Molar entropies from spectroscopic measurements

Statistical mechanical theory applied to spectroscopic measurements provides an accurate means of evaluating the molar entropy of a pure ideal gas from experimental molecular properties. This is often the preferred method of evaluating Sm for a gas. The zero of entropy is the same as the practical entropy scale—that is, isotope mixing and nuclear spin interactions are ignored. Intermolecular interactions are also ignored, which is why the results apply only to an ideal gas. 

The statistical mechanics formula writes the molar entropy as the sum of a translational contribution and an internal contribution 5m = 5m,trans + 5m,int- The translational contribution is given by the Sackur-Tetrode equation  

Here h is the Planck constant and Na is the Avogadro constant. The internal contribution is given by 

, is the energy of a molecular quantum state relative to the lowest energy level, k is the Boltzmann constant, and the sum is over the quantum states of one molecule with appropriate averaging for natural isotopic abundance. The experimental data needed to evaluate int consist of the energies of low-lying electronic energy levels, values of electronic degeneracies, fundamental vibrational frequencies, rotational constants, and other spectroscopic parameters. 

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