Bond Energy Calculations

(Higher Tier only) The whole of this lesson, calculating energy changes from bond energies, is assessed only at Higher Tier in AQA GCSE Chemistry (8462).

During a chemical reaction the bonds in the reactants must be broken and new bonds are made in the products. Each of these steps involves energy, and the two go in opposite directions.

• Breaking bonds is endothermic. Energy has to be supplied to pull bonded atoms apart.
• Making bonds is exothermic. Energy is released when new bonds form.

Bond breaking takes energy in; bond making gives energy out. Remembering this direction is the key to every calculation in this topic.

The bond energy of a particular bond is the amount of energy needed to break one mole of that bond. It is the same value as the energy released when one mole of that bond is formed. Bond energies are supplied in the exam question, measured in kilojoules per mole (kJ/mol); you never have to remember them.

Whether the whole reaction gives out or takes in energy depends on which is larger: the total energy to break the reactant bonds, or the total energy released making the product bonds.

To find the energy change for a reaction, compare the energy needed to break all the reactant bonds with the energy released making all the product bonds.

$\text{overall energy change}=\text{(energy to break bonds in reactants)}-\text{(energy released making bonds in products)}$

The sign of the answer tells you the type of reaction:

Sign of overall energy change	What it means	Type of reaction
Negative	More energy released making bonds than needed to break them	Exothermic
Positive	More energy needed to break bonds than released making them	Endothermic

So a reaction is exothermic when the energy released forming the new bonds is greater than the energy needed to break the existing bonds. It is endothermic when breaking the bonds needs more energy than is released when the new bonds form.

A negative overall energy change means energy is transferred to the surroundings, so the reaction is exothermic. Keep the sign; it carries the meaning.

Calculate the overall energy change for the reaction of hydrogen with chlorine:

$H_2+C{l}_2\to 2HCl$

Use these supplied bond energies: H–H = 436 kJ/mol, Cl–Cl = 242 kJ/mol, H–Cl = 431 kJ/mol.

Step 1 — count and total the bonds broken (reactants).

1 × H–H  = 1 × 436 = 436
1 × Cl–Cl = 1 × 242 = 242
Total bonds broken   = 678 kJ/mol

Step 2 — count and total the bonds made (products).

There are 2 molecules of HCl, so 2 H–Cl bonds are made.

2 × H–Cl = 2 × 431 = 862
Total bonds made    = 862 kJ/mol

Step 3 — apply the formula.

$\text{overall energy change}=678-862=-184\text{kJ/mol}$

The value is negative, so the reaction is exothermic. More energy was released making the two H–Cl bonds than was needed to break the H–H and Cl–Cl bonds.

Calculate the overall energy change for the complete combustion of methane:

$C{H}_4+2O_2\to C{O}_2+2H_{2}O$

Supplied bond energies: C–H = 412 kJ/mol, O=O = 498 kJ/mol, C=O = 805 kJ/mol, O–H = 463 kJ/mol.

Step 1 — bonds broken (reactants). Methane has 4 C–H bonds; there are 2 O=O bonds in the two oxygen molecules.

4 × C–H  = 4 × 412 = 1648
2 × O=O  = 2 × 498 =  996
Total bonds broken  = 2644 kJ/mol

Step 2 — bonds made (products). CO₂ has 2 C=O bonds; each of the 2 water molecules has 2 O–H bonds, giving 4 O–H bonds in total.

2 × C=O  = 2 × 805 = 1610
4 × O–H  = 4 × 463 = 1852
Total bonds made    = 3462 kJ/mol

Step 3 — apply the formula.

$\text{overall energy change}=2644-3462=-818\text{kJ/mol}$

The value is negative, so combustion of methane is exothermic, which fits everyday experience: burning methane releases heat. Counting every bond in the balanced equation, including all four O–H bonds across the two water molecules, is what makes this calculation correct.

Bond energies put numbers on the shape of a reaction profile. The activation energy corresponds to breaking the reactant bonds (climbing the barrier), and the fall to the products corresponds to the energy released when the new bonds form.

• If bond making releases more energy than bond breaking absorbs, the products sit lower than the reactants: an exothermic profile with a negative overall energy change.
• If bond breaking absorbs more energy than bond making releases, the products sit higher than the reactants: an endothermic profile with a positive overall energy change.

Worked check. Suppose the bonds broken total 1500 kJ/mol and the bonds made total 1750 kJ/mol.

$\text{overall energy change}=1500-1750=-250\text{kJ/mol}$

The answer is negative, so the reaction is exothermic and the products are drawn lower than the reactants on the profile. The size of the number, 250 kJ/mol, is the vertical gap between the reactant and product levels.

1. Getting the formula the wrong way round

The order is bonds broken minus bonds made (reactants minus products). Reversing it flips the sign, so an exothermic reaction wrongly looks endothermic. Always subtract the product bond total from the reactant bond total.

2. Not counting every bond in the balanced equation

If two water molecules form, that is four O–H bonds, not two. Multiply the bond energy by the number of that bond across all the molecules in the balanced equation before adding.

3. Dropping the negative sign

A negative answer is not a mistake to be corrected; it is the information that the reaction is exothermic. Keep the sign and use it to state the type of reaction.

4. Saying breaking bonds releases energy

Breaking bonds is endothermic: energy goes in. Making bonds is exothermic: energy comes out. Swapping these leads to the wrong conclusion about the whole reaction.

5. Forgetting to double up diatomic reactants

Two O₂ molecules contain two O=O bonds; two H₂ molecules contain two H–H bonds. Check the large numbers in front of each formula in the balanced equation and multiply the bonds accordingly.