Using Surrogate Equilibrium Constants for Assessing the Energy of Adsorption of Synthetic Organic Substances from Aqueous Phase onto Carbonized Adsorbents

We proposed to evaluate the performance of new adsorption materials in relation to existing commercial products by comparing the values of the standard molar adsorption energy of \(\Delta G_{{\text{a}}}^{^\circ }\) of adsorbates. A typical error in the determination of \(\Delta G_{{\text{a}}}^{^\circ }\) is due to the incorrect calculation of the adsorption equilibrium constant K_e. It is often calculated in isothermal regions that do not correspond to standard adsorption conditions, or the dimensional constant of the Langmuir model equation K_L is falsely used as a thermodynamic constant. The direct use of the Langmuir constant K_L as an equilibrium constant is a thermodynamically invalid approach; however, due to the simplicity of determining K_L, an estimate of the adsorption energy based on it can become an accessible and useful tool for adsorption studies. In this work, we examined two methods to transform the Langmuir constant into surrogate constants, which, according to formal features, are dimensionless quantities and reflect the conditional energy of adsorption. We selected 16 adsorption systems of activated carbon (F300, KAU, KAU/Fe, Akant) with aqueous solutions of sparingly soluble aromatic compounds of the phenol and aniline series. We compared the adsorption energy values obtained from the Langmuir constant and the thermodynamically verified constant of the partial adsorption isotherm, calculated by the procedure developed by A.M. Koganovskii (the Koganovskii method, KM). The deviations of the adsorption energy values calculated from the Langmuir constant are on average 10–15% compared to the results obtained by the Koganovskii method. To plot the adsorption isotherms of aromatic compounds, a simplified algorithm for calculating K_e according to the KM was proposed and tested (without considering the volume of the adsorption phase and the molar volume of adsorbents). Deviations in energy values were within 5% of the KM results. Thus, the considered simplified methods are easy to implement and accurate enough to estimate the standard adsorption energy; therefore, they can be recommended for the initial assessment of the effectiveness of new adsorption materials.