Question
How to calculate the mass percent of MgO in a mixture after reacting with CO2
Answers
GPT-4o mini
To calculate the mass percent of \( \text{MgO} \) in a mixture after reacting with \( \text{CO}_2 \), you first need to know the mass of \( \text{CO}_2 \) that reacted and the stoichiometry of the reaction. The reaction of magnesium oxide (\( \text{MgO} \)) with \( \text{CO}_2 \) forms magnesium carbonate (\( \text{MgCO}_3 \)). The balanced chemical equation for this reaction is:
\[
\text{MgO} + \text{CO}_2 \rightarrow \text{MgCO}_3
\]
### Steps to Calculate Mass Percent of \( \text{MgO} \):
1. **Determine the Mass of \( \text{CO}_2 \) Reacted:**
Measure or calculate the mass of \( \text{CO}_2 \) that was consumed in the reaction.
2. **Calculate the Moles of \( \text{CO}_2 \):**
Use the molar mass of \( \text{CO}_2 \) (approximately \( 44.01 \, \text{g/mol} \)) to convert the mass of \( \text{CO}_2 \) to moles:
\[
\text{moles of } \text{CO}_2 = \frac{\text{mass of } \text{CO}_2}{44.01 \, \text{g/mol}}
\]
3. **Determine the Moles of \( \text{MgO} \):**
According to the balanced equation, 1 mole of \( \text{CO}_2 \) reacts with 1 mole of \( \text{MgO} \). Thus, the moles of \( \text{MgO} \) that reacted will be equal to the moles of \( \text{CO}_2 \) reacted:
\[
\text{moles of } \text{MgO} = \text{moles of } \text{CO}_2
\]
4. **Convert Moles of \( \text{MgO} \) to Mass:**
Use the molar mass of \( \text{MgO} \) (approximately \( 40.30 \, \text{g/mol} \) for \( \text{Mg} \) and \( 16.00 \, \text{g/mol} \) for \( \text{O} \)):
\[
\text{mass of } \text{MgO} = \text{moles of } \text{MgO} \times 40.30 \, \text{g/mol}
\]
5. **Determine the Total Mass of the Mixture:**
You will need the initial total mass of the mixture before the reaction took place.
6. **Calculate the Mass Percent of \( \text{MgO} \):**
Finally, use the mass of \( \text{MgO} \) and the total mass of the mixture to calculate the mass percent:
\[
\text{Mass percent of } \text{MgO} = \left( \frac{\text{mass of } \text{MgO}}{\text{total mass of mixture}} \right) \times 100
\]
### Example Calculation:
Suppose you started with \( 10.0 \, \text{g} \) of a mixture, and you found that \( 2.2 \, \text{g} \) of \( \text{CO}_2 \) reacted.
1. **Calculate moles of \( \text{CO}_2 \):**
\[
\text{moles of } \text{CO}_2 = \frac{2.2 \, \text{g}}{44.01 \, \text{g/mol}} \approx 0.050 \, \text{mol}
\]
2. **Moles of \( \text{MgO} \):**
\[
\text{moles of } \text{MgO} = 0.050 \, \text{mol}
\]
3. **Calculate mass of \( \text{MgO} \):**
\[
\text{mass of } \text{MgO} = 0.050 \, \text{mol} \times 40.30 \, \text{g/mol} \approx 2.015 \, \text{g}
\]
4. **Total mass of the mixture:** \( 10.0 \, \text{g} \)
5. **Calculate mass percent of \( \text{MgO} \):**
\[
\text{Mass percent of } \text{MgO} = \left( \frac{2.015 \, \text{g}}{10.0 \, \text{g}} \right) \times 100 \approx 20.15\%
\]
By following these steps, you can accurately calculate the mass percent of \( \text{MgO} \) in a mixture after it has reacted with \( \text{CO}_2 \).
\[
\text{MgO} + \text{CO}_2 \rightarrow \text{MgCO}_3
\]
### Steps to Calculate Mass Percent of \( \text{MgO} \):
1. **Determine the Mass of \( \text{CO}_2 \) Reacted:**
Measure or calculate the mass of \( \text{CO}_2 \) that was consumed in the reaction.
2. **Calculate the Moles of \( \text{CO}_2 \):**
Use the molar mass of \( \text{CO}_2 \) (approximately \( 44.01 \, \text{g/mol} \)) to convert the mass of \( \text{CO}_2 \) to moles:
\[
\text{moles of } \text{CO}_2 = \frac{\text{mass of } \text{CO}_2}{44.01 \, \text{g/mol}}
\]
3. **Determine the Moles of \( \text{MgO} \):**
According to the balanced equation, 1 mole of \( \text{CO}_2 \) reacts with 1 mole of \( \text{MgO} \). Thus, the moles of \( \text{MgO} \) that reacted will be equal to the moles of \( \text{CO}_2 \) reacted:
\[
\text{moles of } \text{MgO} = \text{moles of } \text{CO}_2
\]
4. **Convert Moles of \( \text{MgO} \) to Mass:**
Use the molar mass of \( \text{MgO} \) (approximately \( 40.30 \, \text{g/mol} \) for \( \text{Mg} \) and \( 16.00 \, \text{g/mol} \) for \( \text{O} \)):
\[
\text{mass of } \text{MgO} = \text{moles of } \text{MgO} \times 40.30 \, \text{g/mol}
\]
5. **Determine the Total Mass of the Mixture:**
You will need the initial total mass of the mixture before the reaction took place.
6. **Calculate the Mass Percent of \( \text{MgO} \):**
Finally, use the mass of \( \text{MgO} \) and the total mass of the mixture to calculate the mass percent:
\[
\text{Mass percent of } \text{MgO} = \left( \frac{\text{mass of } \text{MgO}}{\text{total mass of mixture}} \right) \times 100
\]
### Example Calculation:
Suppose you started with \( 10.0 \, \text{g} \) of a mixture, and you found that \( 2.2 \, \text{g} \) of \( \text{CO}_2 \) reacted.
1. **Calculate moles of \( \text{CO}_2 \):**
\[
\text{moles of } \text{CO}_2 = \frac{2.2 \, \text{g}}{44.01 \, \text{g/mol}} \approx 0.050 \, \text{mol}
\]
2. **Moles of \( \text{MgO} \):**
\[
\text{moles of } \text{MgO} = 0.050 \, \text{mol}
\]
3. **Calculate mass of \( \text{MgO} \):**
\[
\text{mass of } \text{MgO} = 0.050 \, \text{mol} \times 40.30 \, \text{g/mol} \approx 2.015 \, \text{g}
\]
4. **Total mass of the mixture:** \( 10.0 \, \text{g} \)
5. **Calculate mass percent of \( \text{MgO} \):**
\[
\text{Mass percent of } \text{MgO} = \left( \frac{2.015 \, \text{g}}{10.0 \, \text{g}} \right) \times 100 \approx 20.15\%
\]
By following these steps, you can accurately calculate the mass percent of \( \text{MgO} \) in a mixture after it has reacted with \( \text{CO}_2 \).