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

Abstract

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

Activity coefficients of hydrocarbon solutes at infinite dilution in 1,4-dicyanobutane from gas liquid chromatography

“…Everett and Cruickshank et al (3,5) developed the following equation for obtaining the activity coefficient at infinite dilution, γ ∞ 13 , for a volatile solute (1), in an involatile solvent (3), from g.l.c. : (1) where V N denotes the net solute retention volume, p o the outlet pressure which is equal to the atmospheric pressure, J 3 2 p o is the mean column pressure, n 3 is the number of moles of solvent in the column at temperature T , p * 1 is the vapour pressure of the solute (determined by using Antoine equation (6) ), B 11 is the second virial coefficient of the pure solute, V * 1 is the molar volume of the solute, V ∞ 1 is the partial molar volume of the solute at infinite dilution in the solvent, and B 12 is the cross second virial coefficient of the solute and the carrier gas.…”

Activity coefficients of hydrocarbon solutes at infinite dilution in monoethanolamine from gas–liquid chromatography

“…Everett (3) and Cruikshank et al (5) developed the following equation for obtaining the activity coefficients at infinite dilution γ ∞ 13 for a volatile solute (1), in an involatile solvent (3), from g.l.c. : (1) where V N denotes the net solute retention volume, p o the outlet pressure and is equal to atmospheric pressure, J 3 2 p o is the mean column pressure, n 3 the amount of solvent on the column at temperature T , p * 1 is the vapour pressure of the solute determined according to the Antoine equation, (6) B 11 the second virial coefficient of the pure solute, v * 1 the molar volume of the solute, v ∞ 1 the partial molar volume of the solute at infinite dilution in the solvent (here equated to v * 1 ), and B 12 the mixed second virial coefficient of the solute (1) and the carrier gas (2).…”

Note on the Net Retention Volume in Chromatography with a Real Gas as a Carrier

“…It will be seen later on that this is not the case. Cruickshank, Windsor, and Young [4] Ref 4). In frequently cited handbooks [5,6] it is proposed to consider the retention volume calculated with the compressibility correction given by James and Martin [7] for an ideal gas carrier Although this proposal is supported by two groups of experts [8,9] it is obviously inadmissible.…”

“…The thermodynamic interpretation [1,2,4] of the pressure coefficient of the capacity factor, j su , is outside the scope of this note.…”