If $m$ is the mass of a molecule, $k$ is the Boltzmann constant, $P$ is the pressure and $T$ is the absolute temperature, then the density of the gas is given by:

\frac{k T}{P m}

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\frac{P T}{k m}

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\frac{P m}{k T}

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\frac{P k}{T m}

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Solution

The correct option is D $\frac{P m}{k T}$
The ideal gas law is given by $P V = n R T$ , where $n$ is the number of moles of a gas.

$n$ = mass of the gas/molecular weight of the gas.

Density $(d)$ = mass of the gas/volume of the gas.

So, the ideal gas law can also be written as $P M = d R T$ , where, $M$ is the molecular mass of the gas.

$d = \frac{P M}{R T}$
$⟹ d = \frac{P m}{(\frac{R}{N}) T}$ , where $k = \frac{R}{N}$ , $m$ is the mass of one molecule and $N$ is the Avogadro's number.

Hence, the correct answer is option $C$ .

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If m is the mass of a molecule, k is the Boltzmann constant,P is the pressure and T is the absolute temperature, then the density of the gas is given by:

If $m$ is the mass of a molecule, $k$ is the Boltzmann constant, $P$ is the pressure and $T$ is the absolute temperature, then the density of the gas is given by: