Bond Energy Calculations

Breaking a bond needs energy to overcome the attraction holding its atoms together. Making a new bond releases energy as that attraction forms. The energy is not created or used up: it is transferred between the reacting chemicals and their surroundings. A reaction is exothermic overall when making bonds releases more energy than breaking bonds requires. If breaking bonds requires more than making bonds releases, it is endothermic overall.

Calculating from bond energies

A bond energy tells us how much energy is needed to break one mole of a named covalent bond in gaseous substances. Values are given in $\text{kJ mol}^{-1}$. To calculate an energy change, use the balanced equation to count each type of bond in the reactants and products. Multiply each count by its bond energy, add the energies for bonds broken, then do the same for bonds made:

$\Delta H=\sum E_{\text{bonds broken}}-\sum E_{\text{bonds made}}$

The first total is energy required; the second is energy released. For a calculation per mole of reaction as written, a negative $\Delta H$ means energy is transferred to the surroundings and the reaction is exothermic. A positive $\Delta H$ means energy is taken in from the surroundings and the reaction is endothermic.

Counting bonds in a reaction

Consider $2\mathrm{H_2}+\mathrm{O_2}\rightarrow2\mathrm{H_2O}$. Each hydrogen molecule has one H–H bond and the oxygen molecule has one O=O bond. Each water molecule has two O–H bonds, so the two water molecules have four, not two, O–H bonds. The coefficients in the balanced equation matter just as much as the bonds within each molecule.

Calculating the energy change when water forms

For 2H₂ + O₂ → 2H₂O, the reactants contain two H–H bonds and one O=O bond; the products contain four O–H bonds. Using bond energies H–H = 436 kJ mol⁻¹, O=O = 498 kJ mol⁻¹ and O–H = 463 kJ mol⁻¹, calculate the energy change per mole of reaction as written.

The negative result means that, for the reaction as written, forming the O–H bonds releases more energy than is needed to break the H–H and O=O bonds. It is therefore exothermic overall. Bond-energy calculations using mean values give an estimate of the energy change, rather than an exact value for every reaction.