Analysis of the Differences Resulting from the Determination of Langmuir Isotherm Coefficients from Linear and...

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.