$5.[20]$ For a gas mixture of $30\%$ nitrogen, $35\%$ hydrogen and $35\%$ ethane by volume, it is desired to store only $40g$ of this gas mixture in a cylinder having a capacity of $120c{m}^3$ at a maximum temperature of $25C.$ Calculate the pressure inside the cylinder using:

i$).$ Assuming that the mixture obeys the ideal gas laws.

ii$).$ Compressibility factor determine from the pseudo$-$critical point of the mixture.

iii$).$ SRK equation of state and

iv$).$van der Waals equations of state.