Ethanol is a possible fuel. Use average bond energies to calculate \( \Delta H_{\mathrm{rXn}} \) for the combustion of ethanol. \[ \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(\mathrm{g})+3 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})+3 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \]

To calculate the enthalpy change (\( \Delta H_{\mathrm{rXn}} \)) for the combustion of ethanol using average bond energies, we need to follow these steps: 1. **Write the balanced chemical equation**: \[ \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(\mathrm{g}) + 3 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{g}) + 3 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \] 2. **Identify the bonds broken and formed**: - **Bonds broken** in reactants: - In ethanol (\( \mathrm{CH}_3\mathrm{CH}_2\mathrm{OH} \)): - 6 C-H bonds - 1 C-C bond - 1 O-H bond - In \( 3 \mathrm{O}_2 \): - 3 O=O bonds (each O2 has a double bond) - **Bonds formed** in products: - In \( 2 \mathrm{CO}_2 \): - 4 C=O bonds (2 per CO2) - In \( 3 \mathrm{H}_2\mathrm{O} \): - 6 O-H bonds (2 per H2O) 3. **List average bond energies** (in kJ/mol): - C-H: 413 kJ/mol - C-C: 348 kJ/mol - O-H: 463 kJ/mol - O=O: 498 kJ/mol - C=O (in CO2): 799 kJ/mol - O-H (in H2O): 463 kJ/mol 4. **Calculate the total energy for bonds broken and formed**: - **Bonds broken**: - C-H: \( 6 \times 413 = 2478 \, \text{kJ} \) - C-C: \( 1 \times 348 = 348 \, \text{kJ} \) - O-H: \( 1 \times 463 = 463 \, \text{kJ} \) - O=O: \( 3 \times 498 = 1494 \, \text{kJ} \) - **Total energy for bonds broken**: \[ 2478 + 348 + 463 + 1494 = 4833 \, \text{kJ} \] - **Bonds formed**: - C=O (in CO2): \( 4 \times 799 = 3196 \, \text{kJ} \) - O-H (in H2O): \( 6 \times 463 = 2778 \, \text{kJ} \) - **Total energy for bonds formed**: \[ 3196 + 2778 = 5974 \, \text{kJ} \] 5. **Calculate \( \Delta H_{\mathrm{rXn}} \)**: \[ \Delta H_{\mathrm{rXn}} = \text{Energy of bonds broken} - \text{Energy of bonds formed} \] \[ \Delta H_{\mathrm{rXn}} = 4833 \, \text{kJ} - 5974 \, \text{kJ} = -1141 \, \text{kJ} \] Thus, the enthalpy change for the combustion of ethanol is: \[ \Delta H_{\mathrm{rXn}} \approx -1141 \, \text{kJ} \] This indicates that the combustion of ethanol is an exothermic reaction, releasing approximately 1141 kJ of energy.