QJEEAdv23Chc481: JEE Advanced 2023 Chemistry - Class 11 JEEAdv23Chc481 Solution: A gas has a compressibility factor of 0.5 and a molar volume of …

Question

Verified Solution • 2025–26 Session moderate

A gas has a compressibility factor of 0.5 and a molar volume of

0.4 ~\mathrm{dm}^3 \mathrm{~mol}^{-1}

at a temperature of

800 \mathrm{~K}

and pressure

\mathbf{x}

atm. If it shows ideal gas behaviour at the same temperature and pressure, the molar volume will be

\mathbf{y} ~\mathrm{dm}^3 \mathrm{~mol}^{-1}

. The value of

\mathbf{x} / \mathbf{y}

is __________.

[Use: Gas constant,

\mathrm{R}=8 \times 10^{-2} \mathrm{~L}

atm

\mathrm{K}^{-1} \mathrm{~mol}^{-1}

]

Accepted Answer

For gas :

\mathrm{Z}=0.5, \mathrm{~V}_{\mathrm{m}}=0.4 \mathrm{~L} / \mathrm{mol}

\begin{aligned} T = 800 K, P = X atm. \\ \Rightarrow & Z = \frac{{PV}_{m}}{RT} \\ \Rightarrow & \frac{X (0.4)}{0.08 \times 800} = 0.5 \\ \Rightarrow & X = 80 \end{aligned}

For ideal gas,

\mathrm{PV}_{\mathrm{m}}=\mathrm{RT}

\Rightarrow V_{m} = \frac{RT}{P} = \frac{0.08 \times 800}{80} = 0.8 L {mol}^{- 1} = y

Then,

\frac{x}{y}=\frac{80}{0.8}=100

.

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