Answer :
To calculate the percentage composition of oxygen in the given organic substance, follow these steps:
1. Determine the moles of carbon in the CO₂ produced:
- The molar mass of CO₂ is calculated as follows:
[tex]\[ \text{Molar mass of CO}_2 = \text{Molar mass of C} + 2 \times \text{Molar mass of O} = 12.01 \, \text{g/mol} + 2 \times 16.00 \, \text{g/mol} = 44.01 \, \text{g/mol} \][/tex]
- Given the mass of CO₂ is 0.4950 g, the moles of CO₂ can be calculated using:
[tex]\[ \text{Moles of CO}_2 = \frac{\text{Mass of CO}_2}{\text{Molar mass of CO}_2} = \frac{0.4950 \, \text{g}}{44.01 \, \text{g/mol}} = 0.01125 \, \text{moles} \][/tex]
- Since each mole of CO₂ contains one mole of carbon, the moles of carbon are equal to the moles of CO₂:
[tex]\[ \text{Moles of C} = 0.01125 \, \text{moles} \][/tex]
- Calculate the mass of carbon using its molar mass:
[tex]\[ \text{Mass of C} = \text{Moles of C} \times \text{Molar mass of C} = 0.01125 \, \text{moles} \times 12.01 \, \text{g/mol} = 0.135 \, \text{g} \][/tex]
2. Determine the moles of hydrogen in the H₂O produced:
- The molar mass of H₂O is calculated as follows:
[tex]\[ \text{Molar mass of H}_2\text{O} = 2 \times \text{Molar mass of H} + \text{Molar mass of O} = 2 \times 1.008 \, \text{g/mol} + 16.00 \, \text{g/mol} = 18.016 \, \text{g/mol} \][/tex]
- Given the mass of H₂O is 0.2025 g, the moles of H₂O can be calculated using:
[tex]\[ \text{Moles of H}_2\text{O} = \frac{\text{Mass of H}_2\text{O}}{\text{Molar mass of H}_2\text{O}} = \frac{0.2025 \, \text{g}}{18.016 \, \text{g/mol}} = 0.01125 \, \text{moles} \][/tex]
- Since each mole of H₂O contains two moles of hydrogen, the moles of hydrogen are:
[tex]\[ \text{Moles of H} = 2 \times 0.01125 \, \text{moles} = 0.0225 \, \text{moles} \][/tex]
- Calculate the mass of hydrogen using its molar mass:
[tex]\[ \text{Mass of H} = \text{Moles of H} \times \text{Molar mass of H} = 0.0225 \, \text{moles} \times 1.008 \, \text{g/mol} = 0.0227 \, \text{g} \][/tex]
3. Calculate the mass of oxygen in the original substance:
- Given the total mass of the organic substance is 0.2475 g, the mass of oxygen can be calculated by subtracting the masses of carbon and hydrogen from the total mass:
[tex]\[ \text{Mass of O} = \text{Total mass of substance} - (\text{Mass of C} + \text{Mass of H}) = 0.2475 \, \text{g} - (0.135 \, \text{g} + 0.0227 \, \text{g}) = 0.2475 \, \text{g} - 0.1577 \, \text{g} = 0.0898 \, \text{g} \][/tex]
4. Calculate the percentage composition of oxygen:
- Using the mass of oxygen, the percentage composition can be calculated as:
[tex]\[ \text{Percentage of O} = \left( \frac{\text{Mass of O}}{\text{Total mass of substance}} \right) \times 100 = \left( \frac{0.0898 \, \text{g}}{0.2475 \, \text{g}} \right) \times 100 \approx 36.27 \% \][/tex]
So the final answer is approximately [tex]\(36.27\%\)[/tex], which closely matches option D. However, this does not exactly match any of the given options A, B, or C. Consequently, the provided options might contain an error or ambiguity.
1. Determine the moles of carbon in the CO₂ produced:
- The molar mass of CO₂ is calculated as follows:
[tex]\[ \text{Molar mass of CO}_2 = \text{Molar mass of C} + 2 \times \text{Molar mass of O} = 12.01 \, \text{g/mol} + 2 \times 16.00 \, \text{g/mol} = 44.01 \, \text{g/mol} \][/tex]
- Given the mass of CO₂ is 0.4950 g, the moles of CO₂ can be calculated using:
[tex]\[ \text{Moles of CO}_2 = \frac{\text{Mass of CO}_2}{\text{Molar mass of CO}_2} = \frac{0.4950 \, \text{g}}{44.01 \, \text{g/mol}} = 0.01125 \, \text{moles} \][/tex]
- Since each mole of CO₂ contains one mole of carbon, the moles of carbon are equal to the moles of CO₂:
[tex]\[ \text{Moles of C} = 0.01125 \, \text{moles} \][/tex]
- Calculate the mass of carbon using its molar mass:
[tex]\[ \text{Mass of C} = \text{Moles of C} \times \text{Molar mass of C} = 0.01125 \, \text{moles} \times 12.01 \, \text{g/mol} = 0.135 \, \text{g} \][/tex]
2. Determine the moles of hydrogen in the H₂O produced:
- The molar mass of H₂O is calculated as follows:
[tex]\[ \text{Molar mass of H}_2\text{O} = 2 \times \text{Molar mass of H} + \text{Molar mass of O} = 2 \times 1.008 \, \text{g/mol} + 16.00 \, \text{g/mol} = 18.016 \, \text{g/mol} \][/tex]
- Given the mass of H₂O is 0.2025 g, the moles of H₂O can be calculated using:
[tex]\[ \text{Moles of H}_2\text{O} = \frac{\text{Mass of H}_2\text{O}}{\text{Molar mass of H}_2\text{O}} = \frac{0.2025 \, \text{g}}{18.016 \, \text{g/mol}} = 0.01125 \, \text{moles} \][/tex]
- Since each mole of H₂O contains two moles of hydrogen, the moles of hydrogen are:
[tex]\[ \text{Moles of H} = 2 \times 0.01125 \, \text{moles} = 0.0225 \, \text{moles} \][/tex]
- Calculate the mass of hydrogen using its molar mass:
[tex]\[ \text{Mass of H} = \text{Moles of H} \times \text{Molar mass of H} = 0.0225 \, \text{moles} \times 1.008 \, \text{g/mol} = 0.0227 \, \text{g} \][/tex]
3. Calculate the mass of oxygen in the original substance:
- Given the total mass of the organic substance is 0.2475 g, the mass of oxygen can be calculated by subtracting the masses of carbon and hydrogen from the total mass:
[tex]\[ \text{Mass of O} = \text{Total mass of substance} - (\text{Mass of C} + \text{Mass of H}) = 0.2475 \, \text{g} - (0.135 \, \text{g} + 0.0227 \, \text{g}) = 0.2475 \, \text{g} - 0.1577 \, \text{g} = 0.0898 \, \text{g} \][/tex]
4. Calculate the percentage composition of oxygen:
- Using the mass of oxygen, the percentage composition can be calculated as:
[tex]\[ \text{Percentage of O} = \left( \frac{\text{Mass of O}}{\text{Total mass of substance}} \right) \times 100 = \left( \frac{0.0898 \, \text{g}}{0.2475 \, \text{g}} \right) \times 100 \approx 36.27 \% \][/tex]
So the final answer is approximately [tex]\(36.27\%\)[/tex], which closely matches option D. However, this does not exactly match any of the given options A, B, or C. Consequently, the provided options might contain an error or ambiguity.
