Problem $2$: LLE in mixtures of Polystyrene $($PS$)$ and Methyl Cyclohexane $($MCH$)$

Experimental measurements of LLE $($T vs$.$ volume fractions$)$ for $MCH(1)$ and $PS(2)$ at

atmospheric pressure are reported below.

The molecular weight of PS and MCH are $16500\frac{g}{m}ol($average$)$ and $98\mathrm{.}2\frac{g}{m}ol,$ while the

density $(\frac{g}{L})$ of the polymer and solvent is given as a function of $T(K)$ by

${}_{PS}=1175-0\mathrm{.}3976T$

${}_{MCH}=1022-0\mathrm{.}863T$

$2$a$)$ Estimate the critical volume fraction of PS using the simple version of the FH model $($see

problem $1)$ and compare the value with the experimental data above.