Evaluating Activated Carbon−Water Sorption Coefficients of Organic Compounds Using a Linear Solvation Energy Relationship Approach and Sorbate Chemical Activities

A linear solvation energy relationship (LSER) approach was used to investigate the evolving contributions of intermolecular interactions controlling organic compound sorption by granular activated carbon (GAC) from water as a function of sorbate chemical activities. Using a particular GAC (20−40 mesh Darco), 14 sorption isotherms were measured using sorbates with diverse functional groups to represent the range of possible surface interactions, and the data for each sorbate were fit with the Freundlich equation. Using interpolated adsorption coefficients, Kd values (L/kg), LSERs for specific sorbate activities (0.1, 0.01, and 0.001 saturation) were deduced. These expressions revealed that the intermolecular interactions controlling sorption to our particular GAC from water evolved with sorbate activities, such that a global correlation dependent on sorbate activity was found: log Kd (L/kg) = [(3.76 ± 0.28) − (0.20 ± 0.10) log ai]V + [(−0.80 ± 0.14) − (0.48 ± 0.05) log ai]S + [(−4.47 ± 0.20) + (0.16 ± 0.06) log ai]B + (0.73 ± 0.28) − (0.24 ± 0.09) log ai (N = 176, R2 = 0.96), where log ai is the activity of sorbate i, V is McGowan's characteristic volume for the sorbate, S reflects the compound's polarity/polarizability, and B reflects the compound's electron-donation basicity. Hence, sorption was promoted by dispersive forces and was diminished for sorbates capable of proton acceptance/electron donation, although both of these became less important at higher sorbate activities. Other intermolecular interactions were only weakly contributing (e.g., the "S" term) or were not significant at all for this GAC (i.e., the "R" and "A" terms). This result implies the Freundlich coefficients, Kf, for sorbates are given by (3.76V − 0.80S − 4.47B + 0.73) + (0.20V + 0.48S − 0.16B + 0.24) log Ci,wsatn, and their exponents, 1/n, are equal to −0.20V − 0.48S + 0.16B + 0.76. The data set could also be used to deduce a sorbate concentration-dependent LSER which would be useful for estimating equilibrium sorption coefficients for new sorbates of interest: log Kd (L/kg) = [(1.89 ± 0.07) − (0.22 ± 0.06) log Ci,w]V + [(0.90 ± 0.05) − (0.48 ± 0.03) log Ci,w]S + [(−2.36 ± 0.07) + (0.30 ± 0.05) log Ci,w]B + (2.98 ± 0.07) − (0.26 ± 0.06) log Ci,w (N = 176, R2 = 0.98), where log Ci,w is the concentration in water of each sorbate (mg/L).