Question

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Explanation:

Step1: Recall Bond Energy Formula

The heat of reaction \(\Delta H\) is calculated as:
\(\Delta H = \sum (\text{Bond Energies of Reactants Broken}) - \sum (\text{Bond Energies of Products Formed})\)

Step2: Identify Bonds in Reactants

• Reactants: \(2\,\text{CH}_4(g) + 3\,\text{O}_2(g)\)
• \( \text{CH}_4 \): Each \(\text{CH}_4\) has 4 \( \text{C-H} \) bonds. For \(2\,\text{CH}_4\), total \( \text{C-H} \) bonds: \(2 \times 4 = 8\).
• \( \text{O}_2 \): Each \(\text{O}_2\) has 1 \( \text{O=O} \) bond. For \(3\,\text{O}_2\), total \( \text{O=O} \) bonds: \(3 \times 1 = 3\).

Step3: Identify Bonds in Products

• Products: \(2\,\text{CO}(g) + 4\,\text{H}_2\text{O}(g)\)
• \( \text{CO} \): Each \(\text{CO}\) has 1 \( \text{C≡O} \) bond. For \(2\,\text{CO}\), total \( \text{C≡O} \) bonds: \(2 \times 1 = 2\).
• \( \text{H}_2\text{O} \): Each \(\text{H}_2\text{O}\) has 2 \( \text{O-H} \) bonds. For \(4\,\text{H}_2\text{O}\), total \( \text{O-H} \) bonds: \(4 \times 2 = 8\).

Step4: Use Bond Energy Values (from ALEKS or standard tables)

Assume standard bond energies (in kJ/mol):

• \( \text{C-H} = 413 \), \( \text{O=O} = 498 \), \( \text{C≡O} = 1072 \), \( \text{O-H} = 463 \).

Step5: Calculate Reactant Bond Energies

\(\sum \text{Reactant Bonds} = (8 \times 413) + (3 \times 498)\)
\(= 3304 + 1494 = 4798\,\text{kJ/mol}\)

Step6: Calculate Product Bond Energies

\(\sum \text{Product Bonds} = (2 \times 1072) + (8 \times 463)\)
\(= 2144 + 3704 = 5848\,\text{kJ/mol}\)

Step7: Compute \(\Delta H\)

\(\Delta H = 4798 - 5848 = -1050\,\text{kJ/mol}\)

Answer:

\(\boldsymbol{-1050}\) (rounded to nearest kJ/mol, depending on bond energy precision, but standard calculation gives \(-1050\) kJ/mol)