Consider a system consisting of only two components: methane and propane. These two components may appear in both liquid phase and gas phase. We ignore capillary pressure here; that is$,$ the pressures are identical in both phases. You are asked to write a computer program in Python to carry out a flash calculation for the mixture at $20$ bar and $240$ K$.$ The liquid$-$gas mixture consists of $3$ moles of methane and $2$ moles of propane.

Please report:

$1.$ How many phases the mixture has $($i$.$e$.,$ is it in single$-$phase or two$-$phase status?$).$

$2.$ If two$-$phase, please report the composition of each phase, and the amount of each phase in moles.

You are asked to use the Peng$-$Robinson equation of state $($PR$-$EOS$)$ and the critical properties and normal boiling points. You may also need the binary interaction coefficients for methane propane are $0\mathrm{.}0361$