A statistical mechanical perspective on the temperature dependence of the isosteric heat of adsorption and adsorbed phase heat capacity

Statistical mechanical concepts were applied to analyze the temperature dependence of the isosteric heat of adsorption and, consequently, the difference between the adsorbed and gas phase heat capacities for monatomic, diatomic, and linear and nonlinear polyatomic molecules. Expressions were developed at the two extremes of localized and mobile adsorption. Also, the effects of the molecular size and shape on the isosteric heats of adsorption and the dependence on temperature were analyzed. The temperature dependence of the isosteric heat of adsorption was always important, especially for localized adsorption, heavily adsorbed molecules, or relatively low temperatures. At relatively high temperatures, the temperature dependence of the isosteric heat of adsorption became linear with a fixed slope, regardless of the molecular size (for both localized and mobile adsorption) and molecular shape (for mobile adsorption). Depending on the type of molecule and/or temperature, the difference between the adsorbed and gas phase heat capacity could be either negative or positive; and in some cases, significant deviations were exhibited mostly at industrially relevant conditions.