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: He vs CH₄ **Given Information:** - Both gases at same pressure and temperature - Need: relative diffusion rate of He w.r.t. CH₄ **Step 1: Apply Graham's Law of Diffusion** The rate of diffusion is inversely proportional to the square root of molar mass: $$\text{Rate of diffusion} \propto \frac{1}{\sqrt{M}}$$ **Step 2: Set Up the Ratio** For two gases under similar conditions: $$\frac{\text{Rate}_{\text{He}}}{\text{Rate}_{\text{CH}_4}} = \sqrt{\frac{M_{\text{CH}_4}}{M_{\text{He}}}}$$ **Step 3: Substitute Molar Masses** - $M_{\text{He}} = 4$ g/mol - $M_{\text{CH}_4} = 16$ g/mol $$\frac{\text{Rate}_{\text{He}}}{\text{Rate}_{\text{CH}_4}} = \sqrt{\frac{16}{4}} = \sqrt{4} = 2$$ **Step 4: Interpret Result** Helium diffuses **2 times faster** than methane because it has a much lower molar mass and lighter molecules move faster at the same temperature. **Answer: The relative rate of diffusion of He w.r.t. CH₄ is 2:1**