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 masses 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. **Calculate the Rates of Diffusion**: 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. We can compare the rates of diffusion by calculating the square root of the molar masses: - **Propane**: \[ \sqrt{M} = \sqrt{44} \approx 6.63 \] - **Oxygen**: \[ \sqrt{M} = \sqrt{32} \approx 5.66 \] - **Methane**: \[ \sqrt{M} = \sqrt{16} = 4 \] - **Ammonia**: \[ \sqrt{M} = \sqrt{17} \approx 4.12 \] 3. **Determine the Fastest Diffusing Gas**: The gas with the smallest molar mass will have the largest rate of diffusion. From our calculations: - Methane has the smallest molar mass (16 g/mol), followed by Ammonia (17 g/mol), Oxygen (32 g/mol), and finally Propane (44 g/mol). - Therefore, the order of diffusion rates from fastest to slowest is: - Methane > Ammonia > Oxygen > Propane 4. **Conclusion**: Since Methane has the lowest molar mass, it will diffuse the fastest through the porous plug. Thus, the correct answer is **C. Methane**. ### Explanation of Incorrect Options: - **A. Propane**: This gas has the highest molar mass (44 g/mol), making it the slowest to diffuse. - **B. Oxygen**: While it has a lower molar mass than Propane, it is still heavier than both Methane and Ammonia, so it diffuses slower than both. - **C. Methane**: This is the correct answer, as it has the lowest molar mass and will diffuse the fastest. - **D. Ammonia**: Although it has a low molar mass, it is still heavier than Methane, making it slower to diffuse than Methane. ### Revision Summary: - Graham's Law states that lighter gases diffuse faster than heavier gases. - Calculate molar masses to determine diffusion rates. - The gas with the lowest molar mass will diffuse the fastest. - In this case, Methane (16 g/mol) is the fastest diffusing gas through a porous plug.