According to the Ideal Gas Equation in terms of the number of molecules ($N$): $pV = NkT$, where $k$ is the Boltzmann constant . Rearranging for number density ($N/V$): $\frac{N}{V} = \frac{p}{kT}$.

The density ($\rho$) of the gas is the total mass per unit volume. Since the mass of one molecule is $m$, the total mass is $N \times m$. $\rho = \frac{\text{Total Mass}}{V} = \frac{N \times m}{V} = m \left( \frac{N}{V} \right)$.

Substituting the value of $N/V$ from the gas equation: $\rho = m \left( \frac{p}{kT} \right) = \frac{pm}{kT}$.