More Comments, Symmetry Numbers Do Not Lead to Isotope Enrichment

4 More Comments, Symmetry Numbers Do Not Lead to Isotope Enrichment 

Isotope effects on equilibria have been formulated earlier in this chapter in terms of ratios of (s2/si)f values, referred to as reduced isotopic partition function ratios. From Equation 4.80, we recognize that the true value of the isotope effect is found by multiplying the ratio of reduced isotopic partition function ratios by ratios of s2/si values. Using Equation 4.116 one now knows how to calculate s2/si from ratios of factorials. Note well that symmetry numbers only enter when a molecule contains two or more identical atoms. Also note that at high temperature (s2/si)f approaches unity so that the high temperature equilibrium constant is the symmetry number factor. 

In the following an explicit mathematical proof is presented to show that symmetry numbers factors do not lead to isotope enrichment. That result should come as no surprise since the factor on the right hand side of Equation 4.118 can be identified as 

4 Isotope Effects on Equilibrium Constants of Chemical Reactions 

The symmetry number factors are derived from the reduced isotopic partition function ratio of the RHt species. 

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