The relative rate of diffusion of helium w.r.t. methane under similar conditions of pressure and tem — States of Matter and Gaseous State Chemistry Question

💡 Solution & Explanation

# Relative Rate of Diffusion: Helium vs Methane **Using Graham's Law of Diffusion:** At constant pressure and temperature, the rate of diffusion is inversely proportional to the square root of molar mass: $$\text{Rate of diffusion} \propto \frac{1}{\sqrt{M}}$$ **Therefore, the relative rate is:** $$\frac{\text{Rate of He}}{\text{Rate of CH}_4} = \sqrt{\frac{M_{CH_4}}{M_{He}}}$$ **Calculating molar masses:** - Helium: $M_{He} = 4$ g/mol - Methane: $M_{CH_4} = 12 + 4(1) = 16$ g/mol **Substituting values:** $$\frac{\text{Rate of He}}{\text{Rate of CH}_4} = \sqrt{\frac{16}{4}} = \sqrt{4} = 2$$ **Answer: The relative rate of diffusion of helium with respect to methane is 2:1** Helium diffuses **twice as fast** as methane because it has a lower molar mass. Lighter molecules move faster and diffuse more readily through a medium.