Chemistry - Real Gas Question with Solution | TestHub

$\mathrm{PV}=\mathrm{RT}-\frac{A}{V}+\frac{2B}{V^2},\mathrm{P}=\frac{RT}{V}-\frac{A}{V^2}+\frac{2B}{V^3}$

At critical point $\frac{dP}{dV}=0\frac{dP}{dV}=-\frac{RT}{V^2}+\frac{2A}{V^3}-\frac{6B}{V^4}$

$$\begin{array}{rlrl}& 0=\frac{1}{V^2}\left[-RT+\frac{2A}{V}-\frac{6B}{V^2}\right]& & \end{array}$$

$${\mathrm{RTV}}^2-2\mathrm{AV}+6\mathrm{B}=0,\mathrm{D}=4{\mathrm{A}}^2-4\times \mathrm{RT}\times 6\mathrm{B}=0$$

$$T_C=\frac{A^2}{6RB}{T}_C=\frac{6B}{A}{P}_C=\frac{A^3}{108B^2};\mathrm{Z}=\frac{P_C{V}_C}{R{T}_C}\Rightarrow \frac{1}{Z}=3$$