A Classical and Quantum Chemical Analysis of Gaseous Heat Capacity

Physical chemistry is considered to be a scientifically abstract and mathematically intensive course in the undergraduate chemistry curriculum. To most students, the physical chemistry course involves a semester that deals with macroscopic properties and another that deals with microscopic evaluations of chemical systems. They often fail to see the importance of statistical mechanics in making the connection between the content of the two semesters. In this paper, we propose a computational exercise that complements a simple physical chemistry experiment that can be used to understand the chemical basis of a macroscopic property such as the heat capacity of gases using microscopic (classical and quantum) mechanics. Students are given the opportunity to use (1) computational chemistry software to calculate the contributions of translational, rotational, and vibrational motion to the energy of molecules; (2) a graphing program to study the linear and nonlinear dependence of energy on temperature; (3) classical, quantum, and statistical mechanical theory to verify experimental data; (4) regression analysis to approximate the heat capacity constant of simple gases from energy calculations.