A simplified modeling procedure for adsorption at varying pH conditions using the modified Langmuir–Freundlich isotherm

Analytical isotherm models such as Langmuir isotherm, Freundlich isotherm, and other linear isotherms are commonly used for modeling adsorption datasets for a wide range of adsorption studies. Most of these studies consider pH to be fixed. However, pH is an important parameter that varies widely. Hence, the model parameters developed for one set of experiments cannot be used in another scenario where the pH is different. Surface complexation models that can simulate pH changes are complex, multi-parameter models that are difficult to use. The modified Langmuir–Freundlich (MLF) isotherm developed earlier by us could simulate pH-dependent adsorption on goethite-coated sands. However, it has only been tested for arsenic adsorption on goethite-coated sands. Therefore, chromium adsorption datasets were considered to extend this MLF isotherm for other metal ions. Two different adsorbents, viz. coconut root activated carbon (CoAC) and palm male flower activated carbon (PaAC), were selected for the adsorption modeling of Cr(VI) using the MLF isotherm model. An improved modeling strategy was developed for fitting the MLF isotherm, which required only a single pH versus adsorption dataset, instead of several isotherms at different pH values. The new methodology could simulate the pH-dependent adsorption satisfactorily for various experimental datasets. The maximum adsorption capacity was 88.64 (mg/g) and 100.1 (mg/g) for PaAC and CoAC, respectively. The affinity constant for this model (K_a) was found to be 0.007 (L/mg) for PaAC dataset and 0.0106(L/mg) and 0.004 (L/mg) for the CoAC dataset. The average R² values of fitting were calculated and found to be 0.98 for PaAC and 0.85 for CoAC. The average root mean square error (RSME) of the fitting of the model was 0.07 (less than 10%). This modeling strategy required less experimental data and did not require advanced characterization studies. Therefore, this study indicates that the MLF isotherm can be extended to other contaminants and for different adsorbents to model the pH-dependent adsorption.