CH353 - Physical Chemistry I
Spring 2013, Unique 52575

Lecture Summary, 3 April 2013

Statistical Thermodynamics: The energy of an individual molecule or atom has 4 contributions: 1) electronic, 2) translational, 3) rotational, and 4) vibrational.  A monatomic species contains the first two of these energies, and a polyatomic species contains all four.  Today we focused exclusively on applying the Boltzmann distribution to a monatomic species, making the additional simplification that the number of energy states available for the system to fill is dominated by translational states, and so we can ignore contributions from electronic energy in our derivation.  We were able to determine an expression for the partition function of this monatomic species, and from there we were able to derive exact expressions for the system's average energy, heat capacity, and pressure.  We were gratified to see that all of these expressions were very familiar.  We have thus seen a few simple examples of how statistical mechanics can start from the energy of an individual atom or molecule (which can be calculated from quantum mechanics) and using an appropriate partition function and the Boltzmann distribution, results in a macroscopic property that results from a collection of atoms or molecules.  Although we have only done this for a simple example, we could derive expressions for any macroscopic property of any system we wish, no matter how complex.