Study Guide

Bond enthalpies

IB Chemistry HL· 6 min read

1. 1. Bond Enthalpy: Definition and Trends★★☆☆☆⏱ 15 min

📘 Definition

Average Bond Enthalpy

Units:kJmol−1Units: kJ mol⁻¹

The average energy required to break 1 mole of a given covalent bond into separate gaseous atoms under standard conditions. Average values are used because bond strength varies slightly between different compounds.

Example:

The C-H bond enthalpy is averaged across alkanes, alcohols, carboxylic acids and other carbon-containing compounds.

Bond breaking is always endothermic (energy is absorbed), so all bond enthalpy values are positive. Bond forming is always exothermic (energy is released). Bond enthalpy directly correlates with bond strength and inversely correlates with bond length.

Bond

Bond length (pm)

Bond enthalpy (kJ mol⁻¹)

C-C

154

347

C=C

134

614

C≡C

120

839

C-O

143

360

C=O

120

745

📐 Worked Example

Use the table above to identify which bond is stronger, and which has the shorter length: C-O or C=O?

  1. 1

    Compare the bond enthalpy values from the table:

  2. 2
    C−O=360 kJ mol−1,C=O=745 kJ mol−1C-O = 360 \, \text{kJ mol}^{-1}, \quad C=O = 745 \, \text{kJ mol}^{-1}
  3. 3

    Higher bond enthalpy means a stronger bond, so C=O is stronger than C-O.

  4. 4

    Stronger bonds pull atoms closer together, so C=O has a shorter bond length than C-O.

Exam tip:

Examiners regularly test the inverse relationship between bond enthalpy and bond length — never mix this up.

2. 2. Calculating Enthalpy Change of Reaction★★★☆☆⏱ 25 min

✓ Calculator OK

To calculate the total enthalpy change of a reaction, we account for all energy absorbed to break bonds in reactants, and all energy released when new bonds form in products. The core formula is:

ΔH=∑(bond enthalpies of bonds broken)−∑(bond enthalpies of bonds formed)\Delta H = \sum (\text{bond enthalpies of bonds broken}) - \sum (\text{bond enthalpies of bonds formed})
📐 Worked Example

Calculate the enthalpy change for the gaseous combustion of methane, using bond enthalpies: C-H = 414, O=O = 498, C=O = 745, O-H = 463 (all kJ mol⁻¹).

  1. 1

    Write the balanced equation for the reaction (all species gaseous):

  2. 2
    CH4(g)+2O2(g)→CO2(g)+2H2O(g)CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)
  3. 3

    Calculate total energy required to break all bonds in reactants: 4 C-H bonds in CH₄, 2 O=O bonds in O₂:

  4. 4
    Total bonds broken=(4×414)+(2×498)=2652 kJ mol−1\text{Total bonds broken} = (4 \times 414) + (2 \times 498) = 2652 \, \text{kJ mol}^{-1}
  5. 5

    Calculate total energy released when forming all bonds in products: 2 C=O bonds in CO₂, 4 O-H bonds in 2 H₂O:

  6. 6
    Total bonds formed=(2×745)+(4×463)=3342 kJ mol−1\text{Total bonds formed} = (2 \times 745) + (4 \times 463) = 3342 \, \text{kJ mol}^{-1}
  7. 7

    Substitute into the formula for ΔH:

  8. 8
    ΔH=2652−3342=−690 kJ mol−1\Delta H = 2652 - 3342 = -690 \, \text{kJ mol}^{-1}
  9. 9

    The negative sign confirms combustion is exothermic, as expected.

✓ Quick check

Check your understanding of the formula:

  1. What is the correct formula for ΔH using bond enthalpies?

    • ΔH = sum of bond enthalpies of bonds formed minus sum bonds broken

    • ΔH = sum of bond enthalpies of bonds broken minus sum bonds formed

    • ΔH = sum of bond enthalpies of bonds broken plus sum bonds formed

    • ΔH = sum product bond enthalpies minus sum reactant bond enthalpies

    Reveal answer
    1 —

    Bond breaking adds energy to the system (positive), bond formation removes energy (negative), so ΔH = energy in minus energy out.

Exam tip:

Always draw full displayed (structural) formulas before counting bonds to avoid missing multiple bonds.

3. 3. Limitations of Bond Enthalpy Calculations★★★☆☆⏱ 10 min

Calculated enthalpy changes from bond enthalpies are almost always different from actual measured values, because of two core limitations:

  • Bond enthalpies are average values across many different compounds, so the actual bond strength in the specific molecule in your reaction may differ.

  • Bond enthalpies are only defined for bonds in the gaseous state. If any reactant or product is liquid or solid, enthalpy changes from phase changes are not accounted for.

📐 Worked Example

Explain why the calculated enthalpy of combustion of methane (-690 kJ mol⁻¹) differs from the actual standard value (-890 kJ mol⁻¹).

  1. 1

    The actual standard enthalpy of combustion produces liquid water, while the bond enthalpy calculation assumes all products are gaseous.

  2. 2

    When gaseous water condenses to liquid water, additional energy is released, making the actual ΔH more negative than the calculated value.

Exam tip:

Questions asking to explain why calculated values differ from actual values are very common — always mention both key limitations if relevant.

4. Common Pitfalls

Wrong move:

Reversing the ΔH formula, calculating ΔH = sum bonds formed - sum bonds broken

Why:

This gives a ΔH with the opposite sign, so exothermic reactions are incorrectly labelled endothermic and vice versa

Correct move:

Remember: energy in (bonds broken) minus energy out (bonds formed) → ΔH = broken - formed

Wrong move:

Forgetting bond enthalpies only apply to gaseous species

Why:

Any solid or liquid reactant/product adds unaccounted enthalpy from phase changes, leading to incorrect results

Correct move:

Always confirm all species are gaseous when using bond enthalpies, and mention phase change as a source of error if not

Wrong move:

Counting bonds incorrectly (e.g. 1 C=O bond in CO₂, no O=O in O₂)

Why:

Incorrect bond counts lead to wrong total energy sums and final ΔH

Correct move:

Draw the full structural formula of all molecules before counting bonds

Wrong move:

Claiming higher bond enthalpy means longer bond length

Why:

Stronger bonds pull atoms closer together, so the relationship is inverse

Correct move:

Remember: higher bond enthalpy = stronger bond = shorter bond length

Wrong move:

Using negative bond enthalpy values for bonds broken

Why:

All bond enthalpy values are positive by definition, the sign of ΔH comes from the calculation

Correct move:

Use the tabulated positive bond enthalpy values directly in the formula

5. Quick Reference Cheatsheet

Concept

Key Fact / Formula

Definition

Avg energy to break 1 mol of gaseous bond

Bond breaking

Endothermic, ΔH > 0, energy absorbed

Bond making

Exothermic, ΔH < 0, energy released

Trend

Higher bond enthalpy = stronger bond = shorter bond

ΔH formula

Key limitations

  1. Average values 2. Only for gaseous species

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

  • 2022 · 1

    Calculate enthalpy change from bond enthalpies

  • 2023 · 2

    Explain bond enthalpy-bond length trend

What's Next

Bond enthalpies are a core foundational concept for understanding reaction energetics, and connect directly to the next topics of entropy and Gibbs free energy, which let us predict whether a reaction will be spontaneous. Mastering bond enthalpy calculations also complements other enthalpy calculation methods you have learned, including Hess's Law and calorimetry, which are used to get more accurate measured enthalpy change values. This topic also builds on your understanding of covalent bonding structure, linking bond strength to molecular stability.