Modeling of Adsorption Isotherms of Phenol and Chlorophenols onto Granular Activated Carbon—Part III: Additional Isotherm Formulations and a C50-Normalized Descriptor-Coupled Generalized Model

Related adsorbates are commonly fitted with independent adsorption isotherms, limiting parameter transfer across a chemical family. The equilibrium adsorption of phenol (Ph), 2-chlorophenol (2-CP), 4-chlorophenol (4-CP), 2,4-dichlorophenol (DCP), and 2,4,6-trichlorophenol (TCP) on granular activated carbon (GAC) was re-analyzed to extend the model set evaluated in Parts I and II and to develop a family-level formulation. Five additional equations, Dubinin–Radushkevich (D–R), Flory–Huggins, Harkins–Jura, Halsey, and Henderson, were assessed, primarily by nonlinear regression. D–R gave the best pooled performance among the additional direct isotherm models (RMSE = 7.388 mg/g; APE = 2.718%). The generalized Langmuir/Marczewski–Jaroniec function was then reparameterized exactly using the half-saturation concentration C50. Independent C50 values decreased from 34.118 mg/L for Ph to 0.617 mg/L for TCP and were strongly associated with hydrophobicity. A simultaneous descriptor-coupled model constrained C50 and the low-concentration exponent from molecular hydrophobicity, reducing adjustable parameters from 20 to 14 while retaining high accuracy for 45 measured observations (RMSE = 4.434 mg/g; APE = 1.600%). Descriptor coupling supports compact correlation within the investigated family; reliable prediction for unseen compounds remains unestablished.