Adsorption of C1−C7 Normal Alkanes on BAX-Activated Carbon. 2. Statistically Optimized Approach for Deriving Thermodynamic Properties from the Adsorption Isotherm

A new stepwise (SW) statistically optimized model and also a virial-type (VT) model were correlated successfully with adsorption equilibria for the n-alkane series C1−C7 on Westvaco BAX-1100 activated carbon over a wide range of temperatures and pressures. Both models predicted reasonable temperature-dependent isosteric heats of adsorption, and from these slight dependencies, sensible deviations between the adsorbed- and gas-phase heat capacities were indicated. However, the SW model was more reliable under extreme conditions. The SW model also showed that the observed linear dependence of ln(P) on 1/T at constant loading, according to the Clausius−Clapeyron equation, only occasionally contributed to the overall description; statistically, more complicated temperature dependencies of ln(P) were revealed, indicating that the temperature dependence of the isosteric heat of adsorption can be easily overlooked. The ideal-gas assumption, inherent in the Clausius−Clapeyron equation, was also relaxed. The resulting real-gas isosteric heats of adsorption were reduced compared to the ideal-gas values, especially at high loadings and high temperatures. Finally, the temperature-independent isosteric heats of adsorption predicted from the potential theory correlation developed in Part 1 of this series fell almost in the exact middle of the range predicted by the temperature-dependent SW and VT models for the lightly to moderately adsorbed alkanes, but severely underpredicted those for the heavily adsorbed alkanes (i.e., heavier than n-propane).