Problem $2(35$ points$)$

A rigid tank contains $3$ kg of n$-$Hexane $(C_6{H}_{14})$ and $3$ kg of Carbon Dioxide $(C{O}_2)$ at $548$ K and

$5$ MPa $.$ Calculate the volume of the tank in the three following cases:

a$.$ The gases are ideal $(Z_i=1).$

b$.$ The gases are non$-$ideal with compressibility factors $Z_i$ computed with Amagat's law.

c$.$ The gases are non$-$ideal with compressibility factors $Z_i$ computed with Dalton's law.

d$.$ The gases are non$-$ideal with compressibility factor $Z_m$ computed with Kay's rule.

Note:

You need to use the supplied Mathematica notebook to calculate $Z(P_r,T_r)$ for $C_6{H}_{14}$ and

$C{O}_2.$ For part d$)$ use an average between the two.

For a non$-$ideal gas is not true that $\frac{P_i}{P}=y_{i_2},$ therefore part c$)$ must be solved iteratively.

Performs at least two iterations.