I have attempted to describe activity coefficients in two-component system, in
a whole concentration range, using
EHL
equations, so supposing the occurrence of two types of solution (substance "2"
in substance "1" and substance "1" in substance "2"). In transition of one
solution in the other point:
![Q21 = [(x2p+R21·x1p)/x2p]·[(R12·x2p)/(x1p+R12·x2p)]^R12; Q12 = [(x1p+R12·x2p)/x1p]·[(R21·x1p)/(x2p+R21·x1p)]^R21, where: x1p = mole fraction of component 2 in the transition point; x2p = mole fraction of component 2 in the transition point. I assume that K1 = 1 and K2 = 1.](grafika/formula5.png)
Assuming a continuity of activity coefficient derivatives we obtain, after transformations:
![x1p = [R12·(1-R21)]/(R12+R21-2·R12·R21); x2p = 1-x1p](grafika/formula6.png)
which leads to a two-parameter description. On the basis of 18 literature collections of activity coefficient data (calculated from full liquid-vapor equilibrium data in two-component systems in which chemical reactions, and/or associations or dissociations do not occur), including at least 20 data in full concentration range (and seeming sufficiently accurate), I have carried out comparison of foregoing equations with two-parameter Wilson equation (considered to be very good in describing nonelectrolite mixtures with complete mixing of components). I have carried out the calculations using least squares method, minimizing sum of activity coefficient square deviations for both components.
The results give marked superiority of Wilson equation, namely standard deviations count on average to:
- for three hydrocarbon mixtures: 0,0010 for Wilson equation and 0,0018 for EHL equations,
- for six halogenated hydrocarbon mixtures: 0,0022 for Wilson equation and 0,0034 for EHL equations,
- for nine remaining systems: 0,0018 for Wilson equation and 0,0029 for EHL equations.
The results for EHL equations do not seem to be bad so much so we do not take advantage from their properties (straight line for solute and practically one parameter for solvent), especially in limited concentration range.
Assuming a continuity of activity coefficient derivatives we obtain, after transformations:
which leads to a two-parameter description. On the basis of 18 literature collections of activity coefficient data (calculated from full liquid-vapor equilibrium data in two-component systems in which chemical reactions, and/or associations or dissociations do not occur), including at least 20 data in full concentration range (and seeming sufficiently accurate), I have carried out comparison of foregoing equations with two-parameter Wilson equation (considered to be very good in describing nonelectrolite mixtures with complete mixing of components). I have carried out the calculations using least squares method, minimizing sum of activity coefficient square deviations for both components.
The results give marked superiority of Wilson equation, namely standard deviations count on average to:
- for three hydrocarbon mixtures: 0,0010 for Wilson equation and 0,0018 for EHL equations,
- for six halogenated hydrocarbon mixtures: 0,0022 for Wilson equation and 0,0034 for EHL equations,
- for nine remaining systems: 0,0018 for Wilson equation and 0,0029 for EHL equations.
The results for EHL equations do not seem to be bad so much so we do not take advantage from their properties (straight line for solute and practically one parameter for solvent), especially in limited concentration range.
Jump to: Top