A gas has a compressibility factor of 0.6 and a molar volume of $0.4 d m^{3} m o l^{- 1}$ at a temperature of 800 K and pressure x atm. If it shows ideal gas behaviour at the same temperature and pressure, the molar volume will be y $d m^{3} m o l^{- 1}$ . The value of x/y is ___•
[Use: Gas constant, $R = 8 \times 10^{- 2} L a t m K^{- 1} m o l^{- 1}$ ]

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answer is 144.

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Detailed Solution

For gas: Z = 0.6, $V_{m} = 0.4 L / m o l$
T = 800 K, P = X atm.
$\Rightarrow Z = \frac{P V_{m}}{R T} \Rightarrow \frac{X (0.4)}{0.08 \times 800} = 0.6 \Rightarrow X = 96$
For ideal gas, $P V_{m} = R T \Rightarrow V_{m} = \frac{R T}{P} = \frac{0.08 \times 800}{96} = \frac{2}{3} L m o l^{- 1} = y$
Then, $\frac{x}{y} = 144$

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