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

In this paper, adsorbed-phase heat capacities are determined from thermodynamic relations (M. 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.