Understanding Entropy with the Boltzmann Formula

We show how a chemical reaction can be used to suggest the relation between spontaneity and growth of the number of microstates for an isolated system (Boltzmann’s principle) and to motivate the interpretation of entropy via the Boltzmann formula in a chemically relevant way. Using elementary arguments, we obtain an explicit expression for the entropy of a real chemical system as a function of the extent of reaction for a progressing chemical reaction taking place in solution. Enlightened by the insight provided by the chemical-reaction example, we explain how the Boltzmann formula can more generally play a valuable role in classical thermodynamics as a tool to understand the concepts and relations. We use it to explain the peculiar thermodynamic definition of entropy and concepts like temperature and pressure in mechanical terms, thus, connecting the statistical and thermodynamic descriptions.