TO B THAT INVOLVES ONE SOLVENT MOLECULE.k3BH++OH+B+B+HO+HB'IRIRIn solvents of low dielectric constant (0) the proton transfer processes are alteredby ionic association. In t-butyl alcohol ( D = 12.47 at 25") 11 the reactive speciesis the solvated ion-pair rather than the solvated free ion :k4(4) BH+X-+oH+B-+It-BuB +HO+ X-HB+It-BuIn this reaction, a proton that is hydrogen-bonded to the anion in the ion-pair istransferred much less readily than a proton that is hydrogen-bonded to a solventmolecule.In glacial acetic acid (D = 6.22 at 25") 11 the methylamines are converted almostcompletely to the acetate salts, which exist in solution largely in the form of ionpairs, BH+OAc-.12 Proton exchange is first-order in BH+OAc- and probablyinvolves a two step mechanism :( 5 ) BH +OAc-+BHOAckik-1khACOH*+B.HOAC-+B*H*OAC+ACOH.Salts of amines with acids that are stronger than acetic acid, e.g., picric or trichloroaceticacid, seem to react by an analogous mechanism in which the first step is a protontransfer from BH+ to X- within the ion pair.In the following we shall present a brief summary and discussion of results forspecific solvents.WATERSelected values of rate constants for the methyl-substituted amines are listed intable 1. Rate constants kl for acid dissociation have been measured by the p,m.r108 SOLVENT PARTICIPATIONmethod for NH;, (CH3)3NH+ and sarcosinium ion.The values of k-l(= kI/&)for these substrates are of such a magnitude as to suggest that reaction of H3O+with amine takes place at nearly every encounter. Diffusion-controlled processesbetween H3O+ and bases are quite common,19 but this mechanism is not general.For example, the reaction between H3Of and (CH3)3P is probably not diffusion-controlled (table 1).TABLE RATE CONSTANTS FOR PROTON TRANSFER a AND ACID DISSOCIATIONCONSTANTS, WATER, 25"BH+ l o l o K ~ ref.(M)NHZ 25 4.3 11.7~ 108 0.9x 108 5.68 13CH3NH' - - 4 . 0 ~ 108 5.3 x 108 0.242 14(CH3)2NHl - - 0 . 5 ~ 108 9.ox 108 0.168 154.7 3.0 0-ox 108 3.4x 108 1 -57 16HO2CCH2NH&H$ 110 3.2 - I 30 17(CH3)3PH+ 8 0.5 5 1 . 2 ~ 102 5 1 . 2 ~ 102 16 18solutions.(CH3)3NH +Q The rate constants in this table apply to reactions (1)-(3), as indicated in the text, and to diluteValues of kl, in contrast to those of k-1, are quite sensitive to the addition of inertsalts and decrease when salt is added.13~ 1 6 ~ 2 0 Furthermore, there is a strikingreduction in kl upon addition of strong acids. It has been possible, by using sulphuricacid + water mixtures, to reduce kl by as much as six orders of magnitude relative tothe value in water,209 21 and there is every reason to believe that kl goes to zero inthe limit of very high acidity. A detailed study 20 of this phenomenon is consistentwith the following mechanism (6).(6) (a) REVERSIBLE IONIZATION TO PRODUCE AN AMINE-WATERHYDROGEN-BONDED COMPLEXk +BH+ .. . (OH,),+B . . . (HOH),+H(OH&-,k-(b) EXCHANGE OF A WATER MOLECULE BETWEEN BULK SOLVENT ANDTHE SITE ADJACENT TO BkHHOH*+B.. . HOH.. . + B . . . H*OH.. . +HOHThe reversible cycle shown in (6a) does not lead to proton exchange unless theamine during its lifetime undergoes reaction (6b). In strong acid, (6a) becomes aprior equilibrium and (6b) becomes the rate-determining step for proton exchange.The fact that kl approaches zero in very strong acid indicates that the amine is alwaysproduced as a hydrate, that is, m 2 1.Since (n -m) must be 2 1 (the proton is bondedto at least one water molecule), n must be 22, that is, acid dissociation involves atleast two water molecules.20Values of the rate constant k H for exchange of the B . . . HOH hydrogen bond havebeen derived from kinetic data and are listed in table 2. It appears that methyl-substitution on nitrogen strengthens the hydrogen bond.The rate constant k2 for direct proton transfer from BH+ to B decreases sharplywith methyl-substitution on nitrogen (table 1). This could be due to the increasedsteric hindrance or to an increased energy of the desolvation stetl that must precedeproton transferE.GRUNWALD AND M. COCIVERA 109The rate constant k3 for the reaction of BH+, water, and B is not highly sensitiveto methyl-substitution. The small changes that are observed parallel the changesin ~ / K A (table 1). With (CH3)3NH+, water, and (CH3)3N, one water molecule isTABLE 2.-vALUES OF THE FIRST-ORDER RATE CONSTANT kH FOR BREAKINGTHE B . . . HOH HYDROGEN BOND IN WATER AT 25°Camine (B) kH(sec-1)NH3 5x 1011CH3NH2 8x 1010(CH313N 1.1 x 1010HOzCCH2NHCH3 0*8x 1010a ref. (17), (20), (21).involved in this process.22 On the basis of that result and of an analogous resultobtained in methanol (see below), we believe that eqn. 3, which involves one watermolecule, gives a generally correct description of the reaction associated with k3.METHANOLPertinent results obtained by the p.m.r.method are summarized in table 3. Valuesof kl, k-1 and KA are available for p-toluidinium and trimethylammonium ion as wellas for phenyldimethylphosphonium ion. The magnitudes of k-1 suggest that thereaction of hydrogen ion (CH30Hi) is diffusion-controlled with the amines but notwith the phosphine. Also the rate of proton exchange decreases markedly in strongacid24 This phenomenon is similar to that noted in water and can be explainedsimilarly by a mechanism analogous to (6).TABLE RA RATE CONSTANTS FOR PROTON TRANSFER ANDACID DISSOCIATION CONSTANTS, METHANOL, 25°Cki k- 1 k3 KAOBH+ (sec-1) (M-1 sec-1) (M-1 sec-1) (MI ref.p-CH3C6aNH; 2 .9 2 ~ 103 1 . 0 4 ~ 1010 8.1 x 107 2 - 8 ~ 10-7 23(CH3)3M+ 0.6 0.5 x 1010 3-25 x 108 1.20 x 10-10 this workC6H5 * (CH3)zPHf 3 . 7 ~ 103 1 - 3 ~ 108 t i 0 4 2.8 x 10-5 23measured in methanol at 25°C.Values of k3 are available for p-toluidinium ion and for trimethylammonium ion.In the former case only one methanol molecule undergoes proton exchange in thisreaction9 The value of k3 for trimethylammonium ion in methanol is almostidentical with that observed in water (tables 1, 3). The corresponding reaction forphenyldimethylphosphonium ion is very much slower, the upper limit to kl beinglo4 sec-1 M-1.23f-BUTYL ALCOHOLRate constants for reaction (4) have been measured for several methylammoniumand trimethylammonium salts and are listed in table 4.The kinetics of protonexchange is second-order, i.e., first-order in ammonium salt and first-order in amine.In the concentration range employed in these studies (10-3-10-1 M) the salts existlargely in the form of ion pairs.25The data in table 4 show a marked contrast between the behaviour of methyl-ammonium salts and of trimethylammonium salts. For the former, k4 is quiteinsensitive to the nature of the anion and is about one-twentieth of k3 in water110 SOLVENT PARTICIPATIONFor the latter, k4 is highly sensitive to the nature of the anion and ranges from 1/3000to 1/500 of k3 in water. This contrast probably results from the different numbers ofNH-protons in the two cations. Most likely the single proton of (CH3)3NH+ isbound to the anion by a strong hydrogen bond, and as a result its reactivity is greatlyTABLE 4.-RATE CONSTANTS FOR REACTION (4) IN f-BUTYL ALCOHOL, 35°Ck3(H20>"BH+ anion W-(M-I sec-1) kl(t-BuOH)Me3NH+ c1- 1.1 x 105 3500Me3NH+ Br- 5.3 x 105 740Me3NH+ p- t oluenesulphonate 7-OX 105 560MeNH: Cl- 2 .6 ~ 107 23MeNH: p-toluenesulphonate 2 . 4 ~ 107 25a All data at 35" C.reduced. On the other hand, it is most unlikely that all three NH-protons of CH3NHzare bound to the anion by strong hydrogen bonds. One, or perhaps two, of theNH-protons are hydrogen-bonded to solvent molecules and can react freely. Possiblestructures of the hydrogen-bonded complexes are shown in (7).HO-t-Bu(CH&NHf.. . X-HI+ICH3N-H .. . X-H(7)HO-t-BuIn (7) the ion pairs are represented as intimate ion pairs, with cation and anion indirect contact.This assumption is consistent with the strong sensitivity to the natureof the anion of the trimethylammonium salts.ACETIC ACIDProton exchange of the aliphatic amines with acetic acid is first-order in theconcentration of BH+OAc-.12 Rate constants k5 are listed in table 5. The valuesof k5 are nearly proportional to those of the acid dissociation constant, KA, of BHfin water, that is, d log k5/d log K A ~ 1. This remarkable correlation suggests thatthe mechanism of proton exchange involves an ionization step, as suggested in (5).The rate-determining step in this mechanism could be either the initial proton transfer(kt) or the exchange of acetic acid between the solvation shell of B and bulk solvent(k~). Several lines of argument suggest that the second step (kn) is rate-determining.12The effect of changing the anion on the rate of proton exchange was investigatedbrieffy.12P 26 The rate appears to be first-order in BH+X-, and some rate constants(again denoted by k ~ ) are listed in table 5.Theserateconstants are strongly dependenton the nature of the anion and appear to be proportional to its basicity. The basicityof X- relative to OAc- was equated to KA(HOAC)/KA(HX), and the ratio of &-valueswas measured directly in acetic acid, under the conditions of the k5-measurements.2E . GRUNWALD AND M. COCIVERA 111The fact that k5 for the chloride salts is too small to be measured by the p.m.r.technique is consistent with the low basicity of chloride ion.When BH+Cl- is added to a solution of BH'OAc-, the rate of proton exchangedrops markedly.12 For example, the rate of proton exchange drops to nearly one-halfwhen 0.247 M CH3NH3Cl is added to 0-0934 M CH3NH30Ac.Only 30 % of thisTABLE S.-FLRST-ORDER RATE CONSTANTS FOR PROTON EXCHANGE OF AMMONIUMSALTS WITH ACETIC ACID IN GLACIAL ACETIC ACID AT 25"l0lOK~ (in water) Q(MINH,f OAc- 6080 5-69CH3NH; OAc- 230 0.238(CH~)~NH+OAC- 945 1.58TRIS * H+OAc- 41,000 84.0BH+X- ks (sec-1)NI$ picrate- 30 -NH;O~CCCII 2 -0 for BH+-.b TRIS = (tris-hydroxymethy1)aminomethane.decrease can be attributed to increased viscosity. Freezing-point data indicate thatthere is ion-pair association between the two salts to form double ion pairs and higheraggregates. If it is assumed that such ionic aggregates as BH+ - OAc- - BH+ C1-are unreactive," the decrease in rate can be accounted for quantitativeIy.12detected by the p.m.r.technique in these experiments.* " Unreactive " in this context means merely that the rate of proton exchange is too slow to be1 Pople, Bernstein and Schneider, High Resolutioit Nuclear Magnetic Resonance (McGraw-2 Gutowsky and Saika, J. Cltem. Physics, 1953, 21, 1688.3 Gutowsky, McCall and Slichter, ibid. (1953), 21, 279.4 McConnell, ibid., 1958, 28, 430.5 Alexander, ibid., 1962, 37, 967, 974.6 Meiboom, Z. Elektrochem., 1960, 64, 50.7 Meiboom, J. Chem. Physics, 1961, 34, 375.8 Grunwald, Loewenstein and Meiboom, ibid., 1957, 27, 630.9 Grunwald, Jumper and Meiboom, J. Amer. Ci'zem. Suc., 1963, 85, 522.10 Grunwald, Loewenstein and Meiboom, J. Chem. Physics, 1956, 25, 382.11 Dannhauser and Bahe, ibid., 1964, 40, 3058 ; Dannhauser and Cole, J. Amer. Chenz. Sue.,12 Grunwald and Price, ibid., 1964, 86, 2965, 2970.13 Emerson, Grunwald and Kromhout, J. Chem. Physics, 1960, 33, 547.14 Grunwald, Karabatsos, Kromhout and Purlee, ibid., 1960, 33, 556.15Loewenstein and Meiboom, ibid., 1957,27,1067 ; Loewenstein, J. Physic. CIzem., 1963,67, 1728.I6Grunwald, ibid., 1963, 67,2208.17 Sheinblatt, J. Chem. Physics, 1962, 36, 3103.18 Silver and Luz, J. Amer. Chem. SOC., 1961, 83, 786.19 Eigen and DeMaeyer, in Rates and Mechanisms of Reactions, Friess, Lewis and Weissberger,23 Grunwald, J. Physic. Chem., 1963, 67, 2211.21 Emerson, Grunwald, Kaplan and Kromhout, J. Amer. Chem. Soc., 1960, 82, 6307.22 Luz and Meiboom, J. Chem. Physics, 1963,39, 366.23 Cocivera, Grunwald and Jumper, J. Physic. Chem., 1964, 68, 3234.24 Swain, McKnight and Kreiter, J. Amer. Chem. SOC., 1957, 79, 1088.ZsSee, for example, Marple and Fritz, Anal. Chem., 1963, 35, 1223.26 Grunwald and Price, J. Amer. Chem. SOC., 1964, 86, 4517.Hill, 1959).1952,74, 6105.ed., part I1 (Interscience Publishers, New York, 1963), pp. 1031-1050

ISSN:0366-9033    

DOI:10.1039/DF9653900105

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

Acid Catalyzed Hydration Of AcetaldehydeBY M.-L. AHRENS (Mrs.) AND H. STREHLOWMax-Planck-Institut fur Physikalische Chernie, Goettingen,Bunsenstrasse 10, GermanyReceived 8th January, 1965The hydration of acetaldehyde catalyzed by HCl is investigated by the n.m.r. line broadeningtechnique. It is shown that the rate of protonation of the very weak base acetaldehyde is a slow stepin the catalyzed hydration reaction. The influence of intermediate states on kinetically broadenedn.m.r. lines is discussed. In acetaldehyde+water mixtures, rich in acetaldehyde, the formation ofa hemihydrate predominates. The kinetics of this reaction proves to be similar to that of thehydration reaction.A number of papers have appeared dealing with the hydration kinetics ofacetaldehyde and other carbonyl compounds.1-6 These reactions are general acid-base catalyzed.It is the purpose of this investigation to give rather direct evidenceon the elementary steps involved in the H30+-catalyzed hydration of acetaldehyde.EXPERIMENTAL AND RESULTSThe n.m.r. spectra were taken at 56.4 Mc/sec with a Varian HR-60 at (23 & 1)OC.The acetaldehyde was distilled and mixed with the appropriate amounts of aqueousHCl immediately before taking the spectra. Fig. 1 shows a n.m.r. spectrum of a-CHO-CH,Hydra1 A- -FIG. 1.-Proton magnetic resonance spectrum of 25 mole % acetaldehyde+water mixture.25 mole % acetaldehyde+water mixture without addition of acid. In fig. 2 fourspectra at different mole % acetaldehyde and 5 x 10-2 M with respect to HCl arepresented.For the kinetic evaluation of the broadened spectra the followingconsiderations are important. The protons, the resonance lines of which areobserved, neither exchange nor are they spin-coupled to exchanging protons.(This coupling is averaged out by rapid protolysis.) On the other hand, there isspin-coupling between the non-exchanging methyl and aldehyde protons and aconsiderable chemical shift exists between the hydrated and the unhydrated form(53 clsec for the doublet and 260 clsec for the quadruplet). For the " slow case "11M.-L. AHRENS AND H. STREHLOW 113with rtk I (wt-cok) I > 1, every line of the multiplets broadens with AvII2 = l/m andoverlapping of the broadening occurs as shown in fig. 3. The 2nAvl12 havebeen obtained by comparison of the half-line width B of the total multiplet withlines resulting from graphical superposition of appropriate Lorentz-curves.FIG. 2.-Proton magnetic resonance spectra of 5 x 10-2 M HC1 in acetaldehyde+water mixtures.Resonance I : CH3CHO ; resonance I1 : CH3CHO ; resonance I11 : cH3CH(O€&.(a) 1.45 ;(b) 24.3 ; (c) 37.7 ; (d) 56.9 mole % acetaldehyde.FIG. 3.-Construction of line shape broadened quadruplet by superposition of Lorentzcurves.For a solution of 57 mole % acetaldehyde+water mixture A c 0 ~ , ~ / 2 is plotted infig.4 against the concentration of HCl.From the integrals of the lines pertaining to the hydrated and unhydrated formsof acetaldehyde the hydration constant KH = [CH3CH(OH)2]/[CH&HO] has beenevaluated for different aldehyde + water compositions.The results are plotted i114 HYDRATION-KINETICS OF ACETALDEHYDEfig. 5. For the comparison of the acidity of HCl solution in water+acetaldehydemixtures, the Hammett acidity function Ho has been determined with 10-2 and 10-1 MCHCl [MIFIG. 4.-Line broadening in 56.9 mole % acetaldehydefwater mixture as a function of HClconcentration.I, from quadruplet CH3CHO; 11, from doublet CH3CHO; 111, from doublet CH3CH(OH)2 - -0 5 0acetaldehyde [mole %]FIG. 5.-The hydration constant KH = [CH3CH(OH)2]/[CH3CHO] as a functionof acetaldehyde concentration.HCI solutions in these solvents. Because of chemical reaction with the aldehyde,primary and secondary amines were unsuitable for the determination of the Hammet M . - L .AHRENS AND H . STREHLOW 115function 110. Therefore 4-dimethyl-amino-azobenzene was chosen as indicatorwith a pK = 3.19 in water. The pKs were determined spectrophotometrically witha Beckman spectrophotometer DK-2. In fig. 6 the results obtained with 10-2 MHCl are reproduced. Similar to other water + organic solvent mixtures the Hammettacidity function goes through a maximum at about an acetaldehyde mole fraction0.6. The two curves with different concentrations of HCI were virtually parallel,pointing to practically complete dissociation also in concentrated acetaldehydesolution.3I0 5 0 I00acetaldehyde [mole %IFIG. 6.-The Hammett acidity function in 10-2 M HCI in acetaldehyde+water mixtures, deter-mined with 4-dimethyl-amino-azobenzene as indicator.DISCUSSIONThe mechanism of the hydration kinetics in dilute solutions of acetaldehydein water (fig.2a) is formulated asCH3CHO+H30++CH3CHOH+ +H,O+CH,CH(OH)OH,f $CH,CH(OH),+H+C' 2 A -7- B 7 Bl .c-3 2(1)Since acetaldehyde is an extremely weak base, the concentration of the protonatedaldehyde B will be exceedingly low (- 10-9 M) whereas the protonated hydratedaldehyde will have a pK similar to that of H30f and its concentration is accordinglymuch higher than that of B. Compared with A and C', B and B1 are intermediatestates at low concentrations. The rate of the reaction BI+C is very fast and there-fore in the n.m.r. spectrum B1 and C' constitute one averaged species C. Thereaction scheme may thus be condensed t116 HYDRATION-KINETICS OF ACETALDEHYDEIn appendix 1 it is demonstrated that for this system two broadened lines areobserved withUZAC = ~ A B ~ B C K ~ B A + k ~ c hllrc~ = ~ c B ~ B A K ~ B A + ~ B C ) .(3)(4)andThe ratios of the integrals under the resonance lines should bepA/pc = ZAC/ZCA.How-ever, this relationship is only true in dilute acetaldehyde solutions, and fails completelyin acetaldehyde-rich mixtures (fig. 24. The sharp lines of the hydrated aldehydeC and the broad lines of the aldehyde A can be understood on the basis of twoassumptions. One possibility is that in the reaction scheme (1) an intermediateB2 decouples A and C by a slow reaction. Then the concentration of B2 must berelatively high for the slow case to be possible.Since no conceivable species ofthat kind exists, the second possibility applies : a parallel acid-catalyzed reactionoccurs with A. Since H-D exchange on C-H protons in D20 solutions occurswith a rate, orders of magnitude lower than the observed rate, any reaction involvingC-H protons (e.g., keto-enol exchange) is eliminated. The same spectra are ob-served when HC1 is replaced by HC104 or naphthalenesulphonic acid. Thereforethe possibility of the formation of 1,l '-chlorhydrin is also excluded. Furthermore,the dependence of the parallel reaction rate on the overall acetaldehyde concentra-tion shows that a second aldehyde or aldehyde hydrate molecule must be involved.We therefore propose for the parallel reaction of (1) :H H H H H HI I I I I iCH3C0 + CH,C(OH)OHz fCH3COH+ + CH,C(OH),+CH C-0-C-CH, ,-I I (5)OH; OHA + C + B + C + DThis is the same reaction as (1) with H20 being replaced by the aldehyde hydrate C.Since in concentrated aldehyde + water mixtures the concentration of free wateris low and that of the hydrated aldehyde is high, reaction (5) is plausible.1 It is ofthe type A+C+D discussed in appendix 2.According to Shoolery's rule,7 thechemical shifts of the CH and CH3 protons in the hydrate C and in the hemihydrateD should be nearly the same. Therefore, the following conditions occur :ZA I (~A--u)D) I, ZDA I (OA--WD) I >1 and ZCA I (WC--OD) 1, ZD I (UC-UD) I el, thatis, we observe a broad line at COA and a sharp line at OC=:COD.* With the followingarguments, an estimation of the concentration of the hemihydrate D is obtained.At relatively high HCl concentrations, i.e., at high rates, the doublet and the quad-ruplet lines of the aldehyde A do not continue to broaden with increasing rate.This can be understood if ZDA(OA-OD)X 1 under these conditions.In fact, it isobserved that the ratio of CHCl necessary for the deviation from the simple " slowcase theory" for the doublet and the quadruplet is about the same as the ratioof the chemical shifts O A - ~ for these two lines (see fig. 4). This constitutes con-clusive evidence that the deviations of the observed at the two lines are not theconsequence of different z values. Since COA-COD is known, an approximate estima-tion can be made for the mole fraction p~ = PAZDA/ZAD with T D A ~ I (OA--WD) 1-1* Unfortunately because of the small chemical shift between C and D no estimate of the rateof the hydrolysis D+H20+2C is available from the n.m.r.spectraM.-L. AHRENS AND H. STREHLOW 117and z g ~ taken from the line width at A. At a mole fraction 0.57 of acetaldehydep ~ , the mole fraction of the hemihydrate is estimated to be about 10-2.The line broadening at A is thus attributed to the two parallel reactions A-+Cand A-+D.Table 1 gives the values for the rate constants ki = l/~i[H+] for different acetaldehydeconcentrations. The values obtained in 1.4 mole % acetaldehyde may be com-pared with data obtained by Bell and co-workers 3 with the maximum temperaturemethod and by Gruen and McTigue4 with a similar technique.The values k Hreported by Bell et al. have to be multiplied by KH/(~ + KH) before comparisonwith our values kAc. Bell's kAC = 490 M-1 sec-1 at 25°C compares well with ourkAC = 480 M-1 sec-1 at (23 & 1)OC. The difference is smaller than the accuracyof either investigation.TABLE 1mole % acetaldehyde 1 -45 24.3 37.7 56.9Hammett-function HO 2-15 2.88 3-08 3.10kA (M-1 sec-1) 480 i 50 480 f 50 330 f35 330 f35(in 10-2 M HCl)kAc (M-1 Sec-1) N 400 N 240 S 30 < 3(M-1 sec-1) 2 80 - 240 - 300 N 330From the data reported above, some conclusions regarding the elementary stepsof the hydration reaction may be drawn. While at equal HCl concentrations theHammett acidity function HO in acetaldehyde +water mixtures increases by more thanone unit in going from water to 60 mole % acetaldehyde, the rate constant kA dimin-ishes only by about 40 %.This is strong evidence against an established pre-equilib-rium of the step A+B which has been assumed by former investigators.2-4 This stepis common to both reaction paths (1) and (5). That the reaction is not a fast stepas assumed hitherto is a consequence of the extremely weak basicity of carbonylgroups. A direct determination of the pK of protonated acetaldehyde is virtuallyimpossible since very fast polymerization occurs in mixtures of acetaldehyde andstrong concentrated acids. However, from the known pK of protonated acetone(pK = -7.2 8 9 9 ) the corresponding value for acetaldehyde may be estimated tobe about pK = -8, in view of the stronger negative inductive effect of the H atomcompared with that of the CH3 group.A pK = - 8 is also comparable with similardata obtained for aromatic aldehydes 10 and for ketones.11 The large differenceof pK for CH3CHOHf and H2Of is the reason for the relatively slow rate of pro-tonation of acetaldehyde by H3O+PFurther experiments substantiate this conclusion. The dependence of the hydra-tion rate in water + dimethyl sulphoxide and in water + acetone mixtures have beendetermined. The HCl concentration was 5 x 10-2 M, the concentration of acetalde-hyde 1-8 M throughout.The results are interpreted on the basis of the consecutive reactions (1) or (2).In the mixed solvents the rate constants are given byandk m = k&#bO+] ; ~ B C = k&[HzO]kBA = ki~[HZo] +&[XI118 HYDRATION-KINETICS OF ACETALDEHYDEwhere X is the non-aqueous solvent.obtainFor the reciprocal of the overall rate we thusIn fig.7 the reciprocal observed rate is plotted as a function of the ratio of con-centrations of the non-aqueous solvent and the water. The vanishing slope of thewater+acetone curve is readily understood with the weak basicity of acetone and theresulting low value of kgA. From the intercept and the slope of the dimethyl sulph-oxide+water curve we obtain kiB and the ratio kBA/kBC, provided that kiA/kgA isknown. To estimate the latter ratio we assume that the deprotonation of the pro-tonated aldehyde proceeds with the same high rate in the two pure solvents, water0.7 -0.6 -0 5 -9 0.4 23 s - 0 30.20 15.10-2 n HCI1,BM AcelaldehydeAcetone[organ. solvent]/[H20]FIG.7.-The reciprocal rate of hydration of 1.8 M acetaldehyde in 5 x 10-2 M HCl water facetoneand water 4- dimethyl sulphoxide mixtures at 23°C.([HzO] = 55.5 M) and dimethyl sulphoxide ([XI = 12.8 M) which are of compar-able basicity. Then, 12.8 kgA = 55.5 k;BA. With this estimation k i B = 103 M-1sec-1 and khA = 1.1 k;Bc. That is, a water molecule approaching a protonated alde-hyde has about the same chance to be protonated or to be used up for the hydrationreaction. In the solutions with high acetone content the rate of the reaction withthe dilute water is diffusion-controlled, and kLA is estimated to be about 1010 M-1sec-1. Then the pK of the protonated aldehyde in water may be calculated to be-8.5<pK< -7.5.Of course, because of the assumption involved the figures pre-sented should be considered to represent the correct order of magnitude only. Alsowith acetone +water and dimethyl sulphoxide +water mixtures the Hammett acidityfunctions Ho, which vary considerably with the solvent composition, do not seemto exhibit great influence on the kinetics.For the explanation of general acid catalysis of the hydration reaction of acetal-dehyde-for which a Bronsted coefficient a = 0-54 on a very large range of pKhas been found 3-a concerted mechanism for the reaction has been advocated.12With weak acids, the observed rate is greater than the calculated protonation rateof acetaldehyde, even assuming a less negative pK value of the protonated aldehydeM.-L.AHRENS AND H . STREHLOW 119It is the conjugate base set free during the protonation in the immediate neighbour-hood of the carbonyl group which can be effective in accelerating the hydrationrate by a suitable polarization of adjacent water molecules.Such a promoting effect on the &O+-catalysis is not excluded by the aboveconsiderations, since the participation of solvation water in the reaction is stillpossible especially in the acetone + water system, where the H30+-ion will be prefer-entially solvated by water, even in high concentrations of acetone. However, itemerges from these investigations that a push-pull mechanism in H30+ +catalysisshould not increase the rate of hydration of acetaldehyde by orders of magnitude.We are indebted to Dr.M. Eigen for valuable discussion.APPENDIX 1N.M.R. BROADENING FOR A REACTION OF THE TYPE A+B",CThe treatment is analogous to that of McConnell.12 The Bloch equations for the com-plex magnetization G = M,,+iM, in the three states A, B and C are:Here PA, PB and pc are the respective mole fractions of A, B and C, the ctk are defined byak = (l/T2,+i(mk-w), 01 sz yH1 is a measure of the strength of the h.f. irradiation, andthe zk are the average lifetimes of the species k with- = ~ + -). For slow passage,the dGkldt are negligible. When the resulting algebraic equations are solved, the totalcomplex magnetization G = GA+ GB+ Gc is( l l 1 zB ZBA TBC(3)( 9 4(9b)(94- i ~ l M O f p A ~ , f p B ~ B f P C ~ C ] G =(l+ + 'BaB)(l + zcaC)-(rB/zBC)(l + zAaA)- (zB/zBA)(l + zc%)'The functions Pk are :P A = TA(l + zBaB)(l + zCaC) + zB(l + zCaC) - (TB/TBC)(zA - zC),P B = rB[(l + zAaA)(l + rCaC) + (zA/zBA)(l + zCaC) + (zC/TBC)(l + zAaA>]PC = z d l + T A ~ A ) ( ~ + zBaB> + zB(1 -F z A a J - ( ~ B / ~ d ( ~ c - 7,)-One special case for eqn.(8) is of interest. PB and ZB are very small. Furthermore,TA I (CUA-WC) I > 1, TC I (COA-CI)~) 1 > 1, and ZAG 7'2. Then the imaginary parts of Gatw-wA and atw ~ w c , which are proportional to the observed n.m.r. signal, are respectively :andEqn. (10) and (11) correspond to broadened lines with a line width ACOY,~ = 2zB/rATBCand Awlp = ~T&CTB.~ respectively.The time constant z ~ r ~ c / ' t g = ZAC correspond120 HYDRATION-KINETICS OF ACETALDEHYDEto the rate constant kAC = k ~ k B C / ( k B A + k B C ) , which is the overall rate constant forA+C. Similar arguments apply to the time constant ZCZBA/T~ = ZCA.Thus a low concentration intermediate or a transition state is not detectable by n.m.r.methods if ZBA 1 (wB-wA) I 6 1 and ZBC I (u~-uc) I < 1. If for one or both inequalitiesthe reciprocal applies, A and B become independent, and two sharp lines are observedat OA and OC.APPENDIX 2N.M.R. LINE BROADENING FOR A REACTION OF THE TYPE A+C+DThe kinetically modified Bloch equations for this case are :(For the meaning of the symbols, see eqn. (n.) The stationary solution for G iswithWe discuss only the special case which applies to the reaction dealt with in this paper wherez D 1 ( ~ A - U D ) I I oA-mc I 9 I ~ D - u c I TA I ( u A - u D ) 1 > 1, and zc I ( m D - u c ) I < 1-Under these conditions at WA, a broadened line with line width 2/2A is observed, whilethe resonances C and D merge to a single sharp line.where ZD = p&.~c+p&~~ is the frequency of the common line averaged with the molefractions p;1= ZC(ZC+ZD) and p 6 = ~D(TC+TD).1 Bell and Higginson, Proc. Roy. SOC. A , 1949,197,33.2 Bell and de B. Darwent, Trans. Faraday Sac., 1950,46, 34.3 Bell, Rand and Wynne-Jones, Trans. Farahy SOC., 1956,52, 1093.4 Gruen and McTigue, J. Chem. SOC., 1963, 5224.5 Strehlow, 2. Elektrochem., 1962, 66, 392.6 Becker, Ber. Bunsen Ges., 1964, 68, 663.7 Shoolery, Tech. Information Bull., Varian ass., Palo Alto, Calif. 2, no. 3, 1959 (cited in Strehlow,8 Campbell and Edward, Can. J. Chem., 1960,38, 2109.9 Deno and Wisotzky, J. Amer. Chem. Sac., 1963, 85, 1735.10 Culbertson and Pettit, J. Amer. Chem. SOC., 1963, 85, 741.11 Stewart and Yates, J. Amer. Chem. Soc., 1958, 80, 6355.12 Eigen, private communication.13 Eigen, Angew. Chem., 1963,75,489.Magnetische Kernresonanz und chemische Struktur (Steinkopff, Darmstadt, 1962, p. 34 ff)

ISSN:0366-9033    

DOI:10.1039/DF9653900112

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

Kinetics of 1,2-Hydrogen Shifts in Carbonium IonsBY D. M. BROUWER, C. MACLEAN AND E. L. MACKORKoninklijkelShell-Laboratorium, Amsterdam (Shell Research N.V.)Received 30th December, 1964The rates of 1,2-hydrogen shifts for a series of carbonium ions have been determined at varioustemperatures from n.m.r. line broadenings. For the cations studied the rates vary over more thaneight orders of magnitude ; they show no correlation with the basicity of the parent unsaturatedcompounds. It is concluded that the magnitude of the partial positive charge at the carbon atomto which the hydrogen is to migrate largely determines the reaction rate. This leads to a modelwhere in the transition state the positive charge is retained at the carbon atoms, and the hydrogenremains o-bonded to the carbon atoms.The present study deals with intramolecular rearrangements in which a hydrogenis transferred to the positively charged carbon atom in carbonium ions from anadjacent carbon atom :\ //@ I\-# c-cH\ //I @\G-CHThis type of rearrangement reaction is well known in the chemistry of alkylcar-bonium ions and is usually denoted by the term lY2-hydride shift.1 A similar re-action has been observed in carbonium ions of the benzenium ion type, e.g., thehexamethylbenzenium ion? Whether the migrating species should be visualizedas a proton moving along an intermediately formed double bond between the carbonatoms 3 or as a hydride ion is one of the questions which will be discussed.Mean-while we use the term hydride shift.In alkylcarbonium ions the rates of hydride shifts can be extremely high; thus,many of these shifts proceed to completion within the short lifetime of an alkyl-carbonium ion in aqueous solvents.Spectroscopic confirmation of these highrates has been obtained from the n.m.r. spectrum of the 2,3-dimethylbutyl cationin HFy3 which indicated that the rate of the hydride shift between the two equivalenttertiary positions in this cation exceeds 104 sec-1 at - 85°C. This is greater byseveral orders of magnitude than that found for the hexamethylbenzenium ion2In order to obtain more insight into the mechanism of the reaction and the factorsdetermining its rate we have measured by n.m.r. the rates of hydride shifts for aseries of carbonium ions with various stabilities and charge distributions.Car-bonium ions were selected (cf. table l) for which the initial and final states of thereaction are chemically identical and thus the heat of reaction will not influencethe reaction rate.EXPERIMENTALThe spectra were recorded with a Varian dud-purpose n.m.r. spectrometer operatingat 56.4 Mc/sec. The n.m.r. probe was equipped with a variable-temperature Dewar insert.The solvents used were HF+BF3 and HF+SbFs ; the solutions were SufEciently stable121 22 HYDROGEN SHIFTS I N CARBONIUM IONSif prepared and kept at low temperature. After completion of measurements at highertemperatures, spectra were taken at low temperature to ascertain that no chemical changeshad taken place. The prehnitenium ion (111) started to rearrange to the isodureniumion, and the o-dimethoxybenzenium ion to the meta-isomer above -20°C.TABLE RATE CONSTANTS FOR THE ~,Z-HYDROGEN SHIFTSFOR DIFFERENT CARBONIUM IONSion rate constant.sec-1II11IVIC+ H , C / ' CH3CH3 CH,.,Cj++HFH3 HCH3VHVIk> 104 at -885°Ck< 1 at - 20°C(isomerizes to the meta-isomer athigher temperatures)k t l at 0°CChemical shifts were initially measured with respect to benzene or cyclohexane as aninternal reference 4 for which the G(TMS) values of -7-27 and - 1.43 p.p.m. were taken.In later experiments, tetramethylammonium ion was used, the chemical shift of which wasfound to be +4.14 p.p.m. from benzene which corresponds to 3.13 p.p.m. downfield fromtetramethylsilane.The analysis of the rates of the hydrogen shift in the hexamethylben-zenium ion has been described in a previous paper? The more complicated kinetic evalu-ation of the data for the prehnitenium and 5,8-dimethyltetralinim ions is given in theappendixD . M. BROUWER, C . MACLEAN AND E . L. MACKOR(4123S (TMS)FIG. l.-(a) Spectrum at 564 Mc/sec of the prehnitenium ion (LU) in HF+BF3 at -83°C. Thenumbers above the signals refer to the ring and methyl hydrogens at the positions indicated intable 1. (b) Spectrum of the methyl groups at - 18°C.101 0'98Itm10:r(I-10/ I1,1, 30 4 5 4.0 3.5103177FIG. 2.-PIot of log k against 1/T for the 1,Z-hydrogen shift in the prehnitenium ion (.). Includedare some points for the same shift in the 5,8-dimethyltetralinium ion ( x 1124 HYDROGEN SHIFTS IN CARBONIUM IONSRESULTSThe kinetic results are summarized in table 1.The spectrum of the 2,3-dimethyl-butyl cation (I), which is present in equilibrium with the tertiary 2- and 3-methyl-pentyl cations,3 shows a doublet (5 c/sec) at 2.75 p.p.m.* which is the collapsedsignal of the four methyl groups. This doublet does not broaden when the temper-ature is lowered to -85"C, which shows that the rate constant exceeds 104 sec-1at this temperature.The results for the hexamethylbenzenium ion (II) in HF + BF3 have been reportedpreviously 2 ; from the structures at high temperature of the collapsed methylsignals (doublet) and of the ring-proton signal (multiplet) unambiguous proofwas obtained that the reaction proceeds intramolecularly.The reaction rates arethe same in HF+SbFs as in HF+BF3.6 (TMS)FIG. 3.-Spectrum at 56.4 Mc/sec of the carbonium ion of 1,4-benzodioxane (VI) in HF+BF3.The numbers 1, 2, 3 and 6 refer to the ring protons at the positions indicated in table 1. Thesignals marked 7 are from the axial and equatorial protons on the dioxane ring.The low-temperature spectrum of the prehnitenium ion (111) is displayed infig. la. The signals at 8.22 and 4-53 p.p.m. are those of the ortho t ring protonand the ring CH2 group. The p-CH3 signal is a triplet (2.89, 2.83 and 2-77 p.p.m.),the high-field component of which overlaps with the signal of the 0-CH3 group at2.73 p.p.m. The rn-CH3 signals are found at 2.45 p.p.m.Temperature increasecauses broadening and collapse of the two ring proton signals and of the methyl-group signals. The collapsed methyl line at - 18"C, which displays some structure,is shown in fig. lb.The results for the 5,8-dimethyltetralinium ion (IV) are closely analogous. Atlow temperature, the spectrum displays signals centred at 8.22 (ortho ring proton)* All chemical shifts are given in p.p.m. downfield from tetramethylsilane.t ortho, meta and para with respect to the protonated carbon.The Arrhenius plot is given in fig. 2.$ see note 7 this pageD. M. BROUWER, C. MACLEAN A N D E. L. MACKOR 1254.57 (ring CHz), 3-28 (p-CH2), 2-75 (m-CHz), 2.65 (O-C&), 2.32 (m-CH3) and abroad signal at 1.9 p.p.m. of the -CHz-CHz- group. At high temperaturethe first two signals collapse to a peak at 5.8, the p- and m-CH2 signals to one at3.0, and the 0- and m-CH3 signals to one at 2.5 p.p.m.Kinetic results obtainedfor the carbonium ion of 2,4,7-trimethylindane were found to be close to thoseof cations I11 and IV, which shows that incorporation of the substituents in a five-or six-membered ring has no influence on the reaction.The spectrum of o-dimethoxybenzenium ion (V) has signals at about 8 (orthoring protons), 7.02 (meta ring proton), 4.20 (ring CH2), 4-49 (p-OCH3) and 4-30 p.p.m.(m-OCH3). Up to -20°C no change takes place in the spectrum, indicating thatthe rate of intramolecular shifts is lower than 1 sec-1 at this temperature. At highertemperature isomerization to the more stable ion of m-dimethoxybenzene becomesobservable.The spectrum of the carbonium ion derived from 1,4-benzodioxane (VI) is shownin fig. 3.No change takes place up to about 0°C. In HF+BF3, line broadeningsets in at that temperature, but from the fact that the HF line broadens simul-taneously it is concluded that the reaction involved is proton exchange betweenthe ion and the solvent. Attempts to suppress this intermolecular exchange byusing the more acidic HF + SbFs system failed because of decomposition of the ion.The spectrum of fig. 3 indicates that in the dioxane part of the ion-as opposed tothe benzodioxane molecule and the dimethyltetralinium ion-there is no rapid inter-change of the axial and equatorial positions of the hydrogens. This can be at-tributed to the fact that in the ion the alkoxy group at the position para to the ringCH:! group has to be fixed in the plane of the benzenium ring.6 When protonexchange with the solvent becomes fast the axial and equatorial positions equilibraterapidly in the time intervals during which the ion is temporarily converted to themolecule.DISCUSSIONStriking aspects of the present results are (i) the great variation-over morethan eight orders of magnitude-in the rate constants between different molecules,and (ii) the absence of any correlation between the reaction rates on the one hand,and the basicities of the parent molecules on the other.Hexamethylbenzene isabout 104 times more basic than prehnitene or 5,8-dimethyltetralin and yet thehydride shifts in their ions are approximately equally fast.The shifts in the ionsof the o-dialkoxybenzenes-the strongest bases of the series-are much slower,whereas by far the highest rate is observed for the ion of 2,3-dimethylbutene whosebasicity is probably comparable to that of prehnitene.We first discuss the implications of these results for the mechanism of thereaction and its transition state and then consider which factor could be responsiblefor the great differences between the various reaction rates. An attractive hypothesis,proposed earlier,2 for the mechanism of the hydride shift, viz., that it would occurvia a transition state in which the proton is weakly n-bonded (> C=C<), mustbe rejected on the basis of the present results. One would expect for that modelthat as the carbonium ion proper is more stabilized relative to the conjugate base,more energy would be required to form the protonated double bond and, thus,the reaction rate would be lower.As the reaction rates do not correlate withbasicities, i.e., with the extent of stabilization of the carbonium ions, we condudethat the factors that stabilize the ions proper are also operative in the transitionstates. This result can be rationalized by assuming that in the transition state theH126 HYDROGEN SHIFTS IN CARBONIUM IONSelectronic structure resembles that of the unperturbed carbonium ion, i.e., that thepositive charge is still largely retained at the carbon atoms. In valence-bondterminology, the transition state would then be represented as a resonance hybridofAandB:/ @ \ A \ / / \ / @ \ H H H HThis implies that the bonding of the migrating hydrogen atom to the carbon skeletondoes not lose all a-bond character during the reaction.Our results strongly suggest that the magnitude of the formal positive chargeat the adjacent carbon atom (2) is the rate-determining factor, the polarization bythis charge of the C-H bond to be broken contributing to the driving force of thereaction.In agreement with this the reaction rate decreases with decreasing valueof that charge. In the dimethylbutyl cation (I) the-formal-charge is one unitand the reaction rate is correspondingly high. In the alkylbenzenium ions (11-IV)the positive charge is largely delocalized and only a partial positive charge, of about0.25-0.30 unit,4 is present at the adjacent carbon atom; the reaction rate is muchlower.In the alkoxybenzenium ions (V-VI) the strong mesomeric effect of the alkoxygroups results in transfer of negative charge from the electron pairs of the oxygenatoms into the ring, especially to the positions ortho and para to them; thus theexcess positive charge at the carbon atom adjacent to the C-H bond to be brokenis still further lowered and, consequently, the reaction rate is very low.It seems reasonable to assume that the activation entropy is approximately zeroalso for the reaction of ions I, IV and V, and that the differences in rate are entirelydue to differences in activation energy. These differences would then amount to4 kcal/mole or more between ions I and 11-IV and to a similar value between ions11-IV and V-VI.An approximate calculation of the effect of charge delocalizationon the energy of the transition state can be based on a purely electrostatic model.The energy of the transition state is lowered owing to polarization of the-distorted-C-H bond by the positive charge at the adjacent carbon atom. Taking 1.2-13for the distance of that bond to the Cf atom and a value of 0.6 A3 per molecule 7for the polarizability of the C-H bond one finds a polarization energy of about10-20 kcal/rnole per unit of positive charge, which is in fair agreement with theabove results.We realize that a more flexible description of the reaction and the transition statewould be possible in terms of molecular orbital theory.In that approach, themigrating hydrogen is bonded to the two carbon atoms by a three-centre bond,the character of which depends on the geometric path taken by the hydrogen nucleus.If in the transition state the hydrogen should be located right above the C-C bond,it would be bonded through the p z orbitals only of the carbons and the substituentsat the carbons would all lie in the same plane, bonded through carbon sp2 orbitals.The other extreme is the situation where the transition state assumes a geometricconfiguration like that in cyclopropane. In that case the substituents are bondedby carbon orbitals that are between sp2 and sp3 and the three-centre bond betweenthe two carbons and the shifting hydrogen uses not only pz, but also px, pu and scarbon orbitals.We consider that the latter description is to be preferred. Asoutlined before. the positive charge is not Iocated at the hydrogen, which meanD. M. BROUWER, C. MACLEAN AND E. L . MACKOR 127that in the three-centre bond there should be a high electron density near the hydrogennucleus. In its present state of development, however, m.0. theory does not allowany predictions to be made of the effect of further charge delocalization on theenergy of the three-centre bond as compared to that of the starting ion.The experimental assistance of Messrs. J. Gaaf, C. W. Hilbers and J. C. M.Stuiver is gratefully acknowledged.APPENDIXKINETIC ANALYSIS FOR IONS I11 AND I VAt low rates of exchange the ring proton lines of the prehnitenium ion are not particularlysuitable for rate determination.The CH2 signal is a multiplet with overlapping lines( A v ~ = 11 clsec). The CH signal is likewise broadened by spin coupling although toa smaller extent (Avp = 5*6c/sec); moreover it overlaps with the solvent peak. Athigh temperatures the ring proton signals fuse into a single broadened line, the width ofwhich is related to the rate by the expression 5which reduces in our case to2- = 8.3 x 104/(Av; - Av,).The analysis of the methyl-group spectrum is complicated by the interchange involvingmethyl lines in more than two positions. The exchange rates were measured by comparingthe experimental spectra with theoretical ones. The latter spectra were obtained bysolving the Bloch equations including exchange.The chemical shifts in c/sec of the methyl-group lines, with respect to the centre of gravityof the spectrum, are given in table 2.The spin-lattice relaxation times of the ring protonsare long compared with T. The chemical shift of a para methyl group depends on the spinstates of the protons in the CH2 group. The coupling of this group with ortho and metamethyl group is small and will be neglectcd. When intramolecular exchange sets in, theortho methyl group (a in the diagram) will become a meta methyl group ( d ) and vice versa.‘The shifts of the methyl groups in positions b and c switch between those of para and metamethyl groups so that here the spin states of the CH2 group protons have to be specifiedbecause of the long-range coupling of the CH2 hydrogens with the para methyl hydrogens.H HSuppose that the spins of the three ring protons are all (+).Then the low-field coni-ponent of the para methyl group interchanges with the meta signal. Likewise, if the spinsare all (-) the high-field component of the para methyl group interchanges with the metasignal. Thus we have here two independent two-site problems.If the spins of the ring protons are different there is a link between two components ofthe para methyl signal and the meta methyl signal. Suppose that initially the spins in theCH2 group are (+) and the one of the CH group is (-). If an exchange event takes place,the para methyl signal at -15.6 c/sec moves to the meta methyl group position.At th128 HYDROGEN SHIFTS IN CARBONIUM IONSnext exchange there is a chance of 3 that the proton with the minus spin moves into theCH2 group and the methyl group signal is shifted to -12.0 ~ 1 s t ~ . In accordance withthe foregoing considerations we divide the molecules into the fractions given in table 2.TABLE 2.-EXCHANGE PATTERN OF PARA METHYL GROUPS FOR VARIOUSfraction1 CH2 :234 c 56SPIN STATES OF THE RING PROTONSexchange with meta '$2 methyl line number spin states ring protons(+ +> 0-CH: (+) -15.6(++I [T; 1% I;!shift (chemical(+ -) or (- +)(+ -1 or (- +) (-) -12.0 + 10.0 c/sec)f- -) (+) - 8.4 )9(- -1 (-) - 8.4 10The fractions (1,7) and (6,lO) form two independent two-sites problems. Analogouslythe sets (2,3,8) and (4,5,9) form two independent three-sites problems.I he exchange interchanges the methyl groups a and d of the diagram which gives anotherindependent two-sites problem.We label the ortho methyl group by the index 11 (-7.0c/sec) and the corresponding meta methyl group by 12 (+ 10 clsec).The Bloch equations including exchange are in standard notation :d 1-G7 + a7G7 = - -iyHIMo - z,-,1G7 + zL;Gl dt 32and corresponding equations for the fractions (6,lO) and (11,12) for which the statisticalweights are 4 instead of &. For the two three-sites problems, (2,3,8) and (4,5,9) one has,for instance,If z is the lifetime of the proton complex in one of its two configurationsThe five independent sets have been solved in the slow-passage approximation and thesolutions were added in order to simulate the experimental n.m.r. spectrum. The cal-culations have been performed with an analogue computer.At high rates of exchange the collapsed line of the para and meta methyl groups hasa multiplet structure which is caused by the averaged coupling of the ring protons withthese methyl groups. The multiplet structure in fig. lb proves unambiguously that the addedproton exchanges intra-molecularly because an intermolecular exchange reaction wouldaverage out the spin coupling of the methyl groups with the ring protons.For the 5,S-dimethyltetraliniium ion the rates were calculated from the broadeningof single lines at slow passage and from the collapsed ring proton signal at more elevatedtemperatures (cf. eqn. (2))D. M. BROUWER, C . MACLEAN AND E . L . MACKOR 1291 Wheland, Advanced Organic Chemistry (John Wiley & Sons, Inc., New York, 1960), 3rd ed.,2 MacLean and Mackor, Disc. Farahy Soc., 1962,34, 195 ; Pure Appl. Chem., 1964, 8, 393.3 Brouwer and Mackor, Proc. Chem. Soc., 1964, 147.4 MacLean, van der Waals and Mackor, Mol. Physics, 1958, 1,247 ; 1961,4, 241.5 Pople, Schneider and Bernstein, High- Resolution Nuclear Magnetic Resonance (McGraw-Hill6 unpublished results.7 Ingold, Structure and Mechanism in Organic Chemistry (Cornell University Press, Ithaca,chap. 12.Book Company, Inc., New York, 1959), chap. 10.N.Y., 1953), chap. 3.

ISSN:0366-9033    

DOI:10.1039/DF9653900121

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

GENERAL DISCUSSIONProf. M. Eigen (Gottingen) said: Dr. Grunwald mentioned our results on therate of H-bond formation and dissociation. The reaction we have studied was thedimerization of ecaprolactam in non-polar solvents.1 On changing to aqueousmedia the solvent now competes for H-bonding. It turns out, however, that therates of dissociation change only slightly; so that the figure of 109-1010 sec-1 isprobably correct. The rates of H-bond formation are smaller in H20 than in non-polar solvents because of this competition. From studies of the rates of structuralconformation changes (helix +random coil) of polypeptides in aqueous solutionthe above figure for the rate of dissociation of a single H-bond (in the unwindingof the helix) was also obtained. Specific influences which might be related to thephenomena reported by Dr.Grunwald were observed 2 in the recombination ratesof substituted ammonium compounds with OH-. We interpreted these resultsas a strengthening of the H-bond structure at the site of proton transfer induced bythe substituted (non-polar) groups. The strengthening of the H-bond structurewould increase the reaction cross-section for proton transfer and thus lead to anincrease of the rates.Prof. R. M. Noyes (University of Oregon) said: The observation that protontransfer to phosphorus is slower than that to nitrogen raises the interesting questionof the extent to which equilibria and rates of proton transfer reactions can be general-ized in simple terms. The proton is a unique chemical species in that it has no extra-nuclear electrons.Hence it will locate in a region occupied by an electron pairand will be a sensitive probe for indicating regions of high electron density. In anysystem at equilibrium, the protons will be located in regions of maximum electrondensity. That this effect is large can be illustrated by the isoelectronic bases F-,OH-, NH; and CH;. The density of excess negative charge in this series variesby about a factor of 4, but the ionization constants of the acids HF and CH4 probablydiffer by 50 powers of 10 in aqueous solution.Although equilibrium constants can be interpreted from electron densities,rates of proton transfers do not correlate simply with equilibrium acidities. Thus,proton transfers to and from carbon tend to be much slower than those to andfrom oxygen.When acetylacetone ionizes to CH3COCHCOCH; , the electrondistribution in the anion is very different from that in the neutral conjugate acid.Transfer of a proton to the anion will be accompanied by polarization effects thatgreatly shift electron positions. Such polarization will be manifested by a greateractivation energy than when the proton is transferred to an oxygen atom where theelectron cloud is already localized.In summary, the position of equilibrium in proton transfer reactions will bedetermined by electron densities in protonated and unprotonated species, whilethe rates of these reactions (if they are not diffusion controlled) will be determinedby polarizability effects.Prof.B. E. Conway (Ottawa) said : Prof. Noyes raised the question of the isotopeeffect in proton conductance and Wannier’s work.3 In the latter, H3O+ ion rotationwas considered following the work of Huckel.4 This mechanism is now not gener-1 cf. Ber. Bunsenges. physik. Chem., 1963, 67, 819.2cf. Angew. Chem. int. ed., 1964, 3, 1.3 Wannier, Ann. Physik., 1935, 24, 545, 569.4 Huckel, 2. Elektrochem., 1928,34, 546.13GENERAL DISCUSSLON 131ally accepted.1 The H/D isotope effect in the mobility is close to J2 but signifi-cantly temperature dependent.2 The ,/2 value is equal to the expected ratio ofdielectric relaxation frequencies for H20 and D20 3 and hence supports the rotationcontrolled proton conductance mechanism.Prof. M. Eigen (Gottingen) said: Prof.Strehlow concluded from his observationsthat for the catalysis by H30+ the rate-limiting step of the hydration reaction isthe transfer of the proton to the carbonyl group. Assuming a pK-value of thecarbonyl group he gives in his paper the rate of protonation should indeed be ofthat order of magnitude. On the other hand, if we consider the catalysis by acidsother than H30+ there is a linear dependence of log k on pK with a slope appreciablysmaller than one. We must conclude that in those cases the simple protonationof the carbonyl group is slower than the hydration since for protonation log kdepends linearly on pK with a slope of one. (The reverse reaction cannot be fasterthan diffusion-controlled.) Therefore, as I pointed out in my paper, we have toassume a co-operative mechanism for the hydration.It might be possible thatthe two mechanisms, i.e., the stepwise mechanism with a rate-limiting protonationof the carbonyl group (followed by fast hydration) and the co-operative mechanism(requiring the water molecule in the right position for hydration) lead to equal ratesfor H30f. This means that the two lines for log k as functions of pK intersect atthe H30+-pK. (For pK> - 1 the k-values for the stepwise mechanism are belowthose for the co-operative mechanism.) Such an accidental intersection at the H38 +-pK cannot be excluded from the present data, but neither can it be safely concluded.The results for non-aqueous media (dimethylsulphoxide and acetone) might bemisleading if a preferential hydration of H3O+ is present (the H20 concentrationswere >2M).Thus it is also possible that even for H3O+ as a catalyst only theco-operative mechanism is valid. In water as a solvent the lifetime of the proton-ated carbonyl group is so short that it seems a little difficult that all the steps followingprotonation (i.e., orientation, binding and splitting of H20 at the carbonium site)occur faster than the deprotonation of the carbonyl group. Further experimentsin non-aqueous solvents at lower 1320 concentrations might answer this question.The present data are not sufficient to prove either mechanism for H3O+, but theyclearly favour the co-operative mechanism for catalysis by acids with a pK> - 1.Mr. R. P. Bell (Oxford) said: Two pieces of evidence can be quoted to supportthe assumption that a hemihydrate of acetaldehyde is formed in concentratedaqueous solution.(i) The corresponding hemihydrate of monochloroacetaldehydecan be isolated.4 (ii) Cryoscopic and vapour pressure measurements with aqueousformaldehyde solutions show the presence of (CHzOH)20 and of higher polymers.5Prof. Maurice M. Kreevoy (Utziversity of A4innesota) said: Dr. Evans and Dr.Miller, in the Physical Chemistry Laboratory, Oxford, have recently studied theacetaldehyde hydration, dehydration rates in dilute aqueous perchloric acid solu-tion by n.m.r. methods and also by a method based on trappigg the acetaldehydewith semicarbazide as it is formed. Dr. Evans obtained 560 1. mole-1 sec-1 forkCA at 25.0" by the scavenging method.Since the equilibrium constant,1 e.g., see Conway in Modern Aspects of Electrochemistry, vol. 111, chap. 2, ed. Bockris and2 Lewis and Doody, J . Amer. Chem. Sac., 1933,55,3504. LaMer and Mason, J. Chem. Physics,3 Auty and Cole, J. Chem. Physics, 1952, 20, 1309 ; cf. Davidson, Can. J. Chem., 1957, 35, 458.4 Natterer, Monatsh., 1582, 3, 449.5 Bezzi and Iliceto, Chim. Ind., 1951, 43, 212. Bezzi, Dallaporta, Giacometti and Iliceto,Gazz. cliim. Ira!., 1951, 81, 915.Conway (Butterworths, London, 1964).1935, 3, 406132 GENERAL DISCUSSION[CH3CH(OH)2]/[CH3CHO] is 1.17 1 this leads to kAC, 655 1. mole-1 sec-1. Dr.Miller studied n.m.r. line widths as a function of HC104 concentration and obtained605 1.mole-1 sec-1 for kAC and 490 1. mole-1 sec-1 for kcA, both at 26". The generalagreement among these values, the older values, and those of Ahrens and Strehlowgives a good deal of support to the various non-traditional methods used. Muchof the residual scatter seems traceable to the variety of temperatures involved.Prof. F. A. Long (Cornell University) said: Dr. Eigen noted the possibility thattransition states for certain systems where both acids and bases serve as catalystsmay involve a simultaneous attack by an acid and a base with presumably watermolecules playing a connecting role. In his paper Dr. Strehlow does not requiresuch participation, but he does refer to it as sometimes needed; consequently,our data on some kinetic solvent isotope effects may be of interest.Dr. Hung,Dr. Robinson and I have been studying deuterium solvent isotope effects for the muta-rotation of tetramethylglucose as catalyzed by the following acids and bases : HOAc,OAc-, H3O+, H20. The reason for utilizing tetramethylglucose is to eliminatethe irrelevant exchangeable protons of ordinary glucose and to minimize the numberof isotopic fractionation factors which must be considered. For every one of thecatalysts, it is possible formally to fit the data by assuming a conventional mechanism,i.e., direct attack of base on the hydroxylic proton for base catalysis and for acidcatalysis preliminary protonation on the ether oxygen in a pre-equilibrium stepfollowed by attack by a base of the hydroxylic hydrogen, i.e., the familiar two-stepacid-base catalysis mechanism.The alternative is to assume for acid catalysis that there is simultaneous attackby the acid and a solvent molecule.In accordance with Eigen's suggestion thiscould be synchronous by the utilization of some connecting solvent water molecules.We have analyzed our deuterium solvent isotope data for the acid catalysts H3O+and HOAc utilizing a simultaneous mechanism with the intervention of two solventwater molecules. It is possible to get good agreement between the data for experi-mental results by selecting plausible fractionation factors, treated as parameters.Further, the fractionation factors which are needed both for the acid catalysis andfor the related base catalysis form a satisfactory internally consistent set of para-meters, i.e., the fractionation factors needed to explain the data for catalysis bythe base, H20, can be taken over directly and used for catalysis by the acidic speciesH3Of.One cannot utilize this result as proof of a simultaneous mechanism.Thedifficulty is that there are too many parameters to permit a unique solution.However, the simultaneous mechanism does give a satisfactory fit, which is at leastas good as can be obtained by the two-step mechanism.Dr. C. F. Wells (University of Birmingham) said: Dr. Strehlow and Mrs. Ahrenshave suggested as evidence against the rapid pre-establishment of an equilibriuminvolving the formation of protonated aldehyde the fact that their rate constantdoes not decrease proportionately as the Hammett acidity function HO increases.I submit that the use of Ho in such a manner is not valid, as HO measures the totalbasicity of these aldehyde + water mixtures to an added indicator.A knowledgeof the partition of protons between water and aldehyde, such as the concentrationquotient Kc = [CH3CHOH]/[CH3CHO] [(H20)4H+], is really required ((H20)4H+is the hydronium ion). We have shown 2 ~ 3 for various oxygen-containing organic41 Lombardi and Sago, J. Chem. Physics, 1960,32,635.2 Wells, Nature, 1962, 196, 770.3 Gila and Wells, Nature, 1964, 201, 606GENERAL DISCUSSION 133molecules that curves of HO against concentration with p-nitroaniline as the indicator-base B can be analyzed at the water-rich end in terms of the competition of B forprotonated water (H20)4H+ and protonated oxygen-containing molecules.Valuesof the concentration quotient Kc calculated for some carbonyl compounds 2, 3 in5 % solution from such an analysis are given in table 1, together with some valuesfor simple alcohols 1-3 for comparison. Acetaldehyde should have a value a littleTABLE 1.KC KC(moles-1 1.) (moles-1 1.)methanol 0.088 methyl ethyl ketone 0.99ethanol 0.27 ethyl acetate 0-96isopropanol 0.34 acetic acid 0.14acetone 0.63less than that of acetone. Protonation constants obtained in H20 + H2S04 mixtures,such as those quoted by Dr. Strehlow and Mrs. Ahrens, are considerably smallerthan our constants and are not applicable to their largely aqueous system. Ourhigh values of Kc for ketones suggest that the rate constant for protonation ofacetaldehyde will be high.Therefore, the possibility of the rapid pre-establishmentof the protonation equilibrium in the hydration of acetaldehyde is not eliminatedby equilibrium measurements when the appropriate data are used. These highvalues of Kc do not preclude the possibility of a concerted mechanism for thecatalyzed hydration.Prof. Dr. H . Strehlow (Max-PIunck-Inst. Physik. Chem., Gottingen) said : TheHammett function Ho is a measure of the thermodynamic activity of the hydrogenion and therefore determines equilibria involving these ions-only approximately-because of the non-thermodynamic assumptions involved. The observed maxima ofHammett functions in many non-aqueous solvent + water mixtures at constantconcentration of a strong acid, are explained by an increase of the basicity of waterwith its depolymerization brought about by the added organic solvent.4 Thatwater is the stronger base in alcohol containing a small amount of water has beendemonstrated from conductivity measurements (e.g., ref.(5)). A pK-value ofabout - 8 obtained for protonated carbonyl compounds by HO measurements withrather concentrated sulphuric acid is applicable to dilute aqueous solutions sincethe reference state of the Hammett function HO is the aqueous solution of a strongacid at unit molality corrected for non-ideal behaviour at that concentration.Dr. C . F. Wells (University of Birmingham) (partly communicated) : Braude’s 5explanation of the increase in HO in water-rich conditions in terms of the breakdownof the water structure is not applicable at low concentrations of organic molecules.Glycerol has an apparent Kc of zero, and the addition of up to 50-60 % glycerolhas no effect on the pK of p-nitroaniline : 6 the maximum density data 7 suggestthat structure breaking does not occur at low concentrations of alcohols.Structurebreaking will occur at higher concentrations of oxygen-containing organic molecules ;e.g., my relationship 8 ~ 9 gives curved plots 10 at alcohol concentrations > 50-60 %.1 Wells, Nature, 1962, 196, 770.3 Wells, Trans. Faraday SOC., in press.4 Braude and Stern, J. Chem. SOC., 1948, 1976.5 Strehlow, 2. physik. Chem., 1960, 24, 240.6 Braude and Stern, J.Chem. SOC., 1948, 1976.7 Wells, Trans. Faraday SOC., in press8 Mitchell and Wynne-Jones, Disc. Faraday SOC., 1953, 15, 161.10 Giles and Wells, Nature, 1964, 201, 606.2 Giles and Wells, Nature, 1964, 201, 606.McHutchison, J. Chem. SOC.,1926, 1898. 9 Wells, Nature, 1962, 196, 770134 GENERAL DISCUSSIONWynne-Jones has suggested that in H20 + H202 mixtures structure breaking probablyoccurs at very low concentrations of H202, and in agreement with his maximum den-sity data,l plots of my relationship 293 are curved at very low concentrations of H202.2Probably the difference 4 between our measurements and those in H20 + H2SQ4mixtures 5 : 6 is largely due to the different species of hydronium ion (H20)hH+involved: in our aqueous system (and that of Dr.Strehlow and Mrs. Ahrens)/i = 4,7 whereas in the 25-70 % H2S04 mixtures 9 9 6 where the mole fraction ofwater is small h<4 and will approach h = 2.7, 8 These latter H2S04 mixturescorrespond to the breakdown in water structure of Braude.9 The proton affinityin (H20)4H+ will be partially satisfied by the structural hydrogen bonding withinthe entity and will therefore be less than in (H20)2H+, i.e., (H20)2H+ will be aweaker acid than (H20)4H+ to an oxygen-containing organic molecule.Dr. C . F. Wells (University of Birmingham) (communicated) : Prof. Conwayhas suggested that the minimum in proton mobility in water+methanol mixturesmust be related to the basicities of water and methanol. However, the basicity ofwater and methanol vary with cornposition.10, 11 In passing from pure water to puremethanol, the protonated species gradually changes from (H20)4H+ to water-solvated CH30H2,2 until sufficient methanol is present to break down the waterstructure,l2, 13 when the equilibrium will tend to shift from CH30H2 to HiO, withHZO less acidic than (H20)4H+.Only at nearly 100 % methanol will this equilibriumshift to methanol-solvated CH30H2.14, 15 This suggests that (H20)4H+ in structuredwater and methanol-solvated CH30H2 in methanol involve a higher proton mobilitythan CH3OH2 and HZO in the collapsed water structure. Minima in proton mobilityhave also been observed for mixtures of water with ethanol, isobutanol, n-butanoland n-propanol.14~ 16Prof. B. E. Conway (Ottawa) said: I agree substantially with the remarks ofDr.Wells; we had, in fact, made some semi-quantitative estimates of the freeH30+ concentration in methanol+water solutions of HCl and related this to thecomposition at which the minimum conductance occurs. The minimum is ob-served only at high methanol concentrations where MeOH; -+MeOH proton transferevents can compete effectively with the alternative process of MeOHi +H2O protontransfer. The change of basicities of water and methanol with changing com-position will be an important factor in more quantitative calculations as Dr. Wellspoints out.+f++f1 Mitchell and Wyiine-Jones. Disc. Faraday SOC., 1953, 15, 161. McHutchison, J. Chenz. SOC.,3 Giles and Wells, Nature, 1964, 201, 606.5 Campbell and Edward, Can.J. Chem., 1960,38, 2109.6 Den0 and Wisotsky, J. Amer. Chem. Soc., 1963, 85, 1735.7 Bell, The Proton in Chemistry (Methuen, London, 1959), chap. VI.8 Wyatt, Disc. Faraday SOC., 1957,24, 162.10 Salomaa, Acta Chem. Scmtd., 1957, 11, 125.11 Wells, Nature, 1962, 196, 770. Giles and Wells, Nature, 1964, 201, 606.12 Braude and Stern, J. Chenz. SOC., 1948, 1976.l 3 Wells, Trans. Faraday SOC., in press ; see also this Discussion.14Goldschmidt and DahII, Z. physik. Chem., 1925, 114, 1 ; 2. physik. Chem., 1924, 108, 121.Goldschmidt and Thuesen, 2. physik. Chem., 1912, 81, 30. Thomas and Marum, Z. physik.chem., 1929, 143, 191.16 Goldschmidt, Z. physik. Chem., 1926,124,23. Goldschmidt and Mathiesen, Z. physik. Chem.,1926, 121, 153. Goldschmidt and Thomas, Z.physik. Chem., 1927, 126, 24.1926, 1898. 2 Wells, Nature, 1962, 196, 770.4 Wells, Trans. Furaday SOC., in press.9 Braude and Stern, J . Chem. SOC., 1948, 1976.15 De Ligny, Rec. trav. chim., 1960, 79, 733GENERAL DISCUSSION 135Prof. R. J. Gillespie (McMaster University) said: Dr. Brouwer has claimed thatthe collapse of the methyl peaks in the n.m.r. spectra of solutions of hexamethyl-benzene, prehnitene, and 5,8-dimethyltetralene in anhydrous hydrogen fluoride withincreasing temperature shows that an internal proton shift in the formed carboniumions occurs at temperatures lower than that at which exchange with the solventoccurs. It is also claimed that for hexamethylbenzene the reaction rate is the samein the less basic solvents HF+BF3 and HF+SbF,. However, for solution of hexa-methylbenzene in fluorosulphuric acid, Dr. Birchall and I were unable to obtainany evidence for this internal proton shift.1 The n.m.r. spectra obtained were con-sistent with the collapse of the methyl peaks being due to proton exchange betweenthe carbonium ion and the solvent. In support of this conclusion we found thatthe solvent line broadened simultaneously with the collapse of the methyl peaksand that the rate of proton exchange was increased by addition of fluorosulphatewhich increases the basicity of the solvent and decreased by addition of SbF5 whichdecreases the basicity of the solvent. It seems remarkable that an internal protonexchange should be observed in hydrogen fluoride but not in the less basic solventfluorosulphuric acid.1 Birchall and Gillespie, Can. J. Chern., 1964, 42, 502

ISSN:0366-9033    

DOI:10.1039/DF9653900130

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

Influence of Electric Field in the Double Layer on Rate Con-stants Determined with Electrochemical Relaxation Techniquesfor Fast Homogeneous Proton Transfer Reactions in SolutionBY HANS WOLFGANG NURNBERGZentrallabor fiir Chemische Analyse, Kernforschungsanlage Jiilich, GermanyReceived 17th February, 1965Electrochemical relaxation techniques, properly selected with respect to the time scale, offer aconvenient way for the study of fast homogeneous chemical reactions in solution, provided a couplingto a suitable electrode process is possible. But inevitably the measured rate constants are influencedby the electric field in the double layer of the electrode. For the dissociation of uncharged acidsthe dissociation field effect may become dominant. The application of a correction, recently intro-duced by Barker on the basis of the electrical equivalent circuit for the faradaic impedance of theelectrode, is outlined.The same correction may be obtained with the aid of the Gouy-Chapman-theory and Onsager’s theory of the dissociation field effect, if a reasonable value for the distanceof closest approach of the carboxylic group of the acid is presumed. Furthermore, the more com-plicated case of the complementary action of the static $-effect and the dissociation field effectencountered in the study of charged acids is discussed. The conclusions, though drawn in terms ofproton transfer reactions, apply generally to other types of fast chemical reactions.Electrochemical relaxation techniques supply not only information on the kineticsof charge transfer and coupled heterogeneous chemical steps but offer often a con-venient way for the study of fast homogeneous chemical reactions in electrolytesolutions, provided the chemical step can be coupled to a suitable electrode reaction.Besides these possibilities in general studies on fast chemical reactions, the performanceof such measurements by voltammetric techniques is often a necessity for the elucida-tion of complicated electrode processes.A number of methods (from various modesof polarography 1-3 and potentiostatic,4 galvanostatic 4 and coulostatic step methods) 4ato the recently developed technique of high-level faradaic rectification) 5 9 11 havingoverlapping optimal application ranges, especially with respect to the time scale ofthe kinetic measurement, up to a detection limit of around lo* sec-1 for first-orderhomogeneous rate constants are available at present.15 Proton transfer processes,like the dissociation and recombination of weak inorganic 6 9 and organic acids *-12have already been successfully studied. Therefore, the following considerations willbe discussed in terms of such protolytic reactions, though they are generally applic-able to other types of fast chemical reactions.Further, the application of a tech-nique of potentiostatic nature will be assumed, i.e., the electrode potential is adjustedand the resulting current is measured. Analogous arguments could be put forwardfor galvanostatic or coulostatic methods.Consider a solution containing acid molecules HA, anions A-, hydrogen ions Hf *and an excess of an inert salt (for instance, LiCl), which serves as supporting electrolyteand for adjustment of the ionic strength.The electrode reaction consists in the reduction of H+.For a number of reasonsa dropping mercury electrode (DME) might be the best choice as test electrode.14* An abbreviation Hf is written for the hydrogen ions, though one assumes that they are presentin aqueous solutions as hydrated H90i entities.13H. w. NURNBERG 137Lf a potential sufficiently negative to reduce every Hf reaching the transfer layer of theDME is applied, the pseudo-stationary state described below will be established within10-9 sec or less after the electrode potential has reached its predetermined value for theanion concentrations used.While the chemical equilibriumkaHA+H+ +A- (1)frremains unaffected in the bulk of the solution it is shifted to the dissociation side in aregion adjacent to the electrode, or more exactly its transfer layer,16 due to the com-petition of the charge transfer with the recombination.The perturbation of theequilibrium increases with decreasing distance from the electrode. Further there isdiffusion of HA (and to a relatively small extent also of H+) from the bulk of thesolution towards the electrode due to the concentration gradients created. Othermodes of mass transport are normally avoided. In principle, one has convectivediffusion employing a DME or a rotating disc electrode of solid material.However,if the polarization time tp is reduced to intervals <50 msec the diffusion may betreated as linear towards an electrode of practically constant surface area.15 Theelectrode reaction serves simultaneously a dual purpose. It initiates a net chemicalreaction (here dissociation) by perturbing the chemical equilibrium (I) and it indicatesalso the rate of the dissociation via the current passing to the electrode. As thediffusion rate decreases with tf the current i has to be measured before it becomescompletely diffusion controlled. The selection of a method having an optimal time-scale with respect to the expected order of the rate constant is therefore an importantstep in the design of experiments. If one studies very high rate constants demandingvery small polarization times tp, a considerable problem is also the sufficient reductionof the charging time for the double layer capacity.Those difficulties are overcomeby charge injection techniques especially if these are coupled with faradaic rectifica-tion.5~ 1 1 9 17 These aspects in correlation to the individual properties and potentiali-ties of various electrochemical relaxation techniques are discussed elsewhere.15The mathematical treatment of these kinetic measurements is considerablysimplified if the ratio of acid to anion concentration is adjusted <l/lO. Then therecombination becomes a pseudo first-order step and the anion concentration may beregarded as constant throughout the solution up to the electrode for practical purposes.The system may be treated as if adjacent to the transfer layer of the electrode areaction layer 18a existed, having such a thickness p that all H+ formed by dissociationof HA within this layer reach the transfer layer, where they are reduced immediately,before they find a chance to recombine with A-.p is given 18b by eqn. (1) and maybe adjusted via the anion concentration [A-1. This possibility exists only if the backreaction of the studied reaction is second order.P = (h+/k[A-J)', (1)DH+ = diffusion coefficient of H+ in cm2 sec-1, andkr = recombination rate constant in l./mole sec.The dissociation rate constant kd is obtained from the experimentally determinedcurrent ratio i / i ~ or S/SD, if the equilibrium constant Kc is known.One hasi/iD = n* exp a2 erfc d (2)for instantaneous currents after a given polarization time tp, orEliD = (n3/2;1) exp a2 erfc (A) + 1 - 7t3/2dfor the average currents 11 over tp.(3138 ELECTRIC FIELD INFLUENCE O N RATE CONSTANTSi, or 1, is the measured current for a given tp and is controlled by the dissociationand diffusion rate of HA, while iD or i~ is the hypothetical diffusion controlled currentfor the same tp.Though i ~ , or i ~ , might be calculated from the diffusion laws anexperimental determination is preferable due to the lack of exact data for DHA insolutions of higher ionic strength.11The dimensionless parameter 3, is generally defined by eqn. (4) :For the homogeneous dissociation of the acid one has withkdlk, = K,,and eqn.(I),khet is the heterogeneous rate constant of the rate-determining step of the overallelectrode process in cm sec-1. If the rate-controlling step is a homogeneous reaction,for instance a dissociation, khet is a formal entity being related to the dissociationrate constant k d in sec-1 via eqn. (5). Provided the equilibrium constant Kc is knownk d follows using eqn. (7) in principle directly from A, and also k, may be calculatedthen with eqn. (6).SITUATION I N ENVIRONMENT OF ELECTRODEConsidering in more detail the region around the electrode one may adopt withadvantage the picture of the following sequence of partly overlapping layers. Nextto the electrode surface is the discrete part of the double layer. For a negativelycharged electrode its thickness is defined by the distance of closest approach of thecentres of the hydrated cations of the supporting electrolyte and those of the H+-ionsand will therefore be 2-3 A.This layer may be approximately identified with thetransfer layer,l6 i.e., the region where the charge transfer step is possible. Thereforethe outer Helmholtz plane is regarded as the solution-side boundary of the transferlayer. Outwards in the solution follows the dzfuse double layer.Taking a simple view of the whole double-layer problem its so-called thickness pais normally defined by eqn. (8) for a symmetrical 1,l-supporting electrolyte.*with E = dielectric constant, Z = ionic strength.For a given supporting electrolyte pd therefore may be adjusted via I.The diffusedouble layer embraces the whole region in which one has a potential gradient (t,b-potential) and a corresponding electric field between the outer Helmholtz plane and thesolution, while the so-called thickness pd defines a plane where the $-potential hasdecayed to a value given by eqn. (1 5).As the outer Helmholtz plane, or according to the diameter and orientation ofthe acid molecules a plane of slightly greater distance from the electrode, defines alsothe distance of closest approach for HA the reaction layer will expand from this planetowards the solution. Normally its thickness p (eqn. (1)) will be adjusted to appreci-ably larger values than p d . Still further into the solution will extend, even for thepd = 1.988 x lO-''(&T/I)* (8)* As the supporting electrolyte is present in large excess, any contribution of H+ and A- to theformation of the diffuse double layer will be neglectedH .W. NURNBERG 139smallest t,-values applied, the dzflusion layer. Its thickness is given for linear diffusionby6 = (xD,Af,)'. (9)For the practical t,-values the condition 19 d/3>,u is fulfilled. Then the HA-concentration within the reaction layer may be trzated as uniform.Even when p>)Pd as normally adjusted in the study of homogeneous chemicalreactions, the reaction layer will include as its inner section the diEuse double layer.Consequently an electrode cannot serve as a completely ideal probe for monitoringthe course of fast chemical reactions. Inevitably, the $-potential and the electricfield over the diffuse double layer will influence the rate to a degree depending fora given system and electrode potential mainly on the ratio )Pa/& In the double-layerregion one may distinguish between influences on the actual concentration (static$-efect), the transport rate (dynamic $-effect), and the dissociation rate (dissociationfield efect) of the reactants. In the study of the dissociation of an uncharged mole-cule like a monobasic weak acid the dissociation field effect (d.f.effect) may be ofdominating influence. Gierst 20 and Hurwitz 20921 have worked out quantitativecorrections for the action of the static and dynamic $-effect on the rate of chemicalreactions coupled to electrode processes. Though the necessity of a correction alsofor the d.f.-effect had been ackn~wledged,~~ 19, 20 no attempts in this direction havebeen made to the knowledge of the writer until recently. A quantitative correctionhas been deduced by Barker 22 from the electrical equivalent circuit for the faradaicimpedance of the test electrode.We have applied this correction to the experimentalkd-values determined by high-level faradaic rectification for a number of aliphaticand aromatic monobasic acids in aqueous 1 m LiCl solution.5, 11 Later, it will beshown that this correction inay also be derived on the basis of the Gouy-Chapmantheory for the double-layer and Onsager's theory of the dissociation field effect.ELECTRICAL EQUIVALENT CIRCUIT APPROACH TO THE CORRECTIONFOR DISSOCIATION FIELD EFFECTFor the overall electrode process (11) the general electrical equivalent circuit ofthe faradaic impedance 11922 is given in fig.l a : $-effects are neglected.The diffusion of the reactants simulate inductance-free resistive transmission linesTL. They consist of series resistors and shunt capacities uniformly distributed alongtheir length. The kinetics of the chemical reaction are represented by the linkingresistors Rh uniformly distributed between TLEA and TLH*. The increased dissocia-tion rate caused by the d.f.-effect in the double layer is accounted for by the resistorR f d . The charge-transfer resistor is Rct. For the given experimental conditions thiscircuit reduces to a simpler form. As the H+-reduction is a totally irreversible stepat the mercury electrode TLH, can be neglected.Further, it is presumed that theelectrode potential is held sufficiently negative to make the contribution of the chargetransfer rate to the overall rate negligible, i.e., Rct-+O. Then, only the dissociationand diffusion of HA remain rate controlling. Introducing the conditio140 ELECTRIC FIELD INFLUENCE ON RATE CONSTANTSone has usually for a weak acid,and normally a practically uniform acid concentration [HA], across the reactionlayer. Thus, RTL(HA) becomes ineffective for p. Then, R T L ~ ) and Rh may becombined to give Ri according to eqn. (lo), and one arrives at the circuit of fig. lb :with eqn. (l), (5) and (6)follows.DH+[H+] DHA[HA],Ri = (RTL(H+)Rh)'; (10)RA = const./k~,,[HA], (1 1)Finally, the two parallel resistors Rfd and RA may be added :1 1 13.-. -=-Rk Ri RfdFig. l c gives essentially the equivalent circuit for (11) which is seen under the statedconditions by the measuring device, Thus the experimental formal heterogeneousrate constant khet consists of two additive terms :The true kd-value is related to k;let while kfa accounts for the increase due to the d.f.-effect in the double-layer region.khet = kiet+kfd* (13)T L ti2T L HA e >c )FIG. 1 .-Electrical equivalent circuit of the faradaic impedance of the electrode.RTL(H+) = const./D~+[H+] ; RTL(HA) = conSt./&~[HA] ; Rh = const/kd[HA].For p > 4pd, only kLet will depend according to eqn. (5) on p, while kfd has a constantd u e for a given ionic strength and electrode potential.The true kd-value may beobtained if khet, measured at different anion concentrations, constant ionic strength,constant electrode potential and for the condition p> 4pd,is plotted against p. Thenecessity to embrace a reasonable range of p-values may demand the selection of atechnique 15 capable of providing quite short t,-intervals if the chemical reactionis very fast as, for instance, the acid dissociation. In practice,ll a plot of kh&/ JDHA =A/ Jtp (see eqn. (4)) against l/J[A-] is preferable to circumvent at this stage theproblem of the uncertainty in the numerical DHA-value in solutions of higher ionicstrength.Fig. 2 shows experimental plots for two acids.11 The truekd-value follows fromthe slope p of the correction lines.With eqn. (4) to (7) one hasp = (kdKcDH+/DHA)p* (14H. w. NURNBERG 141This procedure has the great advantage that only for the ratio &+IDHA has a numericalvalue to be inserted.A further possibility is to subtract from the experimental kh&/( DHA)*-values theentity k f d / ( D H A ) + given by the intersection with the ordinate and then calculate thetrue ka with eqn. (7).Benzoic acid k”e’’-102 \GAcelic acidBenzoic acid3.8 -2.65.0.2 - /,I I r - 7 - 1 I I I2 4 6 8 10 12 14 161/1/[A-] @/mole),10.810.09.28.476N 26.8 X6.0 I$5.2 =-s:4.4‘223.62.82.01.20.4FIG. 2.-correction lines for d.f.-effect on khet.Clearly a deviation from linear behaviour is expected if p reduces to the dimensionsof the diffuse double layer, because kfd becomes now a function of the adjusted valuefor the reaction layer thickness.This opens interesting possibilities to employrate constants of chemical reactions prior to the charge transfer as a probe for thestudy of double-layer parameters. In this case the linear correction could serve toallow for the contribution to khet which arises without the action of the electric field,i.e., khet (compare dotted line in fig. 2). An inherent advantage of this correction isthat it relies essentially on experimental data. It is generally applicable if the backreaction of the chemical reaction is pseudo-first-order, thus permitting the adjustmentof p via the concentration of the excess reactant.TREATMENT OF THE DISSOCIATION FIELD EFFECT CORRECTION ONTHE BASIS OF THE THEORIES OF GOUY-CHAPMAN AND ONSAGEROne should arrive at the same results concerning the d.f.-effect and its correctionif one starts from the relevant double-layer parameters and allows for their influenceon kd.In a first approximation the diffuse double-layer will be treated on the basi142 ELECTRIC FIELD INFLUENCE ON RATE CONSTANTSof the Gouy-Chapman-theory.23 The $-potential as function of the distance x fromthe outer Helmholtz plane is then given by eqn. (15).X tanh -$x tanh -*H =exp--, (G? )/ (G: ) P dwhere z = charge number of the ions forming the diffuse double layer. For asymmetrical 1,l-electrolyte, z = 1 ; I; = 96500 coulomb mole-1 ; R = 8.31 coulombvolt deg.-1 mole-1 ; T = temperature in OK ; $z = $-potential at distance x in V.pa is obtained from eqn.(8). For the dielectric constant, values corrected forthe nature and concentration of the supporting electolyte according to Hasted andRitson 24 have been inserted.In the absence of ion adsorption, an assumption which seems permissible for thenegative electrode potentials applied in the study of acids at the DME, especially forthe supporting electrolyte used (LiC1),20 the charge density Q of the double layer atthe applied electrode potential may be calculated from 25 eqn. (1 6).where c d l is the differential double-layer capacity per cm2 and ER is the electrodepotential with respect to the potential of the electrocapillary maximum. As c d l is a150500A-.-.-.- ,$-H=somVpd=2-7A.,Pd=9'5A; -I-- ,k= 150mvpd=2.7A; - - - - - - - - ,$hH = lOOmV pd = 2.7W ;FIG.3.-#-potential as function of distance x from the transfer layer.function of the potential one has to perform a graphical integration of the Cdl-ERcurve. With eqn. (17), one gets the value of the $-potential in the outer Helmholtzplane $H 25 :Q = - 11.72dc sinh (;: -$H )for Q in pcoulomb cm-2 and the concentration of the supporting electrolyte Ci inmole/l. In fig. 3, the $%-- x functions for several $H-values and two pd-values corres-ponding to an ionic strength of 0.1 or 1.0 respectively are plotted. From these curveH . w. NURNBBRG 143o L I 4 ' 'pd0 5 10Pd = 2.7Ax , AFiG. 4.-k2[kdo as a function of distance x from the transfer layer.(Note that the scaleof theabscissa is much more extended than in fig. 5).I , I , ,20 28 36 4 I2Pdpd = 9.5Ax, AFIG. 5.-k$/kd,, as a function of distance x from the transfer layer144 ELECTRIC FIELD INFLUENCE ON RATE CONSTANTSthe corresponding 4%-x functions for the electrical field strength & = (~?$~/dx) inV cm-1 are calculated with eqn. (18),2RT 1 4x= ---zF P dAfter evaluation of #% the theory of Onsager 26 for the dissociation field effect (alsoknown in conductivity studies as the 2nd Wien effect) may be employed to calculatethe increase in the dissociation rate constant for a given distance x. One hask: resembles the homogeneous dissociation rate constant for a given 4, while k d ,equals its value for & = 0.The ratio in eqn. (19) is a Bessel function of the para-meter b,. For uncharged molecules forming by dissociation a symmetrical 1,l-electrolyte (H+ and A- in our case), b, is defined asFor the dielectric constant E , the value of the solution for the given ionic strengthand nature of the supporting electrolyte24 has to be inserted.(kLd/kdo)x = f ( b x ) . (19)b, = 9.6364,/&T2. (20)The functionf(b,) may be expanded into the following series :f(b,) = l+b,+b~/3+b~/18+b4/180+b5/2700+ . . . (21)The (kZ/kd,)$ against x-curves resulting for several $H, and pd-values are drawn infig. 4 and 5. One sees that the increase in k d caused by the electrical field falls below10 % for x24pd. Thus, a linear behaviour for the correction function kh,t/(D~~)fagainst l/([A-]* (see fig.2) is to be expected if p-values >. 4pd are adjusted.While the curves in fig. 4 and 5 show the field influence in each plane of distance x,with electrochemical relaxation techniques, average values of the rate constantover the whole respective reaction layer are determined.In fig. 6 the experimentally obtained ratio of the uncorrected experimental kd-valueto the true kd-value, obtained with the correction given in fig. 2, is plotted against xfor two acids.11 The p-values ha! e been calculated from the anion concentration[A-] inserting DH+ = 8.5 x 10-5 cm2 sec-1 and k, = 3.8 x 1010 1. mole-1 sec-1 witheqn. (1). As the ionic strength was adjusted to 1.0 with LiCl, pd = 2.7 x 10-8 cmresulted from eqn.(8). The current was measured at electrode potentials between-2.2 and -2.3 V against N.C.E.* Thus$H= -0.1 V results from eqn. (16) and (17).The average values (z/kd,)% calculated from the relevant (k$/kd0)% against, x-curvein fig. 4 for $H = -0.100 V and pd = 2.7 x 10-8 cm, fit quite well to the experimentalcurves in fig. 6 , if for the (graphical) integration, not the outer Helmholtz plane istaken as lower integration boundary, but a plane at x1m = 0.75Afor acetic acid andXlim = 0-25 A for benzoic acid. This result has to be interpreted by the assumptionthat the distance of closest approach xlim for the carboxylic group of the acid moleculesis given by these planes. As the distance of the outer Helmholtz plane from theelectrode surface (diameter of the discrete double-layer) hardly exceeds 3 A significantlyit might seem difficult at first to account for the length of the acid molecule reachingabout 8 A for some of the acids studied.119 12 However, one has to consider thatdespite the dipole moment of the acid molecules and the relatively high field strengthin the region near the outer Helmholtz plane, one cannot expect on average a perpen-dicular orientation of the acid molecules but rather a more diagonal average position.Thus, in fig.6 values to be inserted for the distance xlm of the carboxylic group fromthe outer Helmholtz plane appear not unreasonable. A lower value of x1m seems to* Cdl-values for 1 m LiCl have been determined employing a square wave polarograph.2H. W. NURNBERG6-5-4 -01452-FIG.6.-Average ratios @kdo as a function of distance x from the transfer layer. Full curves:expt. for acetic acid ( x ) and benzoic acid (0). Dotted curves or points calculated for :X E ~ = 0.25 A (A) ; ~h = 0.50 A (0) ; XI^ = 0.75 A (v) ; = 1.00 A (0).t0 4 12 20 28 36 44 52 60I ' # I t I I ~ " " " " "x, AFIG. 7.-Average ratios a/kdo as a function of distance x from the transfer layer. Full curve :expt. for acetic acid with expt. points (x) ; dotted curves calculated for :x l h = 1.75A; +H= -15OmV(O); xk=0.58,; $-H= -5OrnVf.);xw=O.25A; h= -SOmV(IJ); aUforpd=27A.Further for xlim = 1.0 A ; $H = - 150 mV ; pd = 9.5 A (A), and for HA- of D-tartaric acid withx l h = 0,75r%; #H = -100mV; pd= 2-7A (a)146 ELECTRIC FIELD INFLUENCE ON RATE CONSTANTSoperate for the benzoic-acid type than for fatty acids.This could be understoodif the rotation centre of the somewhat less bulky benzoic acid can approach somewhatnearer to the electrode. The agreement between the final result of the experi-mentally confirmed electrical equivalent circuit approach and the approximatetheoretical considerations based on the Gouy-Chapman theory and Onsager’stheory for the d.f.-effect, may be regarded as satisfactory. To illustrate the orderof discrepancy (kTkd&-ratios for further values of x m at constant +H are plottedin fig. 6.In fig. 7 calculated (@/kd) against x curves for other values of xlm, t , b ~ , pd and forcharged acid molecules are given. For a given pd in general, with increasing t , b ~ andtherefore rising field strength, an increase of the relevant xlm due to the more pro-nounced average orientation towards the electrode is to be expected.Consequently,the more the field increases the degree of average orientation in the direction of thefield the more the negative charge centre of the acid molecule, i.e., the carboxylicgroup, is turned away from the outer Helmholtz plane into a plane of somewhatlower field strength. Thus, the orientating influence of the field will have an anta-gonistic effect on the efficiency of the d.f.-effect.GENERAL CONCLUSIONSIn general, the results give experimental evidence for a dissociation field effect,operating in the double layer region and leading to a net increase in kd and also K,,as k, remains largely unaffected as discussed below.Therefore, postulations 28 abouta decrease of kd and Kc in the diffuse part of the double layer, based on considerationswhich disregard the d.f.-effect, have to be rejected. Onsager26 has stressed that afundamental assumption of his theory is the dissociation via an intermediate ion-pairstage and that the action of the electric field has to be interpreted as causing an increasein the separation rate of these ion-pairs. Our experimental results may therefore beregarded as further corroboration for the existence of such an intermediate ion-pairstage in the dissociation and recombination process of weak acids.Concerning the evaluation of measurements, the curves in fig. 6 and 7 emphasizethe necessity of a correction for the d.f.-effect even if p is made significantly largerthan p d .In this connection p-values above 70 A are hardly experimentally feasiblefor the study of acids, because they require anion concentrations below 5 x 10-3 m.Admittedly, the omission of a d.f.-correction will not cause errors in the order ofxxagnitude for the determined k d . But as the desirable accuracy level for rate constantsof such fast reactions is now -F 10-30 % the d.f.-correction should be applied, at leastif relatively negative electrode potentials causing ~H>50 mV are employed. Dueto the lack of a priuri knowledge of exact values for xlm and t,bH one prefers always todeduce the correction curve experimentally, as outlined above.A practical aspect arises from the theoretical curve drawn in fig.7 for pd = 9.5 A,i.e., I = 0.1, $H = 0.150 V and x l h = 0.75 A. It shows that although the ratiop d / p is much more unfavourable one may expect approximately the same magnitudeof the d.f.-effect as forpd = 2-7 A, i.e., I = 1.0. (t,bH = -0.150 V and$H = -0.100 Vcorrespond to the same region of the electrode potential (-2.2 to -2-3 V against aN.C.E.) for I = 0.1 and I = 1.0 respectively [compare eqn. (16) and (17)l). Thereason for this equal efficiency of the d.f.-effect is due to the fact that at I = 0.1,an electric field of lower strength acts over a larger range on kd, as may be seen fromfig. 3 and 5. At small ~H-values (g50 mV) a low ionic strength may even be advan-tageous for small pH.w. NURNBERG 147INFLUENCES ON THE RECOMBINATION RATE CONSTANTThe influence of the electric field on the recombination rate constant kr remainsneglible.26 Provided the recombination, as is normally the case for acid anions A-and H+, is a diffusion-controlled process there occurs a small increase of kr at lowfield strength due to the destruction of the ion atmosphere, but it levels off for 4 > 104 Vcm-1. This phenomenon is well known as the 1st Wien effect.But even this very slight increase of kr will be, in practice, compensated in thereaction layer. According to Debye’s 29 equation for a diffusion-controlled kr,one has for a given system :k,. = const.(D,+ + DA-), (22)where DH+ is, with DH+$DA-, of dominating influence. As DH+ is also in thenumerator of eqn.(1) the 1st Wien effect cancels practically completely. Neverthelessa correction for the d.f.-effect remains important to get the true value of kn becauseit is obtained from the determined k d with eqn. (6).COMPLEMENTARY ACTION OF $-EFFECTSComplications due to the static $-effect will arise if the acid moZecuZes carrya charge, as, for instance, in the second dissociation stage of a dibasic acid. As themercury electrode has in the potential range of Hf-ion reduction always a high negativecharge there will be repulsion from the double layer part of the reaction layer foran animiic acid HA- and attraction for a cationic acid AH+. Consequently, onehas an opposing action on the dissociation rate by the static $-effect and d.f.effectin the first case and an accumulative result in the latter. Allowance for the static$-effect, which rearranges the acid concentration in the double layer region, is achievedaccording to eqn. (23), where the exponential term accounts for the static $ effecton the charged acid :However, the parameter b in eqn. (19) depends also on the charge of the ions producedby the dissociation of the acid.26 Therefore the rate constant ratio k$/kd will differfor given field strength and solution conditions corresponding to ZHA. For repulsion,this increase in b will partly balance the static $-effect, while for attraction (AH+),the accumulative action of static $-effect and d.f.-effect will be considerably enhanced.The effective ratios eff(k$/kd,,)z of eqn.(23) may be transformed as shown previouslyinto the average ratio for a given p to give the ratio value observed by the measuringdevice. Fig. 7 shows as an example the calculated average ratio for the seconddissociation stage of D-tartaric acid in 1 m LiCl. Comparison with the curve foracetic acid reveals that, for the given conditions, static $-effect and the increase ind.f. effect via b almost compensate each other.The foregoing theoretical considerations on the observed action of the electricalfield on the dissociation rate constant are only of approximative character. This isespecially true for the treatment of the double layer on the basis of the Gouy-Chapman-theory. However, this approach seems suitable to give the general picture and amore rigorous and sophisticated treatment, which would demand in the first placemore precise data on double layer parameters, is not likely to alter the general con-clusions nor to change significantly the numerical values of the corrections148 ELECTRIC FIELD INFLUENCE ON RATE CONSTANTSI am indebted to Dr.G. C. Barker, A.E.R.E. Harwell, and to my colleaguesDr. G. Wolff and Dr. H. W. Diirbeck for various valuable discussions and suggestionsduring the preparation of this paper.1 (a) Niirnberg and v. Stackelberg, J. Electronal. Chem., 1961, 2, 350.(b) BrdiEka, HanuS and Kouteckf, Progress in Polarography, ed. Zuman and Kolthoff,(Interscience Publ., New York, 1962), vol. I, chap. VII.2 Schmidt and v. Stackelberg, Neuartige polarographische Methoden, (Verlag Chemie, Weinheim/Bergstr., 1962).3 Nurnberg and Wow, Chem.Ing. Tech., 1965, 37, 977.4 Delahay in Adu. Electrochem. and Electrochem. Eng., ed. Delahay and Tobias, Interscience4 (a) Delahay, J. Physic. Chem., 1962, 66, 2204.5 Barker and Niirnberg, Naturwiss., 1964, 51, 191.6 Niirnberg, van Riesenbeck and v. Stackelberg, Coll. Czech. Chem. Comm., 1961,26, 126.7 Fleischmann, in Polarography 1964, ed. Hills, (Proc. 3rd Int. Congr. Polarography, Southampton,1964), (Macmillan, London), in press.8 BrdiCka, 2. Elektrochem., 1960, 64, 16.9 Delahay and Vielstich, J. Amer. Chem. SOC., 1955, 77, 4955.Publ. ; New York, 1961, vol. I, chap. 5.(b) Delaliay and Aramata, J . Physic. Chem. 1962, 66, 2208.10 Vielstich and Jahn, 2. Elektrochem., 1960,64,43 ; Giner and Vielstich, 2. Elektrochem. 1960,64,11 Niirnberg in Polarography 1964, ed. Hills, (Proc. 3rd Int. Congr. Polarography, Southampton12 Nurnberg and Durbeck, Z. anal. Chem., 1964,205,217.13 Eigen and De Maeyer, Proc. Roy. SOC., A, 1958,247, 505.14Niirnberg, 2. anal. Chem., 1962, 186, 1.15 Niirnberg, Ber. Bun. physik. Chem., to appear.16 Defay, Ibl, Levart, Milazzo, Valensi and van Rysselberghe, J. Electroarzal. Chem., 1964,7,417.17 Barker in Trans. Symp. Electrode Processes, ed. Yeager, (J. Wiley, New York, 1961), chap. 18.18 (a) Wiesner, Z. Elektrochem., 1943, 49, 164; Chem. Listy, 1947, 41, 6.19 Koryta, 2. Elektroclzem., 1960, 64, 23.20 Gierst and Hurwitz, Z. Elektrochern., 1960, 64, 36.21 Hurwitz, 2. Elektrochem., 1961,65, 178 ; see also Matsuda, J. Amer. Chem. Soc., 1960,64,336.22 Barker, Preprints XIV. CITCE-Meeting, (Moscow, 1963) ; Electrochim. Acta, in preparation.23 Parsons in Modern Aspects in Electrochemistry, ed. Bockris and Conway, (Butterworth, London,24 Hasted, Ritson and Collie, J. Chem. Physics, 1948, 16, 1, 11 ; Haggis, Hasted and Collie, ibid.,25 Grahame, Chem. Rev., 1947,41,441.26 Onsager, J. Cheni. Physics, 1934, 2, 599.27 Barker and Niirnberg, Electrochim. Acta, in preparation.28 Sanfeld, Steinchen-Sanfeld, Hurwitz and Defay, J. Chim. Physique, 1962, 139.29 Debye, Trans. Electrochem. SOC., 1942, 82, 265.128.1964), (Macmillan, London), in press.(b) Kouteckg, ColI. Czech. Chem. Comm., 1953, 18, 597 ; 1954, 19, 857.1954), chap. 3.1952,20, 1452

ISSN:0366-9033    

DOI:10.1039/DF9653900136

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

Examination of Proton Transfer Reactions by TemperatureJump and Electrochemical MethodsBY A. BEWICK, M. FLEISCHMANN, J. N. HIDDLESTON AND LORD WYNNE-JONESThe School of Chemistry, University of Newcastle-upon-Tyne,Newcastle-upon-Tyne 1Received 18th January, 1965Measurements of the kinetics of proton transfer for the systems phenol red+water and p-nitro-phenol+ water by the temperature jump method, and for monohydrogen phosphate+ water andhydroxide ion + water by two electrochemical methods are reported. The concentration dependencedoes not in general agree with the predicted variation for any of these reactions. Some suggestionsfor the deviations and for certain observations of rate constants in excess of the diffusion-controlledvalue are made.The kinetics of fast proton transfer reactions have been investigated by a numberof methods in recent years.1 Two substantial sets of rate constants have been com-piled for solutions by relaxation spectrometric 2 and by electrochemical methods.3The purpose of this paper is to present some data using these techniques and inparticular to examine the concentration dependence of the protolytic reactions.Itwill be shown that for neither of these two methods is this dependence in general inaccord with the predicted variation for the reactions which have been examined.Some suggestions for the deviations and for certain observations of rate constantsin excess of the diffusion controlled rate are made.EXPERIMENTALMeasurements of relaxation times were carried out on the systems p-nitro phenol+water and phenol redfwater using the temperature jump method.2 A block diagram isgiven in fig.1. The equipment was similar to that which has been described except thatFIG. 1.-Block diagram of the equipment used for the temperature jump method. C is the 0.5 pFstorage capacitor, R1 the charging resistor and R2 a resistance adjusted to give critical damping.the performance was uprated. A 0.5 pF rapid discharge condenser could be chargedto 100 kV. This condenser was discharged into the T-jump cell using a triggered sparkgap and an impulse generator delivering 20 kV. The heating pulse was terminated nsiugthe parallel spark-gap, the period being selected by means of a chosen length of coaxial14150 TEMPERATURE JUMP A N D ELECTROCHEMICAL METHODScable.The total circuit was constructed in a coaxial form to minimize inductance.Although the condenser would permit currents up to 200,00OA, the discharge circuit wasadjusted to critical damping which restricted the maximum rate of working to 3000 MW.The rise time was 0.1 psec and the length of the heating pulses for most experiments was0-8 psec. With an E.H.T. of 60 kV and a cell resistance of N 20 ohms, this led to a T-jumpof about 15°C from a starting temperature of 23°C. This gave rise to a 10 P: change inthe equilibrium concentration of the dissociated form of the indicator.The changes in the concentration of the undissociated forms of the indicator wererecorded spectrophotometrically in both cases. The cell is illustrated in fig. 2.It couldbe continuously supplied with solution from a thermostatted reservoir in which the pHwas continuously monitored. The form of the cell is different to that which has been usedpreviously. The initial experiments were carried out with this latter type of cell but withquartz window -solutionperspex bodywindowsolution inletFIG. 2.-Cross-sectional and plan views of the Perspex cell used for the temperature-jump measure-ments. The inlet and outlet tubes are connected to a pump and reservoir which are not illustrated.the very rapid temperature rises generated by the present equipment, shock waves createdoptical disturbances which were clearly marked on the oscilloscope traces. Measurementswere made with suitable systems to show that the cell design, fig.2, does not generate lenseffects due to inhomogeneous heating within the time range used. The supporting electro-lyte (1 MKCl) also does not give any transients at the wavelength used in the measure-ments. The potassium chloride was purified by recrystallization and fusion and the solu-tions were rigorously degassed.Electrochemical determinations of the rate of recombination of hydrogen ions withmonohydrogen phosphate and with hydroxide ions were also carried out. 1 he first systemwas investigated by two methods. In one method the hydrogen ion concentration at thesurface of a rotating palladium disc was reduced to zero and the kinetically controlledcurrent due to the generation of hydrogen ions in the solution was measured as a functionof the rotation speed.4.5 A new small-amplitude continuous perturbation method waA.BEWICK, M. FLEISCHMANN, J . N. HIDDLESTON, WYNNE-JONES 151also used in which a small change in the hydrogen ion concentration was maintained atthe surface of a highly reversible hydrogen electrode (activated Pd or Pd-Ag charged tothe a--B phase transition) and the kinetically controlled current at fixed potentials wasagain measured.5 In this method, in contrast to other electrochemical methods, theconcentrations of all species remain finite and close to their equilibrium values. In con-sequence the kinetically limited current may be measured in the steady state on a stationaryelectrode and, for sufficiently small perturbations, no corrections need be made for them a s transfer of the undissociated acid and base.This method was also used to determinethe recombination rate for hydrogen and hydroxide ions.RESULTSRELAXATION MEASUREMENTSThe simplest scheme for the protolytic equilibria is of the formkz k2k i k tki k5k i kip-nitro phenol phenol-redH+ +In- +HIn, H+ +In2-$HIn-, (1)H++OH-+H20, H++OH-+H20, (2)where HTn and HIn- are the undissociated forms of the indicators. This system oftwo equilibria coupled by the hydrogen ion will be characterized by two relaxationtimes given by3The experimentally determined relaxation times for the two systems for a rangeof concentration of indicator and of hydrogen ion are given in tables 1 and 2. Eachrelaxation time reported is the average value from several determinations (up totwelve separate measurements).It is clear that the measured times do not fit theconcentration dependences described by eqn. (3) unless both k2 and k;l change bymore than one order of magnitude over the range covered and different rate constantsare used to determine 21 and 72. Tables 1 and 2 include values for 21 and 72 calculatedfrom eqn. (3) and using magnitudes for the rate constants reported in the literature.6The deviations between the experimental relaxation times and those predicted bythe current theory are of two kinds. (i) Values for k2 and kb derived from individualrelaxation times and from the slope of plots of 1/71 against ~1n2- at constant pH,are not of the magnitude expected.This indicates that the concentration dependenceis not that predicted by the theory. (ii) The product kzkb can be found from ~ 1 ~ 2using the relationship(5)and then separate values obtained by back substitution into (3). Using the data forphenol red, this procedure leads to complex number rate constants in each case whereboth 71 and 22 were measured. This result shows that the relaxation times do notarise from a reaction scheme with coupling in the manner of eqn. (1) and (2).k2k; = [21Z2(cH+2 + C H + C ~ H - f CH+CInZ-)]-1 52 TEMPERATURE JUMP AND ELECTROCHEMICAL METHODSBoth for p-nitro phenol and for phenol red, if k2 and ki were calculated from 21as the result of a single experiment at a pH about equal to pKmn and at the con-centration of indicator giving an optical density of about unity, the values obtainedwould be close to the published magnitudes.If values of k2 were calculated fromTABLE 1PH7.17.17.17.57.57-57.757.757.757.757.758.08.08.08.08.08.0PH6.656-657-157.157-757.95expt. valuesqn-10-5 mole 1.-1 for relaxation times51, P sec0.230.460.880.440.881 *720.280-561.102.24.10-340.681.342.65.049.35.47.55.315.610.38.1notdetectednotdetectednotdetected-2t lnotdetectednotdetectednotdetected - 1.5<1t l72, P s=574025very smallamplitude552820.617.913.811.410.418.515.512.710.912.210.2calc. valuesfor relaxation times71 ~4 sec8.8 1005.4 833.2 764 4 38072, cc sec2-8 3001.6 1904.0 7203.0 6802.0 6201.2 4500.7 4502.5 12002.0 9501.4 7400.9 6600.55 5900.32 550k2k21.1 x 10220.6 x 10220.7 x 1022derived from 71721.2 mole-2 sec-20.4 x 10220 .5 ~ 1022k2 = 3 x 1010 1. mole-1 sec-1; ki = 1.4 x 1011 1. mole-1 sec-1; y = 0.7.TABLE 2expt. valuesfor relaxation times72, p seccIn-lO-S moIe 1.-171, ,u sec1-4 2.8 143.04 2.3 101.7 3.4 124-05 2.1 143-88 2.0 - 201-7 2.1 N 20Wlc. values k2kiderived from 7 1 ~ 271, P sec 22, P sec 1.2 mole-2 sec-21.8 25 0.44 x 10220.8 23 0.45 x 10221-5 80 1 . 4 ~ 10220-6 70 0.81 x 10220.6 2001.1 440for relaxation timesk2 = 3-6 x 1010 1. mole-1 sec-1; ki = 1.4 x 1011 1.mole-1 sec-1.the individual relaxation times most of the magnitudes derived from 21 would givevalues below and those from 72 values above the diffusion controlled limit (noteparticularly the very low values for 7 2 at high pH). Even though the individualmagnitudes of 21 and z2 do not fit the predicted behaviour, the product 2122, wherethis can be observed, leads to a constant value for k2ki of the expected magnitude, - 5 x 1021 1.2 mole-2 sec-2A . BEWICK, M. FLEISCHMANN, J . N. HJDDLESTON, WYNNE-JONES 153Other possible reactions schemes have also been investigated. The reaction viathe hydroxide ionk2HIn + OH- +In- + H20,k ik5H+ + OH-+H20,k igives relaxation times which show a comparable discrepancy with the experimentaldata. Even if both reactions were simultaneously important it would not be possibleto account for the concentration dependence.The data for p-nitro phenol lead toessentially the same conclusions.The overall conclusion which we would draw from these results is that the expecteddiffusion-controlled rate constant is only observed for certain narrowly defined rangesin coiicentration using the accepted model for fast reactions in solution. These arepresumably the conditions which have previously been used.ELECTROCHEMICAL MEASUREMENTSFigure 3 illustrates the measurements with rotating palladium disc electrodes 5of the kinetically limited currents due to the reactionk2k iH+ + HPOi-+H,PO; (7)In these experiments the hydrogen ions which are discharged at the surface are directlyabsorbed by the electrode and the hydrogen ion concentration at the interface thereforefalls to zero with increasing overpotential.The method of removing the hydrogenions is particularly simple and no secondary recombination steps of the hydrogenatoms need be considered. It can be seen from fig. 3 that a well-defined plateau isobserved at any given rotation speed. The rate constant k2 may therefore be evaluatedfrom the variation of the limiting plateau current with rotation speed LU :i 1cA - DR+ - = constant-a+ K(k2cA, + k,) 1 . 6 1 ~ ~ ’where v is the kinematic viscosity and CA- the concentration of the base. The evalua-tion of k2 from eqn. (8) requires the additional assumption that(9) K = kl/k2.Tt is found that k2 is constant and equal to 2-8 x 1010 1.mole-1 sec-1 over an appreciablerange of pH (5.9-7.52) and total phosphate concentration (10-3-10-2 M). Thisvalue is in good agreement with that determined polarographically.7The kinetically limited current in the electrochemical perturbation method isgiven byThis expression, in common with the equations governing other electrochemicalmethods of determining the rates of reactions in solution, may be derived by solvingthe appropriate differential equation governing the mass transfer of the hydrogenions to the electrodes 59 8 (or in some examples of the undissociated acid) and againassumes the validity of (9). Alternatively, it may be simply derived from the concepti = FD&+k;ci-c,+[exp ( ~ F / R T ) - I].(10154 TEMPERATURE JUMP AND ELECTROCHEMICAL METHODSof the " reaction layer " p in contact with the electrode.9 The lifetime of the hydrogenions is z = 1/kZCA- and ,Y is therefore given byp = (DH+/k2cA-):. (1 1)All the hydrogen ions (or the excess of hydrogen ions) generated within this layermay be assumed to reach the electrode and (10) is therefore directly obtained.Similar considerations apply to methods where the undissociated acid is reducedpreferentially to the base.aoo -I S 0 -I z m-5 0 -4973982 99I8899.55 04-EFIG. 3.-Current i at an empty preactivated palladium disc of area 0,091 cm2 plotted against over-potential ( - E ) with respect to Ag/Ag CI for fixed rotation speeds o (given in rad scc-1) in a solution(pH 6.80) 10-3 M in KH2Po4 and 1 M in KCl.It is found that the slopes of the plots of the current against [exp (qF/RT) - 11vary with cb- in the predicted way.On the other hand, the rate constants deducedwith eqn. (10) vary with pH, fig. 4, and in fact are not true constants. The valuesrange from less than, to greater than, the diffusion-controlled limit which wouldagain only be observed within a very narrow range close to pK,. Rate constantsvarying in a similar manner with pH are found for the systems acetate+water andborate + water. The measurements with Pd-Ag electrodes give the same results,fig. 4, so that the effects cannot be attributed specifically to the electrode material.In the evaluation no allowance has been made for the contribution of the reactionof hydrogen with hydroxide ions ; such a correction would have the effect of bringingthe points izt high pH closer to the straight line in fig.4. It is striking that the changein conditions from the measurements with the rotating disc to those with the per-turbation method, but otherwise using the same electrode material, lead to a changein the concentration dependence. The major difference between the methods iA . BEWICK, M . FLEISCHMAXN, J . N. HIDDLESTON, WYNNE-JONES 155252 0P1 ' IS- 33 -- to5 -too-y"00d9.06 '4 7 * 0 7.5 8-0 8.5 9 - 0 8.0.---PHFIG. 4.-PIot of the logarithm of the rate constant kZ, derived using the electrochemical perturbationmethod, against pH for phosphate buffers. Two different palladium electrodes (0, 0) and apalladium electrode containing 23 % silver (A) have been used.0 00A000000 v000A0 00vvAA0A0 0A000I I I 4 10 I I 12PHFIG. 5.-Plot of pH against current density i at an activated palladium electrode filled with hydrogento the cc-8 phase transition in stirred aqueous solutions of potassium chloride for a constant smallperturbation (overpotential = 5 mv).Different symbols signify different purification methods :(1) 0, 0, A, V, fused recrystallized KCI (approx. 1 M) and fresh triple distilled carbonate freewater ; (2) 0, fused recrystallized KCI (approx. 1 M) and fresh triple-distilled carbonate free water ;(3) 0, as (l), but in addition passed through a column of activated charcoal156 TEMPERATURE JUMP AND ELECTROCHEMICAL METHODSthat in one the hydrogen ion concentration at the surface is zero and in the other it isfinite and close to the bulk concentration.The perturbation method may also be used to determine the rate of the recombina-tion of hydrogen and hydroxide ions.For this simple case, in which the concentrationof base cannot be changed independently of the hydrogen ion concentration, eqn. (10)predicts a decrease of the kinetically controlled current with increasing pH. Althoughthe current varies from experiment to experiment, fig. 5 shows that it is essentiallyindependent of the hydrogen ion concentration.The magnitudes of these currents interpreted with the usual model would lead tothe unrealistic values ki = 4 x 1013 1.mole-1 sec-1 at pH 9 and k; = 6.0 x 1017 1.mole-1 sec-1 at pH 12, which again depend on pH. An explanation for the behaviourcan be given in this extreme example.5 Let us suppose initially that it is inherentlypossible to set up experiments in which the recombination rate can exceed the diffusion-controlled limit. Then, if the reaction layer ,u calculated from (1 1) is less than theorder of molecular dimensions, eqn. (10) will be inapplicable. It will be necessaryinstead to substitute a reaction layer whose thickness il will be independent of con-centration. Such a hypothesis leads to the equationi = Fk&,-c,+[exp (qF/RT)- 11,which is in accord with the experimental data, fig. 5. The constant k$ calculatedusing (12) and A = 10 A gives -4x 1014 1.mole-1 sec-1 which is of the order ofmagnitude which would be derived from the vibration frequency of the hydrogenbond. This must represent the final step of the recombination process when thespecies are in contact and the proton tunnels through the intervening water structure.The assumption of a bimolecular recombination rate in excess of the diffusion-controlled limit may be justified aposteuiori. If the small excess of hydrogen ions isconsumed within the layer of molecular dimensions, molecular collisions cannot berate determining and the rate of a subsequent faster reaction is measured. This rateconstant cannot have the value corresponding to the same step in the body of thesolution, since the reaction near the surface in taking place in an electric field and issubject to special steric restrictions.It is evident that for electrochemical methodsthe diffusion-controlled recombination is also only observed under special conditions.DISCUSSIONThree conclusions might be reached about the data presented in this paper:(a) the results may be wrong; (b) the reactions may follow a complicated reactionscheme ; (c) the collison process is not adequately represented by the Debye diffusionmodel or by any other simple collision model.With regard to the first two points and considering first the T-jump measurements,only two relaxation times were observed and moreover addition of excess phosphatebuffer speeded up the first relaxation time until the optical response followed theheating pulse.The effects are therefore genuine and not in any way controlled bytime constants of the instrumentation. With regard to (b) it has been suggestedthat bimolecular reactions in solution must involve a collision complex since thecollision time will always be large because of the cage effect of the solvent molecules.12, 13The intervention of this complex also avoids the difficulty of making the equilibriumconstant dependent on the collision process, eqn. (9). This complication of thekinetic scheme cannot, however, explain directly the observed results if it is merelyconsidered as an extra step involving an additional species. It is more likely that itwould demand a reformulation of the collision process. This is the third possibility (c)A.BEWICK, M. FLEISCHMANN, J . N. HIDDLESTON, WYNNE-JONES 157It is difficult to account for the concentration variation in the relaxation timesusing any conventional formulation of the kinetics. Since the major terms in theexpressions for the relaxation times are due to the recombination process we wouldsuggest that the model for the collision process must be more complicated than is atpresent accepted. A possibility of this type would be that a proportion of the en-counter complexes undergo further collisions with other particles of the acid andbase during their lifetime which may be longer than is at present thought likely.Statements comparable to those about the interpretation of the relaxation timesmay be made about the electrochemical experiments.It can be seen that the diffusionlimited recombination process is only observed under special conditions and that ingeneral the concentration dependence differs from that which would be predicted.It is difficult to compare the data with published results for electrochemical measure-ments as in cornon with other determinations of the rates of fast reactions, relativelylittle information has been given about the concentration dependence of the kinetics.However, the constants in excess of the diffusion controlled limit given here are notthe only high values which have been observed.3 Electrochemical determinationsof the kinetics of acid-base equilibria have been carried out by the two groups ofmethods : 5 group A in which the hydrogen ion concentration at the surface of anelectrode is reduced to zero, and group B in which the concentration of the acid isreduced to zero, the acid form being preferentially reduced.In this second group,the hydrogen ion concentration is maintained constant with an inert buffer. Alldeterminations by methods based on group A give the diffusion-limited recombinationrate whereas those based on group B give values which are frequently above this limitand depend on the nature and concentration of the buffer. A number of explanationshave been advanced for these high values, e.g., general acid catalysis, changes in therate constants in the high fields near the electrode, adsorption of the reagents.However, the determinations in this second group B have always been carried out inthe presence of high concentrations of the inert buffer so that it is likely that in thiscase N-body collisions (N>3) must be taken into account and the distinction betweengeneral and specific acid catalysis becomes blurred.High rates of recombinationcould arise in this way. It is also difficult to give an explanation for the reason whythe methods based on group A should give the diffusion-limited rate. The calculationof this rate depends on the assumption of the validity of eqn. (9) with kz as thisdiffusion-limited constant. The interventim of a collision complex of finite lifetime,or of any reaction step succeeding collision, makes this assumption invalid. Itappears therefore that the results of electrochemical measurements also point to theneed of re-examining the nature of the collision process.A re-examination of the approach to equilibrium by statistical mechanicalmethods 14 is at present being carried out.15 A general formulation of the collisionprocess taking into account the inelastic nature of the collisions does in fact lead tocorrection terms which change the concentration dependence of the relaxation times.We thank our colleagues and particularly Dr.G. Fowler and Mr. R. Paul forhelpful discussions and comments.1 for general reviews and references see : Technique of Organic Chemistry, vol. 8, part 2 ; ed.Weissberger (Interscience, New York, London, 1963); Bell, Quart. Rev., 1959, 13, 169; seealso collection of review articles, 2. Elektrochem., 1960, 64.2 Eigen and De Maeyer, chap. 18, Technique of Organic Chemistry, as in ref. (1).3 Strehlow, chap. 17, Technique of Organic Chemistry, as in ref. (1).4 Vielstich and Jab, 2. Eiektrochem., 1960, 64,43. Albery and Bell, Proc. Chem. Soc., 1963,169158 TEM PER AT U RE J U M P AND ELECT RO CHE MI C A L M ETH 0 D S5 Bewick, Fleischmann and Hiddleston, Proc. 3rd lnt. Congr. Polarograpky, 1964. Bewick,Fleischmann and Hiddleston, Electrochim. Acta, in press.6Eigen and De Maeyer, Z. Elektrochem., 1955, 59, 986. Diebler, Eigen and Hammes, Z.Naturforsch., 1960, 15b, 554. Eigen and Kustin, J. Amer. Chem. SOC., 1960, 82, 5952.7 Nurnberg, Riesenbeck and von Stackelberg, Coll. Czech. Chem. Comm., 1261,26, 126.sKouteckf, Coll. Czech. Chem. Comm., 1954, 19, 857. Kouteckg and Ci2ek, Coil. Czech.9 Wiesner, Chem. Listy, 1947, 41, 6. Hanu;, Cheni. Zvesti, 1954, 8,702.10 Wiesner, Z. Elektrochem., 1943, 49, 164. Brditka and Wiesner, Naturwiss., 1943, 31, 247,11 von Smoluchowski, 2. physik. Chem., 1917,92,129. Onsager, J. Chem. Physics, 1934,2,599.12 see, e.g., North, The Collision Theory of Chemical Reactions in Liquids (Methuen, London,13 Eigen, Angew. Chem., 1964, 3, 1.14 Prigogine, Non-Equilibrium Statistical Mechanics (Interscience, New York, London, 1962).15 Fowler and Paul, to be published.Chem. Comm., 1956,21,836.391. BrdiCka and Wiesnes, Coll. Czech. Chem. Comm., 1947, 12, 39.Debye, Tram. Electrochem. SOC., 1942,82,265.1964)

ISSN:0366-9033    

DOI:10.1039/DF9653900149

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

GENERAL DISCUSSIONDr. W. J. Albery (Oxford University) said: I would agree with Dr. Niirnbergabout the importance of the effect of the electric field in the double layer on rateconstants determined by electrochemical techniques but I would like to make threecomments. First, I do not think that a plot of kHet against [A-l-t as shown in fig. 2should in all cases give a straight line, especially when the diffuse double and reactionlayer thicknesses are not very different. One may show that when [A14 tendsto zero kH& must also tend to zero and not to a positive intercept as in fig. 2.Writing down the diffusion equation for Hf in the vicinity of an electrode,we may describe the dissociation field effect by a series expression of the form :kD/kg = 1 -k 0, eXp (- i l Z / p ) ,n = lwherep is the thickness of the diffuse double layer. We then substitute this expressioiiin the diffusion equation and by means of Laplace transformations we arrive at acorrecting factor for the dissociation field effect which has the formDr.Nurnberg's correction obtained by integrating the series expression over thereaction layer isa , 1+C- kHet KPk;; k; ! I = 1 nplp'-=-=For small values of p/p, i.e., small values of [A-1, the corrections are approximatelyequal, but for higher values of [A-1, on the left of fig. 2, p/p rises to about 0.3 aiidhence the correcting terms may differ by 20 % or so. Calculations carried out bycomputer since show that this difference is about 10 % for p = 4p and 20 % forp = 2p. When [A-]-%+O, p+O, and whereas Dr.Niirnberg's expression for kHettends to a positive intercept of k&Z,cc,/n, in fact kHet must decrease to zero despitethe dissociation field effect. The fact that this is not predicted by the formuladerived from consideration of electrical analogues and transmission lines must Ithink throw some doubt on this approach especially when p is not much greaterthan p.My second point is that the static and dynamic $ effects cannot be neglectedeven though oppositely charged ions are being produced from a neutral species.The field close to the electrode repels the A- and its concentration there may bedepleted by a factor of 50 or so. Because the H+ is being reduced at the electrodethere is no compensating rise in [H+] ; hence the recombination term is reduced anddissociation is enhanced.We have worked out a treatment 1 for both the staticand dynamic $ effects using hypergeometric functions. They give the followingcorrecting function to kHet for the high field case of a Hg electrode at -2 V :PIP 0 0-1 0.2 0.3f(PlPt) 1.00 1-19 1.35 1 -50At Dr. Niirnberg's highest value of [A-1, p/p is 0-2-0-3 : thus, these correctionsare not negligible and, if included, would pull the left-hand points in fig. 2 down,1 Albery, Trans. Faraday SOC., 1965, 61, 2063.15160 GENERAL DISCUSSIONleading to a smaller intercept and therefore implying that the dissociation fieldeffect was less important.This is quite sensible since the Onsager formula is only applicable as Onsager 1himself stated when " the concentration of free ions is sufficiently small so that theDebye-Huckel radius of the ionic atmosphere is much greater than the effectiverange q of the ions ".In aqueous solution, q is 3.5 A, and in 1 M salt solutions theDebye length is much the same and thus the necessary condition is not fulfilled.Hence the ions are to a certain extent shielded by the electrostatic interactions inthe solution and the dissociation field effect will be less than that predicted by theOnsager formula.To help sort out the interplay of these various field and kinetic effects it seemsto me important to carry out kinetic investigations in which not only [A-] is variedbut also the total ionic strength. Furthermore, the use of electrodes of differentmaterials may be useful since the kinetic effects should remain unchanged butowing to the different overvoltages for the discharge of H+ there will be large variationsin the field effects.Dr.H. W. Niirnberg (Kernforschungsanlage Jiilich) said : Concerning the com-ments of Dr. Albery I would give the following answers. Certainly the relationshipbetween khet/ J D H A and [A-]A will deviate from linearity if the reaction layer isreduced to the region of the diffuse double layer as has been stated already in thepaper. In this connection the equivalent thickness of the diffuse double layer pdrefers only to the distance where the @-potential has decayed to a value given byeqn. (15) while the whole range of the diffuse double layer is somewhat larger andmay be expected to equal say 4pd.However, the present paper is mainly concernedwith the case p>4pd. The lowest experimental point in fig. 2 for acetic acid at[A-]-t = 2-55 corresponds to ,Y = 5.7pd. For all reaction layer thickness adjustedto ,u > 4 pd the amount of all additional influences on khet exerted by effects restrictedto the diffuse double layer region will remain constant and independent of ,u or[A-]+. Therefore they can be accounted for by a constant additional term B/ JD=*,and the experimentally obtained khet/ JDHA will then depend linearly on [A-]+according to eqn. (la) :Consequently the true value of ka free from any side effects caused by the diffusedouble layer of the electrode may be deduced either from the slope of the linearpart of the relationship between khet/JDHA and [A-]+, or the intercept obtainedby extrapolation to the ordinate.This correction is essentially independent ofpossible defects in the interpretation of the nature and relative magnitude of theeffects contributing to B. The situation changes for p<4pd. B now becomes avariable and it is to be expected that it will decrease with decreasing p. The de-crease of B will be for the greater part of 4pd relatively small and would reachappreciable amounts only if p corresponds to very small distances x from the outerHeImholtz plane. However, in practice, p never goes to zero but to a constantminimum value which may equal in the limit the distance Xlim. Therefore B, kLetand consequently khet, will have a finite minimum value which will possibly be smallerthan the intercept obtained by the extrapolation of the linear part of the khet against[A-]+ relationship.As Dr.Albery has stated, the equivalent circuit given in the paper does not account1 Onsager, J. Chem. Physics, 1934,2, 599GENERAL DISCUSSION 161for this decrease of B in the double layer region, because it was designed for thecase p>4pd, i.e., the linear part of the plot khet against [A-]-+, in which we wereexperimentally primarily interested and for which the present equivalent circuitis correct and sufficient. Therefore it is not justifiable to raise fundamental doubtsabout the capability of the equivalent circuit approach. The more complicatedcase of accounting for the situation of p<4p& can be achieved by a more sophisticatedequivalent circuit where RFD, Rh and TLH+ become functions of x for the diffusedouble layer region 4pd.In my paper, uncharged acids B were completely attributed to the dissociation fieldefTect.I agree with Dr. Albery that this is a somewhat too crude approxim-ation. Though the d.f.-effect certainly remains dominant, especially the contribution toB of the static $-effect on the anions should not be neglected, while the dynamic $-effecton H+ seems negligible at least for p > +&as a re-examinationof the problem has shown.1For instance, for an ionic strength of 1.0 we obtain, after allowing only for thestatic $-effect on the anions, a contribution of 20 % to B for p>4pd.Practicallythe same result is obtained from equations derived by Matsuda,;! which accountin principle for both the static $-effect on A- and the dynamic $-effect on H+, whilea similar general correction function tabulated by Albery 3 * yields a $-contributionto B which is 7-3 % larger. This seems to be a satisfactory agreement betweenthe various approaches to the complicated problem of sorting out the differentcontributions of the various double-layer effects for the given conditions. However,any errors in calculating the relative contribution of the various double-layer effectsto B will not affect the accuracy of the correction of khet.After the preparation of my paper the problem has been further examined allow-ing also for the decrease in the dielectric constant E due to the electrical field in thediffuse double layer.2 While details of this treatment will be published elsewheresome essential results are communicated here.For 1 = 1.0, Pd reduces from 2.7to 2.12 A due to the decrease of E . Also for distances x<4 A the ki/kd, againstx-relationship becomes considerably more steep than in fig. 4 due to the increasingdielectric saturation when approaching the outer Helmholtz plane (x = 0). Thedissociation field effect in the portion of the diffuse double layer close to x = 0will therefore be of dominating weight in the d.f.-contribution to B. The decreaseof B from its constant value for p>4pd to its constant minimum value correspondingto the minimum value of p might be therefore slight and difficult to detect.Themain result of the refined treatment allowing for the dielectric saturation is thatthe value for the distance of closest approach XI- of the carboxylic group of theacid molecule to the outer Helmholtz plane is altered for the acetic as well as forthe benzoic acid type to the more reasonable figure of xlimzl*6A. However,none of the general conclusions drawn in my paper is altered by this. Furthermorewith respect to Dr. Albery’s remarks on the limitations of the applicability ofOnsager’s equation due to shielding effects in solutions of high ionic strength, itcan be shown3 that over the greater part of the diffuse double layer due to thedecrease of E the effective external field is strong enough to peel off the shieldingionic atmosphere.Therefore, the demands of the Onsager theory seem to befulfilled in this region.* The supply of these data by Dr. Albery prior to publication is gratefully acknowledged.1 Nurnberg and Wolff, unpublished results.2 Matsuda, J. Amer. Chem. Sac., 1960, 64, 336. Senda and Delahay, J. Amer. Chem. SOC.,3 Albery, Trans. Faraduy SOC., 1965, in press.F1961, 65, 15871 62 GENERAL DISCUSSIONDr. W. J. Albery (Oxford University) said: Taking Dr. Nurnberg’s equation,B is not constant but is a function of the ratio p / p . Hence it is not necessarilytrue that akHet/ap must equal k ~ . For p&p, aB/ap will be unimportant butthis condition is not fulfilled for all of Dr. Nurnberg’s experimental points.Dr. H. W. Nhberg (Kernforschungsanlage Jiilich) said: I agree with Dr.Alberythat in the equation above for khet, kfd and klL are not strictly constants for thewhole reaction layer p. However, for all experimental points given in my papera(kfd+k+)/dp = aB/ap may still be regarded as negligible (see fig. 2, 3 and 4 ofmy paper). The deviation from linearity at the lowest experimental point in fig. 2(acetic acid, [A-]-3 = 2-55) due to the small finite value of aB/ap would fall withinthe stated experimental error of +4 %. This is in excellent agreement with newcalculations employing a computer by Albery 1 * (see table 2 in ref. (1)).Dr. M. Fleischmann (Newcastle upon T’ne) said: There is a general difficultyin the interpretation of electrochemical measurements of the rates of fast homo-geneous reactions which may be illustrated by the evaluation of the effect of highfields on the velocity of dissociation.The mass transfer of the species involved inthe equilibriumkH,t = pkD +BYk lk2HA+A- +H+will be governed by the differential equations,taking into account diffusion and migration. These one-dimensional equationsare solved (usually with simplifying assumptions) with the appropriate boundaryconditions so as to derive the reaction-limited rate. For high field dissociation theelectrical field gradient is additionally determined by the solution of Poisson’sequation for the inert electrolyte. It is instructive to consider the particular con-dition of a steady state (differential with respect to time zero) in the absence ofcurrent. Excluding discontinuous solutions the left-hand side of all the equationsis then zero and the only possible self-consistent solution of the first two is CH+CA- =constant.2 With CHA also a constant, it is impossible to make kl a function of thedistance from the electrode unless k2 exactly compensates the variation of kl.Under these conditions we therefore conclude that there can be no high-fielddissociation in the field of the double layer.While there is difficulty in considering high-field dissociation in the absence ofcurrent flow (or indeed the dynamic 1G/ effect separately from high-field dissociation),this conclusion appears to be unlikely.The cause would seem to lie in the dualuse of the concepts of diffusion, first to derive the variation of kl with field from aformulation in three-dimensions in the bulk of the solution (as well as the evaluation* The supply of these data by Dr.Albery prior to publication is gratefully acknowledged.1 Albery, Trans. Faraday Suc., submitted for publication.2 Bass, Trans. Faraday Soc., 1964, 60, 1656GENERAL DISCUSSION 163of k2) followed by the use of these quantities in the one-dimensional differentialequation in the surface region. A completely self-consistent treatment wouldhave to consider the three-dimensional case in the region of the surface of theelectrode, the kinetically-limited current being derived directly.Dr. W. J. AIbery (Oxford University) said: I think that there is an obviousfallacy in Dr. Fleischmann’s paradox.He states that, because there is no currentflowing, terms of the form D3[X]/W are equal to zero. But this is not true. Theincreased tendency of the acid to dissociate in the region of high field near the elec-trode leads to a fall in [HA] and a rise in both [H+] and [A-] and thereby the estab-lishment of steady-state concentration gradients. Thus 82[HA]/az2 is positivewhile 8[H+]/dz2 and d2[A-]/az2 are both negative; this is quite compatible in allthree equations with an increase in k D , caused by the dissociation field effect, leadingto kD[m] being slightly greater than ~R[H+][A-].Prof. M. Eigen (Giittingen) said : After receiving the preprints, Mr. Ilgenfritzat our laboratory has tried to remeasure the data reported by Bewick, Fleischmannand Wynne-Jones.The error limits are quite high since these measurements haveto be made around pH 7 in unbuffered solutions at small concentrations of the acidsor bases. Furthermore, the measured relaxation times are very short and in manycases close to the heating time. In general, our results agree with those reportedby the authors. The evaluation of the data, however, has to take into considerationthe protolytic (H+ + base) as well as the hydrolytic (OH- + acid) reactions, sincethe pK of the system and the pH of the solution are close to 7. By using the correctexpressions 1 for z, one obtains values whose orders of magnitude agree with themeasured data throughout the whole range of concentration. The agreement isquite good at low concentrations of HIn (phenol red) and OH- (< 10-5 M).How-ever, there is a systematic deviation at higher concentrations : the experimentalvalues of l/z become almost constant whereas they should increase with increasingconcentration of (HIn + OH-). A possible explanation is that at high dye concentra-tions association occurs. Peculiar rate phenomena of this type have been observedby us for a number of dyes (at concentrations around 10-5-10-4 M), and it seemsthat such irregularities exist in phenol red also.The conclusion that these deviations disprove the Debye-theory of diffusion-controlled reactions does not seem to us appropriate. We have studied more thana hundred, more or less simple, acid-base systems, covering about 6 orders ofmagnitude in concentration, and have always found excellent agreement with thetheory.These studies include quite different methods such as sound absorption,high-field pulse and temperature and pressure jump techniques. The results agreealso excellently with those from n.m.r., fluorescence transformation and-wherethe rates are slow enough-flow studies. Some systems (e.g., NH3) have beenstudied in the concentration range from 10-5 to 1 M (employing different tech-niques). At low concentrations we have never observed any concentration de-pendence of the rate constant ; at higher concentrations ionic strength effects, etc.,of course, are present. Deviations of the above-mentioned kind have been observedin some systems, but they could always be quantitatively related to secondaryreactions (such as dimerization or keto-enol tautomerism).We suggest that ainore detailed study of these dye systems be made in order to clarify the nature ofthese deviations. Such T-jump measurements could be complemented also byhigh-field relaxation studies, which can resolve the time range below 1 psec.Dr. A. Bewick (Newcastle upon T’ne) said: We are indebted to Dr. Eigen forrepeating some of our T-jump measurements and eliminating any remaining doubts1 cf. Angew. Chem. int. ed., 1964, 3, 1164 GENERAL DISCUSSIONconcerning conclusion (a) in the discussion section of our paper. We would makethe following reply to his comments concerning the results for phenol red. Al-though we use very dilute solutions which are only self-buffered, we have developeda technique for circulating the solution through the cell from a large capacity reservoirin which the pH is monitored.This enables a good reproducibility to be maintainedwith these solutions.We have calculated relaxation times for the complete protolysis-hydrolysiskinetic scheme represented bykzkik5kikSk iH' + In2 - +HIn-H'+OH-+H,OHIn-+OH-+In2- +H20The literature values were used for kz and k2, and several values for k; wereinvestigated. Table 3 shows the calculated and experimental values for the longerrelaxation time 22, using for k; the value which gives the closest correspondencebetween the calculated and the experimental results. Whereas for the simpleTABLE 3 .-RELAXATION TIMES CALCULATED USING A PROTOLYSIS-HYDROLYSIS KINETICSCHEMEP H 10-5 qn2- mole L-1 ' 2 , psec dc.72, psec expt.7.1 0.23 60 577.1 0.46 38 407.1 0.88 25 257.5 0.44 14 -7.5 0.88 7.7 557.5 1-72 4 287.75 0.28 31 20.67.75 0.56 19 17.97.75 1.10 10 13.87.75 2.2 5 11.47.75 4.1 2.8 10.48-0 0.34 30 18.58-0 0.68 21 15.58.0 1.34 12.5 12.78-0 5.04 3.6 12.28.0 9.3 2.1 10.2k2 = 3 x 1010 1. mole-1 sec-1, k i = 1.4 x 1011 1. mole-1 sec-1, kz = 1010 1. mole-1 sec-1.8-0 2-61 7.3 10.9protolysis scheme, table 1, the calculated z2 values show about the correct percentagevariation with phenol red concentration at fixed pH but are several orders of mag-nitude too long, the protolysis-hydrolysis scheme gives results having the correctorder of magnitude but their concentration dependence is now incorrect, e.g., atpH 8.0 the calculated and experimental values for 22 vary by factors of 15 and 1-8respectively. Therefore our conclusions concerning the inadequacy of the presenttreatment remain as stated.No other case has been reported in which the kinetics of two coupled diffusion-controlled reactions has been investigated over a wide range of concentration, anGENERAL DISCUSSION 165indeed, the data for a single diffusion-controlled reaction are inadequate for veri-fying unequivocally the current theoretical treatment.The accepted theory mustbe regarded as unproved except insofar as the present paper casts considerabledoubt on its validity.The electrochemical perturbation method 5 has also been analyzed using theprotolysis-hydrolysis scheme in order to try to explain the pH dependence of theresults for phosphoric acid. This treatment leads to the following expression forthe currentIf the terms due to the water are small, this gives as before the observed dependenceof the current on the total buffer concentration. Depending upon the relativemagnitudes of the various terms, the pH dependence is either as before or differentin such a sense as to increase the variation of the rate constant with pH.It was suggested also that at higher concentrations phenol red showed deviationsfrom the Beer-Lambert law due probably to association. We have tested this anddo find some small deviations. Over a twenty-fold concentration range extendingfrom the region of the lowest concentration to greater than the highest concentra-tion used in our T-jump experiments, there is only a 20 % discrepancy between thetotal phenol red concentration and that indicated by the optical density. It wouldrequire more than an order of magnitude change over this range in order to accountfor the relaxation times in terms of the theoretical model

ISSN:0366-9033    

DOI:10.1039/DF9653900159

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

Estimation of Very Fast Reaction Rates from the Broadeningof Vibrational Spectral LinesBY MAURICE M. KREEVOY AND C. ALDEN MEADDept. of Chemistry, University of Minnesota, Minneapolis, Minnesota, U.S.A.Received 4th January, 1965The 1435 cm-1 Raman band of the trifluoroacetate ion A- has a width at half-height of about15 cm-1 in neutral aqueous solutions. In acidic solutions this is broadened to as much as 45 cm-1.Evidence is presented that this broadening is due to the shortness of the life of the species, andaverage lifetimes are estimated for A- and HA in a variety of solutions.In a previous, brief, communication1 we described the broadening of the tri-fluoroacetate Raman line at 1435 cm-1 in aqueous solutions containing strongacid, attributing it to exchange broadening.The present paper confirms andextends the earlier observations. The attribution of this phenomenon to exchangebroadening seems to be essentially correct.EXPERIMENTALRaman spectra were measured on a Cary model 81 photoelectric Raman spectro-photometer, equipped with a Toronto-type mercury arc lamp. Solution temperaturesduring the measurements were around 40°, but could not be controlled. A slit of 5 cm-1,double, 10 cm long was used, with a scanning speed of 0.05 x 5 and a period of 10. It wasshown that a five-fold reduction in scanning speed did not appreciably influence eitherband heights, or widths at half-height.On most days when the spectrophotometer was operated, 1-04 M sodium trifluoroacetateNa+A- was scanned to verify the proper functioning of the instrument and to providea calibration for the intensities measured on that day.On a few days some other familiarband was scanned in the place of the 1-04 M Na+A-. For purposes of this paper the in-tensity of the 1435 cm-1 A- band is defined as its height times its width at half-height. Insolutions in which the A- concentration is obvious from the composition it was shownthat the intensity defined in this way is proportional to the A- concentration within theprecision of the measurements (f10 %). In solutions where the composition alone doesnot give the A- concentration it was estimated from this proportionality.THEORYThe theory of the broadening of Raman lines by exchange has been brieflydescribed.1 Space does not permit a full discussion here, but it may be noted thatthe approximation, all Pmz, 9 1 , is not needed to reach the previously indicated con-clusions.The equations used in the present paper are as follows :for the intensity I at frequency v in the neighbourhood of the band maximum cr).The width at half-height is Av+ and C is a constant proportional to the concentrationof the species2.l/z = +(Av+- A v ~ ) , (2)16M. M. KREEVOY A N D C. A . MEAD 167in which z is the mean lifetime of the species and Avi is the width at half-heightof the unbroadened band. Eqn. (2) is an approximation, valid when there is almostno overlap of the bands which are merging. Jt should be noted that, while thefrequencies in eqn. (1) may be expressed in any self-consistent units, those in eqn.(2) must be expressed in rad.sec-1 in order that z will have its usual significanceand units.RESULTSNeutral sodium or ammonium trifluoroacetate (NafA- or NH; A-) solutionsshow an intense Raman band at 1435 cm-1 which has been assigned to the sym-metrical carboxylate stretching frequency.3 To a good approximation this bandis Lorentzian in shape, as shown in fig. 1. This band was scanned a total of 14times during the course of this investigation. The mean band width at half-height,Av+, is 15.1 cm-1 with an average deviation from the mean of 0.3 cm-1 and anextreme deviation from the mean of 0.9 cm-1. This serves to define the precisionwith which Av+ can be measured in favourable cases.FIG. 1.-Typical examples of the 1435 cm-1 Raman band of A-.The solid lines are recordertraces, the circles are calculated for a Lorentzian band, the squares for a Gaussian band. Bothtypes of calculated bands are forced to have the proper height and width at half-weight. Curve Ais 5.06 M NHiA- and curve B is 1.04 M Na+ A-.Table 1 shows Av+ of the 1435 cm-1 trifluoroacetate band in a number of neutraland near-neutral solutions. It will be noted that some self-broadening by thetrifluoroacetate ion occurs. This seems to be attributable to the trifluoroacetateion itself, rather than the cation, as fairly concentrated NaC104 fails to give thiseffect. The ammonium salt behaves much as the sodium salt, and neither produce168 RATES FROM BROADENING OF VIBRATIONAL LINESmore than about 1 cm-1 of broadening below 3 M concentration.Within theprecision of these measurements (+,2 cm-1) the peak position is invariant underthese changes in solution composition. The peak remains Lorentzian, as shownby fig. 1.TABLE ~.-HALF-WIDTH OF THE 1435 cm-1 TRIFLUOROACETATE BAND INVARIOUS NEUTRAL SOLUTIONScationNa+Na+Na+Na+Na+Na+Na+NHiNH;conc. A-, M0.781.041 *943-135.2 10.780.781.013.03width, cm-114.615.1 a15.716.218.316-015.015-416.1a average of 14 determinations, as described above ; b with 3.0 M added NaClO4 ;c with 4.1 M added NaC104.TABLE 2.-cOMPOSITIONS, LINE WIDTHS AND RATES IN ACIDIC SOLUTIONS[H+l0.881 *492.032.142-141 0020.301.682.061.591.802.482.102-763.54[A-I0.881 -492.032.142-143-083.380-700.590.660.870.621-160.880.73[other ions]2 06 M Na+3-08 M Na+0.98 M C1-1 -47 M C1-0.93 M ClO,0.93 M ClO,1 -86 M ClO,0-94 M ClO,1-88 M ClO,2.81 MClO,[HA10.130.511.013.235.392.231.930.360.450.270.680.931 a942.222-3716.417.820.024.523 819.619.418-418-617.717.820.723.027.8-45 =4 tc (I 10-l1/ZA-, sec-10.87 .78 1.20.75 -64 2.50.67 -53 4.60.40 935 8.90.28 * 18 8.24.24.13.13.32.42.55.37.412.028l O - l l / r ~ ~ ,sec-18.17.39.75.93.35.87.26.04.35.93.23.54.44.88.6a interpolated from results given by Hood, Redlich and Reilly ; 4 b somewhat unsymmetricalband, with max.at 1437 cm-1; C somewhat unsymmetrical band with max. at 1450 cm-1.Aqueous HA solutions also show the 1435 cm-1 A- band, as do aqueous HAsolutions containing HCl or HC104, and also solutions partially neutralized withNaOH. However, Av+ varies widely for these solutions. Table 2 shows Av+ andthe concentrations of the various ions in a number of such solutions. The con-centrations were all evaluated from the empirical compositions and the concentra-tion of A- determined from the intensity of its band, as described in the experimentalsection.For solutions made up of HA in water, the degree of dissociation a was evaluatedand compared (in table 2) with that obtained by interpolation from the data of Hood,Redlich and Reilly.4 The present results give consistently higher degrees of dis-sociations, but the discrepancies are not too large, particularly at the lower con-centrations, and the trend is similarM .M. KREEVOY AND C . A . MEAD 169It is clear from table 2 that the band broadens markedly in solutions containingsubstantial quantities of Hf or HA, and most particularly in solutions containingsubstantial quantities of both. In addition, in the most acid solutions, there is avisible tendency for the band to become unsymmetrical and to shift toward higherfrequency. These trends are further illustrated in fig. 2. If this broadening isattributed mainly to the shortness of the lifetime of A- then ~ / z A - can be estimatedby means of eqn. (2), using 15.1 cm-1 for Avg.The analogous quantity for HAcan be obtained from the requirement that equilibrium be maintained. Both ofthese are also given in table 2.FIG. 2.-The 1435 cm-1 band of A- in solutions initially 3.1 M in HA. Curve A is for a com-pletely neutralized solution, B has no additives, C has 0-94 M HC104, D has 1.88 M HC104, E has2-81 M HC104, and F has 6-28 M HC104.A much more cursory examination has also been made of the HA Raman bandat 816 cm-1 and of the ClO, band at 935 cm-1. Pure HA shows a strong peak at816 cm-1 which has been assigned to the carbon-carbon stretching mode.5 It hasa Av+ of 12-4cm-1, but this may not be quantitatively meaningful, as there is ashoulder at -790 cm-1. In aqueous acid (HC1 or HC104) this band has Av+ -27cm-1, not as markedly dependent on the composition of the solution as the 1435cm-1 band of A-, and is Lorentzian in appearance.Trifluoroacetate has a peakat 843 cm-1,3 but this is of lower intensity than the HA band. In acidic solution,the species is also present in substantialIy lower concentration, so that its band isnot visible, but it probably contributes a little of the intensity of the trifluoroaceticacid band. If the broadening of the trifluoroacetic acid band is attributed to theshortness of the life of the species in aqueous solution a value of 14 x 1011 sec-170 RATES FROM BROADENING OF VIBRATIONAL LINESis obtained for ~/ZEA. This is an oversimplification, but, in order of magnitude,at least, it agrees moderately well with the value obtained from the width of the1435 cm-1 trifluoroacetate band.The perchlorate band, assigned to the breathing mode of the ion,6 also has anobvious shoulder. It has an apparent Av, of 11 - 1 cm-1 in 0.5 M NaC104, 11.5 cm-1in 1-88 M HC104 containing 3.1 M CF3COOH, and 12.4 cm-1 in 2.81 M HC104containing 3.1 M CF3COOH.In the latter solution the 1435 cm-1 A- band hasbroadened from 14 cm-1 to -45 cm-1.DISCUSSIONWe believie that the foregoing results are an example of exchange broadeningand we oKer the following detailed scheme to account for them. Three kinds ofA- are distnguished-separated anions, A;;; anions within 5-10A of H+ but,improperly oriented for hydrogen bonding to each other, H+ . . . A-; and anionshydrogen bonded to H+ (probably through one or more water molecules) H+ .A-.All of these are continuously in equilibrium with each other and with HA, sincethe measurement does not disturb this equilibrium. The interconversion of A;and H+ . . . A- is slow on the present time-scale, involving translational diffusion,but this does not influence the overall rate, as there is always an equilibrium con-centration of the latter. It is considered that A; and H+ . . . A- would haveessentially identical 1435 cm-I Raman bands. The rotational orientation of A-is the only thing that distinguishes H+ . . . A- from H+. A-. The fact that theA-bands in neutral solutions are Lorentzian suggests that its rotational reorientationin water is fast.2 It also has about the right Av, for a rapidly rotating species.7However, the 1435 cm-1 band maximum is thought to be slightly shifted in Hf . Ad,giving rise to the small blue shift in fairly concentrated HC104, noted above. Itis postulated that the step determining the spectroscopic lifetime of A- is the con-version of H+.A- to HA. If this is correct, then, in the more dilute solutions,where most of the A- is not Hf . A-, ~ / T A - is klK(H+). The definitions of k1, K, . .and k-1 are given byk iH+ . A- +HA,Hi +A-+H+. A-.k - 1K(3)(4)The last is ~/ZHA. Division of 1 1 ~ ~ - by [Hff does not yield an accurately constantvalue for k&, nor is k-1 constant. The direction of the variations suggest thatthe direct transfer reaction,AH + A--+A-+ HA, ( 5 )may also contribute to I / ~ H A , but non-ideality of solutions, and random, and system-atic errors may also cause considerable deviations from constant values.The mostlikely cause of systematic errors is the possible failure of the interconversion ofH+ . . . A- and H+ . A- to be fast enough to average the various A- bands. Inthat case ~/TA-, as evaluated here, would be smaller than kl . The qualitative inter-pretation of the broadening, as due to exchange, would still be correct, however.There is some reason to believe that K is in the range 10-1-1 1. mole-1.8 If so,using a typical value of I/zA-, kl is N 1012 sec-1. This is a reasonable value since,for other carboxylic acids, the recombination rate is diffusion controlled, meaningthat k1 must be greater than 1011 sec-1.9In further support of exchange as the cause of broadening a number of alter-natives will be discussed brieflyM.M. KREEVOY AND C. A. MEAD 171(a) Simple experimental error ; this is most unlikely in view of the reproducibilityand the precautions taken. In addition, some of the results described here havebeen independently confirmed in at least one other laboratory.10(b) Heterogeneity broadening ; the band becomes broader because of solutioninhomogeneities on a molecular scale, with interconversion of the various A- speciesinadequately fast. This does not happen to the perchlorate band, even in solutionswhich massively broaden the A- band. It also does not happen to the A- bandin neutral solutions. The experimental evidence all points to the conclusion thatrotational reorientation of A- is fairly fast on the present time scale in aqueoussolution.(c) The band is broadened by addition of the 1455 cm-1 band (without specifyingthe origin of the latter).This does not seem to produce the requisite line widths.For example, if the 1455 cm-1 band observed in 6.28 M HC104, 3-1 M HA, is addedto a 1435 cm-1 Lorentzian band, with Av+ of 16 cm-1, and sufficient intensity toreproduce the height of the 1437 cm-1 band in 3.1 M A-, 1.88 M HC104, the result-ing band has " Av+ " of 21 cm-1. This can be compared with the observed, 28 em-1.M. M. Kreevoy thanks the Sloan Foundation for a fellowship which has partiallysupported this work, and C. A. Mead is grateful for the hospitality extended to himby the Physics Department, Birkbeck College, London.1 Kreevoy and Mead, J. Amer. Chem. SOC., 1962,84,4596.2 Seshadri and Jones, Spectrochim. Acta, 1963, 19, 1013.3 Robinson and Taylor, Spectrochim. Actu, 1962,18, 1093.4 Hood, Redlich and Reilly, J. Chem. Physics, 1955, 23, 2229.5 Fuson, Josien and Jones, J. Chem. Physics, 1952, 20, 1627.6 Le Conte, Hundbuch der Physik, Band XXVI (Springer Verlag, Berlin, 1958), p. 825.7 Ramsay, J. Amer. Chem. Soc., 1952,74, 72.8 Robinson and Stokes, Electrolyte Solutions (Butterworths, London, 2nd ed., 1959), p. 394.9 Eigen and de Maeyer, Investigation of Rates and Mechanisms of Reactions, part 2, Friess,10 Weston, private communication.Lewis and Weissberger, ed. (John Wiley and Sons, New York, 2nd ed., 1963), p. 1034

ISSN:0366-9033    

DOI:10.1039/DF9653900166

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

Rate of Proton Transfer in Strong Acids and RamanLine BroadeningBY A. K. COVINGTON, M. J. TAIT* AND LORD WYNNE-JONESDept. of Physical Chemistry, School of Chemistry,University of Newcastle upon Tyne, 1Received 15th January, 1965A recent theory of Raman line broadening has been applied to measurements on perchloricand nitric acid solutions. The second-order rate constant obtained for the reaction of the per-chlorate ion with the proton is a factor of ten lower than that found for the triffuoroacetate ion.The occurrence of line broadening with increased concentration is not restricted to solutions ofacids and consequently some doubts may be raised about its interpretation in terms of the rateof proton exchange between acid and anion.Kreevoy and Mead 1 from a generalization of Heitler's methods 2 have derived anexpression for the second-order rate constant k2 for the reactionkzk iH,O+ +A-+HA+H,O,where A- is an anion species, in terms of the increase in half-width at half-height ofa Raman band of the anion or acid molecule.For slow exchange of the protonthe expression simplifies towhere c is the velocity of light, @-PI is the increased half-width of the line in wavenumbers. It is assumed that the Raman transition does not involve degrees offreedom of the acid molecule which take part in the exchange. Kreevoy and Mead 1applied the theory to measurements on trifluoroacetic acid, taking for the half-width in solutions of the sodium salt.Studies which will be reported elsewhere 3 have been made recently in theselaboratories of the dissociation of perchloric acid by the Raman method.In markeddisagreement with the results of n.m.r. measurements,4-6 perchloric acid was foundto be effectively completely dissociated up to at least 10 M. The basis of the Ramanmethod 79 8 is the determination to a very high degree of accuracy and reproducibility(0.2 %) of the integrated intensity (area under the Raman band), which is proportionalto the concentration of the exciting species. For these measurements the 931 cm-1perchlorate ion band was used. It is of interest to apply Kreevoy and Mead's theoryto results obtained during this study.k2 = 2nc (B-P1)/CH30+1,EXPERIMENTALThe measurements were obtained using 3 the Hilger and Watts E616 recording RamanSpectrometer in conjunction with a very stable Toronto arc source of design similar to thatof Jam, Mikawa and James,9 oFerated at low power (5 kW).Special attention was necessary* present address : Chemistry Department, Rensselear Polyteclmic Iqqtitutq, Troy, New York.17A . K . COVINGTON, M. J . TAIT AND WYNNE-JONES 173to achieve high quality results from the electronic circuitry and for measurements on dilutesolutions a specially developed transistorized amplifier 10 which utilizes a field-effect transistorfor impedance matching was employed with advantage.Perchloric acid solutions were prepared by weight dilution of a stock solution prepareddirectly from A.R. acid without further purification. The molarity of the stock solutionwas determined by potentiometric titration against hydrochloric acid as primary standardthrough borax as intermediate.Intercalibrated interchangeable Raman cells (60 ml) onground-glass joints permitted easy comparison of the intensities from solutions of con-centration up to 11 M in groups of three or four so that scans could be made at optimuminstrumental gains and any slight drifts in source output or amplifier gain could be corrected.RESULTS AND DISCUSSIONThe results of the half-width measurements (p> are shown in table 1. The linewidth in dilute solutions (0.3-3 M) was constant at 6.6 cin-1 and this was taken asthe value of PI. These values refer to slit widths of 0.2 mm (8 cm-1) but the valuesof p -PI were found to be independent of slit width within the experimental accuracy.The second-order rate constant kz for the reaction (1) is shown in the last column,where the perchlorate ion concentration was obtained from the integrated intensities.3The 931 cm-1 perchlorate ion peak is approximately Lorentzian in shape.Insodium perchlorate solutions the peak maximurn occurs at 940 cm-1. The corres-ponding shift in the trifluoroacetate frequency is less than half this. The peakmaximum occurs at about 920 cm-1 in some divalent perchlorates.11 The half-width was the same in 1 M sodium perchlorate as in dilute acid solutions. Hencethe same results would be obtained if following Kreevoy and Mead,l P1 was taken,as the half-width in the sodium salt. The half-width was found to be invariant inmixed sodium perchlorate + potassium chloride solutions of constant perchlorateconcentration (1 -6 M).TABLE 1 .-LINE BROADENING IN PERCHLORIC ACIDC 8-81 10-%t~[H30+] 10-1OkZ 84-03 6-9 0.3 0-6 1.46-06 7.3 0.7 1.3 2.28.36 8.0 1.4 2.6 3.210.54 9.1 2.5 4.7 4.51 1 *44 9.8 3.3 6.2 5.4mole 1.-1 cm- 1 cm-1 sec-1 1.mole-1 sec-1Measurements of the integrated intensities showed 3 that it is only in concentratedsolutions (greater than 10 M) that the concentration of perchlorate ions falls signific-antly below the stoichiometric concentration. That this is due to the formation ofperchloric acid molecules was confirmed 3 by the appearance of a new Raman bandat 974-1 174 cm-1 which is found in solutions of much higher concentration 12 andby the presence of a band in the infra-red.Representing the dissociation formallyby eqn. (1) would lead to a thermodynamic dissociation constant in excess of 103.It was concluded 3 that the appearance of perchloric acid molecules in concentratedsolutions only occurs when there are insufficient water molecules present to solvatethe proton fully as H90: as in dilute solutions.13 If this interpretation is correctthere are no, or certainly very few, perchloric acid molecules present in solutionswhere line broadening is observed.Vollmar has recently 14 studied the variation of the nitrate ion 1048 cm-1 line in anumber of nitrates with increase in concentration. Besides the broadening of theline and a shift in the frequency of the peak, there may be a non-Compensating dropin peak height causing the ratio of the integrated line intensity to the stoichiometri1 74 RAMAN LINE BROADENINGnitrate ion concentration (termed the specific intensity) to vary from a constant valueby 1-2 % for some salts.The only nitrate where no broadening was observed wasthe ammonium salt. He interpreted this as a result of the ammonium ion beingable to fit into the water structure so that it has no effect on the anion. Only if thehydronium ion behaves in the same manner to the ammonium ion is it possible tointerpret the total band broadening in terms of proton jump. Vollmar attributedband broadening in salts to cations of large hydrated radius breaking down the waterstructure thus enabling the nitrate ions to vibrate over a wider frequency range.Frequency shifts, on the other hand, were attributed indirectly to contact ion pairformation causing the release of water molecules which modifies the frequency ofvibration of the nitrate ion.It seems very likely that, in perchloric acid solutions,as the solvation of the proton changes as the solution becomes more concentrated,the changed water structure around the perchlorate ion will lead to line broadening.Krawetz in some unpublished work 15 gives results for line broadening in nitricacid at 25°C. The 1048 cm-1 band in dilute nitric acid (1 M) has a half-width of16 cm-1 which approximately doubles in width at 20 M. Some of Krawetz's resultsare shown in table 2. He found that the half-width of 1048 cm-1 line in sodiumnitrate increased from 15.3 cm-1 in 1 M solution to 16.5 cm-1 in 4-39 M solution,the increase in width with molarity being approximately the same as in acid solutions.The line broadened only slightly (0-2 cm-1) in mixed NaN03 + KC1 solutions.Selecting the value of 16.1 cm-1 the values for k2 in the third column of table 2 haveTABLE 2.-LINE BROADENING IN NITRIC ACID3.143-994-8 16.617-488.079-239-7910.3017-2417.6217-8019.4020.2420.7 121.4621.6422-492.12.63.16.17.88.79.410.412.02.863-503.914.664.975.205.105-044.930.80.80.81.31.61.71.82-12.4been obtained.The values of k2 shown in the last column were obtained from theNO 3 concentrations calculated by Krawetz from integrated intensities.The calcula-tion has not been extended to molarities higher than 10 M since other species such as(H"03)2, NO; are present 169 17 at concentrations higher than 7 My (the molaritywhere the nitrate ion comentration is a maximum) and these will contribute to theline broadening.The parallel increase in line width in nitric acid and sodium nitrate solutions maybe coincidental especially as other nitrates, with the exception of the ammonium andpotassium salts, show greater increases 14 than does sodium nitrate, and also sincethe line widths at the same concentrations of acid and sodium salt are different.New measurements of sodium perchlorate solutions have revealed that the line widthis the same as that in solutions of perchloric acid of the same concentration up to 8 M.Again this may be coincidental and due to entirely different effects as a frequencyshift is involved, but the same question arises here as for intensity measurements 3of the best reference solution to employA .K . COVINGTON, M. J . TAIT A N D WYNNE-JONES 175CONCLUSIONSThe results obtained by the application of Kreevoy and Mead’s theory 1 to threeacids at a concentration 5-6 M are summarized together with other relevant infornia-tion in table 3. The second-order rate constants for the combination reaction(eqn. (1)) range over an order of magnitude. At best, the values must be regardedas estimates only, since other factors, particularly changes in solvent structure insolution, may lead to line broadening ; at worst these factors may be entirely respons-ible for the observed broadening.TABLE 3a 10-llk2 lo-Wcl= 1 0 - 4 2 KK’ = a2c/(1 -4 1.mole-l sec-~ sec-1s toichiome tricmolarity acidperchloric 3 6-06 0-997 1980 0-22 435nitric 15 4.8 1 0.8 13 17.1 0.80 13-7trifluoroacetic 1 5.3 0.34 0.93 3.8 3.5Precise Raman studies of variations in specific intensity, of frequency shifts,as well as of line broadening, preferably coupled with parallel investigations of changesin the Raman water bands 18 should furnish important information about interactionsin concentrated electrolyte solutions.We thank Mr. J. G. Freeman for some additional measurements and Dr. A.Bewick, Dr. M. Fleischmann and Mr. T. H. Lilley for discussions.1 Kreevoy and Mead, J. Amer. Chem. Soc., 1962, 84,4596.2 Heitler, Quantum Theory of Radiation, 3rd edn. (Oxford, 1954).3 Covington, Tait and Wynne-Jones, Proc. Roy. SOC. A, to be published.5 Redlich and Hood, Disc. Farraday Soc., 1957, 24, 87.6 Hood and Reilly, J. Chem. Physics, 1960, 32, 127.7 Young, Rec. Chern. Prog., 1951, 12, 81.8 Young, Maranville and Smith, in Structure of Electrolytic Solutions (ed. Hamer), (Wiley, New9 Janz, Mikawa and James, Appl. Spectr., 1961, 15’47.10 Covington, Molyneux and Tait, Spectrochim. Acta, 1965, 21, 351.11 Jones, Jones, Harmon and Semmes, J. Amer. Chem. SOC., 1961, 83,2038.12 Redlich, Holt and Bigeleisen, J. Amer. Chem. Soc., 1944, 66, 13.13 Eigen, Angewandte Chem. ( I t . Ed.), 1964, 3, 1.14 Vollmar, J. Chem. Physics, 1963,39,2236.15 Krawetz, Thesis (University of Chicago, 1955).16 Chedin, h l e r c and Vandoni, Compt. rend., 1947, 225, 734.17 Chedin and Feneant, Compt. rend., 1949, 22$, 242.18 Covington and Prue, Ann. Rep., Chem. SOC., 1963, 60, 8.Hood, Redlich and Reilly, J . Chem. Physics, 1954, 22, 2067.York, 1959), p. 35

ISSN:0366-9033    

DOI:10.1039/DF9653900172

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

GENERAL DISCUSSIONDr. A. K. Covington (University of Newcdstle upon Tyne) said: I suggest thatthe third explanation (c) of line broadening in trifluoroacetic acid discussed brieflyby Kreevoy and Mead 1 at the end of their paper is the correct one. In anhydroustrifluoroacetic acid there is a band 2 at 1455 cm-1 which has been assigned3 to aC-0 deformation mode and may in part be due to dimers. In the deuterated acidit appears 23 3 at 1426 cm-1. Fig. 1 summarizes the line broadening (half-width)observed for the three acids.194 Some new measurements by Mr. Freeman, Mr.Lilley and myself on trifluoroacetic acid are included for comparison. The closeagreement between these and Kreevoy and Mead’s is striking. The two sets ofmeasurements were made at very different slit widths but the half-width broadening(obtained by subtracting the extrapolated half-width at zero ion concentration) isindependent of the slit width.However, from fig. 1, although the line broadening,,HN03 thwetz1955 d CF$OOH0 Kretvoy4Mcod 1962,19658 Covinrjten FmrnanLLilley 1065Q ,‘#‘O‘965 +0 15 10molarityFIG. 1.in trifluoroacetic acid solutions is linear with concentration up to about 5 M, abovethis it increases sharply. The peak maximum on the other hand shows a steadyfrequency shift from the 1435 cm-1 band found in dilute solutions of the acid andthe sodium salt towards 1455 cm-1 as shown in fig. 2. This seems to be clearevidence that as the solution concentration is increased the 1435 cm-1 band due tothe trifluoroacetate ion, while appearing to broaden as it diminishes in intensity,is being replaced by a band at 1455 cm-1 due to the undissociated acid as the con-centration of this increases.This frequency shift is shown for mixed perchloricand trifluoroacetic acids by fig. 2 of Kreevoy and Mead’s paper.41 Kreevoy and Mead, this Discussion.2 private communication from Dr. Ralph E. Weston, Jr., of Brookhaven National Laboratory.3 Fuson, Josien, Jones and Lawson, J. Chem. Physics, 1952, 20, 1627.4 Covington, Tait and Wynne-Jones, this Discussion.17GENERAL DISCUSSION 177-anhydrous acid 400.00e-sodium salt1 I I I 1 I2 4 6 8 10molarityFIG. 2.I 1.5 10molarityFIG. 3.Raman: x Kreevoy and Mead, 1965 ; +, Covington, Freeman and Lilley, 1965n.m.r. : .. . 0, Hood, Redlich and Reilly, 1955 ; a, Akitt, Covington and Lilley, 196178 GENERAL DISCUSSIONA further disturbing feature of the Raman spectrum of trifluoroacetic acid isthat the 1435 cm-1 band is situated on a sloping base line, which is part of a broadband stretching over some 2000 wave numbers with a maximum at 2000cm-1.This is shown well for sodium trifluoroacetate by Robinson and Taylor 1 in a figuretaken from a microdensitometer trace but a similar broad band is also found in thespectrum of the acid. Until the origin of this band is elucidated the interpretationof interactions in trifluoroacetic acid solutions must remain speculative.Fig. 1 compares the observed line broadening for all three acids for whichmeasurements are so far available23 3 with that observed in sodium nitrate solutionby Vollmar.4 For perchloric acid the line broadening is of similar magnitude asin sodium nitrate while for nitric and trifluoroacetic acids it is greater by a factorof two and three respectively.We think that further evidence must be collectedon many more acids and salts before the phenomenon of line broadening can beunequivocably interpreted.Finally, I should like to comment on the 10 % discrepancy between the valuesof the degree a of dissociation of trifluoroacetic acid found from Raman intensities 2and those found by Hood, Redlich and Reilly 5 from their p.m.r. measurements(see table 2 of Kreevoy and Mead’s paper 2). We have redetermined6 a by thep.m.r. method and find the a values given by Hood, Redlich and Reilly to be incorrect.A critical quantity in the evaluation of a from p.m.r.measurements of the chemicalshift s with respect to water, is s1, the contribution from the hydronium ion.s = s,ap++s,(l -a)p, where’ p = 3x1(2-x),and x is the stoichiometric mole fraction of the acid. Hood, Redlich and Reilly 5assumed for s1 the value found for hydrochloric acid. We have been able to getdown to concentrations as low as 0.1 N and determine s1 experimentally from thelimiting slope of a plot of s1 against p . The value obtained is lower than that as-sumed by Hood, Redlich and Reilly and hence the new a values are higher. Fig. 3compares our results with the earlier results 7 recalculated with the new s1 and withthe values obtained from Kreevoy and Mead’s2 and our own integrated Ramanintensities.All are in good agreement and, in particular, the Raman measurementsare in closer agreement than the modest 10 % accuracy claimed by Kreevoy andMead.2 However, the Raman results lie slightly above the p.m.r. results at con-centrations above 7 M and this may be again symptomatic of the changed natureof the 1435 cm-1 Raman band at these concentrations.Dr. Ralph E. Weston, Jr. (Brookhaven Nat. Lab., N.Y.) (communicated): AsKreevoy and Mead report in their paper, I have also made measurements on Ramanline broadening in aqueous solutions of trifluoroacetic acid.8 These measurements,carried out subsequent to the publication of their first communication,9 have beenlimited to solutions of CF3COOH in H20, CF3COOD in D20, and their sodiumsalts, but have been extended to somewhat higher acid concentrations than thoseused by Kreevoy and Mead.At concentrations where comparison is possible,my results for CF3COOH are similar to theirs. Up to a stoichiometric acid con-centration of 7 M, Av* is linear with concentration; but at higher concentrations1 Robinson and Taylor, Specfrochim. Acta, 1962, 18, 1093.2 Kreevoy and Mead, this Discussion. 3 Covington, Tait and Wynne-Jones, this Discussion.4 Vollmar, J. Chem. Physics, 1963, 39, 2236.5 Hood, Redlich and Reilly, J. Chem. Physics, 1955, 23, 2229.6 Freeman and Lilley, Chem. Comm., 1965, 349.7 Gutowsky and Saika, J. Chem. Physics, 1953, 21, 1688.8 This research was wried out under the auspices of the U.S.Atomic Energy Commission.9 Kreevoy and Mead, J. Amer. Chem. SOC., 1962,84,4596GENERAL DISCUSSION 179it rises sharply. The width of the 1435 cm-1 band in solutions of sodium trifluoro-acetate was essentially independent of concentration. There are, however, certaincomplications attached to the interpretation of the observed broadening.(a) The spectrum of pure CF3COOH exhibits a broad band at 1456 cm-1, witha molar intensity about one-tenth that of the anion band at 1435 cni-1. This bandis presumably due to the dimer, but persists in 10 M CF3COOH, at which con-centration dissociation and dimerization are thought to be negligible.1 In pureCF3COOD (in DzO) the corresponding band is found at 1422 cm-1, while the tri-fluoroacetate band is unshifted in position or intensity.These bands appear tobe present at lower acid concentrations, since the 1435 cm-1 band in 4 M CF3COOHis slightly asymmetric with broadening towards higher frequencies, while the sameband in 4 M CF3COOD is broadened towards lower frequencies.(b) The agreement between values of a determined from intensities of the 1435cm-1 Raman band and from p.m.r. measurements is excellent up to concentrationsof about 7 M CF3COOH. The positive deviation of the Rainan measurementsincreases with increasing concentration, again indicating that a species other thanCF3@OO- is responsible for Raman scattering in this spectral region. The dis-crepancy is larger for solutions of CF3COOD, where the intensity measurementslead to the unlikely conclusion that the concentration of CF3COO- increasesmonotonically with increasing stoichiometric acid concentration.( c ) As Covington, Tait and Wynne-Jones point out, the factors which determineRaman band widths are not well understood.In measurements of the dissociationof perchloric acid by Raman intensities,s Heinzinger and Weston have also deter-mined band widths of the 931 cm-1 perchlorate band. Our results agree with thosereported by Covington, Tait and Wynne-Jones. In particular, we find that theincrease in band width with concentration is essentially the same for solutions ofsodium perchlorate as it is for perchloric acid, up to a concentration of about 8 M(the solubility limit of sodium perchlorate).At higher acid concentrations, wheresome undissociated acid is present, the rate of increase of band width rises sharply.It seems possible that, in addition to the ion-solvent interactions suggestedfor solutions of perchloric and nitric acids, there are hydrogen-bonding effects insolutions of carboxylic acids which will lead to a broadening of vibrational energylevels, and hence to an increase in Raman line width.There are also certain features of the kinetic arguments which do not appearto fit the facts. It is postulated that the spectroscopic lifetime of the trifluoroacetateion A- is determined by the rate of the process,H+ .A-+HA.In this case, it would appear necessary to observe the broadening of a band attribut-able to the H f .A- species, since the conversion of A- to H+ . . . A- and finallyto Hf . A- is too slow (rate constant N 1011 M-1 sec-1) to produce observablebroadening. Yet the authors evidently believe that the 1435 cm-1 band shouldbe assigned to the A- and H+ . . . A- species.Furthermore, there should not be a dependence of the lifetime (as distinguishedfrom the rate of disappearance) of the Hf . A- species on the concentration of Hfor HA, since Hf . A- disappears by a unimolecular process. Of course, the con-centration of H+ . A- may depend on the acid concentration. It therefore appearsdifficult to explain the observed broadening and its concentration dependence onthe basis of the mechanism proposed.The described method of studying very rapid reactions is certainly correct in1 Heinzinger and Weston, J.Chem. Physics 1965, 42, 272180 GENERAL DISCUSSIONprinciple. However, it is my opinion that the systems so far examined are notsufficiently free of complication unrelated to exchange broadening to constituteconvincing experimental evidence that the latter phenomenon is indeed responsible.Prof. M. M. Kreevoy (Univ. of Minnesota) (communicated) : In reply to Weston,I think these comments are answered as best I can in my reply to Dr. Covington.The kinetic scheme is correct if A- and H+ . . . A- have identical bands, whileH+ . . . A- and H+ . A- are rapidly interconverted. I cannot, yet, be certain about theorigin of the 1450 cm-1 band in aqueous HA+HC104 mixtures, but it is not detectablein 1 M HA, while broadening of the expected general magnitude still occurs, sothat I do not think it can be the principal cause of the observed broadening in fairlydilute solutions.Dr.A. K. Covington and Mr. T. H. Lilley (Newcastle upon Tyne) (communicated) :At the present stage of the quantitative study of electrolytes by Raman spectroscopyit would seem unsafe to assume as Dr. Kreevoy does that at zero concentration thehalf-width in HN03 and NaN03 solutions should be the same. Vollmar 1 founda difference of 0-3 cm-1 (corrected for slit width) at zero molarity between variousnitrates. He also found frequency shifts of more than 1 cm-1.The selection of a value for our /31 (Kreevoy and Mead’s Avg) is arbitrary butit would seem preferable to assume a value for a dilute solution of the acid of interestinstead of that for a salt since the ion band in the acid is attributed by Kreevoyand Mead to the three species A-, Hf .. . A-, and H+ . A-; only the first of thesewill be present in the salt solution. Dr. Kreevoy’s recalculated values of k2 using/31 = 15.3 cm-1 differ from ours by less than the one figure significance that Dr.Kreevoy ascribed to them. There is little doubt that the quantum mechanicaltheory of Kreevoy and Mead is essentially correct but there remain some doubtsabout (a) the application of it to any of the acids so far studied and (b) the con-sistency of the theory with the postulated kinetic scheme. We agree that the quali-tative interpretation of line broadening in dilute solutions of trifluoroacetic acid(1-3 M) is correct.Prof.Maurice M. Kreevoy (Univ. of Minnesota) said: We believe that the1450 cm-1 band in strong acid is associated with the oriented, hydrogen-bonded,pair, W+. A-. A modification will account for the 1455 cm-1 band in the liquidacid and the 1426 cm-1 band in the deutero acid. Regardless of the origin of thesebands we have shown that the observed broadening cannot be obtained by simplyadding them to an unbroadened A- band. In 1 M HA, 1.9 M HC104 the bandwidth increases by 5 cm-1 in spite of the fact that no 1450 cm-1 band can be detectedin 1 M HA, 7 M HC104. The increase in line width with concentration in neutralsolutions of NafA- or NH,+A- is less by about an order of magnitude than that inacid solutions of comparable electrolyte concentration.No viable alternativehas been offered to the proposition that the broadening observed in acidic solutionsof trifluoroacetate in the 1-3 M concentration range is due to the shortness of thelifetime of the ion.In most respects the HNO3 system described by Covington, Tait and Wynne-Jones seems comparable. The impression, which might be gained from the text,that the broadening is the same in comparable neutral and acidic solutions doesnot seem to be borne out by the data cited. It seems safe to assume that infinitelydilute nitric acid solutions would give the same NO, width at half-height, as dilute,neutral, NaNO3 solutions ; - 15.3 cm-1. It is mentioned in the text that 4.39 MNaN03 gives a width of 16.5 cm-1, an increase of 1.2 cm-1. In order to achieve asimilar concentration of NO 3 in HNO3 solutions a stoichiometric concentration1 Vollmar, J.Chem. Physics, 1963, 39, 2236GENERAL DISCUSSION 181of -6.5 M would be required and a width of - 19 cm-1 would be observed (asinterpolated from the data in table 2). This indicates a broadening -4 cm-1,more than 3 times the broadening in the comparable neutral solution.If the rate constants cited in table 2 are recalculated using 15.3 cm-1 as the widthof the unbroadened line the following values are obtained.Cmole I.-;3-143.994-816.617.488.079.239.7910.301011 kp1. mole-; sec-10.60.60.60.80.91.01.11.21.41012 klsec-11.81.51.00.90.90.90-70.70.6The values appropriate to dilute solutions would seem to be 0.6 x 1011 1.mole-1sec-1 for k:! and -2 x 1012 sec-1 for kl, the dissociation rate constant. The com-parable values for the trifluoroacetic system are N 1.5 x 1011 1. mole-1 sec-1 and- 4 x 1011 sec-1. The dissociation rate for nitric acid is larger, as befits a strongeracid, and the recombination rate is smaller.None of these rates are diffusion-controlled. The interconversion of A- andH+ . . . A- is relatively slow, but the data for salts strongly suggest that the cor-responding bands are displaced by no more than 1 cm-1. The bands for Hf . . . A-and H+ . A- may be separated by - 15 cm-1, but these species can be interconvertedwithout a translational diffusion, by a rotation of the A- unit.This may well bevery fast. In that case the average lifetime of the A- species (that is, A-, H+ . . . A-,and H+ . A-) will be obtained from the overall line width. This is an approximation,and along with the various experimental uncertainties, suggests that no more thanone significant figure be attributed to the derived rate constants.The perchlorate band is not broadened until very high acid concentrations arereached. This observation in itself supports the " chemical " explanation givenfor the broadening in acidic trifluoroacetate and nitrate solutions, since some un-specified " physical " explanation would, presumably, apply to perchlorate, also.The broadening that is observed all occurs in a region of concentrations where neutralsalt solutions also give considerably broadened bands. The derived rate constantsshould be regarded as no more than upper limits.Prof. R.J. Gillespie (McMaster University) said: Dr. Covington has remarkedthat new measurements of the dissociation of perchloric acid in aqueous solutionby the Raman method are in marked disagreement with the results of n.m.r. measure-ments. Dr. White and I have pointed out that the n.m.r. method is unreliableas it is based on the assumption that the chemical shift of the H3O+ ion is independentof the composition of the acid+water mixture.1 Since the degree of hydration ofthe hydronium ion must decrease with increasing acid concentration this assumptioncannot be justified.Mr. T. H. Lilley (Uniuersity of Newcastle upon Tyne) said : Regarding the degreesa of dissociation of acids obtained by the Raman and p.m.r.procedures, in the p.m.r.method it is assumed 2 that when the acid is completely dissociated the chemical shiftis directly proportional to the function p , defined by Gutowsky and Saika.2 Devi-ations from direct proportionality are attributed to association. For the strong1 Gillespie and White, Can. J. Chem., 1960, 38, 1371.2 Gutowsky and Saika, J. Chem. Physics, 1953,21, 1688182 GENERAL DISCUSSIONacids deviations do not occur until high concentrations and some environmentaleffect, rather than association, might be the cause. The ammonium ion in waterhas similar properties to the hydronium ion1 and since for the ammonium ionassociation does not occur, deviations from proportionality between chemical shiftand the analogous p function for the ammonium ion would indicate the naivity ofthe interpretation of the p.m.r.results. In fig. 1 results obtained by Hindman 2p = 2X/l+xFIG. 1.for ammonium salts have been recalculated. Deviations from linearity occur atabout 5 m for the nitrate, chloride and bromide. The insolubility of the perchlorateprevents measurements at concentrations greater than about 2 m. Raman andp.m.r. work in this laboratory 3 has shown that perchloric acid is completely dis-sociated up to approximately 6 M but at higher concentrations the a values obtainedby the two methods diverge. The differences are possibly due to greater environ-mental effects in the p.m.r. measurements than in the Raman measurements.Prof. €3. E. Conway (Ottawa) said: Wynne-Jones remarked on the minimumfound in Zyate ion mobility in H20+H202 mixtures at the high H202 end of thecomposition range. A similar result is found for Iyonium ion mobility in HCl+methanol +water mixtures 4 where the conductance minimum is around 85-90 %methanol. At that composition, the conductance is close to that of KCl in thesame solvent indicating normal bulk transference of the H3Of ion. Water in themethanol+ water mixture acts as a proton trap ; on one side of the conductanceminimum, anomalous transfers can occur favourably between H20 and H30+,while on the other side of the minimum anomalous transfers can occur betweenCH30H; and CH30H. Transfer between H30+ and CH30H will not be so facileif the base strength of CH3OH is less than that of H2O (the apparent base strengthwill itself depend on composition).1 see, e.g., Frank and Evans, J. Chem. Physics, 1945, 13, 507. Kaminsky, Disc. Faraday Soc.,3 Covington, Tait and Wynne-Jones, Proc. Roy. Soc. A , 1965,286,235. Akitt, Covington, Freeman4 Conway, Borcks, Linton, J . Chem.Physics, 1956,24,834.1957,24, 171.and Lilley, Chem. Comm., 1965,349.2 Hindman, J. Chem. Physics, 1962, 36, 1OOO

ISSN:0366-9033    

DOI:10.1039/DF9653900176

出版商:RSC    

年代:1965

数据来源: RSC