Entropy Explained: The Origin of Some Simple Trends

Density functional theory computational methods were used to calculate the entropies of various molecules; computed entropies correlated closely with measured values. For organic systems, an average of 8.4 kcal/mol for the reaction entropy (one particle to two at 298.15 K) was observed; this value is largely determined by translational entropy gain. The average reaction entropy is slightly lower for reactions that produce two linear molecules and up to 4 kcal/mol higher when no linear molecules are produced, due to differences in rotational entropy of the reactants and products. Translational and rotational entropy are generally independent of molecular identity except for increases in mass and generation of additional moments of inertia; vibrational entropy, which is more dependent on the molecule itself, is a small contributor to the nearly constant entropy of reaction. A variety of inorganic and non-hydrocarbon main group reaction entropies were also calculated; there is an increased contribution of vibrational entropy in inorganic molecules with "softer" vibrations. The trends discussed in this paper can serve as a basis for understanding the contributions of different sources of entropy to the overall reaction T Δ S° for students and practicing chemists; the method employed (i.e., using a commercial program to "discover" trends in a thermodynamic property) can serve as an example of discovery-based learning in the curriculum.