It is pointed out that the possibility of chemical separation of isotopes is a quantum effect. This permits a direct calculation of the difference in the free energies of two isotopic molecules. Tables and approximation methods are given which permit a rapid calculation of equilibrium constants if the frequency shifts on isotopic substitution are known. Several applications are discussed.

The theory of the isotopic enrichment factor is extended to include hyperfine splitting and the nuclear field shift. It is shown that hyperfine splitting is an order of magnitude too small to explain the anomaly in the 238U/235U separation in the U(III)−U(VI) exchange reaction. The “anomalous mass effect” in this reaction and the related U(IV)−U(VI) exchange reactions are shown to be related to the nuclear field shift of the electron energy levels. Calculations of the effects of these shifts exactly reproduce the odd−even staggering in the U(IV)−U(VI) exchange reaction and the separation factors for the even−even nuclei. In the U(IV)−U(VI) exchange reactions the nuclear field effect is three times as large as the absolute value and of opposite sign to the vibrational energy term. It is the nuclear field shift which leads to a preference of the U(IV) for the heavy isotope in each of these exchange reactions. A revision of the reduced partition function ratios of uranium ions in solution, which takes into account the nuclear field shift, is presented.

The rate constants for competitive reactions of isotopic molecules are considered from the theory of ``absolute rates'' and the collision theory. Formulas are derived for the ratio of the rate constants and the difference in the activation energies for reactions of isotopic molecules. The difficulties in the a priori calculation of relative rates are pointed out and discussed. In general the rate constant for the light molecule will be greater than that of the heavy molecule. It is shown that the maximum ratio in the rates occurs when the isotopic atom is essentially free in the activated complex. The conditions for the rate constant of the heavy molecule to exceed that of the light one are formulated. It is shown that the difference in activation energies covers the range from zero to the difference in the differences in the zero-point energies of the reacting molecules and their respective activated complexes.

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