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

The equation of state is given by,
pV = nRT …. (i)

Where, p → Pressure of gas

V → Volume of gas

n→ Number of moles of gas

R → Gas constant

T → Temperature of gas

From equation (i) we have,

p = n RT/V

Where n= Mass of gas(m)/ Molar mass of gas(M)

Putting value of n in the equation, we have

 p = m RT/ MV ------------(ii)

Now density(ρ) = m /V ---------(iii)

Putting (iii) in (ii) we get

P = ρ RT / M

OR

ρ = PM / RT

Hence, at a given temperature, the density (ρ) of gas is proportional to its pressure (P).