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