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

Explanation

`pV=nRT`
`"or "p=(nRT)/(V)`
`"Now, number of moles (n) "=("Mass of substance (m)")/("Molar mass (M)")`
`p=(mRT)/(MV)`
`"But "(m)/(V)="density, d so that"`
`p=(dRT)/(M)`
`"or "d=(pM)/(RT)`
or `d prop p` (for a given gas at constant T)
Thus, at a given temperature, density of a gas is proportional to gas pressure.