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(D) The ideal gas equation is given by $PV = nRT$,where $n$ is the number of moles.We know that $n = \frac{	ext{mass of gas}}{M}$,where $M$ is the mo

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$\frac{Pm}{kT}$

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(D) The ideal gas equation is given by $PV = nRT$,where $n$ is the number of moles.We know that $n = \frac{	ext{mass of gas}}{M}$,where $M$ is the molar mass.Also,the molar mass $M = m N_A$,where $m$ is the mass of one molecule and $N_A$ is Avogadro's number.Substituting these into the ideal gas equation: $PV = \left(\frac{	ext{mass}}{m N_A}ight) RT$.Rearranging for density $ho = \frac{	ext{mass}}{V}$,we get $ho = \frac{P m N_A}{RT}$.Since the Boltzmann constant $k = \frac{R}{N_A}$,we have $R = N_A k$.Substituting $R$ in the density equation: $ho = \frac{P m N_A}{(N_A k) T} = \frac{Pm}{kT}$.

$A$ 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 $?$

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