To solve the problem of how long it will take for 60 cm³ of chlorine to diffuse through a porous pot, given the diffusion of oxygen, we can use Graham's law of effusion. This law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass (or vapor density). ### Step-by-Step Explanation 1. **Understanding Graham's Law**: Graham's law can be expressed mathematically as: \[ \frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}} \] where: - \( r_1 \) and \( r_2 \) are the rates of diffusion of gas 1 and gas 2, respectively. - \( M_1 \) and \( M_2 \) are the molar masses (or vapor densities) of gas 1 and gas 2, respectively. 2. **Identifying the Gases**: - Gas 1: Oxygen (O₂) with a vapor density of 16. - Gas 2: Chlorine (Cl₂) with a vapor density of 36. 3. **Calculating the Rates of Diffusion**: We know that 30 cm³ of oxygen diffuses in 7 seconds. Therefore, the rate of diffusion of oxygen (\( r_{O_2} \)) can be calculated as: \[ r_{O_2} = \frac{30 \, \text{cm}^3}{7 \, \text{s}} \approx 4.29 \, \text{cm}^3/\text{s} \] 4. **Using Graham's Law**: We need to find the rate of diffusion of chlorine (\( r_{Cl_2} \)). Using Graham's law: \[ \frac{r_{O_2}}{r_{Cl_2}} = \sqrt{\frac{M_{Cl_2}}{M_{O_2}}} \] Plugging in the values: \[ \frac{4.29}{r_{Cl_2}} = \sqrt{\frac{36}{16}} = \sqrt{2.25} = 1.5 \] Rearranging gives: \[ r_{Cl_2} = \frac{4.29}{1.5} \approx 2.86 \, \text{cm}^3/\text{s} \] 5. **Calculating Time for Chlorine**: Now, we need to find out how long it will take for 60 cm³ of chlorine to diffuse. The time (\( t \)) can be calculated using the formula: \[ t = \frac{\text{Volume}}{\text{Rate}} = \frac{60 \, \text{cm}^3}{r_{Cl_2}} = \frac{60 \, \text{cm}^3}{2.86 \, \text{cm}^3/\text{s}} \approx 20.98 \, \text{s} \] Rounding this gives approximately 21 seconds. ### Conclusion Thus, the time it will take for 60 cm³ of chlorine to diffuse through the same pot is approximately **21 seconds**. ### Why Other Options Are Incorrect: - **Option A (9.3 sec)**: This is too short and does not account for the higher vapor density of chlorine compared to oxygen, which would slow its diffusion. - **Option B (14 sec)**: This is also too short and does not reflect the calculated diffusion rate of chlorine. - **Option D (28 sec)**: This is longer than expected based on the diffusion rates and would imply a much slower diffusion than what Graham's law suggests. ### Revision Summary: - Graham's law states that the rate of diffusion is inversely proportional to the square root of the molar mass. - Calculate the rate of diffusion for both gases using their vapor densities. - Use the calculated rate to find the time taken for the desired volume of gas to diffuse. - Always check the reasonableness of your answer against the properties of the gases involved.