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)