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A gas has a compressibility factor of 0.6 and a molar volume of $0.5 {dm}^{3} {mol}^{- 1}$ at a temperature of 900 K and $x atm$ . If it shows ideal gas behaviour at the same temperature and pressure, the molar volume will be $y {dm}^{3} {mol}^{- 1} .$ The value of $\frac{x}{y}$ is______.
[Take $R = 0.08 L . atm . {mol}^{- 1} . K^{- 1}$ ]

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answer is 103.68.

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Detailed Solution

$xV = ZRT \Rightarrow x = \frac{0.6 \times 0.08 \times 900}{0.5} = 86.4$

$pV = RT \Rightarrow y = \frac{0.08 \times 900 \times 0.5}{0.6 \times 0.08 \times 900} = \frac{5}{6}$

$\frac{x}{y} = \frac{86.4 \times 6}{5} = 103.68$

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