Ethylene$-$propylene rubber, EPDM, is made in solution using $n-$hexane as the solvent. This solvent must be subsequently removed and the equilibrium between solvent vapor and the polymer$-$solvent solution is an important factor in designing a solvent recovery process. Use the information below to construct a plot of equilibrium hexane vapor pressure above rubber solutions as a function of EPDM volume fraction at $80C.$

An empirical combination of experimental data for rubber$-$solvent systems with the FloryHuggins and the Hildebrand theories has yielded the following correlations:

${}_{12}=0\mathrm{.}34+\frac{V_1}{RT}({}_1-{}_2{)}^2$

For EPDM ${}_2=8\mathrm{.}3(\frac{\text{c}\text{a}\text{l}}{c{m}^3}{)}^{\frac{1}{2}}$ n$-$hexane ${}_1=7\mathrm{.}3(\frac{\text{c}\text{a}\text{l}}{c{m}^3}{)}^{\frac{1}{2}}$

The polymer contains equal molar quantities of ethylene and propylene and has an average molecular weight of $100,000.$