Worked example 1
Estimate ΔH for CH₄(g) + 2 O₂(g) → CO₂(g) + 2 H₂O(g) using D(C-H) = 413, D(O=O) = 498, D(C=O) = 799, D(O-H) = 467 kJ/mol.
Try it first: List every bond on each side with its count before touching a number.
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Thermochemistry & ThermodynamicsBond EnergiesContent level: Core 22 min
Bond Enthalpies and Estimating Enthalpy Change
What you'll be able to do: Estimate a reaction enthalpy from average bond enthalpies and explain why the result is only an estimate.
Best after: Enthalpy of Reaction and Thermochemical Equations, Standard Enthalpies of Formation
Introduction
Bond enthalpies let you predict whether a reaction releases energy using nothing but a Lewis structure and a table of averages. The trade-off is accuracy, and knowing why the answer is approximate is part of the skill.
These are recommended, not required. You can start this lesson at any time.
Learning objectives
- Explain why bond breaking is endothermic and bond making exothermic
- Estimate ΔH from average bond enthalpies
- Count bonds correctly from structural formulas
- Explain the limitations of the bond enthalpy method
Lesson
Breaking costs, making pays
A bond exists because the bonded arrangement is lower in energy. Pulling the atoms apart requires that energy back, so bond dissociation is always endothermic and the tabulated values are always positive. Forming the same bond releases the same magnitude.
There is no such thing as a negative bond enthalpy in a table. The sign appears from which side of the calculation the bond is on.
The estimating relationship
Every reactant bond that changes must be broken and every product bond must be formed. Adding the costs and subtracting the payback gives the net enthalpy change.
ΔH = S(bonds broken) - S(bonds formed)
Counting bonds properly
Draw or visualise the structures. Methane has four C-H bonds, not one. O₂ is a double bond, N₂ is a triple bond, and CO₂ contains two C=O bonds. Miscounting the structures, rather than the arithmetic, is the usual source of error.
CH₄: 4 x C-H; CO₂: 2 x C=O; N₂: 1 x N N triple
Why the answer is approximate
A C-H bond in methane is not identical to a C-H bond in ethanol, so tables list an average across many compounds. The method also assumes every species is gaseous, because condensing to a liquid releases additional energy that bond enthalpies do not capture.
If a question quotes water as a liquid, expect a bond enthalpy estimate to disagree noticeably with the formation-data answer.
When to use which method
Use formation enthalpies when tabulated values exist and states matter, and use bond enthalpies for gas-phase reactions or when you only need to know whether a reaction is exothermic and roughly by how much.
Key ideas
Definition
Bond enthalpy
Energy required to break one mole of a specified bond in the gas phase, always positive.
Rule
Broken minus formed
ΔH is approximately the sum of bonds broken minus the sum of bonds formed.
Key concept
Average values
Table entries are averaged over many molecules, so results are estimates.
Assumption
Gas phase only
The method assumes all reactants and products are gases.
Key concept
Bond strength trend
For the same pair of atoms, triple bonds are stronger and shorter than double, which are stronger than single.
Equation
Enthalpy from bond enthalpies
ΔH = S D(bonds broken) - S D(bonds formed)
- D = average bond enthalpy in kJ/mol, always a positive number
Worked examples
Worked example 2
Estimate ΔH for H₂(g) + Cl₂(g) → 2 HCl(g) using D(H-H) = 436, D(Cl-Cl) = 242, D(H-Cl) = 431 kJ/mol.
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Worked example 3
A reaction has bonds broken totalling 1200 kJ and bonds formed totalling 1150 kJ. Is it exothermic or endothermic, and what does that say about relative bond strengths?
0 of 3 steps revealed.
Common mistakes
Writing bonds formed minus bonds broken.
Why it's wrong: It reverses the sign of the whole estimate.
Check instead: Broken first, because breaking is the cost you pay upfront.
Treating bond formation as requiring energy.
Why it's wrong: Forming a bond moves the system to a lower energy state, releasing energy.
Check instead: Breaking absorbs, forming releases.
Counting one C-H bond in methane instead of four.
Why it's wrong: Every bond present must be accounted for.
Check instead: Sketch the structure and count explicitly.
Expecting the bond enthalpy answer to match the formation-data answer exactly.
Why it's wrong: Table values are averages and the method assumes gases.
Check instead: Report it as an estimate and mention the phase assumption.
Practice this skill
No practice questions are available for this topic yet. You can still practice the whole unit.
What you should now know
Bond breaking always absorbs energy and bond making always releases it, so all tabulated bond enthalpies are positive. For a gas-phase reaction, ΔH is approximately the total energy of bonds broken minus the total energy of bonds formed. The values are averages taken across many molecules, so results are estimates, typically within a few tens of kilojoules. The method also assumes all species are gases, which is why it fails when liquids or solids are involved.
- Bond breaking absorbs energy, bond forming releases it
- Tabulated bond enthalpies are always positive
- ΔH is approximately bonds broken minus bonds formed
- Count every bond from the structure, not the formula alone
- Results are estimates and assume all species are gases
Sources and further reading
- Chemistry 2e, Section 8.1: Valence Bond Theory and Bond EnergiesPaul Flowers, Klaus Theopold, Richard Langley, William R. Robinson · OpenStax, Rice University · Chapter 7.5View source
Chemistry 2e, OpenStax, Rice University, licensed CC BY 4.0. License