# D17.5 Bond Energy and Reaction Enthalpy Change

The enthalpy change for a gas-phase chemical reaction, ΔrH, equals the sum of the enthalpy required to break each of the bonds in the reactant molecules (energy in, positive sign) plus the sum of the enthalpy released when each of the bonds in the product molecules forms (energy out, negative sign). This can be expressed mathematically as:

ΔrH = ∑Ebonds broken – ∑Ebonds formed

Because the bond energy values provided in the Appendix are averaged over many different molecules for each type of bond, such a calculation using those values is not exact. But it provides a very good estimate of the enthalpy change of a reaction. For example, consider this balanced reaction:

H2(g) + Cl2(g) ⟶ 2 HCl(g)

One H–H bond (436 kJ/mol) and one Cl–Cl bond (242 kJ/mol) are broken; two H-Cl bonds (431 kJ/mol each) are formed. Representing bond enthalpies by Ebond, we have:

ΔrH = ∑Ebonds broken – ∑Ebonds formed = [DH-H + DCl-Cl] – [DH-Cl + DH-Cl]
ΔrH = [436 kJ/mol + 242 kJ/mol] – [2(431 kJ/mol)] = -184 kJ/mol

The number of bonds formed here is the same as the number of bonds broken. But because the bonds in the products are stronger than those in the reactants, the reaction has a net release (negative sign) of 184 kJ for every mole of reaction as written. The energy released increases the temperature of the surroundings (the reaction is exothermic).

Note that bond enthalpy calculations assume that all molecules are far from each other (which means that reactants and products must be in the gas phase). Additional enthalpy changes occur when a gas condenses to a liquid or a solid or dissolves into a solution; these transformations are not accounted for by bond enthalpies.

Exercise: Enthalpy Change from Bond Enthalpies 