18
T
HE PREVIOUS CHAPTER INTRODUCED some of the basic concepts
that led to the development of a statistical approach to energy and en-
tropy. This is statistical thermodynamics. By the end of the chapter, equations
were applied to monatomic gases, and thermodynamic state functions—mostly
entropy—were calculated whose values were very close to experimental values.
Also, in some of the exercises you were asked to derive some simple expres-
sions that were also derived from phenomenological thermodynamics. For
example, we know from early chapters in this book that the equation S
Rln (V 2 /V 1 ) is applicable for an isothermal change in volume of an ideal gas.
We can also get this expression using the Sackur-Tetrode statistical thermo-
dynamic expression for S. These correspondences are just two examples where
phenomenological and statistical thermodynamics are consistent with each
other. That is, they ultimately make the same predictions about the state func-
tions of a system, and how they change with a process.
We will see more examples of such correspondence in the current chapter,
because we are going to expand our application of statistical thermodynamics
to include molecules in the gas phase. (We will still be considering the gas
phase almost exclusively.) Recall that we established the partition function,q,
as a central figure in the equations of statistical thermodynamics. Also, re-
member that qwas originally defined as (and ultimately remains) a summa-
tion of negative exponentials involving the energy levels that the gas particles
of a microstate can occupy. For atomic gas particles, the energy levels were
limited to translational states, since we ignored electronic and nuclear energy
levels. We will consider the latter two in this chapter, and make the case that
in most (but not all) systems, these energy levels contribute little to the over-
all q.
But molecules have other energy states that atoms don’t. They have rota-
tional and vibrational energy states that can have an important impact on q.
Indeed, we found in our discussion of rotational spectroscopy that molecules
occupy excited (that is,J0) rotational energy levels at normal temperatures!
This suggests, correctly, that the existence of such energy levels has an impact
on q, and correspondingly on the thermodynamic properties of molecular
gases.616
18.1 Synopsis
18.2 Separating q: Nuclear
and Electronic
Partition Functions
18.3 Molecules: Electronic
Partition Functions
18.4 Molecules: Vibrations
18.5 Diatomic Molecules:
Rotations
18.6 Polyatomic Molecules:
Rotations
18.7 The Partition Function of
a System
18.8 Thermodynamic Properties
of Molecules from Q
18.9 Equilibria
18.10 Crystals
18.11 Summary