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To calculate the enthalpy change ( H) for the reaction C + O2 -> CO2 using bond energies, we use the formula:

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A. -394 kJ/mol\text{A. -394 kJ/mol}

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To calculate the enthalpy change (ΔH\Delta H) for the reaction C+O2→CO2\text{C} + \text{O}_2 \rightarrow \text{CO}_2 using bond energies, we use the formula:

ΔH=∑(bond energies of bonds broken)−∑(bond energies of bonds formed)\Delta H = \sum (\text{bond energies of bonds broken}) - \sum (\text{bond energies of bonds formed})

Let's identify the bonds broken in the reactants and bonds formed in the products.

  • Reactants:

    • C\text{C} (graphite): The energy given for C(graphite) (717 kJ/mol) represents the energy required to atomize one mole of solid carbon into gaseous carbon atoms. This is an energy input, similar to breaking bonds.
    • O2\text{O}_2: This molecule contains one O=O\text{O}=\text{O} double bond. The energy required to break this bond is 498 kJ/mol.

  • Products:

    • CO2\text{CO}_2: This molecule has a linear structure with two C=O\text{C}=\text{O} double bonds. The energy released when these bonds are formed is 2×805 kJ/mol2 \times 805 \text{ kJ/mol}.

  1. Calculate the total energy required to break bonds (reactants).

    Energy to atomize C(graphite) = 717 kJ/mol717 \text{ kJ/mol}
    Energy to break 1 mole of O=O\text{O}=\text{O} bonds = 498 kJ/mol498 \text{ kJ/mol}
    Total energy for bond breaking = 717 kJ/mol+498 kJ/mol=1215 kJ/mol717 \text{ kJ/mol} + 498 \text{ kJ/mol} = 1215 \text{ kJ/mol}

  2. Calculate the total energy released when bonds are formed (products).

    Energy released from forming 2 moles of C=O\text{C}=\text{O} bonds = 2×805 kJ/mol=1610 kJ/mol2 \times 805 \text{ kJ/mol} = 1610 \text{ kJ/mol}

  3. Calculate the enthalpy change (ΔH\Delta H).

    ΔH=(Energy for bond breaking)−(Energy for bond formation)\Delta H = (\text{Energy for bond breaking}) - (\text{Energy for bond formation}) ΔH=1215 kJ/mol−1610 kJ/mol\Delta H = 1215 \text{ kJ/mol} - 1610 \text{ kJ/mol} ΔH=−395 kJ/mol\Delta H = -395 \text{ kJ/mol}

    Comparing this value to the given options, -394 kJ/mol is the closest.

    The final answer is A. -394 kJ/mol\text{A. -394 kJ/mol}.

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