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**: - At S.T.P., 1 mole of gas occupies 22.4 dm³. Therefore, we can find out how many moles of gas are in 0.056 dm³: \[ \text{Number of moles} = \frac{\text{Volume of gas}}{\text{Molar volume}} = \frac{0.056 \, \text{dm}^3}{22.4 \, \text{dm}^3} \approx 0.0025 \, \text{moles} \] 5. **Calculate the Molar Mass**: - Molar mass (M) can be calculated using the formula: \[ M = \frac{\text{Mass of gas}}{\text{Number of moles}} = \frac{0.11 \, \text{g}}{0.0025 \, \text{moles}} = 44 \, \text{g/mol} \] 6. **Calculate Vapor Density**: - The vapor density is half of the molar mass of the gas because vapor density is defined relative to hydrogen (which has a molar mass of 2 g/mol): \[ \text{Vapor Density} = \frac{M}{2} = \frac{44 \, \text{g/mol}}{2} = 22 \, \text{g/mol} \] ### Conclusion The correct answer is **B. 22.00**. ### Explanation of Other Options: - **A. 11.00**: This option is incorrect because it suggests a vapor density that is half of the calculated value. It does not align with the molar mass derived from the given data. - **C. 33.00**: This option is also incorrect as it does not correspond to any logical calculation based on the mass and volume provided. - **D. 44.00**: This option represents the molar mass of the gas, not the vapor density. Vapor density is always half of the molar mass when compared to hydrogen. ### 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 when necessary (e.g., cm³ to dm³). - Molar mass can be derived from the mass and number of moles of the gas. - Vapor density is half of the molar mass when compared to hydrogen. This thorough understanding will help you tackle similar problems in the future!