To calculate the theoretical yield of CO₂ when 24 grams of CH₄ (methane) is added to the reaction, follow these detailed steps:
1. Identify given data and constants:
- Mass of CH₄ given: 24 grams
- Molar mass of CH₄ (methane): 16.04 g/mol
- Molar mass of CO₂ (carbon dioxide): 44.01 g/mol
2. Calculate the moles of CH₄ added:
The number of moles is calculated using the formula:
[tex]\[
\text{moles of CH}_4 = \frac{\text{mass of CH}_4}{\text{molar mass of CH}_4}
\][/tex]
Substituting the values:
[tex]\[
\text{moles of CH}_4 = \frac{24 \text{ grams}}{16.04 \text{ g/mol}} \approx 1.4962593516209477 \text{ moles}
\][/tex]
3. Determine the moles of CO₂ produced:
From the balanced chemical equation:
[tex]\[
\text{CH}_4 + 2 \text{O}_2 \rightarrow \text{CO}_2 + 2 \text{H}_2\text{O}
\][/tex]
We see that 1 mole of CH₄ produces 1 mole of CO₂. Therefore, the moles of CO₂ produced will be equal to the moles of CH₄ reacted:
[tex]\[
\text{moles of CO}_2 = \text{moles of CH}_4 \approx 1.4962593516209477 \text{ moles}
\][/tex]
4. Calculate the theoretical yield of CO₂ in grams:
The mass of CO₂ produced can be calculated using the formula:
[tex]\[
\text{mass of CO}_2 = \text{moles of CO}_2 \times \text{molar mass of CO}_2
\][/tex]
Substituting the values:
[tex]\[
\text{mass of CO}_2 = 1.4962593516209477 \text{ moles} \times 44.01 \text{ g/mol} \approx 65.85037406483791 \text{ grams}
\][/tex]
Therefore, the theoretical yield of CO₂ when 24 grams of CH₄ is reacted is approximately 65.85 grams.
