GENERAL DISCUSSIONProf. J. J. Weiss (University of Newcastle) (contributed) : Several referenceshave been made to a mechanism where the proton transfer occurs along a hydrogenbond, a point which was emphasized particularly by Eigen. In water, this maygo with the intervention of a hydrogen-bonded water molecule whereas in aproticsolvents one should have the direct formation of a hydrogen bond between the tworeactants prior to proton transfer. If the proton transfer goes along a hydrogenbond, the distance which the proton has to travel is relatively short, viz., 0.4-0.6A.Thus, the width of the potential barrier which the proton has to penetrate wouldbe sufficiently narrow to allow processes of tunnelling to compete favourably witha classical mechanism of proton transfer.I am referring here to a real tunnel effectand not to the type of mechanism discussed by Caldin which is essentially a classicalone with a correction for tunnelling only at the very top of the potential barrier. Inthe simple model which I have used,l proton transfer is considered to take placealong a line joining the proton donor and acceptor hence it may be described by aone-dimensional barrier of given height and of width equal to the distance whichthe proton has to travel along the hydrogen bond. This problem, using an Eckartbarrier, which from a physical point of view is the most realistic one, can beformulated in such a way that one can do an exact calculation.The model leads to an expression for the rate constants which gives a reasonableaccount of the isotope effect.Moreover, a Bronsted type of relation can also beobtained from this theory without any further assumptions. As a first approxim-ation (i.e., if one takes only the first term of a particular series expansion) one obtainsfor the Bronsted coefficient a, the following theoretical expression :a = (1 - (2PkT/Q')),where p = (a/h> (2 M)*, where 2a denotes the barrier width and M is the massof the proton (or deuteron). Q is an energy, i.e., the difference between the protonaffinities of the donor and acceptor molecules. Thus the Bronsted exponent adepends also on the value of the energy difference Q. Approximate constancyof a within a certain series therefore presupposes an approximate constant valueof Q, otherwise there should be a variation of the Bronsted coefficient with thevalue of Q. Eigen has discussed the variation of the Bronsted coefficient with thepK difference of the proton donor and acceptor.Eigen's results are fully compatiblewith the above equation as Q, i.e., the difference in the proton affinities of donorand acceptor, is directly related to the difference of their pK values. Eigen'sdiscussion moreover shows that the current derivation of the Brijnsted relation haslittle significance from a theoretical point of view, based as it is on the a prioriassumption of the proportionality between the activation energies and the freeenergies, thereby virtually presupposing what is meant to be derived.Prof. F. A. Long (Cornell University) said: It is true, as Dr.Eigen has said,that the general acid catalysis for the detritiation of azulene-1-t follows the Bronstedrelation over a wide range of acidity. This is similar to the results obtained foressentially the same reaction by Kresge with 173,5-trimethoxybenzene-2-t. Theonly reservation is that the density of points from acids is not high and as a conse-quence, much of the behaviour hinges on the results for the two acids, H20 and1 J. Chem. Physics, 1964,41,1120.446 GENERAL DISCUSSIONH30+, acids which are difficult in Bronsted plots. We also have data giving a moreprecise study of catalysis for groups of acids 1 which show that the catalysis to somedegree depends upon charge type, hence it would be useful to have a greater densityof points for acids of identical charge type to support the statement of Dr.Eigen.Prof. A. J. Kresge (IlZinois Institute of Technology) said: For the detritiation of1,3,5-trimethoxybenzene-2-t, we fowd that the data conform to the Bronstedrelation very well over a wide range of reaction rate (fig. 1). For a spread of 9Ipowers of 10 in catalytic coefficient which corresponds to 17 pK units in catalystacidity, the standard deviation in rate constant from the usual linear log-log relationis only 30 %. On this scale the deviations which Prof. Long found would be small,and this may be the reason why our data appear to obey the Bronsted relation sowell.I would like to add that the reactions with which we are dealing are all slow:none of the rate constants approach the values expected for diffusion-controlledreactions.Therefore, the sort of deviations from the Bronsted relation whichProf. Eigen discussed would not be expected to occur here.Prof. M. Eigen (Giittingen) said: I should like to add a few remarks regardingthe discussion contributions of Lord Wynne-Jones, Mr. Bell, Prof. Long andProf. Kresge. The concerted or co-operative mechanism mentioned in my paperwas introduced in order to remove the inconsistencies occurring in the mechanismof consecutive acid-base action in prototropic changes. Such a consecutive mech-anism would require rate constants for the rate-limiting step which depend linearlyon the pK of the acid or base catalyst-even in the range of diffusion control, whereall directly measured rate constants of proton transfer become independent of pK.(In some cases they even exceed the limiting value of about 1010 M-1 sec-1 appreci-ably, not showing the asymptotic behaviour a-+O).While the concerted or co-operative mechanism must be effective in these cases, it does not necessarily apply1 Thomas and Long, J. Arner. Chern. SOC., 1964,86,4770GENERAL DISCUSSION 47to other cases where a constant a has been observed over a large pK-range. HOW-ever, a necessary condition for a constant a is that the rate constant of the actualprocess is sufficiently below the limiting value mentioned above. This is indeedtrue for all the mentioned reactions, in which one step of proton transfer is probablyrate limiting, especially in the isotope exchange of hydrocarbons discussed by Longand Kresge.The hydrolysis of orthoesters mentioned by Wynne-Jones shows O ~ Yacid catalysis, and inspection of the structure of these compounds suggests thatthere is no suitable place for an attack of the base in the initial (possibly rate-limiting)step. Nevertheless, the co-operative mechanism does not require a symmetricalbehaviour with respect to acid and base catalysis, although in principle both shouldbe possible. In general, all types of mechanisms might be found (e.g., pre-equilibrated protonation or deprotonation leading to specific H+- or OH--catalysis,rate-limiting proton transfer with or without pre-equilibrated protonation or de-protonation and co-operative proton transfers-the latter cases all leading to generalacid or base catalysis).The co-operative mechanism will be preferred only if thetwo sites on the substrate can interact favourably via the solvent structure. Theoxygen groups in the above-mentioned cases fulfil this condition. CK-groups,however-as involved especially in the isotope exchange of hydrocarbons or inketo-enol tautomerism (cf. fig. 26 in my paper) might disfavour the co-operativemechanism.Wynne-Jones also mentioned the fact that a correlation of activation energieswith AH is usually not as good as that of log k with AP (or pK). Since AF andAH, as well as the corresponding kinetic quantities, include contributions fromdifferent sources (e.g., formation of transition complex, solvation, proton transferin H-bond, etc.), one cannot expect that all these contributions are correlated bythe same factor a.Thus, a good correlation for any of the quantities can be ex-pected only for a series of homologous substances. A more detailed treatmentwould require a further knowledge about the structure of the transition state towhich isotope studies might contribute greatly.Prof. B. E. Conway (Ottawa) said: Prof. Eigen remarked on the conditionsunder which a in the Bronsted relation may be expected to be constant over a reason-able range of pK values. A constant a will be expected if the crossing region ofpotential energy curves for the proton transfer in the acid-base reaction is well aboveELECTROCHEM I CAL ACID- BASEAE*=ah(RTlnK1A (RTI R K 1RE ACTION COOR DI N ATEthe zero-point levels of the reactants and/or products.Some justification for thea priori expectation of reasonably constant a follows by comparison with the analogouscase for electrochemical proton transfer at a cathode. Here the energy of the initialstate is changed relative to that of the final state by an energy zFAY for a chang48 GENERAL DISCUSSIONof metal-solution p.d. of AY and the electrocheinical rate i is modified byexp[-zF/3AV/RT]. Hence In i is proportional to AV and a symmetry factorp(+ 0.5) analogous to Bronsted’s a is involved. The activation energy is modifiedby an energy zF’AV. The analogy between the two cases is shown schematicallyin fig. 1, for varying base strength of the entity B. At some electrodes, e.g., Hg,In i is exactly proportional to AY over 9 decades of rate (i.e., for AV changing byca.1 V) so that a similar effect with regard to changing pK values in the Bronstedrelation is entirely reasonable on the basis of potential energy diagrams.1 A changeof 1 V in the electrochemical case is equivalent in RT In K units to a change of about17pK units in the acid-base case, which is a wider range than that normally en-countered in real chemical cases.Mr. R. P. Bell (Oxford) said: Mention may be made of another reaction forwhich it has been claimed that the catalytic power of a series of acids ranging fromH20 (PK 15.75) to H30+ (pK - 1.75) can be represented by a linear Bronsted rela-tion. This is the decomposition of the diazoacetate ion in aqueous solution, studiedby King and Bolinger,2 for which the special mechanism suggested by Eigen for thehydration of carbonyl groups and related reactions does not seem appropriate.However, the dependence of velocity on catalyst concentration in the decomposi-tion of the diazoacetate ion is an unusual one, and the catalytic constants given byKing and Bolinger were derived by an arbitrary extrapolation procedure.It wasshown by Bell and McTigue 3 that the kinetics of this reaction can be interpretedquantitatively by assuming two consecutive steps of comparable rate, making itpossible to derive the velocity constants for the first step N2 : CHCO; +At-+N2 . CH2CO; +Bi, where Ai-Bi is an acid-base pair. (In addition to the valuesalready given we find kA = 1-4 x 104 M-1 min-1 for catalysis by acetic acid.) Therevised catalytic constants do not give a convincingly linear Bronsted plot over thewhole range, and in particular the considerably decreased value found for hydrogen-ion catalysis suggests a flattening of the curve of the kind found by Eigen for normalproton-transfer processes.A further experimental study of the diazoacetate de-composition would be desirable.It is worthwhile emphasizing that the concerted or co-operative mechanismfor proton transfer in aqueous solution is probably confined to a certain type ofreactions, and probably always involves one or more water molecules. Thus,there is no evidence for such a mechanism for keto-enol reactions in water, andno evidence for kinetic terms such as k[AcOH][AcO-] in the hydration of carbonylcompounds or the mutarotation of glucose.4 Additional evidence for the concertedmechanism in carbonyl hydration comes from the results of Strehlow 5 on the kineticsof the reaction MeCOC02H+H20+MeC(0H)2C02H7 which shows a “ spon-taneous ” rate which is much too large to be attributed to catalysis by solvent mole-cules.It was therefore attributed to intramolecular catalysis by the carboxylgroup, and this seems much more probable if the proton transfer takes place throughone or more intervening water molecules.Prof. A. J. Kresge (Illinois Institute of Technology) said: Mr. Bell’s calculationsand the earlier ones to which he referred all predict that the value of the isotope4-1 Bell, The Proton in Chemistry (Cornell Univ.Press, Ithaca, N.Y., 1959), p. 170.2 King and Bolinger, J. Arner. Chem. SOC., 1936, 58, 1533.3 Bell and McTigue, J. Chem. Soc., 1960,2983 ; see also Bell, The Proton in Chemistry (Cornell4Bell and Clunie, Nature, 1951, 167, 363; Proc. Roy. SOC. A , 1952, 212, 33.5 Strehlow, 2. Elektrochern., 1962, 66, 392.U.P., 1959), p. 136GENERAL DISCUSSION 49effect on a given reaction will pass through a maximum as the structure of the transi-tion state is varied from one extreme to the other. I now present some data whichseem to provide the first clear indication of such a maximum. The reaction isaromatic hydrogen exchange, and the isotope effect is that on bond-breaking inthe phenonium ion which is the intermediate in the reaction :kH kDH i- +ArD cHArD+ -+ HAr + D +TABLE 1Ic,lk, exchanging relative rateposition of exchange HArC6H6 - 1 3.4 h0.2C6H5CH3 3 6 3.4 f0.2 *C6HSCH3 2 4 x 102 4-6 f0.4 aC6HSCH3 4 4 x 102 5.5 f0.3 aC6H50CH3 2 2~ 104 7.2C6H50CH3 4 6x 104 6.71 ,3,5-C6H3@CH3)3 2 1 x 1010 6.7 f0-2 Cazulene 1 3x 1011 5.6(a) Olsson, Arkiv.Kerni., 1960, 16, 482. (c) Kresge andChiang, J. Arner. Chern. Soc., 1962, 84, 3976. ( d ) Schulze and Long, J. Arner. Chem. Soc., 1964,86, 331.(b) Russell, M., private communication.These experiments cover a wide range of reactivity and presumably, therefore,a considerable variation in transition state structure. Other data, such as thosepresented by Mr. Bell, are more limited, and this may be the reason why they showonly an upward or downward trend in isotope effect without a maximum.Mr.R. P. Bell (Oxford) said: I should like to amplify two points made in mypaper. First, the conclusions embodied in table 3 are supported by calculationsrecently published by Willi and Wolfsberg,l who examined the dependence of iso-tope effect on the symmetry of the transition state for various values of the barriercurvature. For zero curvature (corresponding to Westheimer’s treatment) there isa fairly sharp maximum in kH/kD for a symmetrical transition state, but for realisticvalues of the curvature this maximum becomes very flat and kH/kD is almost con-stant over a wide range of transition states: this corresponds to the decrease inA1, and the approach of v?/v? to unity shown in my table 3.Secondly, the correlation between kH/kD and p shown in table 2 is improvedif a correction is applied for the secondary isotope effect of the non-ionizing deuteriumatoms in CD2- and CD3-groups.Streitwieser and van Sickle 2 have found that thesubstitution of two deuteriums in the methyl group of toluene diminishes the rateof exchange of a third deuterium by 24 %, i.e., there is a secondary isotope effectof kH/kD = 1.1 5 per deuterium, and in my laboratory Mr. D. M. Goodall has founda similar value for the ionization of nitroethane by hydroxide ions. It is thereforereasonable to correct the observed values of kH/kD by dividing by 1.15 for CD2-groups and by 1-152 for CD3-groups: these corrected values follow the samesequence as /? with the single exception of acetylacetone.One further value maybe added to table 2 by using the observation 3 that k;/kD = 7.7 for the brominationof acetone catalyzed by &0+. The rate-determining reaction is Me& : OH+ + H20,and the appropriate value of p is 1 - a, where a is the Bronsted exponent for acidcatalysis, having the value 4 0.62.1 Willi and Wolfsberg, Chern. and Ind., 1964, 2097.2 Streitwieser and van Sickle, J. Arner. Gem. SOC., 1962, 84, 254.3 Reitz, 2. physik. Chern. A , 1937,179,119. Reitz and Kopp, 2. physik. Chem. A , 1939,184,429.4 Bell, Acid-Base Catalysis (Oxford, 1941), p. 9150 GENERAL DISCUSSIONDr. D. B. Matthews (Univ. of Virginia) said: With regard to the interrelationshipof the Bronsted coefficient, the isotope effect, activation energy and heat of reaction,I shall employ the potential energy profile method of Horiuti and Polanyi :REACTION COORDINATE ( x ) -Change in configuration of the activated state produced by a change in heat of reactionwhere I refers to the initial state and I1 the final state.A change in heat of reactionwill cause a vertical shift of one curve with respect to the other (dotted curve).The effect is a change in activation energy, and also in configuration of the activatedstate with respect to the initial or final state configurations, which causes a changein zero-point energy of the activated state and hence a change in the isotope effect.This direct dependence of the isotope effect on the heat of reaction is often overlookedin comparison with, say, the role played by charge on the acceptor molecule and therole of proton tunnelling. My second point concerns the dependence of the degreeof proton tunnelling on the heat of reaction.Mr. Bell has shown that the isotopeeffect for proton transfer as a function of charge on the acceptor goes through amaximum. Similarly it is found that the dependence of the isotope effect, due toproton tunnelling, on heat of reaction goes through a maximum, the position ofthe maximum corresponding to AH0 = 0.Dr. N. A. J. Rogers (Birmingham University) (communicated) : I should like torefer to a point raised by Dr. Matthews, who pointed out a property of potential energyprofiles, illustrated in fig. 1.He argued that in a situation in which an initial stateFIG. 1.B can lead, via a transition state, TS or TS’, to two final states, A or A’, then thealtering of the final state from A to A’ will not only affect the activation energy ofthe reaction, but will also alter the configuration of the transition state. Thisconsequence is clearly shown in fig. 1. I should like to refer to some of our work,in which the concept appears to be of importance. We have investigated thGENERAL DISCUSSION 51protonation of a series of conjugated dienol ethers of the types I and 11, in which theattached groups are alkyl or hydrogen.We have, in the first instance, studied the preferred site of protonation ( a or y)of these compounds. Broadly, it appears from our results that the transoid-dienolethers (11) are less sensitive in their behaviour to alkyl substitution than are thecisoid-isomers (I).Thus the transoid-dienol ethers examined to date protonate\/I I1exclusively at the y-carbon atom, yielding the more stable, conjugated products.Further, a linear plot of log (k,/k,) against (qa-q,,), the charge densities as calculatedby the simple Huckel m.0. method, has been obtained for the cisoid-dienol ethers.In attempting to rationalize these results, we have found it necessary to invokethe idea of a difference in relative configuration of the transition states for the pro-tonation of these two series of compounds. There appears to be a greater degreeof bonding in the transition state for protonation of the transoid compounds, wherethe more stable products are formed, than in that for protonation of the cisoidisomers, where dependence on a property of the initial state (Aq) is observed.For the reactions below,a cisoid-(111) and a transoid-(1V)-dienol ether give rise to the same product (V)on y-protonation.From our earlier arguments, the initial state for the protonationenergy profile of (111) should lie at a higher level than that of (IV). We havemeasured the equilibrium between I11 and IV and have found that IV is the morestable by about 1 kcal/mole. Thus, on Dr. Matthew's diagram, fig. 1, I11 cor-responds to A', IV to A and V to B.Secondly, Prof. Havinga referred to his studies of the protonation (deuteronation)of the excited state of anisole (I), in which 0- and m- attack is observed, the relativeI I1reactivities at these positions correlating with the calculated charge densities.Wehave been studying the formally similar anion-radical of anisole (11), the calculatedcharge densities of which would predict protonation at the o-position preferentially.This protonation is the crucial step in the metal/ammonia reduction of anisole52 GENERAL DISCUSSIONPreferential protonation at the 0- and at the m-position have been strongly sup-ported by different groups. We now have experimental results, based on an e.s.r.study of the anisole + dimethoxyethane +potassium system, which are most readilyinterpreted in terms of preferential o-protonation of 11. This result, like those men-tioned by Prof.Havinga for I, is the one predicted on the basis of charge densitycalculations.Dr. M. Fleischmann (Newcastle upon Tyne) said: If the viscous relaxation timecan be shown to affect the rate of proton transfer in examples where the solvent isnot directly involved, it would follow that the classical transfer would have to betreated as if the system were non-conservative.1 Both the “ frequency factor ”and the “ energy of activation ” will then depend on the velocity of the particlesinvolved in the transfer, low velocities giving the highest probability of surmountingthe barrier. One would predict that the ‘‘ reaction co-ordinate ” would involvethe movement of the whole molecules or sections of the molecules in the solventcage rather than the stretching of single bonds.In one particular example of proton transfer it is now possible to state thatsolvent reorientation is unimportant.The electrochemical hydrogen ion dischargeon mercury has been measured up to heterogeneous rate constants of the orderI000 cm sec-1.2 The logarithms of these high values of the rate constants plottedagainst eIectrode potential fit on the same “ Tafel line ” as the values measured atless negative potentials. Since the velocity of the nuclei at the high rate constantsis certainly in the range or above that corresponding to the viscous relaxation timeof water, it may be concluded that the reorientation of the solvent is unimportantin this particular discharge reaction.Dr. H. W. Numberg (Kernforschungsanlage Jiilich) (communicated) : Employingthree advanced techniques of polarographic nature (pulse-polarography (PP), square-wave-polarography (SWP) and especially high level faradaic rectification (HLFR) 3),which permit reduction of the measuring time t1 after the start of polarization of theelectrode to finally 1 psec, we have been able to study at 20°C the kinetics of thehydrogen evolution at the mercury electrode up to very negative potentials and con-sequently up to high rate constants for the charge transfer step of this electrodeprocess.4Over the whole range of measurements leading from kct = 5 x 10-5 cm sec-1 at- 1.32 V (SCE) to kct = 800 cm sec-1 at -2.1 1 V (SCE) the results fit to a Tafel-line with a slope of b = 110 mV indicating a constant apparent charge transfercoefficient of aa = 0.53 (fig.1). No double-layer correction has been applied,but as the solutions contained always a constant high supporting electrolyte con-centration of 1 m LiCl the influence of the double-layer effects on b over the wholemeasured range of potential remains quite small (<lo %) and will not exceed 3 %The data between kct = 100 and 800 cm sec-1 could only be obtained withacetic acid making use of the fact that due to the participation of the prior homo-geneous chemical reaction of the dissociation of the weak acid the current-voltage-curve rises less steeply and reaches therefore the limiting current at a more negativeelectrode potential than when a strong acid (HCl) is employed as proton donor.After the homogeneous dissociation rate constant of acetic acid had beenfor aa.1 cp.Bass, Proc. Roy. SOC. A, 1964, 277, 125.2 Barker, Niirnberg and Bolzan, Report Jiil-l37-CA, 1963, Kernforschungsanlage, Julich.4 (a) Barker, Numberg, and Bolzan, Report JiiZ-l37-CA, (Kernforschungsanlage Julich, 1963).Barker and Numberg, Naturwiss., 1964, 51, 191.(b) Barker, Niirnberg, Bolzan and Gardner, Electrochim. Acta, in pressGENERAL DISCUSSION 53determined from the limiting current 1 the charge-transfer rate constant kct could beevaluated from the rising part of the polarogram.The dotted part of the Tafel-line in fig. 1 leads to the most negative potentialobtained in the limiting current region of the polarograms before the discharge ofthe Lif ions occurs.An extrapolation to this potential seems justified if one assumesthat a, remains constant.Several general conclusions relevant to a number of points made by variousauthors at this discussion are possible from our results.(i) Our measurements are concerned with a range of charge-transfer rate constantsand corresponding potentials above that region normally hitherto studied as it isnot accessible by the more conventional techniques due to their larger measuringtimes. Exceptions reaching the lower part of our Tafel range are the experiments10' -10' -loz -10' -.4I 8 l -1 0 ' -10' -1 0 ) -Id' I'amHLFR f-- 4"P*HAC ///S WP, I, = 2.22 rnsec. HClPP. I, =40 msec,HCl-1.3 -1.4 -1.5 -1.6 -1.7 -1.8 -1.9 -1.0 -1.1 -2.2 -23voltsFIG.1 .-Tafel plot for h.e.r. at Hg from 2.5 x 10-4 m HCI, 1 m LiCl and 1 x 10-3 m HAc, 1 x 10-2 mNaAc, 1 m LiCl respectively at 20°C (from ref. (24). The upper measuring limits of the employedtechniques due to their respective measuring time t l and to the respective experimental conditions(strong or weak acid) are indicated. The Tafel-line has been smoothed through a great number ofexperimental points, which had to be omitted because of the small dimensions of the figure.by Bockris and Azzam.2 However, the data obtained by conventional methodsat lower potentials may be fitted fairly well to a Tafel plot of the same slope.3 Con-sequently, for the h.e.r. at mercury from acidic aqueous solutions a constant slopeb and therefore a constant charge-transfer coefficient a over a range of more than1.9 V corresponding to 17 powers of ten in the charge transfer rate constant kot isexperimentally established.This behaviour is consistent with theoretical consider-ations of Christov 4 predicting for an Eckart barrier with a height of Er = 1.5 x 10-12erg at q = 0 a constancy in a over more than 2 V of overvoltage q (see p. 128 in ref.1 Nurnberg, in Proc. 3rd Znt. Congr. Polarography, Southampton, 1964), ed. Hills (Madllan3 cf. Vetter, Elecirochemische Kinetik, (Springer, Berlin, 1961), p. 432.4 Christov, Ber. Bunsen. physik. Chem., 1963, 67, 117.Ltd., London, 1965). 2 Bockris and Azzam, Trans. Fmahy SOC., 1952,48, 1454 GENERAL DISCUSSION(6)). Thus the h.e.r. on mercury may well be regarded as the electrode process onwhich the most extended knowledge with respect to charge transfer rate constantsand charge transfer coefficient is available at present.(ii) With respect to the comparison by Prof.Conwayl between the constancyof the Bronsted coefficient over a certain pK-range and the constant behaviour ofthe charge-transfer coefficient for the h.e.r. at mercury over a given range of elec-trode potentials, the figures have to be enlarged appreciably including our results?In the 2RT In K scale the range of 2 V for which a constant U-value has been ob-served is equivalent to 30.5 pK-units which is a much wider region than generallyobserved in homogeneous proton transfer cases.(iii) One deduces from fig. 1 further that there is no indication for any fast priorchemical reaction in the discharge of hydrogen ions from a strong acid as HCl.On the other hand, we have observed for a number of metal ions reductions studiedat the mercury electrode with the new technique of high level faradaic rectificationa normally fast prior chemical step which is to be attributed to partial dehydrationor decomplexation of the metal ion before electron transfer occurs.2as 2 The absenceof this step in the discharge of hydrogen ions is to be expected by analogy with themechanism pointed out by Eigen 3 for the homogeneous recombination of the H3O+ion and the anion of an acid (see also my discussion remark on the paper of Salomonand Conway and that of Bockris, Srinivasan and Matthews).(iv) Several authors4 have raised the question of the relations between therelaxation time for the reorientation of water molecules and proton transfer.Ourstudy on the h.e.r. at mercury has been cited as furnishing evidence for a protontransfer process where solvent reorientation is unimportant (cf. discussion remarkof Dr. Fleischmann) as well as showing that the dielectric relaxation time of waterseems to be smaller than the time for proton transfer via the interphase electrode/solution (cf. discussion remark of Prof. Christov). A detailed inspection of theproblem reveals that both statements are not strictly correct.Taking our highest (extrapolated) kct value of 2 x 104 cm sec-1 in fig. 1 and assum-ing a " reaction layer " pct for the charge transfer step of only 0.5 A 5 an equivalenttime zct = 2.5 x 10-13 sec is obtained.The dielectric relaxation time z * for H20dipoles in 1 m aqueous alkali halide solutions has been determined 6 as 76 = 9 x 10-12sec at 20°C and is thus a factor 40 larger than our smallest zct. However, the neces-sary rotation of a water molecule into a position favourable for proton transfer isaccelerated by the field of the H3O+ approaching the water molecule.7 For therelevant rotation time in proton transfer one has 'trot = 2 x 10-32,. Regardingfurther that on the average only 1 of 9 rotations leads to a position of the H20molecules adjacent to an H30+ favourable for proton transfer, the effective rotationtime becomes zfrot = 9 x 2 x 10-3 z, as the proton transfer step itself along thehydrogen bridge formed to the favourably orientated H20 molecule occurs in atime negligible with respect to zfrot (see, e.g., ref.(13)) and the measurements on theproton mobility in ice by Eigen and collaborators 8). Inserting these figures one* The viscous relaxation time (cf. Discussion remark Dr. Fleischmann) may be identified with7 0 for practical purposes.1 cf. Discussion remark of Conway.2 Barker, Nurnberg and Gardner, 13 CITCE-Meeting, Rome, 1962 ; Electrochim. Ada, in press.3 Eigen, 2. physik. Chem., 1954, 1, 154.5 (a) Salomon and Conway, this Discussion. (b) Nurnberg, this Discussion.6 Lane and Saxton, Proc. Roy. SOC. A , 1952,214, 531.7 Bockris, Conway and Linton, J. Chem. Physics, 1956,24, 834.8 Eigen and De Maeyer, 2.Elektrochem., 1956, 60, 1037. Eigen, De Maeyer and Spatz, Ber.4 cf. Bell, this Discussion.Bunsen. physik. Chem., 1964, 68, 19GENERAL DISCUSSION 55obtains drat = 1.62 x 10-13 sec. Thus, the Tct value equivalent (with the assumptionfor pet) to our largest (extrapoIated) value of the charge transfer rate constant kctis approaching the order of the effective orientation time Trot' for the H20 moleculesin proton transfer. Though the reorientation of the H20 molecules during protontransfer is therefore not affecting our present results the design of such experimentsseems feasible in principle.(v) In terms of the paper of Salomon and Conway 1la and an earlier published cri-terion by Conway 1 the slope of our Tafel-line in fig. 1 indicates no significant contri-bution of proton tunnelling to the charge transfer step while according to Bockris,Srinivasan and Matthews 2 a moderate tunnel effect cannot be excluded.Dr.Roger Parsons (University of Bristol) said: Some light may perhaps bethrown on the problem of the reorientation of adjacent solvent molecules duringproton transfer by asking the question, " Why are proton transfers fast comparedwith electron transfers? " It is known from the theories of Marcus 3 and Hush 4that homogeneous electron exchange between hydrated transition metal ions andthe electron transfer is retarded by the necessity to reorganize the surroundingsolvent into a configuration intermediate between initial and final states. Thiscan lead to energies of activation in the region of 9 kcal mole-1 for an ion of thesame size as H30+.The absence of such activation energies in proton transferreactions (except when they are endothermic) seems to suggest that solvent reorgan-ization does not play an important role probably because the distance over whichthe proton is transferred is small compared with the electron jump distance and thefield on the surrounding solvent is, relatively, much less altered as a result of thetransfer.Prof. M. C. R. Symons (University of Leicester) said: Although, as stressed byDr. Parsons, the barrier to proton transfer caused by the need for solvent reorgan-ization is likely to be small in comparison with that for many electron-transferprocesses, since the distance through which the proton needs to move is small, thiswill only be true of overall reactions in which the rate-determining step is the transferof a proton.There must be many proton-transfer reactions in solution for whichthis is not the rate-determining step, in which case the solvation " barrier " may beextremely important. Various possibilities may be illustrated by the followingmodel, which also serves to underline in a simple manner several other points raisedduring this discussion.Consider the symmetrical transferThis may be conventionally represented by an energy diagram which showsmovement of the proton as it moves across from one A- to the other (fig. I). How-ever, such curves imply a fixed A - - - A distance, so one needs to draw up a familyof curves for different A - - - A distances.This can be done by imagining a seriesof curves, of the type shown in fig. 1, through each point on the curves given infig. 2, where energy is plotted against the A - - - A distance.Initially, as A- approaches AH, the proton will remain bonded to its initialpartner, and the A - - - H bond length will hardly alter. There will, however, bea solvation barrier to overcome, which could be pictured as a replacement of one ofthe solvent molecules associated with A- by the acid HA. If the system [A - - - H - - - A*Isil,. has some stability, as is often the case, the curves in fig. 2 will now fall.1 Conway, Can. J. Chem., 1959,37, 178.2 Bockris, Srinivasan and Matthews 1 his Discussion.3 Marcus, J. Chem. Physics, 1956, 24, 966 ; for general review see Marcus, Ann.Rev. Physic.A,,,. + HA+(A- - -H- - -A),,,.+AH +A~'lvv. (1)Chem., 1964,15, 155. Hush, J. Chem. Physics, 1948, 28,96256 GENERAL DISCUSSIONOne extreme is that from this minimum there is still a large barrier to protontransfer, so that solvent reorganization will be only a minor effect (cf. Dr. Parsons’explanation). This would be the case, e.g., if the preferred path were a combinationof curve (3), fig. 2, and curve (3) of fig. 1. An important alternative is that, withinthe solvated complex [A - - - H - - - A]& proton transfer is rapid and hence the( A-H -- A )-FIG. 1.( A - - - - A ) h n(A---A) distanceA-SOLV- -- HA ( A-- - H ---A )-SOWFIG. 2kinetic barrier is the initial solvation barrier discussed above.This would be thecase for curves (1) of the figures. One example of this latter situation is the exchange(1) in which A- is F-. Here the HF; ion is stable, and its dissociation will resultin an equal distribution of protons between the two fluoride ions. The same modelmay be used to illustrate the situation envisaged during the discussion, in which aproton is “ pushed across the barrier ” by the group to which it is attached. Thismeans that the A - - - A distance most suitable for proton transfer is less than theequilibrium distance for normal hydrogen bonding. Jn general, the solvent barrieGENERAL DISCUSSION 57considered here will control the rate if xg>yg+zgxd, etc., being the appropriateenergies shown in the figures.The symmetrical exchange used as a model has the advantage that the principleof microscopic reversibility is naturally accommodated.For unsymmetrical ex-changes barrier heights will vary in the manner outlined in the discussion by variouscontributors, but the factors stressed here, viz., (i) the influence of a stable hydrogen-bonded complex; (ii) the need for solvent reorganization during its formation andloss ; (iii) the operation of the principle of microscopic reversibility ; (iv) the needto consider the A - - - A (or A - - - B) distance as well as the A - - - H distance,remain worthy of consideration.Mr. R. P. Bell (Oxford) said: The width of the parabolic barrier at its base isperhaps a rather artificial quantity, since the parabolic approximation is only validnear the top of the barrier.Since the reactions so far investigated involve only arelatively small tunnelling correction (EAIEqmt = 0.79-0.95) the quantity which isdirectly derivable from the experimental data is really the curvature of the top ofthe barrier, and this might be preferable to the width as a basis of comparison.(In terms of the parameters used by Caldin and Kasparian the curvature is 2Eqmt/a2,and it can also be written as 4n%~v$, where m is the reduced mass and iv* theimaginary frequency). At a given temperature the curvature is directly related to&/Eqmt, and the distinction between aqueous and alcoholic solutions, mentionedby Caldin and Kasparian, appears more clearly in terms of curvatures than in termsof barrier widths.Prof.J. J. Weiss (Newcastle) (communicated): I should like to comment onthe question of the barrier width in proton transfer reactions. The distance whichthe proton has to travel along the hydrogen bond between the two reactants wouldbe the mean distance between its initial and final state and this can be deducedfrom known bond distances. The distance of the centres in hydrogen bonds is2.6-2-8 A; as the OH or NH bond lengths are about 1.0-1-1 A, the actual distancewhich the proton has to travel along the hydrogen bond will be 0.4-0-6A. This,however, must not be confused with the closest distance of approach of the reactantsin the initial state (collision diameter) which, on the basis of these figures would benot less than 1.5-1.7 A.These distances cannot, however, be defined very pre-cisely since the molecular surfaces are not infinitely sharp.Prof. M. M. Kreevoy (University of Minnesota) said: Dr. Paul Steinwandand I have recently investigated the reaction of allyl-mercuric iodide with aqueousacid in the presence of traces of iodide ion. The reaction proceeds as shown:H+I -CH,=CH--CH2HgI+CHSCH=CH2 + HgI2.The rate is independent of iodide concentration and the rate-determining step isproton transfer from H+ to the y-carbon. We have studied the primary isotopeeffect on this reaction by a competition method as a function of temperature. Fromthe isotopic difference in the pre-exponential factors we have evaluated the widthof a hypothetical parabolic barrier as 1.3 A.Regardless of its exact physical sig-nificance, this result certainly supports the Caldin and Kasparian generalizationthat the " width " estimated in this way is primarily a function of the solvent. Thereaction is of quite a different type from those reported in table 3, but the width isvery similar to the others reported for aqueous solution.Also, it seems that there is a close relation between proton tunnelling and un-equilibrated transition states. It is the essence of tunnelling that it is very fast.Although the proton apparently moves only about 1 A, the centre of positive charg58 GENERAL DISCUSSIONmoves several times that distance. It seems unlikely that much solvent re-orientationcan take place during the tunnelling. It then follows that the solvent shell will beunequilibrated during much, and perhaps all, of the transfer.I would also like to ask if anyone has thought about tunnelling in the contextof a double jump mechanism :HIA-@ -0-0 +B.Dr.J. R. Jones (Battersea College of Technology, London) (communicated) : Thereare a number of points in Dr. Caldin’s paper upon which I would like to comment.Table 3 contains seven reactions which have been considered in terms of non-classicalbehaviour either by using isotopes or by observing curvature of the Arrheniusplot, and in some cases which involve the use of different catalysts. We believethat curvature alone cannot be taken as conclusive evidence for the existence oftunnelling and would suggest that it should only be used as confirmation when atleast one isotope effect is known together with the activation energy differencesand frequency ratios.This point is important for di-isopropyl ketone where, ifHulett’s account is accepted, a large isotope effect should be observed togetherwith an abnormal ratio for A D / A ~ . Our data for the rates of detritiation showthat ET-EH = 500 cal/mole, AT/& = 1-16 and K H / K ~ = 2-0 at 20°C.Secondly, the calculations of the energy barriers and widths all involve theassumption of a one-dimensional barrier of a symmetric parabolic shape. As manyof the substrates have widely different structures and the kinetic isotope effectsoften cover a wide range of values (cf. the value of 2.0 for di-isopropyl ketone andan equivalent value of 6-0 for acetone), this method is limited and discussion of smalldifferences in barrier widths must be of doubtful value.In the same way as isotopicsubstitution can be used to eliminate a number of uncertainties, then a study of anumber of structurally similar compounds using the same catalyst should be ofconsiderable benefit.Dr. J. R. Hulett (University of Leeds) said: I am interested in the table of barrierwidths given by Dr. Caldin and Dr. Kasparian in their paper. As we gain in-formation upon barrier dimensions, I believe we can use it to decide betweenpossible reaction mechanisms. Since I wrote my review 1 I have examined moreclosely the paper by Stewart and van der Linden.2 Although the Arrhenius para-meters for the permanganate oxidation of PhCH(OWCF3 and PhCD(OH)CF3are not given, they may be calculated from the rate constants shown at threetemperatures for the reaction at pH 13.0.From these results, I find E D - E ~ = 2290 cal mole-1 and AD/& 3-03.These figures are consistent with the author’s suggestion that the large isotope effect,k ~ / k ~ = 16, may be due to tunnelling.I have used Bell’s equations 3 for a para-bolic barrier and find = 11.42 kcal mole-1, ED(^, = 12-73 kcal mole-1, a =0.553Three features call for comment: (i) the degree of barrier penetration issimilar to that found for protons in the bromination of various ketones; (ii) thedifference in barrier heights, 1.3 kcal mole-1 is much the same as the difference inzero-point energies for the stretching modes of C-H and C-D bonds.Thisgiving EH/EH(*, = 0.85 and ED/ED(~, = 0.95.1 Hulett, Quart. Rev., 1964, 18, 227.2 Stewart and van der Linden, Disc. Furuduy Suc., 1960, 29, 211.3 Bell, Trans. Furaduy Soc., 1959, 55, 1GENERAL DISCUSSION 59implies almost complete rupture of the C-H bond in the transition state, unlessthere are considerable contributions from the bending modes. This result may becontrasted with those found for ketone bromination 1 ; (iii) the barrier width issimilar to those observed for proton transfer between an uncharged body and ananion in aqueous solution. Stewart and van den Linden suggest several possiblemechanisms for the reaction. Two involve termolecular collisions of solute species,of which one, the unionized alcohol, is present in only very small proportions atthis pH.- AS* for this reaction is probably too small to support such an unfavour-able process. The two other possible mechanisms are (a) hydride ion transferbetween the alcoholate anion and a permanganate ion or (b), simultaneous protontransfer from the alcoholate anion to water and electron transfer to a permanganateion. The authors favour the first of these mechanisms, although the very smalleffect of substituents in the aromatic nucleus is more easily accommodated by thesecond.The barrier width may help to decide between these alternatives. Mechanism(a) requires the approach of two negative ions and the transfer of a negativelycharged species between them. The electrostatic repulsions should lead to anenergy barrier considerably wider than those obtained for proton transfer betweenan anion and a neutral molecule.This is not the case, and thus the hydride iontransfer mechanism seems unlikely. The calculated barrier width, however, isconsistent with mechanism (b) if the major effect of deuterium substitution is onthe proton transfer, and secondary effects on the electron transfer are small. Atthis point we must leave aside any question of electron tunnelling. Althoughconsideration of the barrier width does not definitely establish mechanism (b),it seems most probable that the reaction involves a proton transfer between ananion and a neutral species-certainly mechanism (a) is unlikely.Prof. G. J . Hills (Southampton University) said: Of the arguments for protontunnelling, the non-linearity of the Arrhenius relation is perhaps the weakest.Thenormal enthalpy of activation defined by the isobaric relationship,(1)consists of two related components, viz., the internal energy of activation AU*and the product of the volume of activation and the so-called internal pressure ofthe system, i.e.,AH' = RT2(a In k/aT),,aTAH: = AU,f+-AV*, (2) Bwhere a and /3 are the coefficients of cubical expansion and compressibility, and AU*is defined by the isochoric relation,AU* = RT2(a In k/aT),,and AV* by the isothermal relation(3)AV* = RT(d In k/dP),. (4)The quantum-mechanical aspects of the reaction will determine the AU* termand thus may contribute to the temperature-dependence of AH*.However, a,/3 and A V are all temperature dependent and, more important, they and possiblyalso AU * are volume or density dependent. Since density is temperature-dependent,the isobaric variation of AH* with temperature is to be expected as a thermodynamicconsequence of eqn. (2). The question then arises as the magnitude of the termccTAV*/P. In aqueous solutions at room temperatures, it is small because a is small1 Hulett, Proc. Roy. Soc. A, 1959, 251, 27460 GENERAL DISCUSSION(zero at 4°C). At other temperatures and in other solvents it is large (1-2 kcal mole-1)even for modest values of AY*. The isobaric temperature dependence is then acomplex quantity even in classical terms and as a criterion of detailed aspects of areaction mechanism, should be used cautiously.Dr.J. R. Hulett (University of Leeds) (contributed): I have tried to apply theequationAH: = AUz+(aTAV:/P>to my results for the bromination of di-isopropyl ketone,l assuming that AU: istemperature independent. Preliminary calculations suggest that the experimentalresults cannot be reproduced by this equation unless AVT varies quite considerablyin the temperature range used (0-SOOC).Prof. B. E. Conway (Ottawa) said: I would like to comment on the questionof barrier widths 2a in proton transfer reactions, e.g., as deduced in the paper ofCaldin and Kasparian and referred to elsewhere in several papers in this Discussion.Most values of 2a seem too large compared with the real barrier width which wecould define as the mean distance between the proton in its initial and final state,and which might be deduced from molecular radii and covalent bond distances.A good example is the autoprotolysis in ice; here the 0-0 distance is relativelyfixed and is close to 2.8 A and the OH internuclear distance in the initial state is0.98 A.After proton transfer, an ion pair OH-H30+ is temporarily created andthe distance the proton is transferred can hardly be greater than about 2.8 - 2 x 0.98 A,i.e., 2a = 0.84A. Similarly, in proton conductance in acids, where the initial andfinal states are identical, 2a f O-SA. The deduced barrier widths, which are largerthan these figures by a factor of 2-3, probably reflect a degree of inapplicability ofthe tunnelling permeability equations as expected; for the Eckart barrier case, agreater “ barrier width ” will be required to reproduce a given curvature at thetop of the barrier, as remarked by Mr.Bell, than would be the case for the parabolictype of barrier model. The real barrier width will probably depend on the strengthof the hydrogen bond between the acid-base pair between which proton transferoccurs.In the model of Bockris, Srinivasan and Matthews, however, the barrier widthof ca. 4 tf seems too large on any basis, e-g., as indicated by Christov’s calculations.2Prof. J. O’M. Bockris (University of Pennsylvania) (communicated) : The Eckartwidth barrier of our calculation is not an assumed one, as is implied by Prof. Conway.It is that which is indicated by the only interpretation which we can make quanti-tatively consistent with the dependence of separation factor on potential (and thevalue that we have used comes out very near to that of Caldin and Kasparian).3Prof.S. G. Christov ( h t . Physic. Chem., Bulgaridn Academy of Sciences) said:The role of the tunnel effect in the proton-transfer processes in solutions and onelectrodes has been investigated by Bell 4 and the writer.5~ 6 Essentially the samemethod for the determination of the dimensions of the potential barriers was appliedindependently in both cases. This method consists in inserting the experimentaldata for reaction rate 0, activation energy E’ and frequency factor K’ in the rate1 Hulett, J. Chem. Sac., 1965, 430.2 Proc.1st Australian Con$ Electrochemistry, ed. Friend and Gutmann (Pergamon Press, 1965),4 (a) Bell, Trans. Fmahy Suc., 1959, 55, 1. (b) Bell, Fendley and Hulett, Proc. Roy. Soc. A,5 Christov, (a) Dokl. Akad. Nuuk. S.S.S.R., 1959,125, 141 ; (b) 2. physik. Chem., 1960,214,40;6 Christov, 2. Elektrochem., 1958, 62, 567.p. 723.1956,235,453.see also (c) Electrochim. Acta, 1961, 4, 306 ; 1963, 9, 575.3 Caldin and Kasparian, this DiscussionGENERAL DISCUSSION 61equation o = K’ exp (-E’/kT) for two isotopes (H and D or T). The quantitiesEk, EI;, KAY KI; (or KH/KA), VH and UD (or OH/UD) are in principle functions of thebarrier width zo and barrier height Ec and also of the corresponding zero-point energies(80 and 60) and entropies (SO and SO) in the initial and the transition states.Thesolution of a system of many transcendental equations by fitting is difficult, but areduction of the unknowns is possible 6 ; in absence of tunnelling we obtainthe relation 0.5 < K b / K h <2 for the ratio of the classical frequency factors, includingthe corresponding activation entropies (So - Sd) ; (ii) by introducing the “ true ”classical activation energies EH and ED (E = E,-(Q-&)) as unknowns. Ac-cording to (i) a low value for the tunnel correction is obtained by assuming Kb /K$ < 1.Accordingly, the decrease of the barrier height (E<E, because he0 = EO-EO>O)leads to an underestimation of the tunnel correction, too. It seems possible in thismanner to determine a lower limit for the net tunnel correction, which is thereforenot cancelled by the contribution of Aeo.The simplest and most direct way for estimating the role of the tunnel effectconsists in the evaluation of the characteristic temperature TK, defined by the con-dition, that the probabilities of transferring through the barrier and over it are equal2For smooth barriers this temperature is given by the relation 1TK = h JG/2nkJ12m, L, = -(d2V/dx2)x=xm,in which rn is the mass of the particle, h the Planck constant, k the Boltzmann con-stant and Lm the barrier curvature at the maximum.Expressions for TK for variousbarrier shapes were derived previously.4 This characteristic temperature permitsthe determination of the temperature ranges 5 : T> 2 T X (negligible tunnelling),TK < T< 2Tx (weak tunnelling), TK/Z < T< TK (moderate tunnelling) and T< T K / ~(large tunnelling).For each of these regions the tunnel correction varies betweenwell-determined limits and corresponding approximations are applicable.2A lower limit for TK can be obtained by insertion for L, the lowest value, corres-ponding to a parabolic barrier with the greatest possible width (e.g., double layerthickness) and the smallest possible height E = E‘ (E’ = experimental activationenergy). Calculations show 3 that proton-transfers normally occur in the regionof moderate or weak tunnelling.Under these circumstances it is not important whether we assume a symmetricalor an unsymmetrical barrier. Calculations of the barrier dimensions on the basisof experimental data give only a barrier equivalent to the real one.29 6 This meansthat both barriers have almost the same permeability in the given temperaturerange, which is possible under the condition that their upper permeable parts nearlycoincide.In this way we obtain different barrier widths for different equivalentbarrier models.2, 6 The effect of non-zero reaction heat (unsymmetrical barrier 39 4)may be important for large tunnelling which normally does not occur in proton-transfer processes. (This seems also to be the opinion of Mr. Bell.)The question, is there justification for the application of a one-dimensionalbarrier in calculating the tunnel corrections, is an important one. It appears,however, that the treatment of Johnston and Rapp 5 does not give a final answer,because they applied the Eckhart potential in evaluating the tunnel corrections fordifferent profiles of the potential energy surface ; this may lead to an underestimationof the tunnel effect.The true barrier profiles may have an intermediate course1 Christov, (a) Dokl. Akad. Nauk., S.S.S.R., 1960, 136, 663 ; (b) Ann. Physik, 1963, 12, 20.ZChristov, Ann. Physik, 1965, 15, 87.3 Christov, Proc. 1st Austral. Con$ Electrochemistry, 1963, p. 723.4Christov, 2. Elektrochem., 1960, 64, 840.5 Jonston and Rapp, J. Amer. Chem. Soc., 1961, 83, 162 GENERAL DISCUSSIONbetween the Eckart and parabolic barrier (with the same curvature at the top),which can be expressed better by means of the generalized Eckhart potential.4bs 5It is therefore possible that the difference between the mean permeabilities ofthe one-dimensional and two-dimensional barriers are not very significant, at leastfor moderate tunnelling.Physically one can expect some cancellation between theeffects of the side-wall repulsion and the more favourable situation, for tunnellingalong the profiles, which are longer than at the saddle point; the tunnel correctionfactor r = V/V' will be larger for these profiles than at the saddle-point, althoughthe barrier height is bigger (and therefore the mean permeability smaller).Finally, the writer agrees with Mr. Bell that relaxation in the water moleculeorientation may contribute to the activation energy of some proton-transfer reactionsin solution.Although it seems that new measurements of hydrogen overpotential 1do not confirm the conclusion that the dielectric relaxation time for water is greaterthan the time of a proton-transfer in the electrode double-layer.Dr. E. F. Caldin (University of Leeds) (partly communicated): I agree withProf. Hills and Dr. Jones that curvature of the Arrhenius plot is not by itself con-clusive evidence for tunnelling ; the evidence is strengthened, however, if (as in ourwork) alternative reasons for the curvature can be eliminated. Isotope effectsshould be investigated wherever possible ; this cannot be done, without changingthe solvent, for the reaction to which our experimental results refer, but work isin progress on the reaction (10) in table 3 of our paper.The possibility of a lag in the reorientation of solvent molecules, mentionedby Mr. Bell, should be investigated further ; it would affect both the isotope effectand the Arrhenius plot.It does not, however, provide a complete explanation ofthe phenomena attributed to tunnelling. In a given solvent the effect of such a lagshould presumably increase (and so the apparent barrier-width should decrease)with increase of - AS*, which reflects the change of solvation on forming the transi-tion state; this does not agree with the data on reactions (7) and (8) in our table 3,which have values of - AS* of 16 and 9 cal deg.-1 mole-1, respectively, and apparentbarrier-widths of 1 -66 and 1 -46 A, respectively.Prof. Hills assumed that AUZ is a simpler quantity than AH*, but for chemicalreactions it does not appear to be so, either in terms of thermodynamic expressions(cf.Dr. Kohnstam's contribution to the discussion of Prof. Hills' paper) or in termsof the physical model. When the transition complex is formed, there is a changein the orientation of solvent molecules, and consequently a change in volume, inthe neighbourhood of the transition complex. Under constant-pressure conditions,the structure and volume of the bulk of the solvent is unaltered, so there is an overallchange in the volume of the solution. Under constant-volume conditions, thelocal volume change around the transition complex must be compensated by anequal and opposite volume change in the bulk solvent, effected by a change in theexternal pressure. Thus, the structure of the bulk solvent is altered, as well as thatnear the transition complex, and the two effects may be difficult to disentangle;AU: will not be determined by the reaction alone.The interpretation would prob-ably be simplest if AV* were kept constant, and this is nearly achieved in constant-pressure experiments at 1 atm.In reply to Prof. Conway, the barrier-widths quoted in our paper are certainlylarger than the distance that a proton would move if it were initially hydrogen-bonded, but (as we point out) if the distance is calculated from the van der Waalsradii there is reasonable agreement. Hydrogen bonding would be expected to beweak in most of the systems reported. If we were to assume that a hydrogen-bonded1 Nurnberg, Barker and Bolzan, Report Jul-1 37-CA, 1963, Kernforschungsanlage Julich)GENERAL DISCUSSION 63complex is formed as a first step in the reaction, followed by proton-transfer withinthe hydrogen bond, we should have to take into account the contribution of the heatof formation of the hydrogen bond to the energy of activation.Dr.M. J. Henchman (Leeds University) said: While tbe concern of this meetingis with proton transfer processes in solution, these processes have been extensivelystudied in the gas phase. Dr. Ausloos has shown how radiation chemistry can bemade to reveal much concerning these processes in the gas phase. The otherinstrumental method uses the mass spectrometer 1 : results by Mr. Ogle and myselfusing this technique indicate some of the factors governing proton transfer reactionsin the gas phase.The reaction chamber is a metal box, traversed by an electron beam: the gasunder investigation flows in through a hole and positive ions are formed by electronimpact in the electron beam : a positively-charged repeller plate pushes these ionsout of the chamber and once they reach the exit slit, they are rapidly accelerated,sorted according to their mass-to-charge ratios by a magnetic field and counted.At low gas pressures, the mass spectrum is an aliquot of the ions formed in theelectron beam and these are the conditions for analytical mass spectrometry. Athigher gas pressures, there is a chance that the positive ion will collide with a moleculealong its track in the reaction chamber, in which case the ion recorded in the massspectrum will be the product of the chemical reaction occurring at that collision.Mass spectra are recorded as a function of increasing pressure when the relativeintensities of the reactant ions decrease and those of the product ions increase.In this way, ion-molecule reactions can be identified and their rate constants measured.We have, e.g., characterized two proton transfer reactions( 2 )CH2NHl + CH3NH2+CH3NH: + CH2=NHoccurring in methylamine and we obtain the following rate constants kl = 9.6 x 10111.mole-1 sec-1, and k?. = 3.6 x 1011 1. mole-1 sec-1. These very high rate constantsare characteristic of ionic reactions in the gas phase and are due to both the ion-permanent dipole and ion-induced dipole interactions. A calculated value for therate constant based on this model 2 gives k = 11.4 x 1011 1.mole-1 sec-1, agreeingwell with the experimental value for kl, and emphasizes here that the rate constantis primarily determined by simple electrostatic considerations. k2 is lower thanthe calculated prediction since here the activated complex may break down by analternative way, according to a hydride ion mechanism,CH2NH,f + CH3NH2+CH3NH2 + CH,NHl.What determines the relative contributions of these two breakdown modes remainsan intriguing question since neither reaction possesses an activation energy.Quite detailed information can be obtained about the mechanism of reaction(1) and the effect of translational velocity upon this.From electrostatic con-siderations, the collision consists of a positive ion striking a dipole and one couldsuggest that, at low incident ion velocities, the ion-dipole interaction will alignthe collision complex in the configuration of minimum potential energy, as shownin fig. 1. Chemically this must be of the form shown and the nitrogen hydrogens1 see Lampe, Franklin and FieId, Progr. Reaction Kinetics, ed. Porter (Pergamon Press Ltd.,2 Moran and Hamill, J. Chem. Physics, 1963,39, 1413.London, 1961), 1, 67, for method and tabulation of reactions and rate constants64 GENERAL DISCUSSIONwill be sterically better placed for transfer. One could predict that the probabilityfor transfer of the nitrogen hydrogen would be greater than that of the carbonhydrogen, i.e., that PN(H)/Pc(H)> 1. On the other hand, at high ion velocities,the ion-dipole interaction will be unimportant, the collision complex will have arandom configuration and both types of hydrogen will be transferred with equalprobability, i.e., PN(H)/Pc(H) +l .CONFIGURATION OF COLLISION COMPLEXCH3NHl+ CH3NH2 +CH3NH: + CHzNH2 { CH3NHLOW ION VELOCITIESIon-dipole interaction determines configurationCH3I n H-N-HHIGH ION VELOCITIESElectrostatic forces unimportant c3- random (+--I configurationFIG.FIG.1.-The configuration of the collision complex at low and high incident ion velocities.4v !3un %,x 2 2 a,00 60 120 I80N molecules/d x 10-13with N, the concentration of methylamine in the reaction chamber.2.-The variation of the functions P@)/Pc(H) and PN(H)/Pc@), as defined in the textGENERAL DISCUSSION 65Differentiation between the two kinds of hydrogen can be achieved using deuteriumlabelling and the proton transfer reaction has been studied for CD3NH2 and CH3NDz.The rate constant for overall proton transfer is in both cases similar to kl, the rateconstant for the reaction for CH3NH2, but in both cases the relative probabilityfor transferring the nitrogen hydrogen increases as the gas concentration in thereaction chamber increases (fig.2). At the lowest gas concentrations, there is littlereaction and so little depletion of the primary ion beam as it passes down the trackout of the chamber. The ions are being constantly accelerated by the repeller fieldand reactive events are occurring over a range of velocities.On the other hand,at the highest gas concentrations, most of the ions react before they leave the chamberand so many ions react at low velocities that few remain to react at high velocities.Increasing the gas concentration emphasizes the low-velocity events and thus theresults in fig. 2 provide powerful support for the model outlined in fig. 1. At lowvelocities, the ion-dipole interaction is aligning the collision complex to give theconfiguration of lowest potential energy but as the velocity increases, this alignmentbecomes less important. In the language of chemical kinetics, the reaction, whichpossesses no activation energy, can proceed through two possible transition states.At high temperatures there is no discrimination between these. At low temperatures,even though there is no activation energy to determine the path, the reaction is stillmade to proceed via the transition state of lower potential energy by the electro-static interaction.These results suggest that both the rate constants and the mechanisms of protontransfer processes in the gas phase are powerfully influenced by electrostatic forcesand this emphasizes the difference between these reactions occurring in the gas andthe liquid phase.Dr.R. A. Ross (University College, London) said: Dr. Ausloos discusses Meyerson’ssuggestion that C3H; ions formed in the mass spectrometer have a protonatedcyclopropane structure. Baldwin, Maccoll and Miller 1 also find that their measure-ments of appearance potentials of C3H; ions from propyl halides are consistent witha common ion being formed. Further, the appearance potentials of the C4Hgions formed from n-butyl, sec-butyl, isobutyl and t-butyl halides again suggest thata common species is formed. While the common ion in the propyl case could be thesecondary ion this is rather improbable in the butyl case and they suggest that asimilar species to that proposed by Meyerson for the propyl ion, with the protonreplaced by CH; , is consistent with the measured appearance potentials.Dr. P. Ausloos (National Bureau of Standards) (communicated): In reply toROSS, the results of recent radiolytic studies have demonstrated conclusively thatthe butyl ions formed in the decompositions of the parent ions of n-pentane andneopentane do not have identical structures. The butyl ion produced in the radio-lysis of n-pentane 1 readily takes part in a hydride-ion transfer reaction with n-pentane-& to form CH3CH2CHDCH3, thus demonstrating that the precursor ionacquires the sec-butyl structure prior to or during reaction. On the other hand,the butyl ion produced in the radiolysis of neopentanez does not react with n-pentane-d12 to form either n-butane or isobutane, demonstrating that this butylion has a different structure from that formed in the n-pentane radiolysis. Thefailure of this ion to undergo a hydride transfer reaction with n-pentane indicatesthat it probably has a t-butyl structure, since reaction between a t-butyl ion andn-pentane is endothermic 3 and thus would be expected to compete efficiently with1 Baldwin, Maccoll and Miller, paper to ASTM Mass Spectrometry Conference (Paris, 1964).2 Ausloos and Lias, J. Chem. Physics, 1964,41, 3962.3 Ausloos and Lias, J. Chern. Physics, in press.66 GENERAL DISCUSSIONneutralization. If the butyl ion in the two systems discussed above were initiallyformed with an identical structure such as the one referred to by Mr. Ross, onewould be faced with the unlikely situation that they rearrange upon reaction todifferent structures whose form is dependent on the nature of the precursor molecule.Finally, if the protonated cyclobutane referred to in our paper, or the butyl ion formedin the radiolysis of n-heptane rearranges to a structure such as the one mentionedby Mr. Ross, one would expect that, contrary to the results, the hydride ion transferreaction with deuterated higher hydrocarbon molecules would result in the formationof CH2DCH2CH2CH3 rather than CH3CHDCH2CH3