This paper extends the theory of gas-chromatographic elution of a highly dilute solute to the second order in gas-phase imperfection terms, yielding a precise expression for the ideal retention volume in terms of the thermodynamic parameters of the system. The effect of carrier gas dissolution in the solvent is included explicitly ; the cross-term second virial coefficient Bl for the system solute+ carrier gas cannot be evaluated unambiguously for an appreciably soluble carrier gas. The use in such cases of polar solvents in which non-polar carrier gases are effectively insoluble is discussed with reference to surface adsorption and chromatographic non-ideality, which are important in polar solvents. Extrapolation of observed retention volume to zero flowrate for each of a series of columns covering a range of solvent loadings should give, corresponding to the limit of infinite loading, unambiguous values of bulk-phase solutein-solvent activity coefficient and of B1 2. The theory has been applied to measurements on the systems benzene+nitrogen+glycerol, and benzene+ carbon dioxide+glycerol, using four columns loaded at 15-7,25.3,33*6 and 23-3 % by weight glycerol on Celite, and the system benzene+hydrogen+glycerol using a column loaded at 44.0 %. The flowrate-dependence of the net retention volume is approximately linear on all columns, the gradient correlating well with empirical plate height and with solvent loading, in accordance with theory and with the known facts about the distribution of a polar solvent on Celite. The zero-flowrate Biz values are effectively the same with all columns. These values of Blz at 50°C are, for benzene+ nitrogen, -98f9 cm3 mole-l, and for benzene+carbon dioxide, -2503~15 cm3 mole-l, both being in fair agreement with theoretical predictions for systems of non-spherical molecules of different sizes. The activity coefficient for benzene at infinite dilution in glycerol at 50°C is logy: = 2.0841 0 0 0 5 .

Values of the mixed virial coefficients Bla are predicted for twenty-eight mixtures where experimental values have been reported. McGlashan and Potter's reduced equation of state is used to calculate corresponding states values, Hudson and McCoubrey's combining rules being used for the mixed critical temperatures. A comparison is made between the experimental and predicted values, using both the Hudson and McCoubrey combining rule and the geometric mean rule for the critical temperatures. In the first six mixtures examined, which are a particularly good test of the procedure (because of differences in ionization potential and size of the two components), agreement is often obtained within the experimental error. In the case of the other twenty-two mixtures, sixteen are better represented by the new procedure.The equation of state for any gas may be written in the formwhere v is the molar volume, p is the pressure, T is the temperature and B, C, . . ., etc., are the second, third, . . ., etc., virial coefficients. These virial coefficients are temperature dependent. It can be shown that the second virial coefficient B characterizes interactions between pairs of molecules. When applied to a mixture of gases, the equation of state is written where the subscript rn refers to the mixture. The second virial coefficient of a binary gas mixture BTn is related to the composition of the mixture by where XI is the mole fraction of component 1, BIl and B22 are the second virial coefficients of the pure components and B12 is a " mixed " second virial coefficient which characterizes interactions between pairs of unlike molecules. There are now available quite a large number of experimental results for mixed virial coefficients and our aim in this paper is to examine how closely these experimental results may be predicted by use of the principle of corresponding states. The most recent corresponding states equation for second virial coefficients is that of McGlashan and Potter 1 which has been shown to apply to a wide range of hydrocarbons and permanent gases. Their equation, for the second virial coefficient of a pure substance, is pv,/WT = 1 + B,/u,, + C,/ui + . . ., (2) B, = x?B, 1 + 2x,(1-x)B,, + (1 -x)2B,,,B / V c = 0~430-0~886(TC/T)-0~694(T"/T)2-0-0375(n-l)(Tc/T)4'5, (4) where Tc and Vc are the critical temperature and critical volume of the pure substance. For permanent gases, n = 1 and the last term in eqn. (4) becomes zero, for n-alkanes and n-alkenes 2 n is equal to the number of carbon atoms in the molecule (n may sometimes be estimated for other substances).3 In order to make

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Activity coefficients at effectively infinite dilution yF3 of various hydrocarbons in n-octadecane at 35°C have been derived from gas-liquid chromatographic retention volume data extrapolated to zero gas pressure. The carrier gas was in most cases nitrogen, or occasionally argon; but three n-alk-1-enes were examined with hydrogen, nitrogen and argon to give a consistency check; the log yF3 values from the three carrier gases agree within 0-002. " Mixed " second virial coefficients B1 have been calculated for every hydrocarbonScarrier gas system. The activity coefficients are discussed in terms of the separability of the configurational (entropy of mixing) part and the interactional (energy of mixing) part. The energy of mixing part is analyzed in terms of the Hildebrand-Scatchard solubility parameter; the alkane systems are analyzed also by considering different types of contact points; and finally thc n-alkane systems are re-analyzed in terms of interactions between " end groups " and " middle groups ". The last analysis is marginally the most successful. The mixed second virial coefficients arecompared with the values predicted by the principle of corresponding states, using the Hudson-McCoubrey combining rule to estimate the mixed pseudo-critical temperatures, together with the McGlashan-Potter reduced equation of state. The agreement is in most cases within the experimental uncertainty. Other combining rules are less successful.

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 ° N is simply related to the thermodynamic activity coefficient of the solute (1) in the stationary liquid (3) and the gradient β 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 ° N and B 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 ° N originally specified over a wide range of flow conditions, even when the carrier gas shows large deviations from ideality. In the case of β , 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.