Question $1($Gas Laws$)$

$150kg$ of ethane $(C_2{H}_6)$ is stored in a $15\mathrm{.}0m^3$ tank$.$ For a temperature of $50C$ estimate the pressure of the gas in the tank assuming that the van der Waals equation is applicable.

The vessel bursts at a pressure of $50$atm. Using the method of successive substitution, how much more ethane $(kg)$ can be pumped into the vessel before it bursts?

Plot the compression factor of the gas as a function of pressure for at least $5$ pressures between $10$ and $50$ bar $($Use either Excel in combination with Goal Seek or Matlab in combination with a root$-$finding function$).$ Describe the figure and explain the observation.

$p=\frac{RT}{(hat(V))-b}-\frac{a}{\text{h}\text{a}\text{t}(V{)}^2}$ where $a=\frac{27R^2{T}_c^2}{64p_c}$ and $b=\frac{R{T}_c}{8p_c}$

For $C_2{H}_6$

$a=0\mathrm{.}558Pa\frac{m}{m}o{l}^2,b=6\mathrm{.}51{10}^{-5}\frac{m^3}{m}ol$

$R=8\mathrm{.}3145\frac{J}{m}ol{K}^5,1$atm$=1\mathrm{.}013{10}^5\frac{N}{m^2}$