Sure! Let's work through the problem step-by-step to find the amount of CO₂ produced from the combustion of 83.29 grams of Ctth, which we are assuming to be octane (C₈H₁₈).
1. Determine the molar mass of octane (C₈H₁₈):
- Carbon (C) has an atomic mass of approximately 12.01 g/mol.
- Hydrogen (H) has an atomic mass of approximately 1.01 g/mol.
- Octane has 8 carbon atoms and 18 hydrogen atoms.
- Thus, the molar mass of C₈H₁₈ is:
[tex]\[
\text{Molar mass of C₈H₁₈} = (8 \times 12.01) + (18 \times 1.01) = 96.08 + 18.18 = 114.26 \text{ g/mol}
\][/tex]
2. Calculate the number of moles of octane:
- The given mass of octane (C₈H₁₈) is 83.29 grams.
- The number of moles of octane is calculated by:
[tex]\[
\text{Moles of C₈H₁₈} = \frac{\text{mass}}{\text{molar mass}} = \frac{83.29}{114.26} \approx 0.729 \text{ moles}
\][/tex]
3. Write the balanced combustion equation for octane (C₈H₁₈):
[tex]\[
2 \text{C₈H₁₈} + 25 \text{O₂} \rightarrow 16 \text{CO₂} + 18 \text{H₂O}
\][/tex]
- According to the balanced equation, 2 moles of C₈H₁₈ produce 16 moles of CO₂.
4. Calculate the moles of CO₂ produced:
- From the stoichiometry of the combustion reaction:
[tex]\[
\text{Moles of CO₂} = \text{Moles of C₈H₁₈} \times \left(\frac{16}{2}\right) = 0.729 \times 8 \approx 5.832 \text{ moles}
\][/tex]
5. Determine the molar mass of CO₂:
- Carbon (C) has an atomic mass of approximately 12.01 g/mol.
- Oxygen (O) has an atomic mass of approximately 16.00 g/mol.
- CO₂ has 1 carbon atom and 2 oxygen atoms.
- Thus, the molar mass of CO₂ is:
[tex]\[
\text{Molar mass of CO₂} = 12.01 + (2 \times 16.00) = 12.01 + 32.00 = 44.01 \text{ g/mol}
\][/tex]
6. Calculate the mass of CO₂ produced:
- The mass of CO₂ produced is given by:
[tex]\[
\text{Mass of CO₂} = \text{moles of CO₂} \times \text{molar mass of CO₂} = 5.832 \times 44.01 \approx 256.65 \text{ grams}
\][/tex]
Therefore, the amount of CO₂ produced by the combustion of 83.29 grams of Ctth (octane) is approximately 256.65 grams.
