$($i$)$ Explain how the van der Waals equation of state can be used to estimate the

molar volume of a gas at a pressure, $p,$ and temperature, $T.$

$($ii$)300kg$ of ethane $(C_2{H}_6)$ is stored in a $15\mathrm{.}0m^3$ tank$.$ For a temperature of $21C$

estimate the pressure of the gas in the tank assuming that the van der Waals equation

is applicable.

$30\%$

$($iii$)$ If the vapour pressure of ethane at $21C$ is $38\mathrm{.}3$atm estimate how much more

gas can be pumped into the vessel before it begins to condense.

$20\%$

$($iv$)$ If it is assumed that $C_2{H}_6$ behaves as an ideal gas, estimate the pressure of the

gas in the vessel for the conditions specified in $($iii$)$

$($v$)$ Determine the compression factor of $C_2{H}_6$ for the conditions in $($iii$).$

$15\%$

The van der Waals equation of state is$,$

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

For $C_2{H}_6$

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

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