as mentioned in the following table, how do I arrange those kinetic models for five soils based on the highest determination coefficient( R2) and the lowest root mean square error (RMSE) please?
You can subject your data of the models equation to regression analysis using statistical softwares such as XLSTAT. Based on the obtained statistical values of R2, adjusted R2, MSE, RMSE and AIC, you can justify the fitting of your models. Usually lower RMSE and AIC signifies the best fitting.
Since you have done the regression, you can arrange the finding from the model with the lowest RMSE and AIC to the most highest values. That is the simplest justification you can make. Good luck.
Kamal Hama Karim, It's best to start with the physics of the process. Presumably it is about adsorption. It's good if you also include kinetic data along with the adjustments. Information about the numerical methods used would also be useful. On the basis of the attached data, no reliable differentiation between the individual functions is possible.