$11\mathrm{.}5.$ The NRTL model for the excess Gibbs energy of mixing in a binary solution $[$H$.$ Renon

and J$.$M$.$ Prausnitz $(1968),$ AIChE J$.,14,$ p $135]$ is

$\frac{G^{Ex}}{RT}=x_1{x}_2(\frac{{}_{21}{G}_{21}}{x_1+x_2{G}_{21}}+\frac{{}_{12}{G}_{12}}{x_2+x_1{G}_{12}})$

where $x_1$ and $x_2$ are the liquid mole fractions of $1$ and $2,{}_{12}$ and ${}_{21}$ are binary parameters,

and $G_{12}=$exp$(-{}_{12}),G_{21}=$exp$(-{}_{21})*$ is a third parameter for the mixture. Let

$x_1=x_2$ and choose a symmetric mixture where ${}_{21}={}_{12}.$ What is the largest value of $$

that can be used for this correlation if it is to show phase splitting? What happens if the

mixture is not equimolar?