Isotherms for Sorption of Dye: A Comparison of Linear and Non-linear Methods Sing-On Teng#, Wen-Ta Chiu and Yuh-Shan Ho* Taipei Medical University - Wan-Fang Hospital Introduction Equilibrium studies in adsorption give the capacity of the adsorbent for an adsorbate. Equilibrium relationships between adsorbent and adsorbate are described by adsorption isotherms. Isotherms can be obtained by batch reaction at various pH values, temperature, and they vary with the adsorbent type, the adsorbate type and other parameters of the adsorption processes. In this study, a comparison of linear least-squares method and non-linear method of three widely used isotherms, Langmuir, Freundlich, and Redlich-Peterson, were examined to the experiment of Methylene blue adsorption on activated carbon. A trial and error procedure was used for non-linear method by using the solver add-in with Microsoft’s spreadsheet, Microsoft Excel. Methods Batch adsorption studies were carried out by contacting 0.01 g of activated carbon with 50 ml of dye solution of known initial dye concentration in 125 ml capped conical flasks. The contact was made using water bath shakers at a constant agitation speed of 95 strokes with a stroke length of 1.5 cm at four different solution temperatures 32C, 40C, 50C, and 60C. After 48 h, the dye solutions were separated from the adsorbent by centrifugation. The left out concentration in the supernatant solution was analyzed using a UV Spectrophotometer. Table 3. Isotherm parameters obtained by using non-linear method Results Table 1. Isotherms and their linear forms Table 2. Isotherm parameters obtained by using linear method Figure 1. Isotherms obtained by using linear method for the adsorption of Methylene blue using activated carbon at temperature 323 K Figure 2. Isotherms obtained by using non-linear method for the adsorption of Methylene blue using activated carbon at temperature 305 K Conclusion It is not appropriate to use the coefficient of determination of linear regression method for comparing the best-fitting of isotherms. Non-linear method could be a better way to obtain the isotherm parameters. Langmuir is a special case of Redlich-Peterson isotherm when constant g was unity. Both two-parameter Langmuir and three-parameter Redlich-Peterson isotherms were the best-fitting models for the adsorption of Methylene blue on activated carbon.