Excess Gibbs energy equivalent

Equation 9.9-3 does not give values tor the mixture parameters a and b separately, but only for their sum. A second equation comes from requiring that the excess Gibbs energy predicted from an equation of state at liquidlike densities be equivalent to that from excess Gibbs energy or activity coefficient models discussed in Secs. 9.5 and 9.6. Since, from an equation of state, as F —> oo, V b and Ymix mix. so that liquid densities are obtained, the second equation that is used is... 

So there is complete equivalence between the use of the activity coefficient and the excess Gibbs energy. In a sense there is hardly any difference at all. If the correction for nonideality is in a logarithmic form (7 Tin 7) it can be combined with the ideal term (RT In x) as a correction to x. If it does not have a logarithmic form (wx ) it becomes a correction to the AG or A/i term. 

Relation [A 1.33] forms the link between the description of the solutions by the Lewis activity coefficients method, and that by die excess Gibbs energy. The two methods, therefore, are equivalent. 

The relation [3.87] hnks the solutions described by the Lewis method of coefficients of activity and the excess Gibbs energy method. Both methods are therefore equivalent. 

We have seen two equivalent methods to charaeterize the imperfection of a solution via the eoeffieienls of activity and the excess Gibbs energy. On rare occasions, we find other methods we will briefly describe two of them in this section. 

Still with the aim of having mathematical expressions for the representation of the solution, Redlich and Kister offered a representation that provides an expansion of the excess Gibbs energy, a pure-substance reference in the same state of segregation as the solution (reference (I)), the equivalent of ihe Margules expansion for the activity coefficients. For a two-component solution, the pol5momial expansion up to order m is written ... 

According to Eq. (5.70) 7 can be only identified with the surface-related excess Gibbs energy (G /a) if we ignore effects caused by changes in the mole number at the cost of the bulk composition. The validity of Eq. (5.70) is equivalent to the... 

Many mixtures of interest in the chemical indu.stry exhibit strong nonidealities that can not be described by the EOS with any form of the van der Waals mixing rules. Mixing rules that combine equations of state with liquid excess Gibbs free-energy (or, equivalently, activity coefficient) models are more suitable for the thermodynamic... 

Clearly these two forms are ultimately equivalent via a simple expression, whieh we will estabhsh later (expression [3.83]), which links the activity coefficients of different components of the solution and their excess partial molar Gibbs energies. 

The most explicit recognition of macromolecular energies as surface energies of solvent excess or deficit is in the work of Blank (28, 29), who showed the essential equivalence of Gibbs adsorption isotherms and the changes in the energy of alternate protein states. 

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