Regular solution theory

The regular solution describes a method for assessing the activity coefficient ( ) in mixtures whose behavior only slightly from the Raoult's law differs. Such solutions are called regular in this model . ${\displaystyle \gamma }$

Determining equations

The following applies to a binary mixture

${\displaystyle R\ T\ ln\ \gamma _{1}=V_{1}^{L}\phi _{2}^{2}\left(\delta _{1}-\delta _{2}\right)^{2}}$

${\displaystyle R\ T\ ln\ \gamma _{2}=V_{2}^{L}\phi _{1}^{2}\left(\delta _{1}-\delta _{2}\right)^{2}}$

With

Activity coefficients
${\displaystyle \gamma _{1},\gamma _{2}\ }$

Volumes of pure liquids
${\displaystyle V_{1}^{L},V_{2}^{L}\ }$

Volume fraction
${\displaystyle \phi _{1}={\frac {x_{1}V_{1}^{L}}{x_{1}V_{1}^{L}+x_{2}V_{2}^{L}}},\ \phi _{2}={\frac {x_{2}V_{2}^{L}}{x_{1}V_{1}^{L}+x_{2}V_{2}^{L}}}}$

Solubility parameters
${\displaystyle \delta _{1}=\left(c_{11}\right)^{1/2},\ \delta _{2}=\left(c_{22}\right)^{1/2}}$

${\displaystyle c_{11}={\frac {\Delta U_{1}}{V_{1}^{L}}},\ c_{22}={\frac {\Delta U_{2}}{V_{2}^{L}}}}$

${\displaystyle \Delta U\approx \Delta H_{v}-RT}$

${\displaystyle T\ }$ temperature

${\displaystyle R\ }$ Gas constant

${\displaystyle \Delta H_{v}\ }$ Enthalpy of evaporation

Summary

With the regular solution theory, the activity coefficients of the components of a mixture can be determined solely from the easily accessible pure substance properties, the enthalpy of vaporization and the solution volume. It should be noted that a number of simplifications and assumptions severely limit the quality of the forecast.

literature

1. ↑ Hildebrand JH, "Solubility. XII. Regular Solutions", J.Am.Chem.Soc., 51, pp. 66-80, 1929
2. ^ Reid RC, Prausnitz JM, Poling BE, "The Properties of Gases and Liquids", 4th edition, McGraw-Hill, 1988