Topic: Equation of state of a perfect gas, work done on compressing a gas· Kinetic Theory of Gases

An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressure at temperature 27^°C. The mass of the oxygen withdrawn from the cylinder is nearly…

An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressure at temperature 27$^\circ$C. The mass of the oxygen withdrawn from the cylinder is nearly equal to :

[Given, $R = \frac{100}{12}$ J mol$^{-1}$K$^{-1}$, and molecular mass of O$_2$ = 32, 1 atm pressure = $1.01\times10^5$ N/m]

1. 0.125 kg

2. 0.144 kg

3. 0.116 kg

4. 0.156 kg

Doubtly Asked 30 Oct 2026 NEET UG 2025 Practice test neet Save WhatsApp Report

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Answer: 3. 0.116 kg

Key idea: use $PV=nRT$ for the gas left, then subtract from the initial moles. The gauge pressure must be converted to absolute pressure.

Absolute pressure $=11+1=12$ atm $=12\times1.01\times10^5=1.212\times10^6$ Pa. $V=30\times10^{-3}\ \mathrm{m^3}$, $T=300$ K, $RT=\tfrac{100}{12}\times300=2500$ J/mol.

$$n_{\text{left}}=\frac{PV}{RT}=\frac{1.212\times10^6\times0.03}{2500}\approx14.54\ \text{mol}$$

Moles withdrawn $=18.20-14.54=3.66$ mol, so mass $=3.66\times32\approx117\ \mathrm g\approx0.116$ kg (nearest option).

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressure at temperature 27^°C. The mass of the oxygen withdrawn from the cylinder is nearly…

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