QUESTION $4$

A binary liquid system exhibits LLE at $25C.$ Determine from each of the following sets of miscibility data

estimates for parameters A and $B$ in the $3-$suffix Margules equation at $25C$ using:

a$)$ Equations for $3-$suffix Margules

b$)$ Miscibility limit charts for the $3-$suffix Margules equation

i$),x_1=0\mathrm{.}10,x_1^{**}=0\mathrm{.}90$

ii$)x_1=0\mathrm{.}20,x_1^{**}=0\mathrm{.}90$

iii$),x_1=0\mathrm{.}10,x_1^{**}=0\mathrm{.}80$

$ln(\frac{x_1^{**}}{x_1})=A[x_2^2(1+2(\frac{B}{A}-1)x_1)-(x_2^{**}{)}^2(1+2(\frac{B}{A}-1)x_1^{**})]$

$ln(\frac{1-x_1^{**}}{1-x_1})=B[x_1^2(1+2(\frac{A}{B}-1)x_2)-(x_1^{**}{)}^2(1+2(\frac{A}{B}-1)x_2^{**})]$

$\frac{A}{B}=\frac{2{}_{2}ln(\frac{x_2^{**}}{x_2})+{}_{1}ln(\frac{x_1^{**}}{x_1})}{2{}_{1}ln(\frac{x_1^{**}}{x_1})+{}_{2}ln(\frac{x_2^{**}}{x_2})}$

where

${}_i=x_i^2-(x_i^{**}{)}^2-x_i^3+(x_i^{**}{)}^3$

${}_i=x_i^2-(x_i^{**}{)}^2-2x_i^3+2(x_i^{**}{)}^3$