Question

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 ?

• A. $P/(kT)$
• B. $Pm/(kT)$
• C. $P/(kTV)$
• D. $mkT$

Answer 1

Answer: (B)

$PV = nRT $
$\frac{n}{V} = \frac{P}{RT} $
$ \frac{n}{V} = \frac{P}{kN_{A}T} \left(k = \frac{R}{N_{A}}\right) $
$\frac{nN_{A}}{V} = \frac{P}{kT} $
$\frac{mnN_{A}}{V} = \frac{mP}{kT}$
$ \rho= \frac{mP}{kT}$