The integrated rate equations are given for various mechanisms by which three substances may be interconverted by first-order reactions. These equations are of special interest in the interpretation of isotopic exchange in the presence of an over-all chemical reaction. When certain rate constants in the mechanism are equal or have the same ratio as the ratio of concentrations of isotopic species in the reaction medium, considerable simplification of the integrated rate equation occurs.
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Alberty et al. (1957) studied this question.
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