โ Scribed by Rogers, Donald W.
No coin nor oath required. For personal study only.
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 in statistical thermodynamics, as we now call the new science, is the partition 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.
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 is K eq = n B /n A = 3/5 = 0.600. Knowing K eq , we can calculate the energy separation between levels A and B from the Boltzmann equation:
For example, at 298 K, in Fig. 8.1, K eq = 0.600 leads to (ฮต B -ฮต A ) = 2.10 ร 10 -21 J.
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