To determine which gas will diffuse fastest through a porous plug, we can use Graham's Law of Effusion. This law states that the rate of effusion (or diffusion) of a gas is inversely proportional to the square root of its molar mass. In simpler terms, lighter gases will diffuse faster than heavier gases. ### Step-by-Step Explanation: 1. **Identify the Molar Masses**: We need to calculate the molar mass of each gas based on the atomic weights provided: - **Propane (C₃H₈)**: - Molar mass = (3 × 12) + (8 × 1) = 36 + 8 = **44 g/mol** - **Oxygen (O₂)**: - Molar mass = 2 × 16 = **32 g/mol** - **Methane (CH₄)**: - Molar mass = 12 + (4 × 1) = 12 + 4 = **16 g/mol** - **Ammonia (NH₃)**: - Molar mass = 14 + (3 × 1) = 14 + 3 = **17 g/mol** 2. **Apply Graham's Law**: According to Graham's Law, the rate of diffusion (r) is given by: \[ r \propto \frac{1}{\sqrt{M}} \] where \(M\) is the molar mass of the gas. Therefore, the lighter the gas (lower molar mass), the faster it will diffuse. 3. **Calculate the Rates of Diffusion**: We can compare the rates of diffusion by looking at the square roots of the molar masses: - For **Propane**: \( \sqrt{44} \approx 6.63 \) - For **Oxygen**: \( \sqrt{32} \approx 5.66 \) - For **Methane**: \( \sqrt{16} = 4 \) - For **Ammonia**: \( \sqrt{17} \approx 4.12 \) 4. **Determine the Fastest Diffusing Gas**: The gas with the lowest molar mass will have the highest rate of diffusion. From our calculations: - Methane (16 g/mol) has the lowest molar mass, thus it will diffuse the fastest. ### Conclusion: The correct answer is **C. Methane**. ### Explanation of Other Options: - **A. Propane (44 g/mol)**: This gas has the highest molar mass among the options, so it will diffuse the slowest. - **B. Oxygen (32 g/mol)**: While it is lighter than propane, it is still heavier than methane and ammonia, making it slower than both. - **D. Ammonia (17 g/mol)**: Although ammonia is lighter than oxygen and propane, it is still heavier than methane, which means it will diffuse slower than methane. ### Revision Summary: - Graham's Law states that lighter gases diffuse faster than heavier gases. - Calculate molar masses to determine which gas is the lightest. - Methane (16 g/mol) is the lightest gas among the options, making it the fastest to diffuse. - Always compare the square roots of molar masses to assess diffusion rates effectively.