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 . Which of the following gives the density of the gas? [2016]

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Solution

Q.
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 [2016]

1 $\frac{P}{(k T)}$

2 $\frac{P m}{(k T)}$

3 $\frac{P}{(k T V)}$

4 $m k T$

Ans.
(2)

As $P V = n R T$

or $n = \frac{P V}{R T} = \frac{mass}{molar mass}$ ...(i)

$Density, ρ = \frac{mass}{volume} = \frac{(molar mass) P}{R T} = \frac{(m N_{A}) P}{R T}$

$∴$ $ρ = \frac{m P}{k T}$ $(∵ R = N_{A} k)$

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