Question

A gas has a compressibility factor of 0.5 and a molar volume of 0.4 dm3 mol−1 at a temperature of 800K and pressure x atm. If it shows ideal gas behavior at the same temperature and pressure, the molar volume will be y dm3 mol−1. The value of $\frac{x}{y}$ is ___. [Use: Gas constant, R = 8 × 10−2 L atm K−1 mol−1]

Answer 1

The compressibility factor (Z) = $\frac{V_{real}}{V_{ideal}}=0.5$
$V_{real}=0.4\,dm^3mol^{-1}=0.4$ L/mol
$V_{ideal}=\frac{0.4}{0.5}=0.8\,L/mol$
$\therefore\,$ y = 0.8 L/mol
Using the equation PV = nRT,
P = $\frac{1\times8\times10^{-2}\times800}{0.8}$
x = 80 atm
$\therefore\,$ $\frac{x}{y}=\frac{80}{0.8}=100$