Calculating energy change from bond energies (HT)
The total energy change of a reaction is the difference between the energy needed to break bonds (in reactants) and the energy released when new bonds form (in products).
The key formula
ΔE = (energy in to break bonds) − (energy out forming bonds)
Or equivalently:
ΔE = sum of bond energies (reactants) − sum of bond energies (products)
Note: bond energies are positive numbers (energy required to break a bond).
Sign convention
- Negative ΔE → exothermic (more energy released than absorbed).
- Positive ΔE → endothermic (more energy absorbed than released).
Method (step-by-step)
- Write the balanced equation.
- Draw the displayed (full structural) formulae to count bonds.
- List bonds in reactants × number of each.
- List bonds in products × number of each.
- ΔE = sum(reactant bonds) − sum(product bonds).
✦Worked example— Worked example: H₂ + Cl₂ → 2HCl
Bonds in reactants:
- 1 × H–H = 436 kJ/mol
- 1 × Cl–Cl = 243 kJ/mol
- Total = 679 kJ/mol
Bonds in products:
- 2 × H–Cl = 2 × 432 = 864 kJ/mol
ΔE = 679 − 864 = −185 kJ/mol → exothermic.
✦Worked example— Worked example: combustion of methane
CH₄ + 2O₂ → CO₂ + 2H₂O
Bond energies (kJ/mol): C–H 413, O=O 498, C=O 805, O–H 463.
Reactants:
- 4 × C–H = 1652
- 2 × O=O = 996
- Total = 2648
Products:
- 2 × C=O = 1610
- 4 × O–H = 1852
- Total = 3462
ΔE = 2648 − 3462 = −814 kJ/mol → exothermic.
Why the formula works
Breaking bonds costs energy; making bonds gives energy back. If more is given back (products) than was paid (reactants), the reaction is exothermic and energy is released to the surroundings.
⚠Common mistakes
- Forgetting to multiply by the number of bonds. CH₄ has FOUR C–H bonds, not one.
- Wrong sign. ΔE = reactants − products (not products − reactants).
- Using bond ENTHALPY values from a different table — answers will differ from mark scheme.
- Counting bonds in molecules incorrectly — draw out the displayed formulae.
Links
Extends C5.1, C5.2. Used in C7.3 (combustion energy of fuels) and links to A-level enthalpy.
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