A given sample of an ideal gas occupies a volume, V at a pressure,...

$PV = nRT ⇒ PV = \left(\dfrac{m}{M}\right)RT$

$P = \left(\dfrac{R}{M}\right)\dfrac{m}{V}T ⇒ \dfrac{P}{ρ} = \left(\dfrac{R}{m{N}_{A}}\right)T$

$⇒ \dfrac{P}{ρ} = \dfrac{kT}{m}$

$ρ = \dfrac{Pm}{kT}$.