A test of the polynomial-fitting method of determining binary-gas-mixture adsorption equilibria

The polynomial-fitting method is used to determine the adsorption isotherms of binary gas mixtures. The method involves measuring retention times in a chromatographic column at different compositions; a polynomial is then fitted to a specific function of the retention time versus composition data. An algebraic expression can be obtained for each isotherm, with the coefficients depending on the polynomial coefficients. In this paper we examine the detailed working of the method assuming perfect experimental data is available. We use hypothetical systems that obey the binary-Langmuir theory. Starting with the hypothetical system, the set of retention times is calculated, and these are used in the polynomial-fitting method to estimate the binary isotherms. Comparison of the original and estimated isotherms allows a direct assessment of the precision of the method. The results show that the method is best suited to systems where both binary isotherms are close to linear.