8 THE KINETICS OF REACTIONS IN SOLUTION By D. M. Goodall (Uniuersity of York) Introduction.-THE papers presented at the Nobcl Symposiuni, 1967, in honour of Professors Norrish, Porter, and Eigen, have now been published;1 this reviewer has no hesitation in placing them first among the 1968 references. Norrish on ‘Kinetic Spectroscopy,’ Porter on ‘Flash photolysis and primary processes in the excited state,’ and Eigen on ‘Kinetics of reaction control and information transfer in enzymes and nucleic acids’ are all eminently readable, and lavishly illustrated. Reviews by H. Eyring, Chance, Dainton, and Witt are included and an excellent picture of the foremost problems facing kineti- cists at the end of 1967, with the ideas and instrumentation being developed to meet them, is presented.This report is divided into sections as follows : 1. General theory 2. Diffusion control in photochemical and pulse-radiolytic studies 3. Solvent and ionic charge effects 4, Proton- and hydrogen atom-transfer reactions 5. Kinetic isotope effects 6 . Electrochemical studies of solution reaction kinetics 7. Fast-reaction techniques applied to biochemical problems The uses of kinetics in deduction of organic and inorganic reaction niech- anisms are reviewed in other articles in this Annual Report. Readers un- familiar with the rapid-reaction techniques which are mentioned frequently are referred to the excellent monograph by Caldin,2 and the Interscience compilation ‘Investigation of rates and mechanisms of reactions.3 This review takes up many of the topics considered in the previous Annual Report by Crooks4 and Challi~,~ and the excellent survey of the 1965-1967 literature on fast reactions in solution by Eyring and Bennion,6 which also has a section on biochemical applications.1. General Theory.-Klopman7 sets out to marry organic and inorganic chemistry in a generalised treatment of chemical reactivity; his semi-quantita- tive theory gives simultaneous theoretical foundation to the hard and soft acid ‘Fast Reactions and Primary Processes in Chemical Kinetics,’ ed. S. Claesson, E. F. CaIdin, ‘Fast Reactions in Solution,’ Oxford University Press, Oxford, 1964. ‘Investigation of Rates and Mechanisms of Reactions, Part 2,’ ed. S. L. Friess, J. E. Crooks, Ann. Report Chem. SOC. ( A ) , 1967, 64, 37. B. C. Challis, Ann.Report Chein. Soc. (B), 1967, 64, 99. E. M. Eyring and B. C. Bennion, Ann. Rev. Pliys. Clietn., 1968, 19, 129. G. Klopman, J . Amer. Chern. Soc., 1968, 90, 223. Interscience, New York, 1967. E. S. Lewis, and A. Weissberger, Interscience, New York, 1963. 149150 D. M. Goodall and base concept, to nucleophilic order, and to other reactivity indices. The interactions between a Lewis acid and Lewis base plus their solvating shells are subdivided into : (1) coulomb, (2) electron transfer and delocalisation, and (3) Born solvation effects. A perturbation treatment of the interaction energies suggests classification of reactions as charge- or frontier-controlled [( l), or (2) and (3) predominate respectively]; and reactivity orders can be computed with a knowledge of fundamental atomic and molecular parameters such as ionisation potential, electron affinity, atomic orbital coefficients, charges, and solvent dielectric constant. Dixon8 gives a simple molecular-orbita, method for predicting the direction of alternative proton-abstraction reactions in x-electron systems, based, via a discussion on non-bonding orbital coeffic- ients, on n.m.r.coupling constants between these protons and the remaining atoms in the molecule. The vast accumulation of data on substituent effects in the rates and equilibria of organic reactions has been rationalised by Swain and Lupton:9 they find from statistical analysis of 43 reaction series that any remote substituent constant can be written as: G = fF+ rR where Fand R are field and resonance constants specific for a given substituent and f and r are empiricial weighting factors independent of substituent but different for each reaction series.All parameters are at present given no theoretical content; it would lend weight to the treatment if a correlation with fundamental molecular parameters such as inter-group bond distances and charges could be made (cf. Dewar and Grisedale, ref. 10). A Huckel molec- ular-orbital study suggests that part of the efficiency of bifunctional catalysis, in systems such as the mutarotation of glucose in the presence of pyridine and phenol, arises from delocalization of the transferring charge over the x- electron systems of the two catalysts.ll An important paper by Schwarz12 builds the theoretical framework of chemical relaxation spectroscopy, and gives a general solution to the relaxa- tion problem.Evaluation of complex spectra with many interacting rate constants is best done in terms of the experimentally accessible mean reciprocal relaxation time, and the dispersion about the mean; these quantities can be related to rate constants of individual steps. Applications to the conforma- tional changes of biopolymers are considered later in this report. In another theoretical treatment of relaxation spectra, Hayman13 enquires whether it is possible to distinguish a charge-transfer reaction between aromatics to give a dimer, AB, from a series of steps which utilise both sides of the molecules to give sandwiches ABA, BABABA etc. When all association and dissociation 8 W.T. Dixon, Tetrahedron, 1968, 24, 5509. C. G. Swain and E. C. Lupton, J . Amer. Chem. SOC., 1968,90,4328. lo M. J. S. Dewar and P. J. Grisedale, J. Amer. Chem. SOC., 1962, 84, 3548. l1 H. J. Gold, J . Amer. Chem. SOC., 1968, 90, 3402. l2 G. Schwarz, Rev. Mod. Phys., 1968,40,206. l3 H. J. G. Heyman, J . Chem. Phys., 1968, 48, 3273.The Kinetics of Reactions in Solution 151 rate constants are degenerate, one relaxation time is predicted for both systems, but distinction is in theory possible if this degeneracy is removed (c.J ref. 12). Chal4 has given a simplified treatment for deriving the rate equations in complex interconnected systems where several blocks of reactants are at equilibrium. Shear15 has presented a mathematical proof that a homogeneous chemical reaction system has one, and only one, equilibrium position.Following partial disproval of the classic oscillating chemical reaction between iodate and peroxide, distinction between homogeneous and heterogeneous systems must be made carefully.16 More studies of self-oscillations in open systems involving enzymes have been made,17 and several authors suggest testing of theories with constant source and sink concentrations. Swinkels and Wojcie- chowski describe in detail a matrix approach to the kinetics of such open systems.l* Two papers elaborate the theoretical background for modulation of laser light scattered from a liquid undergoing both thermal diffusion and chemical reaction.19 From measurements of the widths of the central Rayleigh linesz0 (split according to the number of reactions) as a function of scattering angle, rate constants may in principle be evaluated.This technique has yet to be experimentally tested, but holds much promise. The relative merits for kinetics of n.m.r. lineshape analysis and the newer spin-echo technique have been discussed by ReevqZ1 following careful experiments on the determination of hindered rotation rates in amides. 2. Diffusion Control in Photochemical and Pulse Radiolytic Studies.-Using a statistical treatment, Steinberg and Katchalskiz2 have given a new derivation of the diffusion-control kinetic equations; this includes the Forster equation for non-radiative energy transfer, and also accounts for the case where diffusion alters the distance between donor and acceptor during the energy- transfer process.The theory is successfully testedz3 using the excited naphthal- ene (lifetime sec.)-anthranilic acid system in solvents over a viscosity and diffusion coeficient range of lo3, where the Forster equation is inadequate. Wagner and K ~ c h e v a r ~ ~ also find that a simple inverse viscosity dependence for triplet energy transfer probability does not hold for low-viscosity solvents and slow energy transfer, and like Katchalski recognise that at high quencher l4 S. Cha, J . Bio?. Chem., 1968, 243, 820. l5 D. B. Shear, J . Chem. Phys., 1968,48,4144. D. H. Shaw and H. 0. Pritchard, J . Phys. Chem., 1968,72,1403,2693; H. Degn and l7 H. Degn, Nature, 1968,217, 1047; E. E. Sel’kov, European J . Biochem., 1968,4, 79. 18 G. M. Swinkels and B.W. Wojciechowski, Trans. Faraday SOC., 1968, 64, 43. l9 L. Blum and Z . W. Salsburg, J . Chem. Phys., 1968,48,2292; B. J. Berne and H. L. 20 B. Chu, J . Chem. Educ., 1968,45, 224. 21 P. T. Inglefield, E. Krakower, L. W. Reeves, and R. Stewart, Mol. Phys., 1968,15, 22 I. Z . Steinberg and E. Katchalski, J . Chem. Phys., 1968, 48, 2404. 23 Y. Elkana, J. Feitelson, and E. Katchalski, J . Chem. Phys., 1968, 48, 2399. 24 P. J. Wagner and I. Kochevar, J . Amer. Chem. SOC., 1968,90,2232. J. Higgins, J . Phys. Chem., 1968, 72, 2692. Frisch, J. Chem. Phys., 1967,47,3675; ibid., 1968,49,2864. 65.152 D. M. Goodall concentrations the energy-transfer distance is satisfied without any need for diflusion. Protic solvents seem to give an abnormal increase in fluorescence quenching rates with certain aromatic donors containing phenoxide groups, and Umberger25 propounds solvent assistance by proton transfer during the energy donation process.Intermittent photochemical generation of alkyl radicals using rotating sector methods has been used to find rate constants for the reaction of radical pairs in solution. Burkhart26 varied the sector rotation speed and analysed for products after each run, whereas Weiner and H a m r n ~ n d ~ ~ followed the decay of the radical transients in the millisecond dark intervals by use of e.s.r. Both find rate constants in the range 1-4 x lo9 1. mole-l sec.-l, considerably higher than polymer chain termination rates, and in satisfactory agreement with diffusion control theory, when a correction for the three in four anti-bonding triplet collisions is taken into account.The ‘solvent cage’ effect and the primary recombination of photochemically produced radical pairs must always be taken into account in photochemical diffusion control studies. Analogously, some of the most interesting papers on pulse radiolysis are concerned with the search for spurs, i.e. groupings of reactive intermediates, generated by the 7-ray pulse close enough together for there to be a significant probability that they will react with one another. Freeman’s2* recent theoretical analysis of this kinetic problem, predicting a fast, followed by a slow, phase (combination of oppositely charged ions within the spur, then the homogeneous reaction of these ions) has been substantiated by several studies using non-aqueous solvent^.^^^ 30 The two investigations by Thomas and his co-w~rkers~~ use nanosecond pulses so that the fast phase of the decay is not masked. There are now two more theoretical treatments of recombination rates for a pair of oppositely charged ions generated within a spur: Mo~umder~~ uses random walk of the ions in their mutual coulomb field to compute half-lives of neutralisation from a given distance as a function of viscosity, temperature, and other variables, whilst Williams32 concludes that the Nernst-Einstein equation is adequate for a description of recombina- tion from typical initial separation values of 40-120 A.Klein et aZ.33 looked for spurs after 50 nsec. pulses into aqueous solutions of various pH values and ionic strengths, but found no evidence of non-homogeneous distribution of the hydrated electrons in their time frame; an initial fast decay of the hy- J.Q. Umberger, J . Phys. Chem., 1968, 72, 1350. ZG R. D. Burkhart, J . Amer. Chern. SOC., 1968, 90, 273. 27 S. Weiner and G. S. Hammond, J . Amer. Chem. SOC., 1968, 90, 1659. 28 G. R . Freeman, J . Clietn. Phys., 1968,46,2822. 29 K. N. Jha and G. R. Freeman, J . Chern. Phys., 1968, 48, 5480; J. C. Russell and 30 J. K. Thomas, K. Johnson, T. Klippert, and R. Lowers, J . Chern. Phys., 1968, 48, 31 A. Mozumder, J . Chem. Phys., 1968,48, 1659. 32 F. Williams, J . Chem. Phys., 1968, 48, 4077. 33 N. Klein, C. N. Trumbore, J. E. Fanning, and J. W. Warner, J . Phys. Chem., 1968, G. R . Freeman, ibid., p. 90. 1602; R. Cooper and J. K.Thomas, J . Chem. Phys., 1968,48,5103. 72, 880.The Kinetics of Reactions in Sohition 153 drated electron in air-free alkali was attributed to a reaction with excited water. HamilP4 postulates that the hydration of a pulse-generated electron takes sec. in water, and that differences in reactivity of the free and hydrated electrons could account for anomalies in the radiation chemistry of water, usually attributed to spurs ; for instance, solutes in concentrations greater than 1 0 - 2 ~ will scavenge all free electrons before hydration. Dainton’s review, ‘The chemistry of the electr0n,’~5 gives a concise rate constant summary and discussion of the role of diffusion control in reactions of the hydrated electron. The usual activation energy in these reactions is ca.3.5 kcal. mole-1, the diffusional activation energy of the electron; Cer~ek3~ has recently reported measurements of lower activation energies in its reac- tions with the hydronium and nitrite ions, and prefers to discuss these as electron-migration reactions, with anupper limit of 2.3 kcal. mole-l calculated from the known equivalent conductance of the electron and absolute reaction- rate theory 3. Solvent and Ionic Charge Effects.-Parker and his c o - ~ o r k e r s ~ ~ continue to amass data about solvent effects on solubilities and kinetics in a variety of protic and dipolar aprotic solvents. They have analysed the rates of 78 bi molecular nucleophilic substitution and bimolecular elimination react ions in various solvents, and the free energies of transfer of reactants from these solvents to methanol, and make deductions about transfer free energies and solvation of the transition states.Their short cuts in assessing transfer free energies of individual ions by extra-thermodynamic assumptions (e.g. by allotting equal contributions to the tetraphenylboride and tetraphenylar- sonium ions) are rightly criticised by Rodewald, Mahendran, Bear, and Fuchs;38 these workers measure enthalpies of transfer of alkali halides, and give an alternative explanation for some of the S,2 solvent effects. More superficially unrewarding work on the thermodynamics of transfer between solvents is required for a resolution of these problems. K o s ~ w e r ~ ~ has observed a striking solvent effect in the reaction between the 1 -ethyl-4-methoxycarbonylpyridyl radical and 4-nitrobenzoyl chloride.The rate increases by a factor of 104 in changing solvent from 2-methyltetrahydro- furan to dimethylformamide or acetonitrile, and this indicates a charge- transfer transition state ; other benzoyl chlorides react via an atom-transfer transition state. Solvent effects are discussed in terms of Kosower’s 2 value model,40 assuming equilibrium solvation of the transition state. An interesting study of the competing reactions of disproportionation and 34 W. H. Hamill, J . Ctiem. Phys., 1968, 49, 2446. F. S. Dainton, ref. 1 , p. 185. 36 B. Cercek and M. Ebert, J . Phys. Chetn., 1968, 72, 766; B. Cercek, ibid., p. 2279. 37 R. Alexander, E. C. F. KO, J. Parker, and T. J. Broxton, J . Amer. Chem. SOC., 38 R.F. Rodewald, K . Mahendran, J. L. Bear, and R. Fuchs, J . Amer. Cliem. SOC., 39 E. M. Kosower and M. Mohammad, J . Amer. Chem. SOC., 1968,90,3271. 40 E. M. Kosower, ‘An Introduction to Physical Organic Chemistry,’ Wiley, New 1968, 90, 5049. 1968,90, 6698. York, 1968.154 D. M. Goodall recombination of a pair of ethyl radicals has been madc, both in the gas phase and in various non-polar solvents. kc kd c4H10 +-- 2c2H.!je+ C2M4 + CZH6 The logarithm of the rate ratio is a linear function of the square root of the internal pressure of the solvent, and Stefani41 gives a number of other examples which suggest that Hildebrand’s theory is as successful as dielectric constant correlations for a number of electroneutral reactions. Measurements of activation volumes are uniquely suited to the study of solvation changes during a reaction.Browef12 has considerably extended the range of application of this technique by describing a pressure jump apparatus with optical monitoring of equilibrium shifts : positive or negative pressure jumps may be made in 5 msec. from any pressure in the range 50-1400 atm. H i r ~ t a ~ ~ has used e.s.r. to distinguish different degrees of solvation of ion pairs in ethereal solvents. The extent of splitting of the e.s.r. spectrum of the naphthalenide radical anion by its alkali counter-ion depends on the separation between the two, and, in the presence of naphthalene, electron exchange was shown to proceed only via the loosely bound ion pairs; the rate constants in the pre-equilibrium formation of this from the tight ion pair have been evalu- ated.In liquid ammonia, all proton exchange from the ammonium ion occurs via the free ion rather than ion pairs, and the n.m.r. data can be used to derive ion-pair formation constants as well as exchange rates.44 Gigantic ‘primary salt effects’ have been found in a study of anion-anion reactions in the presence of cationic polyelectrolytes,45 and cation-cation reactions with anionic macro-ions. There is, presumably, a high concentration of counter-ions in the neighbourhood of the polyelectrolyte molecule, and electrostatic repulsion between the like ions are reduced. In fact the rate enhancement arises predominantly from a lowering in the activation enthalpy term, as is also observed in the more complex systems where micelles are used to catalyse reactions of their counter-i0ns.~6* 47 Interestingly, one particular reaction between negative ions is not accelerated by use of a cationic micelle;46 if the reactants bind at the same type of site, competitive binding could occur, and neighbouring sites might be too far apart to promote reaction.4. Proton- and Hydrogen Atom-transfer Reactions.-Marcus4s has extended his successful theory for weak- overlap electron transfers to cover proton- and atom-transfers, and strong- overlap electron transfers. The free energy of 41 A. P. Stefani, J . Amer. Chem. SOC., 1968, 90, 1694. 42 K. R. Brower, J . Amer. Chem. SOC., 1968, 90, 5401. 43 N. Hirota, J . Amer. Chem. SOC., 1968, 90, 3603; N. Hirota, R. Carraway, and 44 D. R. Clutter and T. J. Swift, J .Amer. Chem. SOC., 1968, 90, 601. 45 N. Ise and F. Matsui, J . Amer. Chem. SOC., 1968, 90, 4242. 46 C. A. Bunton, E. J. Fendler, L. Sepulveda, and K-U Yang, J . Amer. Chem. SOC., 1968,90, 5512. *? R. B. Dunlap and E. H. Cordes, J . Amer. Chem. SOC., 1968,90,4395; L. R. Romsted and E. H. Cordes, J. Amer. Chem. SOC., 1968,90,4404. 48 R. A. Marcus, J . P/JYS. Chem., 1968, 72, 891 W. Schook, J . Amer. Chem. SOC., 1968,90, 3611.The Kinetics of Reactions in Solution 155 activation for the reaction of AH and B- may be calculated if the energy difference between reactants and products is known, and the rates of the symmetrical exchanges AH + A-, BH + B- have been measured. Predic- tions are made about the magnitudes of the Br~lnsted exponents and kinetic isotope effects and it will be of interest to obtain magnetic resonance data for symmetrical transfers and test these relations.A provocative paper by Pshenichnov and Sok01ov~~ suggests that a reaction with rate-deter- mining proton transfer be treated as a process of consecutive vibrational excitation steps within a hydrogen-bonded complex of donor acid and acceptor base, of lifetime 10-10 sec. Energy transfer would occur by resonant interaction between the randomly tumbling solvent and the complex, and solvents with a vibration frequency near to the A-H fundamental are predicted to be particularly effective. Ritchie and Kingso present detailed LCAO-MO-SCF calculations on potential energy surfaces for proton abstraction from the series HH, HF, HzO, H3N, H4C by the hydride ion. With the exception of the first reaction, shallow energy minima along the reaction co-ordinate are found, rather than activation energy maxima.In the absence of gas-phase data, Ritchie and King add solvation-energy correction factors and use their, by now approximate, calculations to give a rather unsatisfactory account of some solution results. Current problems in the kinetics of proton-transfer reactions in solution have also been discussed by Khristov.51 Ahrens and ma as^^^ have extended Eigen’s survey53 of proton-transfer rates to include S-H . . . N and S-H . . . S transfers. The general trend of Bramsted-plot curvature is still present, but at large ApK values, rates for S-H . . . S transfer level off below the diffusion control limit, and individual deviations from a smooth plot are present, as in proton transfer from carbon acids.An analogous Brcansted plot over the range ApK = - 10 to + 14 has been constructed for proton transfers between fluorenes and bases in dimethyl- sulphoxide solution54. Ritchie and Uschold obtained their latest data from stop-flow studies using benzoate ions as bases. The diffusion control rates are attained within these ApK limits, but diffusion control cannot be obtained when methanol is considered as solvent; for this solvent, considerable free energy is required for de-solvation of the reactants in the pre-equilibrium which precedes proton transfer. Recent papers from the Grunwald group have also highlighted the differences in proton transfers which occur uia a ‘solvent bridge’ Grotthus-type mechanism, and those which necessitate direct contact between acid and base molecules. The transfer from the imidazolium ion to imidazole is diffusion controlled, and has a large reaction diameter: 49 E.A. Pshenichnov and N. D. Sokolov, Znternat. J. Quantum Chem., 1967, 1 , 855. C. D. Ritchie and H. F. King, J. Amer. Chem. SOC., 1968,90, 825, 833, 838. 51 S. G. Khristov, Zhur.fiz. Khim., 1968, 42, 1553. 5 2 M. L. Ahrens and G. Maass, Angew. Chem. Znternat. Edn., 1968, 7 , 818. 53 M. Eigen, ref. 1, p. 245; Angew. Chem. Internat. Edn., 1964, 3, 1. 54 C. D. Ritchie and R. E. UschoId, J. Amer. Chem. Soc., 1968,90, 3415. E. K. Ralph and E. Grunwald, J . Amer. Chem. SOC., 1968,90, 517.156 D. M. Goodall n.ni.r. studies55 of both substrate and 170-enriched water-line broadenings show that there is a mean of 1-4 water molecules mediating in this reaction. Thus, approximately half the proton exchanges here are quadrimolecular, or of higher order.For direct proton transfers between ammonium ions and a m i n e ~ , ~ ~ exchange is relatively slow but does not conform to the Brarnsted rule when the acceptor base is varied. This leads to the conclusion that dehydration of the solvent-separated encounter complex, rather than proton transfer, is the rate-determining step. Long and GoodalF7 studied the rate of proton transfer between acetic acid and the anions of nitroalkanes in mixtures of light and heavy water; here proton transfer is rate determining, and donor and acceptor are in contact. Other studies of proton transfers to carbon bases confirm the lack of solvent bridging in such 59 Kreevoy’s review59 on ‘Developments in the study of A-SE~ reactions in aqueous solution’ starts with identification of the overall mechanism, and progresses to hypotheses on fine details of the transition state; general acid catalysis and isotope effect determinations are the most powerful aids to such studies.The classic way of demonstrating solvent involvement in solution reactions is to look for a dependence on solvent concentration in the rate equation. Bell and co-workers60 have been able to do this in a study of the reversible hydration of ketones, by using mixtures of water with high mole fractions of dioxan or acetonitrile. Their results are striking, and indicate involvement of 0, 1, 2, or 3 water molecules in the transition state according to the catalyst present and whether hydration or dehydration is being studied.Evidence points to a stepwise mechanism with no diffusion apart of reactants: for instance, one water molecule is involved in hydration catalysed by benzoic acid. I1 ir A powerful argument for a stepwise proton-transfer sequence is that a fully concerted mechanism cannot be written for a monofunctional catalyst such as triethylamine. A simple electrostatic model predicts that a stepwise sequence has lower activation energy than a concerted one, but the concerted scheme still has proponents.49, 61 Close analogies can be drawn between this 56 E. Grunwald and A. Y . Ku, J. Amer. Chem. SOC., 1968,90, 29. 57 D. M. Goodall and F.A. Long, J . Amer. Chem. SOC., 1968,90,238. 58 V. Gold and D. C. A. Waterman, J . Chem. SOC. (B), 1968,839,849. 59 J. M. Williams and M. M. Kreevoy, Ado. Phys. Org. Chem., 1968, 6, 63. 6O R. P. Bell, J. P. Millington, and J. M. Pink, Proc. Roy. SOC., 1968, A , 303, 1. 61 W. J. Albery, Progr. Reaction Kinetics, 1967, 4, 353.The Kiiietics of Reactions it1 Solution 157 reaction and the reversible addition of hydrogen peroxide to aldehydes, studied by Jencks: this system shows the interesting feature of a Brransted exponent, a , equal to unity during acid catalysis.62 Swift63 has analysed lH n.m.r. lineshape data to find rate and activation parameters for proton exchange from the hydration spheres of several cations, and these suggest different push-pull mechanisms for weak (1) and strong (2) acid catalysis: in both cases the solvent functions as a base: H H H H M-0-H .. . A-H . . , 0-H -4 M-0- . . . H-A , . . H-0-H 1 1 I I (1) + H M H H M H H-9-H . . . -0-H . . .O-H- H-0 . . . H-0- . . . H-0-H + + 1 I I I I I (2) At low exchange rates the nature and number of solvent molecules bound in the primary hydration sphere may be found from peak area meas~rements.~~ Loewen~tein~~ generated radicals from alcohols, and studied their proton exchanges with the hydronium ion using e.s.r. line-broadening. The rate constants and substituent effects parallel those found with neutral alcohols. Stop-flow with e.s.r. detection was used to follow the hydrogen atom exchange between 2,4,6-tri-t-butylphenol and its ring-deuteriated phenoxy radical in carbon tetrachloride.66 Reaction proceeds in two steps via a symmetrical intermediate [ROHOR].of lifetime sec., and the asymmetry of the actual transition state is demonstrated by the low kinetic isotope effect. Kastening67 has taken account of both the variation in e.s.r. sensitivity, and non-homogeneity in radical concentrations, within a capillary flow tube mounted in the spectrometer waveguide. The theory is then applied to find the rate constant for dismutation of the nitrobenzene negative ion, under conditions of laminar flow in the capillary. An interesting flask photolytic reaction is reported by Weller;68 at acidities where azulene is present predominantly as its protonated cation, a flash generates azulene via the primary formation of the excited azulinium ion, a very strong acid which deprotonates as it is quenched.The restoration of the Ga E. G. Sander and W. P. Jencks, J. Amer. Chem. SOC., 1968, 90, 4377. 63 T. A. Stephenson, T. J. Swift, and J. B. Spencer, J . Amer. Chem. SOC., 1968, 90, 64 R. G. Wawro and T. J. Swift, J. Amer. Chem. SOC., 1968,90,2792; N. A. Matwiyoff 65 R. Pouko and A. Loewenstein, J . Chem. SOC. (A), 1968, 949. 67 B. Kastening, Ber. Bunsengesellschaft Phys. Chem., 1968, 72, 20; B. Kastening and K. H. Grellman, E. Heilbronner, P. Seiler, and A. Weller, J . Amer. Chem. SOC., 4291. and H. Taube, J . Amer. Chem. SOC., 1968, 90, 2796. M. R. Arick and S. I. Weissman, J . Amer. Chem. SOC., 1968, 90, 1654. S. Vaviizka, ibid., 1968, 72, 27. 1968, 90, 4238.158 D. M.Goodall ground-state equilibrium after termination of the flash occurs with a rate constant known from previous flow studies.69 5. Kinetic Isotope Effects.-By use of a sufficiently wide range of donor acid and acceptor base strengths to ensure variations on either side of the sym- metric transition state, maxima in change of primary kinetic isotope effects in a reaction series are now well d~cumented.~O-~~ Kresge71 shows that a smooth correlation of isotope effect with rate constant is found in proton transfer from the hydronium ion to carbon-carbon double bonded systems only when substituents of the type -OR are considered. More diverse substitution in the olefin obscures any correlation. Studies in water suggest maxima near the point of equal pK values of donor and a~ceptor.~O In tetrahydrofuran, with phenyl-lithium as the base, the maximum occurs with donor acids of pK ca.25.72 Benzene has a pK near 36, and the divergence between these two figures is presumed to be due to the fact that the pre- dominant, ion-paired species is a considerably weaker base than the bare phenyl anion. Kreevoy has reported a primary isotope effect which remains constant through large changes in dimethylsulphoxide-water compositions, and it is assumed that the hydrogen ion proton donor remains the H30f unit.59 Competitive abstraction of hydrogen and deuterium from [c~-~H-] toluene by bromine atoms has been studied both in the gas phase73 and in solution, and it is difficult to explain alterations in the observed isotope effects, particularly when similar abstraction studies using chlorine atoms yield concordant gas phase and solution results.Caldin and Tomalin74 have studied the rates of proton and deuteron transfer between 4-nitrobenzyl cyanide (or its [2Hz]-isomer) and ethoxide ion, by a combination of low temperature and stop-flow techniques. Devia- tions from Arrhenius behaviour at the lowest temperatures are attributed to proton tunnelling, and, using the Bell model of a parabolic one-dimensional barrier, concordant results are obtained by independent analyses of the two systems. They then proceed to use the model to analyse recent data where proton tunnelling is indicated, and calculate barrier widths and heights; symmetric transition states are found to show the maximum difference in H and D barrier heights, as expected. Lewis and Robinson75 obtain tritium isotope effects to compare with deuterium isotope effects in cases where tunnelling is suspected; deviations from the Swain relation are small, and a justification is offered.The anomalous isotope effects in the reaction between 89 B. C. Challis and F. A. Long, J . Amer. Chem. SOC., 1965, 87, 1196. 70 R. P. Bell and 4. M. Goodall, Proc. Roy. SOC., 1966, A, 294,273; J. L. Longridge and F. A. Long, J . Amer. Chem. SOC., 1967,89, 1287; A. F. Cockerill, J. Chem. SOC. (B), 1967,964. 71 A. J. Kresge, D. S. Sagatys, and H. L. Chen, J. Amer. Chem. SOC., 1968,90, 4174. 72 Y. Pocker and J. H. Exner, J . Amer. Chem. SOC., 1968,90,6764. 73 R. B. Timmons, J. de Guzman, and R. E. Varnerin, J . Amer. Chem. SOC., 1968,90, 7* E.F. Caldin, M. Kasparian, and G. Tomalin, Trans. Furaday SOC., 1968,64, 2802; 5996. E. F. Caldin and G . Tomalin, ibid., p. 2814.The Kinetics of Reactions in Solution 159 2,6-lutidine and 2-nitropropane continue to haunt experimentalist^,^^ 76 and Davis and Lehman’s76 activation parameters are so widely divergent from those of Lewis that the tunnelling explanation cannot be assumed proved. Willi77 continues his important experimental and theoretical investigations of secondary hydrogen isotope effects in simple SN2 reactions of methyl iodide and [2H3] methyl iodide. Temperature dependence studies are reported, with cyanide ion as the nucleophile. From an accurate knowledge of ground- state force constants, and isotope effects in similar reactions, the best fit of the data is obtained by a set of transition-state force constants which include unchanged C-H stretching contributions.(It is normally assumed that an sp3 to sp2 change increases the stretching vibration frequency.) In this instance alterations in the bending force constant dominate the isotope effect. In the SN1 solvolysis of t-butyl chloride, the secondary isotope effect is constant in solvent mixtures which promote ionization at the same rate,78 and equal to the isotope effect calculated on the assumption of an equilibrium with t-butyl and chloride ions.79 This gives more evidence for the ion-pair nature of the transition state. In interpreting results of remote secondary isotope-effect studies, there seems to be a consensus of opinion in favour of Shiner’s hyperconjugative explanation.8O Servis, BoreiC, and SunkoS1 also suggest hyperconjugation as the reason for their observation of an excellent linear free-energy correlation between the solvolytic rate enhancement on making the change from RR’XCaH to RR’XCCH3, and the secondary isotope effect on solvolysis after the methyl hydrogens have been replaced by deuteriums.Assuming hyperconjugation as the explanation for the first effect, the extension to the second seems logical. 6. Electrochemical Studies of Solution Reaction Kinetics.-The application of electrochemical methods in reaction-rate studies is introduced by Caldin,2 and reviewed rigorously by Strehlow.g2 A 1968 review of developments in alternating current polarography also has references to work in homo- geneous kinetics.83 Most investigations are carried out at constant voltage, and for the case where reaction in solution modifies the diffusion gradient of the electro-active species, explicit solutions for the value of the average current (in a polarographic measurement) or the decay of current with time (at a fixed electrode) are available. These hold only for a first-order reaction 75 E.S. Lewis and J. K. Robinson, J . Anter. Chem. SOC., 1968, 90, 4337. 76 T. A. Lehman, Diss. Abs., 1967, 28, B, 632. 77 A. V. Willi and Chong Min Won, J . Amer. Chem. SOC., 1968,90, 5999. 78 G. J. Frizone and E. R. Thornton, J . Amer. Chem. SOC., 1968,90, 121 1. 79 J. C. Evans ana G. Y-S. Lo., J . Amer. Chem. SOC., 1966, 88,2118. 80 V. J. Shiner, W. E. Buddenbaum, B.L. Murr, and G. Lamarty, J . Amer. Chem. SOC., 1968, 90, 418; J. G. Jewett and R. P. Dunlap, J. Amer. Chem. SOC., 1968, 90, 809; D. S. Noyce and M. D. Schiavelli, J . Amer. Chem. SOC., 1968,90, 1023. 81 K. L. Servis, S. BorEik, and D. E. Sunko, Tetrahedron, 1968, 24, 1247. 83 H. Strehlow, ref. 3, p. 799. 83 W. H. Reinmuth, Analyt. Chem., 1968, 40, 185R.1 60 D. M. Goodull in solution, and Birk and PeroneS4 find that they may be used in the rather special case where the electro-reducible species are ketyl radicals generated by flash photolysis; instead of the normal constancy of concentration in the bulk solution, this concentration follows a second-order decay, and the rate constant for the radical recombination can be found from chronoampero- metric measurements.The majority of papers are concerned with the ECE inechanism, where a chemical reaction is interposed between two charge-transfer steps. These steps may occur at different electrodes, normally a combined ring-disc arrangement spinning in the solution. Theoretical and experimental con- siderations combine to make this the most tractable arrangement.85 It may be illustrated by Bruckenstein’s study of the kinetics of oxidation of arsenic(n1) by iodine in alkaline iodide solutions.86 The iodine is produced at the disc electrode by oxidation of iodide ion, at a rate controlled by the disc current, then moves by connective diffusion towards the ring, where it is rzduced back to iodide; en route it reacts with arsenic(m), and the ring current is diminished according to the rate of this reaction.As before, the method treats first-order reactions only, and reactions with half-lives in the region of lo-’ sec. com- Pete usefully with diffusion between the electrodes. The example above was a new kinetic and mechanistic study, but studies by AlberyE7 and Bruckenstein8* using well-documented reactions confirm the essential validity of the theory. Karp has recently suggested a slight modification of the Albery treatment.8g ECE Processes can be observed using a single electrode, provided both reactant and product are electro-active. One possible scheme is : *nn,e k i n a c A f B - + - C + D If C is reduced at a considerably less cathodic potential than A, the electrode potential may be stepped from an initial high value, where the reaction is proceeding smoothly from left to right, to a lower value where B is being oxidized whilst C is still being reduced.Blount and Hermango have followed the decay of current with time (and also the change in potential with time at constant current) in the sequence where B is p-hydroxyphenylhydroxylarnine and C its dehydration product. The dehydration is found to be catalysed by general acids and bases, and with this conclusion the catalysis scheme sug- gested could be improved by following the arguments of Bell.91 A more complex system is the two-electron oxidation of o-tolidine to the di-i~nine.~~ 84 J. R. Birk and S. P. Perone, Analyt. Cizem., 1968, 40, 496. 85 W. J. Albery and S. Bruckenstein, Trans. Faraday SOC., 1966,62, 1946, W. J. Albery, 86 D. C.Johnson and S. Bruckenstein, J. Amer. Chem. Soc., 1968,90, 6592. 87 W. J. Albery, M. L. Hitchman, and J. Ulstrup, Trans. Faraday SOC., 1968,64,2831. 88 P. Beran and S. Bruckenstein, J. Phys. Chem., 1968, 72, 3630. 89 S . Karp, J . Phys. Chem., 1968, 72, 1082. 90 H. N. Blount and H. B. Herman, J . Phys. Chern., 1968,72, 3006. 91 R. P. Bell, ‘The Proton in Chemistry,’ Methuen, London, 1959, ch. 9. 92 J. W. Strojek, T. Kuwana, and S. W. Feldberg, J. Amer. Chem. SOC., 1968, 90, 1353; T. Kuwana and S. W. Feldberg, Discuss. Faraday SOC., 1968,45, 134. ibid., 1967, 63, 177 1.The Kitretics of Reactions in Solutiora 161 The reaction sequence here is A f B + e : B + C + e ; A + C + 2B. The electrochemical data were supplemented by spectrophotometric concentra- tion-time studies of the reactive species, made possible by the use of a transparent doped tin oxide glass electrode.Careful analysis of the data suggests that 2B is in fact the ion pair AC, though e.s.r. demonstrates that B is a true one-electron oxidised species in some solvents. A paper by Nelson also deals with the distinction between two-electron and ECE processes.93 To acquaint more chemists with these useful electrochemical techniques, Crooks and Bulmer have introduced an undergraduate experiment on kinetics from polarograp hy . 94 7. Fast-reaction Techniques Applies to Biochemical Systems-Rapid- reaction techniques have already made great advances in our understanding of short-lived intermediates in biochemical pathways, enzyme-substrate binding processes, and conformation changes of Many advances in technique are prompted by biochemical challenges, as will be illustrated below.Eigen’s two lucid reviewsg5 describe advances in instrumentation which have gone hand-in-hand with the chemical and biochemical studies in his Institute. These include a pressure-shock wave method with 10 nsec. dead time, combined stop-flow temperature jump, and a square-wave electric-field jump apparatus with 50 nsec. dead time. This last apparatus is used to study haemoglobin relaxations, where unexplained data still remain despite the introduction of a detailed scheme of conformation changes and substrate bindings. The functional unit of haemoglobin here is a tetramer of two weakly interacting ap-dimers. Antoninig6 has been able to study the rate of dissociation of the dimer into cc- and P-monomers, displacing the equilibrium position by flash photolysis, or rapid addition of carbon monoxide in a stop- flow apparatus. Kirschner and Eigen’s studyg7 of allosteric binding to glyceraldehyde-3-phosphate dehydrogenase is a key example of the applica- tion of stop-flow and temperature-jump methods to investigate fundamental operations in enzyme control processes.The observed relaxation times correspond to the Monod model of stepwise substrate binding and ‘all-or- nothing’ conformation change, and only one of the enzyme’s two conforma- tions has catalytic activity. P0h198 has presented an elegant study of the reversible denaturation of chymotrypsin and trypsin in water and aqueous ethanol. Denaturation follows a linear Arrhenius activation energy plot, but the renaturation rate goes through a maximum with temperature.A large heat capacity of activation is indicated, and promises to yield much new infor- mation about solvation changes in protein unfolding. This work was made 93 R. F. Nelson, J. Electroanalyt. Chem. Interfacial Electrochem., 1968,18, 329. g4 J. E. Crooks and R. S. Bulmer, J . Chem. Educ., 1968,45, 725. 95 Ref. 1, p. 333; M. Eigen, Quart. Rev. Biophys., 1968, 1, 3. g6 E. Antonini, M. Brunori, and S. Anderson, J . Biol. Chem., 1968, 243, 1816. 97 K. Kirschner, in ‘Proceedings of the 4th Meeting of the Federation of European 98 F. M. Pohl, European J . Biochern., 1968, 4, 373; 1968, 7, 146. Biochemical Societies, Oslo, 1967.’162 D.M . Goodall possible by development of a simple temperature-jump apparatus ; cooling or heating is achieved with 3 sec. dead time by switching thermostatting water flows. Temperature jump and stop-flow studies by Hammesg9 compare rates of binding of aspartate (the natural substrate) and a-methylaspartate to aspartate aminotransferase, and subsequent relaxations of the enzyme- substrate complex are analysed. Schimmello0 showed that lysozyme binds di- and tri-N-acetylglucosamine with equal rates. Since X-ray data on the mono- and tri-saccharide showed one sugar residue to be identically bound in each case, and the third residue rather loosely bound,lol identity of rates is understandable. Gutfreundlo2 has studied phosphorylation and dephos- phorylation of the enzyme E.coli. phosphatase. Here different phosphory- lating esters react at the same rate, and rearrangement of the active site is presumed to be rate determining. There is currently much theoretical and experimental activity in the fields of conformational changes of proteins, and association of nucleic acid strands. A key experimental paper by Schwarzlo3 describes how transitions between helices and random coils are accompanied by large decreases of dipole moment, and provide a mechanism for dielectric relaxation. This relaxation occurs at higher frequency than rotational relaxation of the polymer; the latter is effective only below lo5 c./sec. With poly-(y-benzyl-L-glutamate) as the polypeptide in solvent mixtures of ethylene dichloride and dichloroacetic acid, the observed mean relaxation time for conformational change is in excellent agreement with theory;lo4 the individual growth step of forming one helical unit of the chain from a coil has a rate constant, k = 1.3 x 1010 sec.-l, which is consistent with diffusion of a peptide group over several A.Poly- (L-lysine) helix-coil changes in water have been investigated by the ultra- sonic-absorption method, but the results are difficult to interpret.lo5 The stability and fast association-dissociation rates of pairs of the different nucleotides A, U, C , G, and some substituted derivatives have been measured in non-aqueous solvents by ultrasonic absorption,lo6 and by dielectric loss in the presence of a high d.c. field gradient.lo7 Differences in stability of the various pairs are alone far too small to account for the invariable biological A-U and C-G pairings.Rates here are very fast, but when the formation of double helices of oligonucleotides containing 3-10 residues of A and U was studied by Eigen and POrschke,lo7 the relaxation time was found in the milli- 99 G. G . Hammes and J. L. Haslam, BiocRemistry, 1968, 7, 1519. loo D. M. Chipman and P. R. Schimmel, J . Biol. Chem., 1968, 243, 3771. lol C. C. F. Blake, G. A. Mair, A. C. T. North, D. C. Phillips, and V. R. Sarma, lo2 Ref. 1 , p. 429. lo3 G. Schwarz and J. Seelig, Biopolymers, 1968, 6, 1263. lo4 G. Schwarz, Biopolymers, 1968, 6, 873; see also ref. 12. lo5 R. C. Parker, L. J. Stulky, and K. R. Applegate, J . Phys. Chem., 1968, 72, 3177. loci G. G. Hammes and A. C. Park, J .Amer. Chem. SOC., 1968, 90, 41 5 1 , lo7 Ref. 1, p. 358. Proc. Roy. SOC., 1967, B, 167, 365.The Kinetics of Reactions in Solution 163 second range. Only one relaxation was found, and from the magnitude of its activation energy the following mechanism was suggested : I I I I I \ I I 1 I I \ I I 1 I \ G i 3 fi I \ I I I \ I I I \ I 1 I I i b 8 I I I I I I I I I 1 I I 1 1 1 1 .i There is a pre-equilibrium, with formation of the third base-pair in a sequence rate-determining for complete helix formation. The renaturation of DNA has been followed using fast electrolytic heating to rapidly perturb the equilibrium position.108 Chance, De Vault, Legallais, Mela, and Yonetanilog provide a comprehen- sive survey of the kinetics of electron transfer in biological systems. Their researches are centred on the role of the cytochromes, essential electron- transfer catalysts in the respiratory chain. Flow studies were carried out with mitochondria as well as with the isolated electron-transport mediators. A pulsed flow apparatus has been developed, with the continuous flow phase (dead time 100 psec.) succeeded by stop-flow observation. Berger has described an optimally designed flow apparatus,l1° and his suggestions for mixer design were incorporated into the Chance system. Chancel09 also demon- strated that laser-activated electron transfer from chlorophyll to cytochrome-c takes less than 2 psec., and Witt has detailed reviews of the use of single and periodic light pulses of lifetime 10-1-10-8 sec. in studies on the photo- synthesis pathway.lll Flash photolytic studies of the role of flavins as photo- oxidizers have been reported by Green and Tollin.l12 The nanosecond flash photolysis apparatus described by Porterll3 and Novak and Windsor114 are of potential interest for biochemists. Postscript--The Landolt ‘iodine clock’ experiment, a classic kinetics demonstration experiment dating from the 1890s,ll5 is now available with lasers and fast recording gear.l16 To the fast-reaction kineticist, nothing is sacred ! lo* J. G. Wetmur and N. Davidson, J . Idol. Biol., 1968, 31, 349. log Ref. 1, p. 437. R. L. Berger, B. Balko, and H. F. Chapman, Rev. Sci. Instr., 1968, 39, 493; R. L. Berger, B. Balko, W. Borcherdt, and W. Friauf, ibid., p. 486. ll1 Ref. 1, pp. 81 and 261. 112 M. Green and G. Tollin, Photochem. and Photobiol., 1968, 7 , 129, 145, 155. 113 Ref. 1, p. 159. 114 J. R. Novak and M. W. Windsor, Proc. Roy. SOC., 1968, A , 308,95. 115 H. Landolt, Chem. Ber., 1885, 18, 249; G. W. A. Fowles, ‘Lecture Experiments in Chemistry,’ Bell, London, 1963, p. 602. J. A. Church and S. A. Dreskin, J. Phys. Chern., 1968, 72, 1387.