4. THE KINETICS OF REACTIONS IN SOLUTION By J. E. Crooks (University of Kent at Canterbury) A LARGE proportion of the 4500 papers listed in the ‘Kinetics and Mechanism’ section of Current Chemical Papers for 1967 concern reactions in solution, so that this review must be highly selective. The papers chosen make some point relevant to solution kinetics as a whole as distinct from those in which the concentration-dependence of a reaction rate is used as part of the evidence for a particular reaction mechanism. Papers of such general significance include those concerned with mathematical and theoretical aspects and those concerned with the effect of the solvent on the rate of reaction. Kinetic isotope effects are frequently measured but their significance is still debatable.The study of fast reactions is still sufficiently novel to warrant a more detailed account of methods and results than that for reactions followed by con-ventional techniques. The award of a Nobel prize to Professor Norrish, Professor Porter and Dr. Eigen reflects the rapidly growing interest in this field. Mathematical Aspects.-TTlt~~.orc.tic.ul. There have been several developments in the theory of rates of diffusion-controlled reactions. Bass -and Greenhalg show that the Smoluchowski treatment in which the reaction rate is calcu-lated by assuming that particles of one species are stationary whilst particles of the other species diffuse towards them can lead to a self-contradiction. If the concentrations of the species are not equal the reaction rate depends on which of the species is replaced by stationary sinks.Watts2 gives an alternative treatment for the rate of a diffusion-controlled reaction between ions which predicts slightly faster rates than those calculated from the Debye modification of the Smoluchowski equation. Watts3 extends his treatment to describe slower reactions between ions and to include the contribution due to dissoci-ation of the products of the reaction which gives a lower value of the rate constant. The result agrees with that given by Eigen et ~ 1 . ~ to within the limits of the approximations used. In the derivation of the Smoluchowski equation it is assumed that the concentrations of the diffusing species are zero at a distance from the stationary sinks equal to the sum of the radii of the particles of the two species.Noyes’ takes this concentration as finite and related to the rate at which reaction would occur if diffusion were infinitely fast. Logan6 uses this boundary condition of Noyes to calculate the effect of temperature ’ L. Bass and W. J. Greenhalg Trans. Faraday Soc. 1966,62,715. A. M. Watts Truns. Faraday SOC. 1966,62,2219. ’ A. M. Watts Trans. Faraday SOC. 1966,62,3189. ‘ M. Eigen W. Kruse G. Maass and L. de Maeyer Progr. Reaction Kinetics 1964,2 285. ’ R. M. Noyes Progr. Reaction Kinetics 1961,1 129. S. R. Logan Trans. Faraday SOC. 1967,63,1712 38 J . E. Crooks on the rate of a diffusion-controlled reaction and shows that the observed Arrhenius activation energy is similar to the activation energy of self-diffusion in the solvent i.e.about 3.5 kcal. mole-1 in water. This value has been verified experimentally for ionic reactions by the temperature-jump method and for free-radical reactions by pulse radiolysis. Logan' also calculates the dependence of diffusion-controlled rates on ionic strength using Noyes' boundary con-dition and finds the dependence is less than that predicted by the Brernsted-Bjerrum equation although the discrepancy is small at low ionic strength. The calculated rate is less than that predicted by the simple Debye-Smoluch-owski equation and Logan points out that this makes doubtful the assertion that certain reactions of the hydrated electron are too slow to be diffusion-controlled. Friedman' discusses another weakness in the Smoluchowski equation namely that the molecular nature of the solvent is ignored.There is a hydrodynamic effect due to interactions between solvent and solute molecules similar to that responsible for the electrophoretic effect on the conductance of electrolyte solutions. Smoluchowski himself considered colloidal particles as the solute and so was quite justified in ignoring this effect. The effect is shown to make a reduction of about 15 % in the computed rate constants for ions or neutral species in water which is not really significant in view of the other possible errors. However despite all these criticisms experimentalists still find the Smoluchowski equation adequate as will be shown. Calculation ofrate constants. A method for the elucidation of the kinetics of complex systems is described by Cover.' An 'applied stress' i.e.the volu-metric or electrolytic addition of reagent is imposed on a reacting system at a predetermined rate. If the stress is programmed correctly the behaviour of the system is simplified and rate constants can be calculated. Some prior knowledge of the system is required so that the most useful stress function can be applied. A simple examplelo would be the use of a pH-stat to follow the kinetics of a reaction in which OH- is consumed. The rate at which alkali has to be added to keep the pH constant gives the rate of the reaction. Computers both digital and analogue are being used for the elucidation of complex kinetic schemes. D. F. DeTar and C. E. DeTar" give a general discussion of the design of computer calculations for the kinetics of systems including those with steady-state concentrations of labile species and those involving equilibria.As an example they consider an enzyme reaction the glycolytic pathway in cell metabolism for which Garfinkel and Hess12 pro-duced a model mechanism consisting of 89 equations 24 normal reactants and 13 different enzyme systems containing a total of 41 enzyme intermediates. D. F. DeTar and C. E. DeTar offer to supply a copy of the Fortran I1 pro-gramme and an instruction manual to those interested. However they point ' S. R. Logan Trans. Faraday SOC. 1967,63,3416. * H. L. Friedman J . Phys. Chem. 1966,70,3931. R. E Cover J . Phys. Chem. 1967,71,1990. l o R. P. Bell and B. Coller Trans. Furaday SOC. 1965,61 1445. l 1 D. F. DeTar and C. E. DeTar J .Phys. Chem. 1966,70,3842. '* D. Garfinkel and B. Hess J . Biol. Chem. 1964,239,971 The Kinetics of Reactions in Solution 39 out that no computer programme can be a substitute for chemical knowledge and research judgement. D. F. DeTar13 uses the same programme REMECH, to calculate theoretical yields of various products from the thermal decom-position of benzoyl peroxide for various values of the rate constants in 300 possible elementary reaction steps. Comparison with experimental values shows that only 101 of these steps are significant and the rate constants for these are found. MahoneyI4 investigates the complex kinetics of the oxygen absorption of 9,lO dihydro-anthracene and 2,2’,3,3’-tetraphenylbutane cata-lysed by peroxy- and phenoxy- radicals. The rates of the eleven consecutive and competitive reactions involved are found by fitting the observed rates of oxygen uptake to calculated values using a digital computer.Markisz and Gettlerl5 use a similar method to study the addition of a-hydrogen donor compounds to methyl vinyl ketone a concurrent first- and second-order reaction. Analogue computers can also be used as in Walles and Platt’s16 study of the thermal decomposition of an oxazolidone. Oscillatory reactions. Lindblad and Degn17 use a digital computer to investigate oscillatory reaction systems i.e. those in which a reagent concen-tration increases and decreases in a periodic manner rather than decreasing monotonically. The basic theory was first considered by LotkaI8 for ecological systems to account for periodic variations in the numbers of animals in the wild.A most interesting review of the whole problem is given by Higgins,” whose examples are mainly taken from biochemistry. His article is illustrated with concentration-time plots taken from an analogue computer. There is an intriguing analogy with the oscillations which can be set up in an electronic amplifier in which feedback is excessive autocatalysis being the chemical feedback. Higgins speculates ‘Virtually all the dynamical characteristics associated with modern electronics can be generated through chemical reactions . . . such dynamics may play a role in biological functions including transmission of information and control’. The Role of the &lvent.-Albery2* gives an interesting review of the part played by solvent water in aqueous proton-transfer reactions.The fundamental question is whether the proton is transferred directly from acid to base or by a Grotthus-type mechanism via an H,O bridge i.e. whether the transition-state is like (A) or (B). H \ 0 -___ H ____ S O--H--o--H--S H‘\ / / I D. F. DeTar J . Amer. Chem. SOC. 1967,8!4,4058. l4 L. R. Mahoney J . Amer. Chem. SOC. 1967,89,1895. J. A. Markisz and J. D. Gettler J . Phys. Chem. 1967,71 3053. l6 W. E. Walles and A. E. Platt Ind. Eng. Chem. 1967,59 No. 6,41. P. Lindblad and H. Degn Actu Chern. Scund. 1967,21 791. A. Lotka 2. Phys. Chem. (Leipzig) 1910,72 508. l9 J. Higgins Ind. Eng. Chern. 1967,59 No. 5,19. *’ W. J. Albery Progr. Reaction Kinetics 1%7,4,353 40 J. E. Crooks Albery correlates a large amount of information from relaxation and electrochemical methods n.m.r.Raman line broadening and isotope effects in isotopically-mixed aqueous solutions. His findings are illustrated with detailed potential-energy surfaces showing the difference between stepwise and concerted proton transfer to oxygen and to carbon. The general conclusion is that for diffusion-controlled proton transfers to oxygen and nitrogen the rate-determining step is the formation of a hydrogen-bonded complex between an H,OZ species and the anion followed by fast translations of protons in a Grotthus manner to protonate the anion. However for proton transfer to carbon the reaction occurs via the H30+ species as predicted from con-sideration of the potential-energy surfaces and suggested experimentally by the mixed-solvent isotope effects.Huyser” reviews solvent effects on free-radical reactions explicitly omitting reactions where the solvent is a reactant. Most work has been done on reactions in which the solvent affects the behaviour rather than the formation of a free-radical intermediate. By changing the solvent the reactive intermediate can be made to give different products e.g. the photochemical chlorination of hydrocarbons can be made to occur mainly at tertiary C-H by the use of carbon disulphide as solvent. Variation of rate with solvent properties. It has long been known that the rate of a reaction in solution often depends on the solvent and that large differences may be observed not only between aqueous and non-aqueous solvents but even between different non-aqueous solvents.Predictions of the variation of rate with solvent can be made from thermodynamic data con-cerning the solvent as discussed in a review by EckertZ2 Kondo and Tokuraz3 calculate rates of reaction in mixed solvents from rates in the pure solvents, which are components of the mixtures. Several workers have correlated rates of reaction with some bulk parameter of the solvent such as the dielectric constant or some other measurement of solvent polarity. Del Castillo et ~ 1 . ~ find a linear relationship between the logarithm of the rate of trypsin-catalysed esterolysis and the reciprocal of the dielectric constant of the solvent. Campbell and Hoggz5 use the ET scale of solvent polarityz6 to correlate rates of the reaction of 2,4-dinitrobenzene sulphenyl bromide with cyclohexene in carbon tetrachloride benzene chloroform and acetic acid and find a good straight-line plot of log k against ET over a range of four orders of magnitude in k.Jones and T h ~ r n t o n ~ ~ find the rates of solvolysis of methyl chloromethyl ether in a large number of binary mixed solvents to obey the Winstein equation :28 log k = mY + log k, 21 E. S. Huyser Ado. Free-Radical Chem. 1965,1,77. 22 C. A. Eckert Ind. Eng. Chem. 1967,59 No. 9,20. 23 Y. Kondo and N. Tokura Bull. Chem. SOC. Japan 1967,40,1433. 24 L. M. Del Castillo Y. Bustamente and M. Castaneda-Agullo Biochim. Biophys. Acta. 1966, ” D. S. Campbell and D. R. Hog& J . Chem. Soc. (B) 1967,899. 26 K. Dimroth C. Reichardt T. Siepmann and F.Bohlmann Annalen 1963,661,l. ’’ T. C. Jones and E. R. Thornton J . Amer. Chem. SOC. 1967,89,4863. E. Grunwald and S. Winstein J . Amer. Chem. SOC. 1948,70,846. 128,578 The Kinetics of Reactions in Solution 41 where k is the rate of solvolysis of X in some solvent ko is the rate of solvolysis of X in 80 20 v/v ethanol-water and Y is a measure of the ionising power of the solvent obtained by defining rn as unity for the solvolysis of t-butyl chloride in that solvent. Despite the above it seems likely that good correlations between rates and solvent polarity are rare. There is little or no correlation for the reaction of n-butyl nitrite with a~etamide,~’ the solvolysis of hex-5-enyl p-nitrobenzene-s ~ l p h o n a t e ~ ~ ester and acetal hydrolysis the reaction of isopropylamine with 2-acetylbromo na~hthalene,~ the Curtius reaction of 2-naphthoyl a ~ i d e ~ and the solvolysis of o-halogeno-substituted 2-alkyl t ~ s y l a t e s .~ ~ Cox and McTigue3’ state that it now seems certain that for reactions with no net change in charge the dielectric constant of the solvent has little connection with the rate. It is the solvent-solute interactions often quite specific which are all-important. Soloation. A more fruitful approach to the problem of the variation of reaction rates with solvent is to consider solvation of both reactants and transition states. Parker35 gives a comprehensive review of the kinetic conse-quences of the difference in solvating ability between protic solvents which interact by hydrogen bonding and dipolar aprotic solvents such as dimethyl-sulphoxide.Solvent activity coefficients show that the dipolar aprotic solvation energy for polar molecules can be up to fifty times more than that of protic solvents as long as the solute is not a strong hydrogen-bond donor or acceptor. Protic and dipolar aprotic solvents differ in their ability to solvate anions. Protic solvents have a general hydrogen-bonding interaction with small anions whereas dipolar aprotic solvents which are highly polarisable have a mutual polarisability with large polarisable anions. In terms of what Parker calls ‘the colourful Hard and Soft Acids and Bases principle’ ‘hard’ anions, have strong interactions with protic solvents which are ‘hard’ whereas ‘soft’ anions have strong interactions with dipolar aprotic solvents which are ‘soft’.Parker discusses a large number of S,2 reactions of the type: Y- + R3CX -+ YCR + X -which are much faster in dipolar aprotic solvents than in protic solvents. It is still a matter for debate whether the origin of these large solvent effects lies in differences in the solvation of the reactants or the transition states. Ritchie and Uschold find that proton transfer from 9-methyl f l ~ o r e n e ~ ~ and triphenyl methane37 is much faster in dimethylsulphoxide than in protic 29 Z . Kricsfalussy A. Bruylants and A. Dalcq Bull. SOC. chim. befges 1967,76 168. ’O W. S. Trahanovsky and M. P. Doyle J . Amer. Chem. SOC. 1967,89,4867. ” B. G. Cox and P. T. McTigue Austral. J . Chem. 1967,20 1815. 32 P. J. Taylor J . Chem.SOC. (B) 1967,904. 33 D. C. Berndt J . Org. Chem. 1967,32,482. 34 P. E. Peterson R. J. Bopp D. M. Cheuli E. L. Curran D. E. Dillard and R. J. Kamat J . 35 A. J. Parker Adv. Phys. Org. Chem. 1967,5 173. 36 C. D. Ritchie and R. E. Uschold J . Amer. Chem. SOC. 1967,89 1730. ’’ C. D. Ritchie and R. E. Uschold J. Amer. Chem. SOC ’1967.89,2960. Amer. Chem. SOC. 1967,89 5902 42 J. E. Crooks solvents and consider that proton transfer is slow in protic solvents on account of the need for solvent reorganisation around the transition state. Ritchie et aL3* also attribute to solvation the great acceleration in dimethylsulphoxide solution of the rates of combination of various anions with the stable carbonium ion of 4,4'-bis(dimethylamino)triphenylmethyltetrafluoroborate.On the other hand Cockerill and Sa~nders,~' who find the reaction between 2-phenyl-ethyldimethylsulphonium bromide and OH- to be a thousand times faster in 9.8 M. aqueous dimethylsulphoxide than in water attribute this solely to the greater nucleophilicity of OH - in dimethylsulphoxide. Solvation due to hydrogen-bonding has also received some study. Miotti4' interprets rates of S,2 reactions of benzyl halides in mixed protic solvents in terms of hydrogen-bonding in the transition state. Illuminati et aL4' find that rates of piperidino-dechlorination of meta-substituted chloroquinolines in methanol do not vary much with the nature of the meta-substituent since the substituent affects the strength of hydrogen-bonding in such a way that the change in solvation compensates for the change in reactivity.The course of many organic reactions may be directed by solvation. The stereochemistry of the photo-dimerisation of a~enaphthylene~~ and of cou-marin43 is influenced by the nature of the solvation of the transition state. Wagner44 finds that solvation of the biradical intermediate in the photolysis of ketones favours bond cleavage rather than radiationless decay. Huyser and Kim4' show that solvation of the trichloromethanesulphinyl radical determines whether it adds to cyclohexene or abstracts hydrogen radical solvation favouring addition. Shapiro Duncan and C10pton~~ find that the base-catalysed decomposition of camphor toluene-p-sulphonylhydrazone can give either camphene or tricyclene polar aprotic solvents favouring camphene formation.It is still by no means clear whether reactant or transition-state solvation is more generally important. It might be objected that transition-state solvation is unlikely to be significant since there is not enough time for solvent molecules to orient themselves around a transition state as suggested by Bell.47 Con-clusive evidence on this point is difficult to find but Kresge et ~ 2 1 . ~ ' find that values of ASs for proton transfer to 1,3,5-trimethoxybenzene in aqueous solution suggest that transition-state solvation is possible even for such a rapid process as a proton jump. 3e C. D. Ritchie G. A. Skinner and V. G. Badding J . Amer. Chem. SOC. 1967,89,2063. 39 A. F. Cockerill and W. H. Saunders jun. J . Amer. Chem. SOC. 1967,89,4985. 40 U.Miotti Gazzetta 1967,97,254. 41 G. Genel G. Illuminati and G. Marino J . Amer. Chem. SOC. 1967,89,3516. 42 D. 0. Cowan and R. L. Drisko Tetrahedron Letters 1967,1225. 43 H. Morrison H. Curtis and T. McDowell J . Amer. Chem. SOC. 1966,88,5415. 4* P. J. Wagner Tetrahedron Letters 1967,1753. *' E. S. Huyser and L. Kim J . Org. Chem. 1967,32,618. 46 R. H. Shapiro H. J. Duncan and J. C. Clopton J . Amer. Chem. SOC. 1967,89 1442. *' R. P. Bell Discuss. Faraday SOC. 1965,39,16. 48 A. J. Kresge Y. Chiang and Y. Sato J . Amer. Chem. SOC. 1967,89,4418 The Kinetics of Reactions in Solution 43 Information on solvation from AH* AS* and AC;. Kohnstam4’ reviews the methods of obtaining AC and the interpretations of the values obtained for SN2 solvolyses in mixed organic and aqueous solvents.He gives a thorough account of the difficulties in measuring AC; from the variation of AH* with. temperature as Arrhenius plots generally appear to be linear. Accurate experimental work and careful statistical analysis are needed but it is possible to measure A c t to an accuracy of a few per cent. In conjunction with AS* values information is obtained about the extent of build-up of the reactant solvation shell on formation of the transition state. Solvent transition-state interactions increase the heat capacity of the system so that the increase of solvation consequent on formation of the transition state causes AC to be negative. Robertsonso also gives an account of the precautions necessary to obtain reliable AC values and interprets the results found for SN2 hydrolyses in aqueous solution.He considers that the cause of the variation of AH* with temperature is the temperature-dependence of the free energy of the reactant solvation shell rather than the change in heat capacity of the solvent around the reacting species. This is suggested by the observation that the enthalpy of solution of methane in water changes with temperature at the rate of -52 cal. mole- deg. - ’ at 50° the solvation shell of water around methane becoming less stable with rising temperature. This value is in striking agreement with the typical value of - 50 cal. mole- ’ deg. - found for the AC of SN2 hydrolysis. In conformation of this theory Martin and Robertsons1 find a large variation in AC; for the solvolysis of t-butyl chloride in ethanol-water mixtures in the composition range where there is a rapid change in structural stability with composition.Fagley et a1.” find that AH* and AS* for the solvolysis of fluorobenzyl chlorides in isopropanol-benzene solutions can be entirely accounted for in terms of the thermodynamic properties of the isopropanol component in the mixture. AH* bears no relationship to the heats of solution of the substrates in contrast to the observation of Arnett et aLS3 who find endothermic maxima in the heats of solution of t-butyl chloride in the com-position range where AH’ for solvolysis is at a minimum. Fagley et al. account for the difference in behaviour by saying that solvation of the fluorobenzyl chlorides is not at the reactive centre of the molecule.Parker et al. 5 4 investigate AH’ and AS* for the reversible sN2 decomposition of trimethylsulphonium bromide to methyl bromide and dimethyl sulphide, in dimethylacetamide and in 88 % w/w methanol-water a protic solvent of the same dielectric constant. Both the forward and back reactions are observed, and Parker et al. show that solvent and ionic strength have much more effect 49 G. Kohnstam Ado. Phys. Org. Chem. 1967,5 121. R. E. Robertson Progr. Phys. Org. Chem. 1967,4,213. J. G. Martin and R. E. Robertson J . Amer. Chem. SOC. 1966,88,5353. 52 T. F. Fagley G. A. Von Bodungen J. J. Rathmell and J. D. Hutchinson J . Phys. Chem. 1967, ’’ E . M. Arnett W. G. Bertrude J. J. Burke and P. M. Duggleby J . Amer. Chem. SOC. 1965, 54 Y. C. Mac W. A. Millen A. J. Parker and D.W. Watts J . Chem. SOC. (B) 1967,525. 71 1374. 87,1541 44 J . E. Crooks on the anion-cation reaction than on the reverse dipole-dipole reaction, although both pass through the same transition state. Their conclusion is that it is differences in solvation of the reactants rather than of the transition state, which are important. A similar conclusion is reached by Hiller and Kreuger” who interpret AHS and ASS for the oxidation of formate ion by iodine in aqueous dimethylsulphoxide in terms of weaker solvation of formate by dimethylsulphoxide than by water. Information on solvation and solvent efectsfrorn AVS. Le Nobles6 gives an interesting account of the kinetics of reactions in solution under pressure. He comments that chemists avoid this field because they believe ‘the apparatus is cumbersome expensive and dangerous and the work requires a taste for engineering’.This he says is a misconception the apparatus being as cheap and convenient as a spectrophotometer and. considerably more reliable. The variation of rate with pressure gives the volume of activation AV* which is related to the changing density of the surrounding solvent as the reagents approach the transition state. Pressure is thus a probe uniquely suited to the study of solvation changes during a reaction. Le Noble discusses the experi-mental methods used and tabulates 456 reactions for which A V has been measured. Reactions of different types have different ranges of AVS values; e.g. free-radical formation reactions have AVS ca. + 10 ~m.~/rnole-’ whereas ionisation reactions have AV* ca.- 20 C M . ~ mole-’. It seems that AVS values are not necessarily unambiguous. Golinkin Lee, and HyneS7 find that -AV* for the solvolysis of benzyl chloride in ethanol-water mixtures has a maximum value at a certain solvent composition, paralleling the changes in AHS and AC; already discussed. They show that the changes in AVS are due almost entirely to changes in the partial-molar volume of the benzyl chloride i.e. to changes in the reactant solvation rather than the transition-state solvation. Baliga and Whalle~,’~ in their study of the pressure-dependence of benzyl chloride solvolysis in ethanol-water mixtures find no such maxima or minima in AV* but only a smooth increase in -AT/$ with increasing proportion of ethanol.They also have an explanation for their results stating that maxima and minima in the solvating power of ethanol-water mixtures are to be expected only for measurements at constant pressure, and not for measurements at constant volume. Ewald and Ottley’’ find -AVS for the cyclisation of 4-chlorobutanol to form tetrahydrofuran to be markedly less than - AVS for analogous non-cyclic reactions and attribute this to exclusion of solvent from the centre of the cyclic transition state. Adamson and Stranks6’ find a large -AV* for the thallous-thallic electron-exchange reaction which shows that the transition state must 5 5 F. W. Hiller and J. H. Kreuger Inorg. Chem. 1967,6 528. 56 W. J. Le Noble Frog. Phys. Org. Chem. 1967,5 207. 5 7 H. S. Golinkin I. Lee and J.B. Hyne J . Amer. Chem. SOC. 1967,89 1307. ’* B. T. Baliga and E. Whalley J . Phys. Chem. 1967,71 1166. 59 A. H. Ewald and D. J. Ottley Austral. J . Chem. 1967,20 1335. 6o M. G. Adamson and D. R. Stranks Chern. Comrn. 1967,648 The Kinetics of Reactions in Solution 45 involve a water molecule between the ions. AV* values for transition states involving the expulsion of an aquo-ligand are large and positive. Homolytic scission reactions are characterised by relatively large positive AV* values which are in general presumed to reflect the volume difference between reactant and transition state. However Neuman and B:har6' suggest these large pressure effects are really due to an increase in the rate of the back reaction which occurs before the radicals can escape from the solvent cage.As proof of this hypothesis Neuman and Behar show that AV* is nearly zero for the decomposition of t-butylphenyl peracetate which is not subject to recombination in the cage as the products are stable molecules. Walling and Waits62 also point out that the cage effect determines the efficiency of radical production in homolysis. The rate of decomposition of di-t-butyl peroxide is reduced in solvents of high viscosity which form stronger cages and the reduction in rate at high pressures can be entirely attributed to the increase in solvent viscosity. Lieber Rehm and Wellier63 look for an increase in fluo-rescence with increasing pressure as the increasing viscosity of the solvent slows down the quenching reaction but find the reverse for P-naphthol.They suggest the reason for the observed increase in the rate of diffusion-controlled reactions with increasing pressure is that the faster collision rate means a greater number of collisions between correctly oriented molecules. However the effect of pressure on fluorescence spectra is complex as shown by Braun and F O r ~ t e r ~ ~ who interpret a similar phenomenon for naphthalene in terms of the change in the association equilibrium between the electronically-excited state and the dimeric excimer. Isotope Effects.Cimon and Palm65 review the origins and significance of primary and secondary hydrogen isotope effects in solution with especial reference to enzyme kinetics. Stern and Wolfsberg66 find by detailed calcula-tions that it is legitimate to consider only the parts of the molecule near to the site of isotopic substitution when calculating hydrogen isotope effects.They predict that large changes in parts of the molecule far removed from the position of isotopic substitution will have little effect on the calculated magnitude. This conclusion must be interpreted with care as both theoretical and experi-mental work show that the symmetry of the transition state is of great signifi-cance in determining the magnitude of a primary hydrogen isotope effect. This symmetry may in some circumstances be influenced by substitution in a 'distant' part of the molecule e.g. at the para-position in a benzene ring. More O'Ferrall and Kouba6' carry out model calculations of primary isotope effects for four- and five-centre transition states taking account of bending vibrations and proton tunnelling.Their calculations agree with the usual 61 R. C. Neuman jun. and J. V. Behar J . Amer. Chem. SOC. 1967,89,4549. 62 C. Walling and H. P. Waits J . Phys. Chem. 1967,71 2361. 63 C. 0. Leiber D. Rehm and A. Wellier Ber. Bunsengesellschufr Phys. Chem. 1966,70 1086. 64 H. Braun and Th. F h t e r Ber. Bumengese!lschujt Phys. Chem. 1966,70 1091. 6 5 H. Simon and D. Palm Angew. Chem. Internat. Edn. 1966,5,920. 66 M. J. Stern and M. Wolfsberg J . Chem. Phys. 1966,45,4105. '' R. A. More O'Ferrall and J. Kouba J . Chem. SOC. (B) 1967,985 46 J . E. Crooks simple calculations which take account only of stretching vibrations and confirm that a maximum effect is to be expected from a symmetrical transition state.They also find that the Swain6* relationship relating deuterium and tritium isotope effects i.e. (kH/kD)1.442 = kH/kT is valid. Experimental evidence in favour of this relationship is found by Kresge et aL6’ for the acid-catalysed aromatic hydrogen exchange in 1,3,5trimethoxybenzene. Albery7’ gives a full discussion of the reasons why a more symmetrical transition state should cause a larger isotope effect for proton transfer. The results of his calculations are summarised diagrammatically. An interesting agreement between theoretical and experimental isotope effects is found by Ohno71 for the reaction of the solvated electron with the hydroxonium ion. Arrhenius plots give a difference in activation energy of 1340 cal. mole- for OH and OD bond-fission in the hydroxonium ion which agrees with the theoretical value of 1200 cal.mole-found from i.r. data. Primary hydrogen-isotope efects. Jones et ~ 2 2 . ~ ’ find that kH/kT for proton loss from p - and m- substituted acetophenones varies with the activation energy in a manner consistent with the theory that increasing transition-state symmetry increases the isotope effect. Davis and Kens0n7~ make a similar observation on the hydrolysis of arylboranes; k,/kD for B-H bond breaking increases as the strength of the B-H bond as measured by the stretching frequency decreases. There has been some interest in the use of hydrogen-isotope effects to detect proton tunnelling. Lewis and F ~ n d e r b u r k ~ ~ find values of kH/kD up to 24.2 at 25” for proton transfers from 2-nitropropane to sterically-hindered pyridine bases.They suggest that steric hindrance may favour tunnelling. Jones et also suggest tunnelling to account for anomalous isotope effects in the detritia-tion of o-methyl acetophenone. Bell and O n ~ o o d ~ ~ in a careful study of the kinetics of oxidation of formate and deuterioformate ions by permanganate, find that the isotope effect appears almost entirely in the activation energies, so that the contributions of tunnelling is insignificant. The large variations in isotope effects which can be found in a series of similar reactions due to variations in transition-state symmetry and also possibly to variations in the extent of tunnelling render doubtful any attempt to assign a reaction mechanism on the basis of the magnitude of the isotope effect, but such attempts are not uncommon.Fife77 chooses a mechanism for the hydrolysis of 2-(p-substituted phenyl)-4,4,5,5-tetramethyl-1,3-dioxalans partly on the grounds that the observed isotope effect is 2-4 whereas isotope effects 68 C. G. Swain E. C. Stivers J. F. Reuwer jun. and L. J. Schaad J . Amer. Chem. SOC. 1958, 69 A. J. Kresge and Y. Chiang J . Amer. Chem. SOC. 1967,89,4411. ’O W. J. Albery Trans. Faraday SOC. 1967,63,200. ” S. Ohno Bull. Chem. SOC. Japan 1966,39,2560. 72 J. R. Jones R. E. Marks and S. C. Subba Rao Trans. Faraday SOC. 1967,63,111. 73 R. E. Davis and R. E. Kenson J . Amer. Chem. SOC. 1967,89 1384. 74 E. S. Lewis and L. H. Funderburk J . Amer. Chem. SOC. 1967,89,2322. 75 J. R. Jones R. E. Marks and S.C. Subba Rao Trans. Faraday SOC. 1967,63,993. 76 R. P. Bell and D. P. Onwood J. Chem. SOC. (B) 1967,150. ’’ T. H . Fife J. Amer. Chem. SOC. 1967,89,3228. 80,5885 The Kinetics of Reactions in Solution 47 for reactions known to proceed by the alternative mechanism are in the range 1.4 to 1-7. E. M. Eyring et d7' hope to characterise the reacting moieties in enzyme reactions involving proton transfer by comparing isotope effects with those found for simple proton-transfer systems; e.g. k& = 2 suggests an 0-H . . 0 transfer whereas kH/kD = 3 suggests a N-H . . 0 transfer. However Kohn and Gill,79 as a result of their work on the alcoholysis of tri-n-octyl aluminium stress the need for caution in using isotope effects as a mechanistic criterion. The unpredictability of isotope effects is also demonstrated by de la Mare and El Dusouqui" who find a solvent isotope effect of 1.9 on the bromination of phenol in acetic acid despite the prediction of Swain et aLS1 that such an effect would be negligible.The most reliable use of hydrogen iso-tope effects is in deciding which of the two mechanisms is correct when one predicts a large effect and the other none at all. For instance Cerfontain and Telder's' observation of k,/kD = 6.1 for the nitration of anthracene in aceto-nitrile is a clear indication that the breaking of the C-H bond is rate-determining. Similarly the variation of fluorescence intensity with isotopic substitution is used by Stryers3 to diagnose whether excited species are involved in proton-transfer reactions.Solvent isotope efects. The validity of solvent isotope effects appears to be much greater than that of primary isotope effects. Golds4 has shown that the rate of slow proton-transfer reactions should depend 06 the deuterium content of the H,O-D,O mixed solvent in a predictable way partly determined by the Brarnsted exponent a. Gold" tests his theory by evaluating a for the general acid-catalysed hydrolysis of cyanoketone dimethylacetal both from the varia-tion in rate in various H,O-D,O mixed solvents and from the variation in rate with the pKA of the acid catalyst. Excellent agreement is found. A similar agreement is found by Salomaa et aLE6 for the general acid-catalysed hydrolysis of vinyl ethers using the theoretical equations of Salomaa Schlaeyer and LongE7 and of Kresge.88 Kresge and Chiang" also study the hydrolysis of ethyl vinyl ether with similar success.They point out that although the solvent isotope effect in H,O-D,O mixed solvents cannot be regarded as a useful criterion of reaction mechanism it can in favourable cases provide valuable information concerning the nature of the transition state in reactions of known mechanism. In particular it can show the position which the transition state occupies on the reaction co-ordinate for reactions in which proton transfer from the hydro-xonium ion to the substrate occurs in the rate-determining step. 78 M. H. Miles E. M. Eyring W. W. Epstein and M. T. Anderson J . Phys. Chem. 1966,70,3490. 79 E. Kohn and J. M. Gill J . Organometallic Chem. 1967,7 359. P.B. D. de la Mare and 0. M. H. El Dusouqui J . Chem. SOC. (B) 1967,251. C . G. Swain D. A. Kuhn and R. L. Schowen J . Amer. Chem. SOC. 1965,87,1553. H . Cerfontain and A. Telder Rec. Truv. Chim. 1967,86,371. 83 K. Stryer J. Amer. Chem. SOC. 1966,88 5708. 84 V. Gold Trans. Faraday SOC. 1960,56,255. 86 P. Salomaa A. K. Kankaanpera and M. Lajunen Acta Chem. Scand. 1966,20 1790. 8 7 P. Salomaa L. L. Schlaeger and F. A. Long J . Amer. Chem. SOC 1964,86,47. 89 A. J. Kresge and Y. Chiang J. Chem. SOC. (B) 1967,58. V. Gold and D. C. A. Waterman Chem. Comm. 1967,40. A. J. Kresge Pure Appl. Chem. 1964,243 48 J . E. Crooks Secondary hydrogen isotope eflects. Stern and Wolfsberggo show theoretically that there cannot be a secondary hydrogen isotope effect of more than about 1.5% unless there is a force constant change at the isotopically substituted position between reactant and transition state.Kresge and Pretogl agree with this conclusion and point out that the crucial issue in the interpretation of secondary isotope effects is the origin of these changes in force constant. Brown et aLg2 have suggested that the changes are of steric origin the -CD, group being smaller than the -CH group since the amplitude of a C-H vibration is greater than that of a C-D vibration with the same energy. Kresge and Preto test this hypothesis by measuring the equilibrium constant for the ionisation of triphenylcarbinol for varying degrees of ring deuteriation. Ring deuteriation at any point increases triphenyl cation formation but the effect is greatest for deuteriation at the para-position whereas the steric hypothesis would suggest the effect would be greatest for ortho-substitution.Kresge and Preto conclude that the effect is caused by the inductive effect of the C-D group by hyperconjugation as discussed by Halevig3 Heitner and L,effekg4 also test the steric hypothesis by measuring the secondary isotope effect on the racemisation of a highly hindered biphenyl and find no change in the rate when the hindering -CH groups are replaced by -CD3 groups. Koenig and WolP’ measure the secondary isotope effect on the formation of the t-butyl radical by the decomposition of t-butyl perpivalate. They find k Jk, = 1-02 as compared with k JkD = 1.11 for the formation of the t-butyl cation and are able to account for the effect in terms of the hyperconjugative stabilisation of the radical without involving steric effects.Karabatsos et dg6, in a theoretical and experimental study of the solvolysis of 8-methyl naphthyl and naphthoyl chlorides find that less than 10% of the observed secondary isotope effect can be attributed to non-bonded (i.e. steric) interactions most being caused by hyperconjugation. Lee and N0szk6~’ find secondary isotope effects around 1.15 for solvolysis of dimeth~xyphenyl-[~H,]-ethyl p-bromo-benzenesulphonates in accordance with the hypothesis of non-classical carbonium-ion intermediates. Following Streitwieser et aLg8 they attribute secondary isotope effects to the decrease in bending force constant from an initial C-H tetrahedral bending to the lower frequency out-of-plane motion in the transition state.This latter is affected by the proximity of the leaving or entering group. If these are close the out-of-plane bending will have higher M. J. Stem and M. Wolfsberg J . Chem. Phys. 1966,45,2618. 91 A. J. Kresge and R. J. Preto J . Amer. Chem. SOC. 1967,89 5110. 92 H. C. Brown M. E. Azzaro J. G. Koelling and G. J. McDonald J . Amer. Chem. Soc. 1966, ” E. A. Halevi Prog. Phys. Org. Chem. 1963,1 109. 94 C. Heitner and K. T. Leffek Canad. J . Chem. 1966,44,2567. 95 T. Koenig and R. Wolf J . Amer. Chem. SOC. 1967,89,2948. 96 G. J. Karabatsos G. C. Sonnichsen C. G. Papaioannou S. E. Scheppele and R. L. Shone, ’’ C. C. Lee and L. Noszk6 Canad. J . Chem. 1966,44,2491. 88,2520. J . Amer. Chem. SOC. 1967,89,463.A. Streitwieser jun. R. H. Jagow R. C. Fahey and S. Suzuki J . Am-. Chem. SOC. 1958,80, 2326 The Kinetics of Reactions in Solutions 49 energy and so be at a higher frequency. An alternative explanation of a similar phenomenon is given by NikoletiC et dg9 who find secondary isotope effects around 1.1 for the solvolysis of methyl-substituted cyclopropylcarbinyl and cyclobutyl derivatives. They explain this deviation from the theoretical maxi-mum value of 1.4 in terms of hyperconjugative charge delocalisation in the non-classical carbonium ion. Eflectsfor isotopes other than hydrogen. The masses of isotopes of other elements differ proportionally much less than those of hydrogen so that the isotope effects are very small. It is in general not possible to measure the different rates directly and the effects are measured by competitive techniques.The reactants are analysed by mass spectrometer at various intervals after the start of the reaction. Yankwich and Buddenbaum'" discuss sixteen reactions reported in the literature for which the kinetic carbon-isotope effects vary with the inverse-square of the temperature rather than with the reciprocal as theoretically predicted. They attribute this behaviour to the existence of alternative mechanisms for each reaction one of which is favoured in a different temperature range from the other. Smith and Bourns"' use the existence of a nitrogen isotope effect of 1.0091 & 00007 to decide between two possible mechanisms for the carbonyl-elimination reaction of 9-fluorenyl nitrate with acetate ion.Brown and Druryl'' compare experimental and theoretical values for the nitrogen isotope effect in the reduction of nitrate nitrite and hydroxylamine to ammonia to find out whether the cleavage of the N-0 bond is rate-determining. Agarwala Rees and Thodelo3 use a similar tech-nique with sulphur isotope effects to find points of cleavage in the sulphur chains when polythionates are decomposed by acid. Fast Reactions.-Pulse radiolysis. Pulse radiolysis continues to be a popular and fruitful field. In 1967 more work was published concerning this technique for the study of fast reactions than any other. Anbar and Nets"* tabulate rate constants for 660 reactions of the solvated electron 270 reactions of the hydrogen atom in solution and 480 reactions of the hydroxyl radical in solution.Only 19 of the 164 references are to work published more than five years ago, and the more recent results are obtained almost exclusively by pulse radiolysis. Freemanlo' gives a theoretical treatment of the kinetics of the initial reactions after a radiolytic pulse discussing the scavenging of positive ions and solvated electrons in the radiolysis of liquid hydrocarbons. The good agreement with experiment suggests that solvated electrons are formed in non-polar solvents as well as in water. Dainton et aZ.'06 account for differences between rate constants obtained by pulse radiolysis and those obtained by product analysis, 99 M. NikoletiC S. BorEiC and D. E. Sunko Tetrahedron 1967,23,649. loo P. E. Yankwich and W. E. Buddenbaum J .Phys. Chem. 1967,71,1185. lo' P. J. Smith and A. N. Bourns Canad. J . Chem. 1966,44,2553. L. L. Brown and J. S. Drury J . Chem. Phys. 1967,46,2833. Io3 V . Agarwala C. E. Rees and H. G. Thode Canad. J . Chem. 1967,45 181. lo4 M. Anbar and P. Neta Internat. J . Appl. Radiation Isotopes 1967,18,493. G. R. Freeman J . Chem. Phys. 1967,46,2822. G. V . Buxton F. S. Dainton and G. Thielens Chem. Comm. 1967,201 50 J . E. Crooks after continuous radiolysis in terms of the transfer of electrons from one unstable species to another during radiolysis. Anbar et al.107 find that the activation energy of all reactions of the type ea; + X -+ X- is around 3.5 kcal. mole-' the energy of activation of diffusion in water despite the wide range of rate constants. The rate is determined by the probability of finding an electron vacancy on the substrate molecule and low rate constants are caused by a large number of collisions in which the substrate molecule is in an unfavourable electronic configuration.For example for hydroxonium-ion substrate k = 4.0 x 10" 1. mole-' set.-' and ASt = -2.2 cal.deg.-' mole-' whereas for urea substrate k = 2.7 x lo5 1. mole-' set.-' and ASt is -25 cal.deg.-' mole-' This conclusion is borne out by the work of Kevan'08 who finds that the relative rates of reactions of the solvated electron in ice at 7 7 " ~ quantita-tively parallel those in water at 300°K. Gottschall and Hartlog find from the temperature variation of the products from steady-state radiolysis that the activation energy of all reactions of the type eai + X -+ X - is around 3.5 kcal.which they state to be the activation energy of self-diffusion in water taking the value of Wang.'" A clearer picture of the solvated electron is beginning to emerge. Dainton et al.' ' ' show that the kinetic salt effect on the reactions of the solvated electron in methanol is consistent with the solvated electron having a unit negative charge and a diameter of 5 A. Anbar and Neta'12 use the rates of the reaction between the hydrogen atom and the fluoride ion to calculate the redox potential of the solvated electron to be 2.5 volt. This agrees with the value of 2.1 volt found by Baxendale'13 from the rate of reaction between the hydrogen atom and the hydroxide ion. However there are still some mysteries even about the simplest reactions.Barker and Sammon''4 find the rate of combination of hydroxonium and hydroxyl ions produced by pulse radiolysis to be 7.3 x 10" 1. mole-'sec.-' much less than that found by Ertl and Gerischer'" using the temperature-Jump method. The discrepancy is too great to be written off as experimental error. The number of systems studied by pulse radiolysis in 1967 is so great that it is only possible to give a list to indicate the fields of activity. Inorganic species studied include CO,' l6 CNS-,'" and Oi.118 Organic species studied include lo' M. Anbar Z. B. Alfassi and H. Bregmann-Reisler J . Amer. Chem. SOC. 1967,89 1263. lo' L. Kevan J . Amer. Chem. SOC. 1967,89,4238. Io9 W. C. Gottschall and E. J. Hart J . Phys. Chem. 1967,71,2102. J.H. Wang J . Amer. Chem. SOC. 1951,73.510. G. V. Buxton F. S. Dainton and M. Hammerli Trans. Faraday SOC. 1967,63 1191. M. Anbar and P. Neta Trans. Faraday SOC. 1967,63,141. J. H. Baxendale Radiation Res. Suppl. 1964,4 139. G. C. Barker and D. C. Sammon Nature 1967,213,65. 'I5 G. Ertl and H. Genscher. Z . Elektrochem 1961,65,629. 116 Y. Raef and A. J. Swallow J . Phys. Chem. 1966,70,4072. J. H. Baxendale and D. A. Stott Chem. Comm. 1967,699. W. D. Felix B. L. Gall and L. M. Dorfman J . Phys. Chem. 1967,71 384; G. Czapski ibid., p. 1683 The Kinetics of Reactions in Solution 5 1 phenol,' l9 acrylamide,120 pyridine,121 nitrobenzene,'22 nitro~obenzene,'~~ phenylhydr~xylamine,'~~ and the nitroparaffns. l 25 Hagemann and Schwarz'26 study the benzyl radical produced by pulse radiolysis of a-chlorotoluene and ThomasI2' studies the methyl radical in aqueous solution produced by pulse radiolysis of aqueous methyl iodide.N.rn.r. The measurement of the rate of a chemical reaction from the width of the n.m.r. absorption peak of the nucleus whose movement causes the reaction is a popular and successful technique. Several workers have tested its validity by comparing the rates thus obtained with rates for the same reaction found by an independent technique. Griffths and Socrates'28 find good agreement between the rate of hydration of pyruvic acid measured by n.m.r. line-width and the value found by S t r e h l ~ w ' ~ ~ by the pressure-jump method, with conductimetric detection. Luz et al. 30 find that the rate of the acid-catalysed oxygen-exchange on acetaldehyde measured by the width of the "0 peak is the same as the rate of dehydration of acetaldehyde hydrate.' 31 The inversion of the cyclohexane ring is not perhaps a chemical reaction in the strict sense of the term but its rate can be measured.Anet and Bourn'32 measure the rate of chair- to boat-inversion for cyclohexane-C2H by two different methods, line-shape analysis and double resonance. In the less familiar double-resonance technique the equilibrium distribution of spin states for protons on a given site is perturbed by saturation with a strong radio-frequency field. If protons are transferred to another site by a chemical reaction the change in intensity at the second site gives a measure of the rate of the chemical reaction.The range of observable rates is severely limited as the chemical-relaxation time must be of the same order of magnitude as the spin-lattice relaxation time. Anet and Bourn find excellent agreement between values of A H f and ASf found by the two methods although a direct comparison between rates is not possible as the methods are only applicable in different ranges. Rates of internal rotation also hardly count as kinetics but Gutowsky et find good agree-ment between the rates of rotation about the C-N bond in N-methyl-N-benzylformamide calculated from n.m.r. line-width and observed in a mixture 'I9 E. J. Land and M. Ebert Trans. Faraday SOC. 1967,63,1181. K. W. Chambers R. Collinson F. S. Dainton W. A. Seddon and F. Wilkinson Trans. B. Cercek and M. Ebert Trans.Faraday soc. 1967,63 1687. Faraday SOC. 1967,63 1699. "' K.-D. Asmus A. Wigger and A. Henglein Ber. Bunsengesellschaft Phys. Chem. 1966,70,862; K.-D. Asmus B. Cercek M. Ebert A. Henglein and A. Wigger Trans. Faraday SOC. 1967,63,2435. lZ3 K.-D. Asmus G. Beck A. Henglein and A. Wigger Ber. Bunsengesellschaft Phys. Chem., 1966,70 869. I 2 4 A. Wigger A. Henglein and K.-D. Asmus Ber. Bunsengesellschaft Phys. Chem. 1967,71 513. ''' J. Sutton and Tran Dinh Son J . Chim. phys. 1967,64,688. lZ6 R . J. Hageman and H. A. Schwarz J . Phys Chem. 1967,71,2694. ''' J. K. Thomas J . Phys. Chem. 1967,71 1919. 12* V. S . Grifiths and G. Socrates Trans. Faraday SOC. 1967,63,673. lZ9 H. Strehlow 2. Elektrochern. 1962,66,392. 130 P. Greenzaid Z . Luz and D. Samuel J . Amer. Chem.SOC. 1967,89,756. 13' R. P. Bell and P. G. Evans Proc. Roy 'SOC. 1966 A 291,297. 13' F. A. L. Anet and A. J. R. Bourn J . Amer. Chem. SOC. 1967,89,760. 133 H. S. Gutowsky J. Jonas and T. H. Siddall jun. J . Amer. Chem. SOC. 1967,89,4300 52 J . E. Crooks enriched in one rotamer. A similar agreement is found by Mannschreck, Mattheus and R i s ~ m a n ' ~ ~ for the interconversion rate of the rotamers of N-benzyl-N-2,4,6-tetramethyl benzylamide. A considerable amount of work has been done on proton exchange on oxygen nitrogen and carbon. Puar and G r ~ n w a l d ' ~ ~ look for but fail to find, evidence for a Grotthus-type mechanism for proton exchange between salicyclic acid and methanol (c$ Albery2'). Grunwald et al. measure proton exchange rates for phenol in aqueous acid'36 and substituted phenols in methan01.l~' Rabideau and H e ~ h t ' ~ use 1 7 0 n.m.r.line-widths to measure the rates of acid- and base-catalysed proton exchange in water and find rates for the ionic-recombination reaction similar to those found by pulse radiolysis. l4 Ralph and Gr~nwald'~' measure the rate of exchange of triethylammonium ion with H 2 0 by proton line-width and with D20 by observation of the change with time of the height of the HOD proton peak. The symmetrical exchange B + HOH + HB' + BH+ + HOH + B is five times slower than expected from the rate for trimethylammonium and Ralph and Grunwald attribute this to steric hindrance. Grunwald and Ralph'40 measure the rate of breaking the R,N-HOH hydrogen bond and find it to be the rate of diffusion of the water molecule into the bulk solvent.In aqueous sulphuric acid the rate varies inversely with the viscosity over a five-fold range of bulk viscosity as predicted by the Smoluchowski equation. Grunwald and Ralph point out that no dis-continuity is observed in passing from trimethylamine to triethylamine which is evidence against the theory that special ice-like water structures are built up near non-polar organic groups. One of the ethyl groups in triethylamine must be adjacent to the water molecule that is hydrogen-bonded to nitrogen but it does not noticeably affect the kinetics. Day and Reille~'~' find the isotope effect for the diffusion-controlled proton-transfer from trimethylammonium ion to water to be 1.23 as expected for a diffusion-controlled reaction.G r ~ n w a l d ' ~ ~ finds that rates and equilibria for proton exchange of trimethyl-ammonium ion in methanol are similar to those in water. Brauman McMillen, and Kana~awa'~ use the double-resonance technique to measure the rate of proton exchange between fluorenyl lithium and fluorene in dirhethylsulphoxide, as the rate is too slow (k2 = 0.5 1. mole-'sec.-') to observe by the line-width method. The rate of exchange of solvent in the first co-ordination sphere of a metal ion is observed by Wuthrich and C ~ n n i c k ' ~ ~ for vanadyl ion in water, 134 A. Mannschreck A. Mattheus and G. Rissman J . Mol. Spectroscopy 1967,23 15. 13' M. S. Puar and E. Grunwald J . Amer. Chem. SOC. 1967,89,4403. 136 E. Grunwald and M. S. Puar J . Phys. Chem. 1967,71 1842.13' E. Grunwald C. F. Jumper and M. S. Puar J . Phys. Chem. 1967,71,492. 138 S. W. Rabideau and H. G. Hecht J . Chem. Phys. 1967,47,544. 139 E. K. Ralph jun. and E. Grunwald J . Amer. Chem. SOC. 1967,89,2963. f40 E. Grunwald and E. K. Ralph jun. J . Amer. Chem. SOC. 1967,89,4405. 14' R. J. Day and C. N. Reilley J . Phys. Chem. 1967,71 1588. 142 E. Grunwald J . Phys. Chem. 1967,71 1846. 143 J. 1. Brauman D. F. McMillen and Y. Kanazawa J . Amer. Chem. SOC. 1967,89 1728. 14* K. Wuthrich and R. E. Connick Inorg. Chem. 1967,6,583 The Kinetics of Reactions in Solution 53 and by Fratiello Miller and Sch~ster’~’ for AlCl, BeCl, GaCl, SbC15 and TiC1 in NN-dimethylformamide. Line-width measurements can sometimes be interpreted incorrectly. The width of the satellite lines produced by Ig9Hg-H spin-coupling in the ‘Hn.m.r.spectrum of methylmercuric iodide have been taken to give the rate of alkyl but S i m p ~ o n ’ ~ ~ shows the line broadening is caused by relaxation of spin-coupling with the quadrupole halogen nucleus. A similar explanation is also given by Ham Jeffery Mole and Stuart,148 although they still invoke alkyl exchange to explain the collapse of the satellite lines on the addition of AlCl,. Relaxation methods. The temperature-jump method continues to be the most widely used of the relaxation methods. Bewick and Robertson149 test the theory of coupled reactions by measuring the relaxation times for systems in which zinc and copper ions compete for murexide. Good agreement with the generally accepted theory is found in contradiction to earlier work in the same 1ab0ratory.l’~ Rorabacherl” finds that the rate of formation of the monoammine complexes of the divalent first-row transition-metal ions is controlled by the rate of water loss from the M(H,O)i+ .. . . NH complex. There is good agreement with the rate of water exchange in the inner solvation sphere as found by n.m.r. line-width1 ’ This rate-controlling desolvation is common but by no means universal. Kustin et find the rate of formation of the P-aminobutyrate complexes of Mi2+ and Co2+ to be controlled by the rate of chelate-ring closure whereas the a-aminobutyrate complexes form by the usual mechanism. Hurwitz and Kustin’” find the rate of formation of uranyl complexes decreases with de-creasing nucleophilic character of the anionic ligand.The temperature-jump technique has been used by Stuehr’56 for a detailed study of the tautomerism of diacetylacetone which turns out to be a surprisingly complex process. Bio-chemistry seems to offer the most promising field for temperature-jump work. Hammes and S~hirnrnel’~~ apply matrix techniques to the often very difficult problem of calculating rate constants from relaxation times with special reference to enzyme systems. Erman and Hamme~’’~ apply a temperature-and by ultrasonic absorption.’ 14’ A. Fratiello D. P. Miller and R. Schuster Mol. Phys. 1967 12 11 1. 146 E. F. Kiefer and W. L. Waters J . Amer. Chem. Soc. 1965,87,4401. 147 R. B. Simpson J . Chem. Phys. 1967,46,4775. 14’ N. S. Ham E. A. Jeffery T. Mole and S.N. Stuart Chem. Comm. 1967,254. 14’ A. Bewick and P. M. Robertson Trans. Faraday SOC. 1967,63,678. lSo A Bewick M. Fleischmann J. N. Hiddleston and Lord Wynne-Jones Discuss. Faraday SOC., 1965,39 149. D. B. Rorabacher Inorg. Chem. 1966,5 1891. T. J. Swift and R. E. Connick J . Chem. Phys. 1962,37,307. M. Eigen and K. T a m 2. Elektrochem. 1962,66,107. lS4 A. Kowalak K. Kustin R. F. Pasternack and S. Petrucci J . Amer. Chem. SOC. 1967,89,3126. Is’ P. Hurwitz and K. Kustin J . Phys. Chem. 1967,71,324. 15’ G. G. Hammes and P. R. Schimmel J . Phys. Chem. 1967,71,917. J. Stuehr J . Amer. Chem. SOC. 1967,89,2826. J. E. Erman and G. G. Hammes J . Amer. Chem. SOC. 1966,88,5607 54 J . E. Crooks jump to the sample in a stopped-flow apparatus to investigate the reaction of ribonuclease with cytidine 2,3'-cyclic phosphate.There have been some advances in instrumentation for relaxation tech-niques. Caldin and Crooks'59 describe an apparatus in which a temperature-jump is produced by a microwave pulse and use it to measure the rates of the proton-transfer reactions between 2,4-dinitrophenol and the butylamines in chlorobenzene solution. Eyring et al. 16' describe a dissociation field-effect relaxation apparatus used to study the hydrolysis of the uranyl ion. Hoffmann and Pauli'62 describe a pressure-jump apparatus for the study of relaxation processes in the microsecond region. A rectangular pressure-jump of 12 micro-seconds duration and 25 atmospheres amplitude is produced by discharging a capacitor through a flat coil in front of a copper membrane.The formation of the Co2+-malonate complex is studied. In these sophisticated kinetic techniques care must be taken to relate the apparatus design to the system studied. It is a pity that on the evidence of their own published oscilloscope traces many users of the temperature-jump technique seem unaware that a small capacitor of the correct value in the detector circuit would greatly reduce noise and so lead to more accurate results. Flash photolysis. Hayon and M ~ G a r v e y ' ~ ~ produce solvated electrons by flash photolysis in the vacuum u.v. which then react with SO;- COZ- and OH-. Strong and per an^'^^ study the transient iodine atom o-xylene charge-transfer complex produced by flash photolysis. It is more stable than the iodine molecule o-xylene complex as predicted by the Mulliken theory.The variation of the rate of formation with temperature follows the general pattern predicted by the Smoluchowski equation with Stokes-Einstein diffusion coefficients. Wagner'65 shows that the rate of decay of triplet acetone is due to hydrogen-atom abstraction from the solvent in contradiction to the hypothesis of Borkman and Kearns,'66 who state that triplet acetone has only a very short lifetime in solution so that a triplet-energy transfer in pure acetone must be faster than diffusion-controlled. Hammond et ~ 1 . l ~ ~ study steric effects on the rate of energy transfer from triplet fluorenone to various substituted stilbenes. Flash photolysis like temperature-jump is also applicable to systems of biochemical interest e.g.proflavin'68 and the photochromic spiropyrans.'69 Other methods. Gorrell and Dubois' 7 0 use the fluorescence-quenching 159 E. F. Caldin and J. E. Crooks J . Sci. Instr. 1967,44,449. 160 E. F. Caldin and J. E. Crooks J . Chem. SOC. (B) 1967,959. 16' D. L. Cole E. M. Eyring D. T. Rampton A. Silzars and R. P. Jensen J . Phys. Chem. 1967, 71 2771. H. H. Hoffmann and K. Pauli Ber. Bunsengesellschuf. Phys. Chem. 1966,70 1052. 163 E. Hayon and J. J. McGarvey J . Phys. Chem. 1967,71,1472. 164 R. L. Strong and J. Perano J . Amer. Chem. SOC. 1967,89,2535. 166 R. F. Borkman and D. R. Kearns 1. Amer. Chem. SOC. 1966,88,3467. 16' W. G. Herkstroeter L. B. Jones and G. S. Hammond J . Amer. Chem. SOC. 1966,88,4777. K. Kikuchi and M. Koizumi Bull.Chem. SOC. Japan 1967,40,736. 169 M. Mosse and J.-C. Metras J . Chim. phys. 1967,64 691 ; J. Arnauld and M. Mosse Compt. ''O J. H. Gorell jun. and J. T. Dubois Trans. Faraday SOC. 1967,63,347. P. J. Wagner J . Amer. Chem. SOC. 1966,88,5672. rend. 1967,264<= 1145 The Kinetics of Reactions in Solution 55 technique to measure the encounter rate between biacetyl and polycyclic aromatic hydrocarbons. They test the Smoluchowski equation using experi-mental diffusion coefficients rather than those calculated from the Stokes-Einstein equation and find good agreement. The Stokes-Einstein diffusion coefficients are up to three times less than the experimental values as these large, flat molecules can slip sideways through the solvent. Petrucci' 71 measures the rate of association between solvated Mg2 + and SO:- to form Mg2+(H2O),SO;- in water-glycol mixtures from the ultrasonic absorption in the frequency range 50-170 MHz and finds the rate varies with viscosity as predicted by the Smoluchowski equation.Petrucci and Battistini' 72 use the same apparatus to measure the rate of formation of the tetrabutyl-ammonium bromide ion-pair in nitrobenzene-methanol mixtures. Gui'tyai and Mairanovskii' 7 3 use the dropping-mercury electrode to measure the rate of protonation of pyridine 2,6-lutidine and maleate ion in aqueous dioxan. The rates at high dioxan concentration are an order of mag-nitude higher than that predicted by the Debye-Smoluchowski equation, which suggests that the approximations necessary in solving the polarographic equations are invalid under the conditions used.Niirnberg' 74 gives a careful and detailed account of high-level Faradaic rectification a modification of the polarographic technique which enables accurate measurements to be made on the fastest reactions. During the lifetime of each mercury drop a stream of high-voltage microsecond pulses at a repetition frequency of 10 kHz is applied, and the rectified current is plotted against the applied potential. The effective drop-time is thus reduced to one microsecond. Niirnberg gives an extensive review of the theory the apparatus and its applications with 164 references. The ionisation rates for seventeen carboxylic acids are given in good agreement with results from relaxation methods'75 and the rotating-disc electrode.'76 Bimolecular rate constants for fast reactions can also be found by classical methods if the reagents can be used at sufficiently low concentrations.A controlled low concentration of reagent can be maintained by a two-phase liquid system the reagent reacting in say an aqueous layer but being mostly present in the other organic layer. This technique is used by Nanda and S h a ~ m a ' ~ ~ to observe fast alkaline hydrolysis of esters and by Hogeveen et ~ 2 . ' ~ ' to observe the reduction of trimethylcarbonium ions by molecular hydrogen. The concentration of a reagent may also be low as the result of an unfavourable equilibrium constant. Coombes Moodie and Schofield 17' 17' S. Petrucci J . Phys. Chem. 1967,71 1174. 17' S. Petrucci and M. Battistini J . Phys. Chem. 1967,71 1181. V. P. Gui'tyai and S. G Mairanovskii Elektrokhimiya 1966,2 1414. 174 H. W. Niirnberg Fortschr. Chem. Forsch. 1967,8,241. M. Eigen Angew. Chem. Internat. Edn. 1964,3 1. 17' W. Vielstich and D. Jahn 2. Elektrochem. 1960,64,43. 17' A. K. Nanda and M. M. Sharma Chem. Eng. Sci. 1967,22,769. A. F. Bickel C. J. Gaasbeek H. Hogeveen J. M. Oelderik and J. C. Platteeuw Chem. Comm., 1967,634. 179 R. G. Coombes R. B. Moodie and K. Schofield Chem. Comm. 1967,352 56 J . E . Crooks point out that the rate of nitration of alkylated aromatic hydrocarbons is independent of the nature of the alkyl groups and suggest that the rate is controlled by the encounter rate between the hydrocarbon and the nitronium ion. The observed rate is slow because of the low concentration of nitronium ion