$(50$ points$)$ Please answer parts A through D below!!

a$.(5$ points$)$ Write the molecular formula for $n-$hexatriacontane. What are the $T_C,P_C,$ and $$ for n$-$hexane and n$-$hexatriacontane, according to values found online?

b$.(10$ points$)$ Plot the Px diagram for $n-$hexane $+n-$hexatriacontane at $621\mathrm{.}8K$ found in the table in the image below. What is the critical pressure?

c$.(15$ points$)$ Compare calculation results from the PR EOS with the experimental data $($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 the table'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.