A given sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas?

1. $Pm/(kT)$

2. $P/(kTV)$

3. $mkT$

4. $P/(kT)$

Doubtly Asked 30 Oct 2026 NEET UG 2016 Phase 2 Practice test neet Save WhatsApp Report

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Answer: 1. $Pm/(kT)$

Density $\rho=\dfrac{\text{mass}}{\text{volume}}$. Use the ideal gas law in terms of the number of molecules $N$: $PV=NkT$.

Mass $=Nm$, so

$$\rho=\frac{Nm}{V}=\frac{Pm}{kT}$$

Option (1). Option (4) is the number density $N/V$, missing the factor $m$.

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

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