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Q.

A gas has a compressibility factor of 0.5 and a molar volume of 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 $y {dm}^{3} {mol}^{- 1} .$ The value of 𝐱/𝐲 is ___.[Use: Gas constant, $R = 8 \times 10^{- 2} L atm K^{- 1} {mol}^{- 1}$ ]

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Detailed Solution

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$PV = ZRT$
$P = \frac{0.5 \times RT}{0.4} = 1.25 RT = x$
$1.25 RT \times V_{m} = RT$ $V_{m} = \frac{1}{1.25} = y$
$\frac{x}{y} = \frac{1.25 RT}{(\frac{1}{1.25})} = {(1.25)}^{2} RT = 8 \times 10^{- 2} \times 800 \times {(1.25)}^{2} = 100$

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A gas has a compressibility factor of 0.5 and a molar volume of 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 dm3mol−1. The value of 𝐱/𝐲 is ___.[Use: Gas constant, R=8×10−2 L atm K−1mol−1 ]