Adsorbed-Phase Heat Capacities: Thermodynamically Consistent Values Determined from Temperature-Dependent Equilibrium Models

Abstract

In this paper, adsorbed-phase heat capacities are determined from thermodynamic relations (Ind. Eng. Chem. Res. 2003, 42, 6938−6948; J. Phys. Chem. 1999, 103, 2467−2479) applied to temperature-dependent adsorption equilibrium models and are shown to vary widely depending on the equation used. Two common gas adsorption models, the Langmuir and Dubinin−Astakov (D−A) equations, are used to determine thermodynamically consistent heat capacities. The common temperature-dependent Langmuir equation results in an adsorbed-phase heat capacity that is equal to the gas-phase heat capacity, while the original kinetic theory derivation of Langmuir (J. Am. Chem. Soc. 1918, 40, 1361−1403) gives a value less than the gas-phase value by a constant amount. The D−A equation as modified by Ye et al. (Carbon 2003, 41, 681−686) leads to an adsorbed-phase heat capacity that is equal to the liquid-phase heat capacity. We also determine adsorbed-phase heat capacities from the standard Dubinin−Radushkevich equation in which the adsorbed-phase molar volume is set equal to that of liquid at the adsorption temperature. This analysis shows that, for n-hexane on BPL carbon, the isosteric heat and adsorbed-phase heat capacity behave unrealistically at high loadings; the heat capacity can become negative with increasing temperature, indicating a deficiency in this adsorption equilibrium model.