Problem $[5$ points$]$: A $0\mathrm{.}04m^3$ rigid tank contains $0\mathrm{.}15$ kg of Methane and $0\mathrm{.}40kgo{f}_2$ at $320$ K $.$

$($a$)$ Using the ideal gas equation of state, determine:

i$.$ the average molar mass of the mixture

ii$.$ the average gas constant of the mixture, and

iii. the partial pressure of each gas.

$($b$)$ In addition, determine the total pressure of the mixture using:

i$.$ the ideal gas equation of state

ii$.$ the van der Waals equation and compare the results.