Exam Survival Guide: Physical Chemistry by Jochen Vogt

Author:Jochen Vogt
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

(8.15)

different structures. A conventional pocket calculator cannot display this number in the usual way. What we can do is to rewrite this number as follows:

Thus,

(8.16)

An astonishing fact about the molecule is that under cellular conditions the molecule only occurs in a few well-defined conformational structures characterized by a few special sequences out of 6150. For simplicity, we assume that there is only one such functional form of the molecule. If the molecule had to find this unique structure in a random-walk process where each conformational change takes only a few picoseconds, this process would take a very long time. In contrast, real folding times are less than 1 s [2]. This discrepancy is called Levinthal paradox . Moreover, if the folding process were driven by the minimization of the Gibbs free energy Δ G = Δ H − T Δ S of the molecule, then this unique functional form would have to be characterized by a steep minimum in enthalpy that balances the large entropic contribution − T Δ S to Δ G, where Δ S is the conformational entropy. It is our task to calculate this entropy using Boltzmann’s statistical approach to entropy. We assume two macrostates: (1) the functional state, which is realized by W 1 = 1 configuration of the molecule, and (2) the dysfunctional state, realized by all remaining W 2 = N − 1 conformational sequences. As N is so large, we can safely assume W 2 = N. Thus,

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