Concise Physical Chemistry

c08 JWBS043-Rogers September 13, 2010 11:25 Printer Name: Yet to Come

8 A Statistical Approach to Thermodynamics

In the late nineteenth century, Ludwig Boltzmann made the connection between

Maxwell’s statistical-atomic equations and the deterministic equations of chemical

thermodynamics, which were only emerging at the time of his work. (Gibbs was not

widely read in Europe at that time.) A central concept instatistical thermodynamics,

as we now call the new science, is thepartition function. We shall see the relation

between the partition function and the thermodynamic properties including the Gibbs

free energy and the equilibrium constant. Actual calculation of partition functions

falls anywhere within the range of easy to impossible. We shall calculate some of the

easy ones and approximate some of the others.

8.1 EQUILIBRIUM

If two very simple gaseous systems, A and B, are in equilibrium and each system has

only one energy level as shown in Fig. 8.1, the equilibrium constant isKeq=nB/nA=

3 / 5 = 0 .600. KnowingKeq, we can calculate the energy separation between levels

A and B from theBoltzmann equation:

Keq=e−(εB−εA)/kBT

For example, at 298 K, in Fig. 8.1,Keq= 0 .600 leads to(εB−εA)= 2. 10 × 10 −^21 J.

Concise Physical Chemistry,by Donald W. Rogers

Copyright©C2011 John Wiley & Sons, Inc.

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