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

Explanation

The equatin of state is given by,
pV=nRT……..(i) where,
p `to` Pressure of gas
V `to` Volume of gas
R `to` Gas constant
T `to` Temperature of gas
From equation (i) we have,
`n/V=p/(RT)`
Replacaing n with `m/M` we have
`m/(MV)=p/(RT)..........(ii)` where,
m `to` Mass of gas
M `to` Molar mass of gas
But, `m/V=d` (d= density of gas)
Thus, form equation (ii), we have
`d/M=p/(RT)`
`rArrd=(M/(RT))p`
Molar mass (M) of a gas is always constant and therefore, at constant temperature
`(T),M/(RT)`= constant.
= (constant) p
`rArr d prop p`
Hence, at a given temperature, the density (d) of gas is proportional to its pressure (p)