Question

Using the equation of state $pV=nRT$, show that, at a given temperature the density of a gas is proportional to its gas pressure $p$.

Answer 1

$PV=nRT=\frac{w}{M}RT$

Hence, $PM=\frac{w}{V}RT=\rho RT$

$\rho \propto P$

Here, $\rho =\frac{w}{V}$

$n=\frac{w}{M}$

$\rho$ is the density, P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, T is the temperature and M is the molar mass.