The Method of Successive Product Fractions

The methods of continuous isotopic analysis of the product or of successive product fractions have been applied to tracer systems, where k/k —l l, by Ropp, Weinberger, and Neville,51 Downes,51 and Schmitt, Myerson, and Daniels.55 The expressions for (k/k —l) can be developed conveniently from Eqs. V.22and V.23. Consider an experiment in which the reaction is allowed to proceed to an extent ft of completion. The product formed between ft and /, of completion is isolated for isotopic assay. From Eq. V.23 one obtains 

For continuous isotopic analysis of the. product or the removal of small samples, (/g—/x)/(l—/x) -C 1, we may limit the expansion of the logarithm to the first power and obtain the equation of Downes51 

A log-log plot of Rx/i versus (l—fi) yill give a straight line of slope (k/k —l). The method is entirely analogous to that of cumulative isolation of the product (cf. Section V.B-2). Any increase in precision results from the greater ease, in some cases, of increasing the number of experimental observations. Furthermore, a knowledge of RM is not required. The latter is mainly a matter of convenience, since it can usually be obtained ex- 

For the case where (/a—/x) is appreciable one obtains the result given by Schmitt, Myerson, and Daniels,64 

If a compound A BA decomposes to form A B and A, then the decomposition of ABA into AB and A or into A B and A will show an intramolecular isotope effect or an intramolecular isotopic competition. The general solution to the kinetics of such a system involving the species A BA, ABA, and ABA all reacting at different rates to give the products A B, AB, A, and A is rather unwieldy. We shall present several particular solutions to the kinetics of the system. 

The methods of continuous isotopic analysis of the product or of successive product fractions have been applied to tracer systems, where by Ropp, Weinberger, and Neville, Downes,  

First we consider the case where ABA is present at tracer concentration. The general formulation of the kinetics at the tracer level has been given by Bigeleisen. The assumption made is that one neglects the contribution of A from ABA in comparison with its formation from A BA and neglects the presence of ABA. The results are, in the present notation. 

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