Statistical model residual entropy

The Bernal-Fowler-Pauling statistical model for the proton arrangements in ice presents a very subtle problem in the actual evaluation of the number of possible configurations in a macroscopic crystal. This is not just an academic exercise for, if we suppose there are configurations, all of which are equally likely, then the entropy of the system due to this cause is k In Further, if these configurations become frozen at some temperature where the disordering is still essentially complete, the measured entropy of the ice crystal will still have the residual value In at o °K, entropy from all other sources having vanished. 

This analysis in many ways parallels the theoretical treatment presented by Dafforn and Koshland [see Ref. (37)] as an extension and refinement of the initial proposal of orbital steering. They clearly established that the total effect could be large even after allowing for residual internal freedom in the transition state and that a loose complex as exemplified by bromine combination could occur with little loss of entropy. The point which is developed more fully here is that the microscopic model used for the statistical mechanical calculations is not the same macroscopic model used in the original definition of orbital steering. 

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