Comparison of linearization methods for modeling the Langmuir adsorption isotherm

The Langmuir isotherm model is widely used for modeling adsorption equilibrium data. The linearization method is mostly applied for estimations of the Langmuir parameters. However, it is not unified and requires further study. In this paper, the applicability and accuracy of four linearization methods of the Langmuir isotherm (equilibrium adsorbate concentration ( C e )/equilibrium adsorption capacity ( q e )- C e , 1/ q e -1/ C e , q e - q e / C e and q e / C e - q e ) in parameter estimations by linear least squares regression (LSR) were compared. The influence of linearization on the assumption about errors in the LSR variables was analyzed. The results showed that Langmuir-1 ( C e / q e - C e ) and Langmuir-4 ( q e / C e - q e ) followed the assumption for all evaluated conditions whereas Langmuir-3 ( q e - q e / C e ) violated the assumption for all conditions. Langmuir-2 (1/ q e -1/ C e ) obeyed the assumption of LSR only when C e approached the initial adsorbate concentration ( C 0 ). Langmuir-1 ( C e / q e - C e ) provided the most accurate estimations of the Langmuir parameters, particularly at low levels of random errors in C e and when the errors (%) in estimated maximum adsorption capacity ( q m ) and constant ( K a ) ranged from −5% to 5% and from −15% to 15% at low levels of errors (−0.5–0.5 mg/L), respectively. The Langmuir-1 isotherm model adequately represented the experimental equilibrium data of sulfamethoxazole (SMX) onto activated carbon with an R 2 value of 0.96.