Analysis of the Differences Resulting from the Determination of Langmuir Isotherm Coefficients from Linear and Non-Linear Forms—A Case Study

The sorption process is most commonly described by Langmuir isotherms, which can be calculated from either a non-linear form or various linear forms. Despite the fact that the non-linear model is now preferred, articles using linear models continue to be submitted to journals. On the basis of 68 isotherms, it was found that the linear Hanes-Woolf model (the most commonly used) gives the most similar q_m and K_L values to the non-linear model. The largest differences were obtained by determining the isotherm from the non-linear and linear forms of the Lineweaver-Burk model (this is the model often used by researchers). The evaluation of isotherms should not be performed solely on the basis of the coefficient of determination R², which was intended for linear equations. Statistical measures such as the mean relative error, sum of squares of errors, chi-square statistic, sum of absolute errors, hybrid fractional error function, mean squared error were analysed. On the basis of the coefficient of determination, the Hanes-Woolf linear model was found to best describe the actual results, and on the basis of the other statistical measures, the isotherm determined from the non-linear form was found to be the best fit for the study.