1. Chi-Square Test Evaluation on Sorption Isotherms
Chung-Hui Hua*, Chung-Chi Wang and Yuh-Shan Ho#
School of Public Health, Taipei Medical University
Introduction
Three sorption isotherm models, Langmuir (1916), Freundlich (1906) and Redlich-Peterson (1959) have been widely applied and linear regression has been used to determine the most fitted model throughout the years. In this study, the sorption of three basic dyes namely Basic Violet 10, Basic Violet 1 and Basic Green 4 onto sugar cane were studied. Equilibrium isotherms were measured and analyzed using the three isotherms. Linear coefficient of determination and the Chi-square statistic test were used to determine the best-fit isotherm for each system.
Materials and Methods
Raw sugar cane was washed, dried and then screened through a set of sieves to get geometrical size 351 – 589 µm. Basic Violet 10, Basic Violet 1 and Basic Green 4 solution were prepared in distilled water.
50 ml of dye solution with properly ranged concentrations and 0.25 g accurately weighed sugar cane sample were placed in a 125 ml conical flask. A series of such conical flasks was then shaken at a constant speed of 100 rpm in a 25°C water bath for 24 h. Then the sugar cane was separated by centrifugation and the solution was analyzed for the remaining dye concentration by using spectrophotometer.
Table 2. Comparison of linear coefficient of determination, r2, and Chi-square test statistic, 2.
Table 3. Sorption isotherm constants for BV1, BV10 and BG4.
Table 1. Isotherms and their linear forms
Figure 1. Theoretical isotherms and experimental data
Results and Discussion
The advantage of using Chi-square test was comparing all isotherms on the same axial setting. Original idea of Chi-square used in biostatistic was to observe whether the experimental data was related to the theoretical data. Based on this idea, we have calculated the 2 value which is defined as followed:
Conclusion
The results revealed the potential of sugar cane, a waste material, could be a low-cost sorbent.
Chi-square test provided better optimum determination for the three sets of experimental data.
The best fit isotherm was Redlich-Peterson isotherm.
The sorption capacities were: BV1 > BG4 > BV10.
where qe,m equilibrium capacity obtained by calculated from model (mg/g) and qe was the equilibrium capacity (mg/g) from the experimental data. 2 indicated the “closeness” between the experimental data with the various isotherms. As 2 value approaches to 0, the experimental data is behaving more toward that certain isotherm. 2 value showed the relationship between the experimental data and the various isotherms clearly (Table 2). The 2 values suggested that the Redlich-Peterson isotherm provided a good model of the sorption system. Figure 1 showed the isotherm plots and the experimental data for sorption of BG4 on sugar cane. The isotherm constants for the sorption of three basic dyes on sugar cane were obtained by using the method of least squares and shown in Table 3.
References
Langmuir, I. (1916), The constitution and fundamental properties of solids and liquids. Journal of the American Chemical Society, 38,
Freundlich, H.M.F. (1906), Über die adsorption in lösungen. Zeitschrift für Physikalische Chemie, 57,
Redlich, O. and Peterson, D.L. (1959), A useful adsorption isotherm. Journal of Physical Chemistry, 63, 1024.