Answer :
To determine how many grams of CO₂ can be produced from 100 grams of C₇H₆O₂ (benzoic acid), we need to perform stoichiometric calculations based on a balanced chemical equation. The combustion reaction for benzoic acid is:
[tex]\[ \text{C}_7\text{H}_6\text{O}_2 + 8 \, \text{O}_2 \rightarrow 7 \, \text{CO}_2 + 3 \, \text{H}_2\text{O} \][/tex]
### Step-by-Step Solution:
1. Calculate the Molecular Weight of C₇H₆O₂:
- Carbon (C): [tex]\( 12 \, \text{g/mol} \)[/tex]
- Hydrogen (H): [tex]\( 1 \, \text{g/mol} \)[/tex]
- Oxygen (O): [tex]\( 16 \, \text{g/mol} \)[/tex]
[tex]\[ \text{Molecular weight of C}_7\text{H}_6\text{O}_2 = (7 \times 12) + (6 \times 1) + (2 \times 16) \][/tex]
[tex]\[ = 84 + 6 + 32 \][/tex]
[tex]\[ = 122 \, \text{g/mol} \][/tex]
2. Calculate the Molecular Weight of CO₂:
- Carbon (C): [tex]\( 12 \, \text{g/mol} \)[/tex]
- Oxygen (O): [tex]\( 16 \, \text{g/mol} \)[/tex]
[tex]\[ \text{Molecular weight of CO}_2 = 12 + (2 \times 16) \][/tex]
[tex]\[ = 12 + 32 \][/tex]
[tex]\[ = 44 \, \text{g/mol} \][/tex]
3. Determine the Number of Moles of C₇H₆O₂:
- Given mass of C₇H₆O₂: [tex]\( 100 \, \text{g} \)[/tex]
[tex]\[ \text{Number of moles of C}_7\text{H}_6\text{O}_2 = \frac{\text{mass}}{\text{molecular weight}} \][/tex]
[tex]\[ = \frac{100 \, \text{g}}{122 \, \text{g/mol}} \][/tex]
[tex]\[ \approx 0.8197 \, \text{moles} \][/tex]
4. Use the Stoichiometric Ratio from the Balanced Equation:
- According to the balanced equation, 1 mole of [tex]\( \text{C}_7\text{H}_6\text{O}_2 \)[/tex] produces 7 moles of [tex]\( \text{CO}_2 \)[/tex].
[tex]\[ \text{Moles of CO}_2 = 0.8197 \, \text{moles of C}_7\text{H}_6\text{O}_2 \times 7 \][/tex]
[tex]\[ \approx 5.7379 \, \text{moles of CO}_2 \][/tex]
5. Calculate the Mass of CO₂ Produced:
- We now have the number of moles of CO₂ and we know the molecular weight of CO₂ is [tex]\( 44 \, \text{g/mol} \)[/tex].
[tex]\[ \text{Mass of CO}_2 = \text{moles of CO}_2 \times \text{molecular weight of CO}_2 \][/tex]
[tex]\[ = 5.7379 \, \text{moles} \times 44 \, \text{g/mol} \][/tex]
[tex]\[ \approx 252.468 \, \text{g} \][/tex]
### Conclusion:
Under the given conditions, 100 grams of C₇H₆O₂ can produce approximately 252.47 grams of CO₂.
[tex]\[ \text{C}_7\text{H}_6\text{O}_2 + 8 \, \text{O}_2 \rightarrow 7 \, \text{CO}_2 + 3 \, \text{H}_2\text{O} \][/tex]
### Step-by-Step Solution:
1. Calculate the Molecular Weight of C₇H₆O₂:
- Carbon (C): [tex]\( 12 \, \text{g/mol} \)[/tex]
- Hydrogen (H): [tex]\( 1 \, \text{g/mol} \)[/tex]
- Oxygen (O): [tex]\( 16 \, \text{g/mol} \)[/tex]
[tex]\[ \text{Molecular weight of C}_7\text{H}_6\text{O}_2 = (7 \times 12) + (6 \times 1) + (2 \times 16) \][/tex]
[tex]\[ = 84 + 6 + 32 \][/tex]
[tex]\[ = 122 \, \text{g/mol} \][/tex]
2. Calculate the Molecular Weight of CO₂:
- Carbon (C): [tex]\( 12 \, \text{g/mol} \)[/tex]
- Oxygen (O): [tex]\( 16 \, \text{g/mol} \)[/tex]
[tex]\[ \text{Molecular weight of CO}_2 = 12 + (2 \times 16) \][/tex]
[tex]\[ = 12 + 32 \][/tex]
[tex]\[ = 44 \, \text{g/mol} \][/tex]
3. Determine the Number of Moles of C₇H₆O₂:
- Given mass of C₇H₆O₂: [tex]\( 100 \, \text{g} \)[/tex]
[tex]\[ \text{Number of moles of C}_7\text{H}_6\text{O}_2 = \frac{\text{mass}}{\text{molecular weight}} \][/tex]
[tex]\[ = \frac{100 \, \text{g}}{122 \, \text{g/mol}} \][/tex]
[tex]\[ \approx 0.8197 \, \text{moles} \][/tex]
4. Use the Stoichiometric Ratio from the Balanced Equation:
- According to the balanced equation, 1 mole of [tex]\( \text{C}_7\text{H}_6\text{O}_2 \)[/tex] produces 7 moles of [tex]\( \text{CO}_2 \)[/tex].
[tex]\[ \text{Moles of CO}_2 = 0.8197 \, \text{moles of C}_7\text{H}_6\text{O}_2 \times 7 \][/tex]
[tex]\[ \approx 5.7379 \, \text{moles of CO}_2 \][/tex]
5. Calculate the Mass of CO₂ Produced:
- We now have the number of moles of CO₂ and we know the molecular weight of CO₂ is [tex]\( 44 \, \text{g/mol} \)[/tex].
[tex]\[ \text{Mass of CO}_2 = \text{moles of CO}_2 \times \text{molecular weight of CO}_2 \][/tex]
[tex]\[ = 5.7379 \, \text{moles} \times 44 \, \text{g/mol} \][/tex]
[tex]\[ \approx 252.468 \, \text{g} \][/tex]
### Conclusion:
Under the given conditions, 100 grams of C₇H₆O₂ can produce approximately 252.47 grams of CO₂.
