JEE Advanced · 2023 · 04 Jun 2023 · Paper 1 · States of Matter

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

0.4 dm^{3} mol^{- 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 dm^{3} mol^{- 1}

. The value of

x / y

is ____.

[Use: Gas constant,

R = 8 \times 1 0^{- 2} L atm K^{- 1} mol^{- 1}

]

Answer: 100

Solution

The compressibility factor is defined as:

Z = \frac{P V _{m}}{R T}

Given:

Z = 0.5

V_{m} = 0.4

L/mol,

T = 800

K.

Solving for pressure x:

0.5 = \frac{x \times 0.4}{0.08 \times 800}

x = \frac{0.5 \times 0.08 \times 800}{0.4} = 80 atm

For ideal gas behavior at the same T and P:

P V_{m} = R T

y = \frac{R T}{P} = \frac{0.08 \times 800}{80} = 0.8 L/mol

Therefore:

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

JEE Advanced · 2023 · 04 Jun 2023 · Paper 1 · Integer answer

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