Page 187 - Chemical equilibria Volume 4

Appendix 2

Recap of statistical thermodynamics

The aim of this appendix is to recap, but not demonstrate, certain results
in the field of statistical thermodynamics, which are used in this fourth
volume in this series. These concepts are presented in detail and
demonstrated in the first volume: Phase Modeling Tools: Applications to
Gases [SOU 15b].
We know that in the microscopic approach to a phase, we consider that
phase to be a collection of molecule-objects whose energies are distributed
in accordance with a statistical law. The state of a collection of molecule-
objects changes constantly, but over time, the collection reaches a certain
type of distribution in which the molecule-objects may be found in different
states. The term number of complexions denotes the number of distributions
of molecule-objects between the different states they are liable to occupy.
Out of all the possible distributions, there is one which corresponds to the
maximum number of complexions. Boltzmann’s law allows that the number
of complexions corresponding to the most probable type of distribution is
practically equal to the total number of complexions, and vice versa. The
state of the collection is then that which corresponds to the maximum
number of complexions.

Most calculations in statistical thermodynamics are based on Stirling’s
approximation, which enables us to simplify the expression of the factorial
logarithm n if the number n is large. It is written:

≅
−
ln ! n ln n n ≅ n ln n [A2.1]
n

Chemical Equilibria, First Edition. Michel Soustelle.
© ISTE Ltd 2015. Published by ISTE Ltd and John Wiley & Sons, Inc.