Virial Coefficient B2 Research Articles

Gas-liquid chromatographic determination of cross-term second virial coefficients using glycerol. Benzene + nitrogen and benzene + carbon dioxide at 50°C

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 B12 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 solute-in-solvent activity coefficient and of B12. 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 B12 values are effectively the same with all columns. These values of B12 at 50°C are, for benzene + nitrogen, –98 ± 9 cm3 mole–1, and for benzene + carbon dioxide, –250 ± 15 cm3 mole–1, 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 logγ∞13= 2.084 ± 0.005.

Thermodynamics of mixtures from gas chromatography. The activity coefficients of hydrocarbon solutions and the second virial coefficients of hydrocarbon vapour and permanent gas mixtures

This paper reports work designed to establish the reliability of the gas chromatographic method for the determination of the mixed second virial coefficients B12 of mixtures of hydrocarbon vapours and permanent gases, and of activity coefficients γ∞1 at infinite dilution in hydrocarbon liquid mixtures. This work confirms for eight carrier gases that, except for CO and methane, the activity coefficients are independent of carrier gas employed to within about ±0.003 in log10γ. The values of B12, determined with three stationary phases, agree to within about ± 10 cm3 mole–1; in five cases comparison was possible with values of B12 obtained by independent experimental methods and agreement within the above limits was found. The B12 values determined in this and earlier work are correlated using the principle of corresponding states. The Hudson and McCoubrey rule for the estimation of the mixed critical temperature gives values of B12 in closer agreement with experiment than the geometric mean rule. The former procedure gives excellent agreement over a wide range of temperature for the system benzene + N2, but predicts values which are somewhat too high for longer chain n-alkanes. The activity coefficients at infinite dilution have been used to evaluate the interaction parameter χ of the Flory-Huggins theory : values of χ for aliphatic + aliphatic, aromatic + aromatic and aliphatic + aromatic systems are compared.

The phase and volumetric relations in the helium—n‐butane system: Part II. Second virial coefficients for helium—n‐butane mixtures

AbstractThe second virial coefficients of pure n‐butane and of two mixtures of helium and n‐butane were determined in the range 100° to 225°C. from isothermal compressibility measurements. Values of B11 (pure n‐butane) agree closely with those of McGlashan and Potter (11) at low temperatures and of Hirschfelder et al. (7) at higher temperatures. Values of the mixed second virial coefficient B12 were computed from the mixture data. B12 shows little variation with temperature over this interval. The interpretation of the data as the behavior of a mixture composed of hard sphere (helium) in a real gas (n‐butane) is discussed.

Prediction of second virial coefficients of mixtures from the principle of corresponding states

Values of the mixed virial coefficients B12 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.