No abstract

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

The classical mathematical description of critical points of binary mixtures and the computer technique used to solve the relevant equations are described. The techniques used here are applicable to any closed equation of state and one fluid model prescription.The critical points, in a given range of temperature and volume are located as the solution of two simultaneous equations :( ~P / ~u ) T , x (a2G/a&,p = 0 ( Z P / ~U ) T , X (a3G/ax9h,p = 0 with reduced volume 8 and reduced temperature f as independent variables. The search procedure

This review is part 10 of a series of contributions by the critical properties group of the previous IUPAC Commission I.2 on Thermodynamics, Subcommittee on Thermodynamic Data and the present IUPAC Project #2000-026-1-100, Critical Compilation of Vapour Liquid Critical Properties, sponsored by the Physical and Biophysical Chemistry Division. It presents all known experimental data for the critical constants of hydrocarbons containing halogens. Recommendations are given together with uncertainties. Critical temperatures have been converted to ITS-90, and the molar masses are based on the relative atomic masses recommended by the IUPAC-CIAAW in 2005.