Isotope Distillation The Fenske Equation

Vapor-liquid equilibria of isomeric or isotopic mixtures perhaps come closest to showing perfect ideal behavior and a separation factor, which for all practical purposes remains constant over the entire range of compositions. Distillation is the most commonly used technique for the separation or enrichment of several important isotopes. Both and are produced 

Suppose we wish to gain an idea of the requirements for distilling the isotopic pair C O-C O, for which the value of a is 1.01 (see Table 6.9) with the equilibrium curve very close to the diagonal, which represents total reflux conditions. Here, a graphical construction on the McCabe-Thiele diagram does not recommend itself, since the operating and equilibrium curves are 

We start by applying the definition of the separation factor. Equation 6.22a, to the reboiler and obtain 

At total reflux the operating line coincides with the 45+ diagonal so that = Xjv- Equation 7.22a becomes 

A further simplificahon results for separation factors close to 1, for then we have by a Taylor-expansion of the denominator 

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