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The Transition State in Chemical Kinetics by Prof APRIL 3, 1937 NATURE 575 The Transition State in Chemical Kinetics By Prof. M. Polanyi, University of Manchester """'HE energy barrier separating the initial and The 'transition state method' of treating 1 final states of a reaction has ceased to be a problems of reaction velocity consists in a general­ fictitious concept since the main principles of ization of this procedure to other variations than chemical inertia were discovered by F. London those of temperature. Supposing the reaction rate (1927). For some simple cases, we can now cal­ in solution changes under the influence of hydro­ culate the energy changes occurring during the static pressure 71", then applying thermodynamics process of reaction, and follow the paths along to equation (A) we obtain which the atoms move. We can, in particular, obtain in many cases a clear picture of the con­ dlogk1 V 1 -V-r dlogv/2 figuration which corresponds to the top of the d1t = RT energy barrier. This configuration is called the where V is the volume of a solution containing transition state " of the reaction. 1 one mol of the initial state and V the volume It is interesting to deduce Arrhenius's equation 1 of a solution containing one mol of the transition by thermodynamical considerations relating to the state. We can again neglect the differential of v transition state. At chemical equilibrium we see and set the atomic configuration changing forwards and k ex; e (V1 - Vr)/RT backwards between the initial and final states of 1 a reaction, and passing on each occasion through The fruitfulness of this deduction depends on the transition state -r. The positions which the our capacity to interpret the values of V 1 - V" atomic system takes up between the initial and derived from observation. This is easiest in the final states form a continuous sequence and can, case of reactions of the type A + B = AB ; for therefore, be defined by one co-ordinate l which these we can predict V 1 - V" with some accuracy. is called the 'reaction path'. At equilibrium we The configuration of the transition state must have a certain infinitesimal number of reacting here be intermediate between the configuration of systems in the transition state, that is, near the the initial and final states and quite near to that top of the energy barrier. This number (population) of the final state, and the same will hold for the can be equated to the concentration product of volume V "" V -r will lie between V and V (the the reactants, say, c'.r/ ... into an infinitesimal 1 2 volume of the final state) close to V 1• This has, equilibrium constant K 1dl. in fact, been confirmed by experiment. It thus Population ( -r) = c' .c" ... K 1dl seems that the rate at which reaction velocity Since varies with hydrostatic pressure is predictable for Population = birth-rate x average life, certain types of reactions. we can calculate the birth-rate by noting that the The method is capable of further generalization. average life of " is equal to a thermal velocity v Variations in reaction velocity can be observed over dl, and that thus : under the influence of an electric field, for example, when the rate or" electrolytic evolution of hydrogen Birth-rate (-r) = c'.c" ... K v. 1 is governed by the polarization (e) of an electrode. Now the birth-rate of" is equal to the rate of the for­ In this case we might write for the equilibrium ward reaction (l) plus the rate of the back reaction constant K which relates the concentration of (2), and since at equilibrium, rate (I) = rate (2) the hydrogen ions in solution to that of the hydrogen gas at the electrode, rate (l) = c'.c" ... K 1vj2 and the rate constant k 1 is d log K n de = RT' k1 = K 1v/2 ... (A) Applying van t'Hoff's isochor to K 1 , we obtain: where n is the effective (molar) charge of the proton. The effective charge is equal to F = 96,500 dlogk1 q dlogv/2 =-RT+ coulombs for the hydrogen ion which constitutes the initial state, and equal to zero for the final The second term on the right being negligible, this state when the proton is neutralized at the elec­ gives k1 ex e ....q,;RT, that is, Arrhenius's equation. trode. If we assume that in the transition state © 1937 Nature Publishing Group 576 NATURE APRIL 3, 1937 the effective charge has an intermediate value, The principle consists in introducing a parameter say, IXn, IX being about 0·5, we obtain of the transition state arising from the general equation d log K 1 = IXF • IX ,....., . 0 5 p,- P-. de RT ' . ' (B) RT which on comparison of the differential of equation . d logvj2 A with respect to e and by neglectmg de where x is an external parameter causing the variation in reaction rate and p 1 - p-. is the change in the corresponding parameter accompanying the can b e 1'd ent1 'fi e d w1t· h d log k, If we measure k, -----a:;-· formation of the transition state from the initial by the intensity i of the current, we have log k, state. oc log i and finally The advance in the various directions to which I have referred is, as yet, tentative, but the method . IXFe 1og = --RT + const .,· IX,....., 0·5 ·' seems to provide a rational framework for the interpretation of many empirical rules of reactivity which is the well-known over-voltage equation of as well as a guidance to the discovery of new Tafel. This equation is thus interpreted as in­ relationships. dicating that the effective charge of the transition REFERENCES state lies about half-way between that of the The derivation of a reaction velocity from a statistical treatment initial and the final states of the reaction. of the transition state was first put forward by Wigner and Pelzer (Z. phys. Ghem., B, 15, 445 ; 1932) in their treatment of the reaction The field of such generalizations has been H + H,para = H, + H; this treatment was generalized by Eyring extended to other variations of reaction velocity (J. Ghem. Phys., 3, 107; 1935) and by Evans and Polanyi (Tram. Far. Soc., 31, 875; 1935). The thermodynamic formulation equa· arising from changes in chemical constitution, from tion (A) is due to the latter authors and to Wynne-Jones and Eyring the transfer of a reaction from the gas phase into (J. Ghem. Phys., 3, 492; 1935). Equation (B) and its various applica· tions sketched out in this paper are due to Evans and Polanyl (Trans solution, and from variations of solvents. Far. Soc., 31, 8i5; 1935; 32, 1333; 1936). Obituary Notices Sir Albert Kitson, C.M:G., C.B.E. widening circles, not only on account of the remark­ IR ALBERT KITSON, whose death occurred on able discoveries which have already been referred to, S March 8, was a geologist of world-wide repute, but also on account of the energy and drive which and the discoveries which he made and which are now he put into his work. By many of the Gold Coast being exploited in many parts of the world entitle natives he was regarded as a fetish doctor owing to him to be classed as one of the foremost economic his seemingly reckless handling of snakes, an ability geologists of his time. which he had acquired during his boyhood in the Kitson was born in Manchester in 1868, but when Australian bush. Nor did he know what fear meant. six years old accompanied his parents to Australia. In the early days of his Southern Nigerian appoint­ He entered the Civil Service of Victoria by com­ ment, when he was geologizing in the wake of a petitive examination, and having a bent for geology punitive expedition, he was continually in trouble he took courses in this subject at the University with the military authorities as he was always getting and School of Mines, Melbourne. Later on, he also ahead of them. took courses in mining and surveying, thereby Among Kitson's discoveries on the west coast of equipping himself for the career which he was after­ Africa may be mentioned the black and brown coal­ wards to follow. fields (Nigeria), manganese, bauxite, diamonds (Gold As a result of his studies, Kitson was transferred Coast) and many others of lesser importance, the to the Geological Survey of Victoria. In 1903 he development of which has contributed enormously became senior geologist, and while he occupied this to the prosperity of these two colonies. But he post was responsible for some magnificent field work. followed up these discoveries by coming home and In 1906 he went to Southern Nigeria as principal of describing their possibilities to interested parties in the Mineral Survey, but resigned in 1911. In 1915 the business world of London for, as already indicated, he was appointed director of the Geological Survey he had the economic side of geology very strongly of the Gold Coast, which position he held until 1930 developed. Moreover, he was a great enthusiast and when he retired, having reached the age limit. So he managed by some subtle gift to impart his valuable were his services considered, however, that enthusiasm to others. his period of service was extended five years beyond After his retirement, Kitson was requested by the the usual period. It was while he occupied this Government of Kenya to carry out a preliminary position that his name became known in ever- geological survey with special reference to the © 1937 Nature Publishing Group.
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