Kinetic Theory NCERT Solutions Class 11 Physics - Solved Exercise Question 13.12

Question 13.12:

From a certain apparatus, the diffusion rate of hydrogen has an average value of 28.7 cm³ s^–1. The diffusion of another gas under the same conditions is measured to have an average rate of 7.2 cm³ s^–1. Identify the gas.
[Hint: Use Graham’s law of diffusion: R₁/R₂ = (M₂/M₁)^1/2, where R₁, R₂ are diffusion rates of gases 1 and 2, and M₁ and M₂ their respective molecular masses. The law is a simple consequence of kinetic theory.]

Solution:

Rate of diffusion of hydrogen, R₁ = 28.7 cm³ s^–1
Rate of diffusion of another gas, R₂ = 7.2 cm³ s^–1
According to Graham’s Law of diffusion, we have:
R₁ / R₂  =  (M₂ / M₁)^1/2
Where,
M₁ is the molecular mass of hydrogen = 2.020 g
M₂ is the molecular mass of the unknown gas
∴ M₂ = M₁(R₁ / R₂)²
= 2.02 (28.7 / 7.2)²
= 32.09 g
32 g is the molecular mass of oxygen. Hence, the unknown gas is oxygen.