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,

Replacing n = m/M we have

⇒

because the number of moles is given as:

Where,

M - Mass of gas

M - Molar mass of gas

But,

(where, d = density of gas)

Thus, from equation (ii), we have

⇒

⇒

Molar mass (M) of a gas is always constant and therefore, at constant temperature T,

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