Determine the molar volume and compressibility factor of methanol vapour at $280K$ and $6$ bar using Redlich $-$ Kwong equation. $P=\frac{RT}{V-b}-\frac{a}{T^{0\mathrm{.}5}V(V+b)}.$ The constants $\text{'}a\text{'}$ and $\text{'}b\text{'}$ are evaluated using limiting conditions as ; $a=\frac{0\mathrm{.}4278R^2{T}_C^{2\mathrm{.}5}}{P_C}$;$b=\frac{0\mathrm{.}0867R{T}_C}{P_C},$ where the Critical Temperature and Pressure are respectively $512\mathrm{.}6K$ and $81$ bar.