By Ilya Prigogine, Stuart A. Rice

The *Advances in Chemical Physics* sequence offers the chemical physics and actual chemistry fields with a discussion board for serious, authoritative reviews of advances in each zone of the self-discipline. choked with state-of-the-art study suggested in a cohesive demeanour now not came across in different places within the literature, every one quantity of the *Advances in Chemical Physics* sequence serves because the ideal complement to any complicated graduate classification dedicated to the learn of chemical physics.

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The roots of ’physical arithmetic’ could be traced again to the very starting of man's makes an attempt to appreciate nature. certainly, arithmetic and physics have been a part of what used to be known as traditional philosophy. speedy development of the actual sciences, aided via technological growth and lengthening abstraction in mathematical examine, brought on a separation of the sciences and arithmetic within the twentieth century.

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These are tabulated in Table I which is 27 ISOTOPE EFFECTS I N CHEMICAL KINETICS TABLE I. Estimated Maximum Ratios in Specific Rate Constants at 25' C. 2 Maximum values for inverse isotope effects may be similarly calculated by setting f of the reactants equal to unity, which is indeed the case if the isotopic reactants are atoms. ,* may be taken as unity which is the minimum value of this ratio. Maximal values are estimated by taking the values for normal strongly of bonded molecules. This maximum value of inverse effects may be obtained from the values in Table I by dividing by the square root of the ratio of masses of the heavier to the Iighter isotope.

Furthermore, a knowledge of R,, is not required. The latter is mainly a matter of convenience, since it can usually be obtained ex- 44 JACOB BIGELEISEN A N D MAX M’OLFSBERG perimentally either by extrapolation or by successive approximation in the cumulative product method. If R,, is known in the successive fraction method, the intercept gives (k/k’- 1). This is the equivalent of an additional experiment in the cumulative product met hod. For the case where ( f 2 - f l ) is appreciable one obtains the result given by Schmitt, llyerson, and Daniels,Ss which is valid only for small differences between Rr(3-4) and Rr(1--9, in addition to assumptions implicit in Eqs.

27 shows that the method of isotopic analysis of the substrate is a very poor one a t small amounts of conversion. B-l and shown in Fig. 2 . Eq. 28 is a simple and useful one. 54 The expressions for (k/k'-- 1) can be developed conveniently from Eqs. 23. Consider an experiment in which the reaction is allowed to proceed to an extent fl of completion. The product formed between fl and f 2 of completion is isolated for isotopic assay. From Eq. 33) A log-log plot of R,, versus (1-fJ will give a straight line of slope (k/k'-1).