Calculate reaction enthalpy from bond energies
Estimate ΔHr by adding the energy to break reactant bonds and subtracting energy released when product bonds form.
AS Level; Cambridge International Chemistry 9701, 2025–2027 syllabus. Report signs, states, units and significant figures consistently. Standard conditions use 298 K and 101 kPa in this syllabus. Written practice is self-checked
Before you begin
- Rearrange a formula, balance a chemical equation and use temperature differences.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which expression estimates ΔHr from bond energies?
What you will learn
- Calculate ΔHr from bond energies
- Count each bond using balanced molecular equations
- Interpret the sign and the limits of average bond energies
Count bonds broken and formed from the balanced equation
For the reaction as written, ΔHr ≈ Σ(bond energies of bonds broken) − Σ(bond energies of bonds formed). Breaking reactant bonds is positive; forming product bonds contributes energy release, so it is subtracted.
Multiply each bond energy by the number of bonds in the balanced equation. For a double bond count two shared pairs as specified by the data, and include all bonds in every reactant and product molecule.
Use the estimate with its stated scope
Bond-energy calculations commonly use average energies for bonds in gaseous molecules, so the calculated reaction enthalpy is an estimate. Compare results at sensible precision and do not present an approximate average-data result as an exact measurement.
Check whether the question asks for the reaction as written or per mole of a particular product. Changing the equation coefficients changes the enthalpy amount proportionally.
Pause and explain
How many H–Cl bonds form in H₂ + Cl₂ → 2HCl?
Worked example
Calculate ΔHr for H₂(g) + Cl₂(g) → 2HCl(g), using H–H 436, Cl–Cl 242 and H–Cl 431 kJ mol⁻¹.
Show the worked solution
- Break one H–H and one Cl–Cl bond: 436 + 242 = 678 kJ mol⁻¹.
- Form two H–Cl bonds: 2 × 431 = 862 kJ mol⁻¹ released.
- ΔHr = 678 − 862.
Answer ΔHr = −184 kJ mol⁻¹ for the equation as written.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
For H₂ + Cl₂ → 2HCl, calculate ΔHr from H–H 436, Cl–Cl 242 and H–Cl 431 kJ mol⁻¹.
Give me a hint
Add energies for one H–H and one Cl–Cl bond, then subtract two H–Cl energies.
Compare my reasoning
- Broken = 436 + 242 = 678.
- Formed = 2 × 431 = 862.
- ΔHr = 678 − 862.
ΔHr = −184 kJ mol⁻¹.
Look for these in your work
- Bond counts correct
- Formula used
- Negative exothermic result stated
Estimate ΔHr for N₂ + 3H₂ → 2NH₃ using N≡N 944, H–H 436 and average N–H 390 kJ mol⁻¹.
Give me a hint
Break one triple bond and three H–H bonds; form six N–H bonds.
Compare my reasoning
- Broken = 944 + 3×436 = 2252 kJ mol⁻¹.
- Formed = 6×390 = 2340 kJ mol⁻¹.
- Subtract formed from broken.
ΔHr ≈ 2252 − 2340 = −88 kJ mol⁻¹ for the equation as written.
Look for these in your work
- Reactant bond count correct
- Six product N–H bonds counted
- Sign and estimate labelled
A student obtains +120 kJ mol⁻¹ for a reaction described by data where forming product bonds releases more energy than breaking reactant bonds absorbs. Diagnose the likely error.
Give me a hint
Use the physical energy direction to test the reported sign.
Compare my reasoning
- The verbal energy balance predicts net energy release.
- A releasing reaction has negative ΔH.
- Check whether product bond energies were added instead of subtracted.
The sign should be negative because more energy is released in bond formation. The student likely reversed the subtraction or bond-energy convention.
Look for these in your work
- Net energy direction assessed
- Sign related to exothermicity
- Likely arithmetic/convention error identified
Common mistakes
- Subtracting broken bonds and adding formed bonds
- Forgetting the product coefficient
- Counting two HCl bonds when the equation makes two molecules
- Reporting the value as exact when average data are used
What can you explain now?
Which expression estimates ΔHr from bond energies?
Compare with the explanation
Bonds broken − bonds formed
Breaking absorbs energy and forming releases it.
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Make it stick
Why do bond energies for product bonds appear with a minus sign in the ΔHr estimate?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.