# Bond enthalpies

> IB Chemistry HL · R1: What drives chemical reactions?
> Source: https://www.owlsprep.com/study/ib-chemistry-hl-u4-bond-enthalpies/

This sub-topic explains how to use average bond enthalpy values to calculate enthalpy changes of reaction, connects bond enthalpy to bond strength and length, and outlines key limitations of this calculation method.

**Prerequisites:** [Enthalpy change and Hess's Law](https://www.owlsprep.com/study/ib-chemistry-hl-u3-enthalpy-hess-law/)

## Learning objectives

- Define average bond enthalpy and relate it to bond strength and length
- Calculate enthalpy change of reaction using average bond enthalpy values
- Explain the key limitations of bond enthalpy-based calculations
- Identify common errors in bond enthalpy problem-solving

## 1. Bond Enthalpy: Definition and Trends

**Average Bond Enthalpy** — 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.

*Notation:* Units: kJ mol⁻¹

*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. Compare the bond enthalpy values from the table:
2. $$C-O = 360 \, \text{kJ mol}^{-1}, \quad C=O = 745 \, \text{kJ mol}^{-1}$$
3. Higher bond enthalpy means a stronger bond, so C=O is stronger than C-O.
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. Calculating Enthalpy Change of Reaction

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:

$$\Delta H = \sum (\text{bond enthalpies of bonds broken}) - \sum (\text{bond enthalpies of bonds formed})$$

**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. Write the balanced equation for the reaction (all species gaseous):
2. $$CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)$$
3. Calculate total energy required to break all bonds in reactants: 4 C-H bonds in CH₄, 2 O=O bonds in O₂:
4. $$\text{Total bonds broken} = (4 \times 414) + (2 \times 498) = 2652 \, \text{kJ mol}^{-1}$$
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. $$\text{Total bonds formed} = (2 \times 745) + (4 \times 463) = 3342 \, \text{kJ mol}^{-1}$$
7. Substitute into the formula for ΔH:
8. $$\Delta H = 2652 - 3342 = -690 \, \text{kJ mol}^{-1}$$
9. The negative sign confirms combustion is exothermic, as expected.

**Check your understanding**

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

   *Answer:* ΔH = sum of bond enthalpies of bonds broken minus sum bonds formed

   *Why:* 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.

*Calculator:* allowed

## 3. Limitations of Bond Enthalpy Calculations

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. The actual standard enthalpy of combustion produces liquid water, while the bond enthalpy calculation assumes all products are gaseous.
2. When gaseous water condenses to liquid water, additional energy is released, making the actual ΔH more negative than the calculated value.

> **info**
>
> Despite these limitations, bond enthalpy calculations still give a useful approximate value for ΔH, and are great for comparing the relative reactivity of different compounds.

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

## Common pitfalls

- **Wrong:** Reversing the ΔH formula, calculating ΔH = sum bonds formed - sum bonds broken
  - Why it fails: This gives a ΔH with the opposite sign, so exothermic reactions are incorrectly labelled endothermic and vice versa
  - Correct: Remember: energy in (bonds broken) minus energy out (bonds formed) → ΔH = broken - formed
- **Wrong:** Forgetting bond enthalpies only apply to gaseous species
  - Why it fails: Any solid or liquid reactant/product adds unaccounted enthalpy from phase changes, leading to incorrect results
  - Correct: Always confirm all species are gaseous when using bond enthalpies, and mention phase change as a source of error if not
- **Wrong:** Counting bonds incorrectly (e.g. 1 C=O bond in CO₂, no O=O in O₂)
  - Why it fails: Incorrect bond counts lead to wrong total energy sums and final ΔH
  - Correct: Draw the full structural formula of all molecules before counting bonds
- **Wrong:** Claiming higher bond enthalpy means longer bond length
  - Why it fails: Stronger bonds pull atoms closer together, so the relationship is inverse
  - Correct: Remember: higher bond enthalpy = stronger bond = shorter bond length
- **Wrong:** Using negative bond enthalpy values for bonds broken
  - Why it fails: All bond enthalpy values are positive by definition, the sign of ΔH comes from the calculation
  - Correct: Use the tabulated positive bond enthalpy values directly in the formula

## 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 | $\Delta H = \sum (\text{bonds broken}) - \sum (\text{bonds formed})$ |
| Key limitations | 1. Average values 2. Only for gaseous species |

## 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.

- [Energy cycles](https://www.owlsprep.com/study/ib-chemistry-hl-u4-energy-cycles/)
- [AHL: Extended enthalpy and entropy calculations](https://www.owlsprep.com/study/ib-chemistry-hl-u4-ahl-extended-enthalpy-and-entropy/)
- [AHL: Gibbs free energy and reaction spontaneity](https://www.owlsprep.com/study/ib-chemistry-hl-u4-ahl-gibbs-free-energy-and/)

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