Bond Enthalpies

Bond enthalpy (also known as bond energy) is defined as the amount of energy required to break one mole of the stated bond. For example, the bond energy of a O-H single bond is 463 kJ/mol. This means that it requires 463 kJ of energy to break one mole of O-H bonds. Note: In order to break any bond, energy must be absorbed. Therefore, bond breaking is always an endothermic change (ΔH > 0). Conversely, energy is always released upon the formation of a bond. Therefore, bond making is always an exothermic change (ΔH < 0). Find a list of bond energies in the table shown at the bottom of this page.

Change in reaction enthalpy (ΔH_rxn) can be approximated from bond energy data. One can assume that during a chemical change, all bonds in the reactants are broken yielding free atoms as shown in step 1 in the diagram below. Then those atoms recombine to form the new bonds found in the products (step 2).

The overall reaction enthalpy change is easily obtained via Hess' Law:

\[\Delta H_{\rm rxn} = \Delta H_1 + \Delta H_2\]

To summarize, the change in enthalpy for a given reaction will the combined total of the energy required to break any bonds that are broken and the energy released from any bonds that are formed.  

\[\Delta H_{\rm rxn} = \Sigma \Delta H_{\rm breaking} + \Sigma \Delta H_{\rm making}\]

This is the sum of the bond enthalpies of the broken bonds minus the sum of the energies of the bonds that are formed (since forming bonds will release energy).  One advantage of this method is that you only need to look at the bonds that are changing in a given reaction.

Example: Consider the hydrogenation of ethene to give ethane.

\[\rm C_2 H_4 (g) + H_2 (g) \rightarrow C_2 H_6 (g)\]

Here, we need to break the C=C bond in ethene, and the H-H bond in H₂. Then we need to form two new C-H bonds and a C-C bond in ethane. (See Bond Energy table at the bottom of this page) A H-H bond enthalpy (BE) is 436 kJ/mol, a C=C bond is 602 kJ/mol, a C-C bond is 346 kJ/mol, and a C-H BE is 413 kJ/mol. All of the changing energies for the reactants and products for this reaction are shown in the table below.

Combining both sides gives: +1038 -1172 = -134 kJ/mol

Although the above method is the most efficient in that you only break what you have to, you can also calculate the enthalpy by breaking all the reactant bonds and forming all the product bonds.  This results in the change in enthalpy being the sum of the all the reactant bond enthalpies minus the sum of all the product bond enthalpies. "Bond Enthalpy" or "Bond Energy" is simply shown as BE in the formula below:

\[\Delta H_{\rm rxn} = \Sigma BE_{\rm reactants} - \Sigma BE_{\rm products}\]

This can often be a very lengthy calculation if there are a lot of bonds, so you should practice to just look and calculate for the bonds that are changing as in the example above.

In the table of bond energies shown below, please note that the top table is for single bonds and the bottom table is for double and triple bonds. Make sure you have the right bond for your specific compound(s).