Calculation of Entropy for a Two-Dimensional (2D) Ideal Gas with a Statistical Thermodynamic Method

Predicting adsorbate entropy is an essential prerequisite for surface science, heterogeneous catalysis, and microkinetic modeling. The linear correlation between adsorbate and gas-phase entropy has been widely found in various experiments, and it is considered as a simple and effective method to predict adsorbate entropy. In this work, the two-dimensional (2D) ideal gas model was used to calculate adsorbate entropy with the statistical thermodynamic method. The rotational entropy was obtained by solving the Schrodinger equation for a two-dimensional rotator. Combining the translational and vibrational entropy, an extended reversible adiabatic equation for 2D ideal gas can be derived, which is identical in form to the three-dimensional (3D) equation. Then the linear correlation between the 2D and 3D entropy can be proved theoretically, and the slope of this linear correlation is the heat capacity ratio. According to the characteristics of vibrational contribution to the heat capacity, the temperature is divided into three ranges, each of which has its own linear correlation. From the statistical thermodynamic computation data of benzene, perfect linear correlations can be fitted, and each slope is much close to the predicted value from our derived equation. The widely used Campbell-Sellers correlation matches our correlation in the low temperature range. We predict that there may be another linear correlation for different molecules in the medium temperature range, which is more appropriate in most heterogeneous catalytic reactions.