The use of gas-liquid chromatography to determine activity coefficients and second virial coefficients of mixtures I. Theory and verification of method of data analysis

Abstract

This paper reformulates the differential equation describing the local elution rate in a g.l.c. column in terms of the local pressure and the carrier gas outlet flow rate. Analytical integration for an ideal carrier gas suggests an accurate method for extrapolating a function of the retention volume linearly to zero pressure, where the intercept V$^0_N$ is simply related to the thermodynamic activity coefficient of the solute (1) in the stationary liquid (3) and the gradient $\beta$ gives B$_{12}$ for the mixture solute + carrier gas (2). We argue that a simple extension of the method should apply also, with fair accuracy, to a non-ideal carrier gas. We support this argument with data obtained by a numerical integration procedure which gives retention volume in terms of specified V$^0_N$ and $\beta$ for a range of inlet and outlet pressures. The reliability of the numerical integration procedure is established by comparing results for the ideal gas case with the results of analytical integration. The retention volumes obtained by numerical integration for a non-ideal carrier gas are then treated as 'experimental' observations, using in addition to our extrapolation procedure, two previously published procedures. Our procedures are consistently more successful than the others and recover accurately the V$^0_N$ originally specified over a wide range of flow conditions, even when the carrier gas shows large deviations from ideality. In the case of $\beta$, our method is significantly in error only when the carrier gas deviates largely from ideality in a low pressure column with large pressure drop. A simple refinement of our method is satisfactory for even this case.