Residual activity coefficient

If one lets af = Xjy then it follows that a[ = y[- Thus, in this treatment the residual activity and residual activity coefficient are the same whether or not one expresses concentration in mole fractions or weight fractions. 

The residual activity coefficient of group k in the given solution is given by the following equation... 

The residual activity coefficient of group k in a reference solution containing only component i, rksimilarly determined using Equations (3C-9) through (3C-11) with the exception that the summation indices k, m, and p refer only to the groups present in the pure component and the summations over each component j are calculated only for the single component present in the reference solution. 

Step 14 Calculate the residual activity coefficient of each group k in the polymer solution, rk, using Equation (3C-9)... 

In Equation (39), Tk is the residual activity coefficient of subgroup k in the mixture and Tk is that value in a pure solution of the component i. This term is added so when the mole fraction approaches unity, the term lnytR tends to zero (y(R -> 1). The residual activity coefficient of subgroup k in a solution is given by... 

Fil is the residual activity coefficient of the functional group in a reference mixture which contains only i molecules. The activity coefficient for the group k in molecule i depends on the molecule i in which the k group is situated. The following relation gives the activity coefficient of each group ... 

The residual activity coefficient contribution for each component is given by... 

The values corresponding to the functional groups will be written with the same letter as the same value in a solution of molecules, but in uppercase. Thus, the coefficient of activity of the group k will be, its volume parameter R, its surface parameter Q., its molar fraction X,.In the energy exponential of relation [3.153], the letter T would be replaced by, its surface fraction 0 would be replaced by 0. . Only the term a in the equivalent relations [3.154] would retain the same notation, a. By transposition of relation [3.163] to the group solution, the residual activity coefficient F. for a group k will be written as ... 

In this e q)ression, is the chemical potential of the group in the group solution studied, and ii is the chemical potential of component in a hypothetical substance in which the component k is pure. Evidently, such a substance can neither be formulated nor conceived. However, we are able to conceive a pure solution of /, considered to be a solution of its groups, in which the group k has a chemical potential and we can write the following for the chemical potentials and the residual activity coefficients ... 

---