$(50$ points$)[$PVTsim$]$ See the paper by Joyce et al$.(2000)$ on "Vapor$-$Liquid Equilibria for the Hexane $+$ Tetracosane and Hexane $+$ Hexatriacontane Systems at Elevated Temperatures and Pressures," which has been posted on Canvas.

a$.(5$ points$)$ Write the molecular formula for n$-$hexatriacontane. What are the $T_C,P_C,$

$1$

and $$ for $n-$hexane and $n-$hexatriacontane, according to the PVTsim database in the Sl unit system?

b$.(10$ points$)$ Plot the Px diagram for $n-$hexane $+n-$hexatriacontane at $621\mathrm{.}8K$ by using Table $2$ on page $426$ of the paper. What is the critical pressure?

c$.(15$ points$)$ Compare calculation results from the PR EOS with the experimental data from Joyce et al$.($as you plotted for part b$).$ You can perform PT flash for n$-$hexane $+7$mol$\%$ n$-$hexatriacontane$]$ at $621\mathrm{.}8K$ at the pressures used in Joyce et al$.\text{'}$s experiment $($i$.$e$.,791$kPa,$1480$kPa,$2514$kPa,$3549$kPa,$4583$kPa, and $5500$kPa in the SI unit system$).$ Use the default value, zero, for the binary interaction parameter $($BIP$)$ between the two components.

d$.(20$ points$)$ In order to represent the critical point of this binary fluid system at $621\mathrm{.}8$ K more accurately, should the BIP be increased or decreased from the default value of zero? Demonstrate the effect of BIP on the two$-$phase envelope in order to support your answer.