Question

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

Answer 1

According to ideal gas equation :

pV = nRT or p = \(\frac{nRT}{V}\) 

n = \(\frac{Mass\ of\ gas(m)}{Molar\ mass\ of\ gas(M)}\) 

p = \(\frac{mRT}{MV}\) 

Now density, d = \(\frac{m}{V}\) 

∴ p = \(\frac{dRT}{M}\) 

Or d ∝ p at constant temperature.