To determine the vapor density of the gas, we need to follow a series of steps that involve understanding the relationship between mass, volume, and molar volume at standard temperature and pressure (S.T.P.). ### Step-by-Step Explanation 1. **Understanding Vapor Density**: - Vapor density is defined as the mass of a certain volume of gas compared to the mass of an equal volume of hydrogen at the same temperature and pressure. It can also be calculated using the formula: \[ \text{Vapor Density} = \frac{\text{Mass of gas}}{\text{Volume of gas at S.T.P.}} \] 2. **Given Data**: - Volume of gas = 56.00 cm³ - Mass of gas = 0.11 g - Molar volume of a gas at S.T.P. = 22.4 dm³ (which is equivalent to 22,400 cm³) 3. **Convert Volume to dm³**: - Since the molar volume is given in dm³, we need to convert the volume of the gas from cm³ to dm³: \[ 56.00 \, \text{cm}^3 = \frac{56.00}{1000} \, \text{dm}^3 = 0.056 \, \text{dm}^3 \] 4. **Calculate the Molar Mass of the Gas**: - To find the vapor density, we first need to find the molar mass of the gas. The molar mass can be calculated using the formula: \[ \text{Molar Mass} = \frac{\text{Mass of gas}}{\text{Volume of gas at S.T.P.}} \times \text{Molar Volume} \] - Plugging in the values: \[ \text{Molar Mass} = \frac{0.11 \, \text{g}}{0.056 \, \text{dm}^3} \times 22.4 \, \text{dm}^3 \] 5. **Perform the Calculation**: - First, calculate the mass per dm³: \[ \frac{0.11 \, \text{g}}{0.056 \, \text{dm}^3} \approx 1.9643 \, \text{g/dm}^3 \] - Now, multiply by the molar volume: \[ \text{Molar Mass} \approx 1.9643 \, \text{g/dm}^3 \times 22.4 \, \text{dm}^3 \approx 44.00 \, \text{g/mol} \] 6. **Calculate Vapor Density**: - The vapor density is half of the molar mass (since vapor density is defined relative to hydrogen, which has a molar mass of 2 g/mol): \[ \text{Vapor Density} = \frac{\text{Molar Mass}}{2} = \frac{44.00 \, \text{g/mol}}{2} = 22.00 \] ### Conclusion The correct answer is **B. 22.00**. ### Explanation of Other Options: - **A. 11.00**: This value is incorrect because it suggests a molar mass of 22 g/mol, which does not match our calculations. - **C. 33.00**: This value is also incorrect as it implies a molar mass of 66 g/mol, which is not supported by the data provided. - **D. 44.00**: While this is the molar mass we calculated, it is not the vapor density. The vapor density is half of the molar mass. ### Revision Summary: - Vapor density is calculated using the mass of the gas and its volume at S.T.P. - Convert volumes to the same units (dm³) when necessary. - Molar mass can be derived from the mass and volume of the gas. - Vapor density is half the molar mass when compared to hydrogen.