JEE Advanced 2023 Paper 1 · Q09 · Solutions & Colligative Properties

Question

A gas has a compressibility factor of $0.5$ and a molar volume of $0.4$ dm$^3$·mol$^{-1}$ at a temperature of $800$ K and pressure $x$ atm. If it shows ideal gas behavior at the same temperature and pressure, the molar volume will be $y$ dm$^3$·mol$^{-1}$. The value of $x/y$ is ___. [Use: Gas constant $R = 8 	imes 10^{-2}$ L·atm·K$^{-1}$·mol$^{-1}$]

SolveKar AI · Accepted Answer

Real gas: $Z = PV_m/RT \Rightarrow 0.5 = x \cdot 0.4/(0.08\cdot 800) \Rightarrow x = 0.5\cdot 64/0.4 = 80$ atm. Ideal gas at same $T, P$: $y = RT/P = 0.08\cdot 800/80 = 0.8$ dm$^3$/mol. Therefore $x/y = 80/0.8 = 100$.