error functions

Heavy metals are considered as one of the important factors threatening water quality in many areas, so they have attracted the attention of many researchers. In this research, the temporal variations of arsenic removal from aqueous solution were investigated using a photocatalytic-adsorbent composite TiO2-Fe2O3 for 360 minutes. Then the capability of linear and nonlinear models of Pseudo-first-order, Pseudo-second-order, Elovich, and power was evaluated in describing the kinetic process.

To determine the kinetics of arsenic adsorption from aqueous solution by TiO2-Fe2O3 composite, batch adsorption experiments were performed at pH 7, initial concentration of 40 mg/L, and adsorbent dose of 1 g/L. After linear and nonlinear fitting of the kinetic models on the adsorption data and finding the constants of each model, the adsorption amount was calculated at different times and compared with the values measured in the laboratory.

The results showed that the amount of adsorption increased with increasing time, and the concentration of arsenic reached equilibrium in 25 minutes. Considering the values of error functions in linear fitting, it was observed that the Pseudo-second-order equation with the lowest errors and the highest coefficient of determination (99.92%) was better agreed to the laboratory data. After this model, the Pseudo-first-order equation performed better, and the weakest simulation was for the Elovich model. In nonlinear analysis, the coefficients of determination of all models were high and very close to each other, so according to the values of error functions, the Elovich model had the lowest error value, which indicates the best fit on the kinetic data. Afterward, power, Pseudo-second order, and Pseudo-first order models had the best fit on the kinetic absorption data, respectively.

Comparison of models up to 360 minutes using the coefficient of determination and error functions (R-squared, root-mean-square error, sum of squares error, sum of absolute errors, absolute relative error, HYBRID, Marquardt’s percentage standard deviation), showed that the use of linear shape can lead to a completely different result and interpretation than the nonlinear shape of the model. So that based on linear methods, Pseudo -second-order model and based on nonlinear methods, the Elovich model had the best fit on kinetic data. Nonlinear fits of kinetic models were also superior to linear forms. In general, the results showed that TiO2-Fe2O3 composite has a high potential for arsenic removal from an aqueous solution.