Entropy isomer group thermodynamics

The harmonic oscillator approximation has generally been used in calculations of thermodynamic contributions from inversion at tetrahedral carbon. Inversion in a molecule having four different groups bound to a carbon atom results in the presence of two optical isomers. To calculated values of entropy and Gibbs free energy a contribution LkXnl should be added for each pair of optical isomers. 

In (212) the substituent is situated in an axial position with respect to a cyclohexane ring, but in (213) the substituant is exclusively equatorial and hence (213) might be expected to be the more thermodynamically stable. In fact at 200°C compound (212) is the more stable but below 48°C (213) is the more stable. These results can be explained by analysis of the symmetry of (212) and (213) and the consequences upon entropy factors. Isomer (212) has C, symmetry, but isomer (213) has 3 symmetry and hence the entropy for (213) should be lower by U In 3. This however, is balanced by the enthalpy factor, which as mentioned favours (213). The above case might be complicated by the entropy of mixing of different conformations of the hydroxy-substituent In (214) and (215) with a symmetrical substituent this problem is avoided, and equilibration of (21 and (215) confirms the above analysis fully equilibration of (216) and (217) also establishes a similar effect However, the interpretation of the results by the Belfast group differs in an important respect from that of the Princeton group. 

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