Bond enthalpy

Bond enthalpy is the energy needed to break one mole of a particular covalent bond, with everything in the gas state. Breaking bonds always takes in energy, so bond enthalpies are positive. Because the same bond has a slightly different strength in different molecules, data tables give the mean bond enthalpy: an average over many compounds. You use them to estimate the enthalpy change of a reaction: ΔH = bonds broken − bonds formed.

What is bond enthalpy?

A covalent bond holds two atoms together. To pull them apart, energy must go in. For example, breaking one mole of H-H bonds in hydrogen gas to make two moles of hydrogen atoms takes 436 kJ, so the H-H bond enthalpy is +436 kJ mol⁻¹. Making the bond releases the same amount.

A C-H bond in methane is not quite as strong as a C-H bond in ethanol, because the rest of the molecule affects it. AQA A-level Chemistry asks you to define mean bond enthalpy, and notes that bond enthalpies are mean values across a range of compounds containing that bond.

These are the values used in the examples below. Different books give slightly different values, and exam questions always give you the ones to use.

How to calculate ΔH from bond enthalpies

AQA GCSE Chemistry explains it like this: energy must be supplied to break bonds in the reactants, and energy is released when bonds in the products are formed. The overall change is the difference:

1. Write the balanced equation and draw out every molecule so you can see each bond.
2. Add up the bond enthalpies of every bond in the reactants (bonds broken). Remember to multiply by the number of molecules.
3. Add up the bond enthalpies of every bond in the products (bonds formed).
4. Subtract: broken minus formed. A negative answer means exothermic; a positive answer means endothermic.

In an exothermic reaction, more energy is released forming the new bonds than was needed to break the old ones. In an endothermic reaction it is the other way round.

Worked examples

Example 1: burning methane

CH₄ + 2O₂ → CO₂ + 2H₂O, with everything as gases.

• Bonds broken: 4 C-H + 2 O=O = 4 × 413 + 2 × 498 = 1652 + 996 = 2648 kJ.
• Bonds formed: 2 C=O + 4 O-H = 2 × 805 + 4 × 463 = 1610 + 1852 = 3462 kJ.
• ΔH = 2648 − 3462 = −814 kJ mol⁻¹. It is exothermic.

Example 2: hydrogen and chlorine

H₂ + Cl₂ → 2HCl. Broken: 436 + 243 = 679 kJ. Formed: 2 × 432 = 864 kJ. ΔH = 679 − 864 = −185 kJ mol⁻¹.

Example 3: only count the bonds that change

C₂H₄ + H₂ → C₂H₆. Ethene has 4 C-H bonds and ethane has 6. You can count every bond, or only those that change: a C=C and an H-H break (612 + 436 = 1048 kJ), and a C-C and two new C-H bonds form (347 + 2 × 413 = 1173 kJ). ΔH = 1048 − 1173 = −125 kJ mol⁻¹. The four C-H bonds that stay the same cancel out.

Example 4: finding an unknown bond enthalpy

For N₂ + 3H₂ → 2NH₃, ΔH = −92 kJ mol⁻¹. Use N≡N = 945 and H-H = 436 to find the N-H bond enthalpy, x.

There are six N-H bonds because each of the two NH₃ molecules has three.

Try a bond energy calculation in this question from the Chemical Bonding course, then press Mark.

Why bond enthalpy answers are estimates

AQA asks you to explain why values from mean bond enthalpy calculations differ from those found with Hess's law. Two reasons:

• Mean values: each bond enthalpy is an average over many compounds, not the exact value for the molecules in your reaction.
• States: bond enthalpies apply to gases. Standard enthalpy changes use standard states, so if water is formed as a liquid, extra energy is released as it condenses.

That is why the methane answer, −814 kJ mol⁻¹, is less negative than the standard enthalpy of combustion of methane, which is about −890 kJ mol⁻¹ with liquid water as a product. Enthalpies of formation give more accurate answers: see the enthalpy calculator guide, or try both methods in the Enthalpy Calculator.

Check your understanding.

Common mistakes

• Subtracting the wrong way. It is broken minus formed. Formed minus broken gives the wrong sign.
• Forgetting the numbers in the equation. 2O₂ means two O=O bonds; 2H₂O means four O-H bonds.
• Missing double bonds. CO₂ has two C=O bonds, not two C-O bonds.
• Saying bond breaking releases energy. Breaking bonds always takes energy in.
• Treating the answer as exact. Mean bond enthalpies give an estimate.

Practise with a short timed paper

Bond energies come up in GCSE Chemistry Higher and in the first year of A-level Chemistry. The daily A-level Chemistry: Year 1 and GCSE Chemistry Higher papers are short timed papers of 8 questions, with a new one every day.

Read next

Chemistry · EnergeticsEnthalpy calculator: ΔH by Hess's law or bond enthalpiesFind the enthalpy change of a reaction from enthalpies of formation or combustion, combined equations or bond enthalpies, with working and worked examples.