Question

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

Answer 1

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 with , we have

Where,

m → Mass of gas

M → Molar mass of gas

But, (d = density of gas)

Thus, from equation (ii), we have

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

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