A one lb mixture of ethane and methane contains $30\%$ by volume of methane. Mixture pressure is $500$ psia and temperature is $300$ F$.$ Calculate the mixture volume. Use Papay's equation to calculate the Z$-$factor. The critical pressure of ethane is $708$ psia and critical temperature is $90$ F$,$ and the critical pressure of methane is $673$ psia and critical temperature is $-116$ F$.$