Relation between density, molar mass and pressure

The ideal gas equation can also be recast in terms of a gas's density. Starting from $PV = nRT$ and rearranging to $\frac{n}{V} = \frac{P}{RT}$, then substituting $n = m/M$ gives $\frac{m}{MV} = \frac{P}{RT}$. Since $m/V$ is the density $d$, this becomes $\frac{d}{M} = \frac{P}{RT}$, or equivalently $M = \frac{dRT}{P}$. This form lets the molar mass of a gas be calculated directly from a measurement of its density at known temperature and pressure, without needing to separately measure its mass and volume. It also restates Boyle's law in terms of density: at constant temperature, the pressure of a fixed mass of a ga …