IB Chemistry SL — Reactivity 1.2: Energy Cycles (Bond Enthalpies & Hess's Law)

In R1.1 you measured ΔH with calorimetry. This sub-topic lets you calculate it two ways: from average bond enthalpies (R1.2.1) and using Hess's law (R1.2.2). Both rest on one idea — breaking bonds costs energy, making bonds releases it, and total energy is conserved.

👆 Pick a reaction in the bond-enthalpy calculator · reveal the two routes in the Hess cycle

1. Breaking and making bonds R1.2.1

Breaking a chemical bond always absorbs energy — it is endothermic (positive). Forming a bond always releases energy — it is exothermic (negative). A reaction's enthalpy change is just the balance between the two:

ΔH = Σ(bonds broken) − Σ(bonds formed)

The values we use are average bond enthalpies: the mean energy needed to break one mole of a particular covalent bond in the gaseous state, averaged over many different molecules that contain it. Because they are averages, a bond-enthalpy calculation gives an estimate of ΔH — the real bond in a specific molecule differs slightly from the average, and the method only works when every species is a gas. It is least reliable when liquids or solids are involved (their intermolecular forces are ignored).

2. Bond-enthalpy calculator R1.2.1

Pick a gas-phase reaction. The calculator breaks every bond in the reactants (energy in, +) and forms every bond in the products (energy out, −), then takes the difference. Values are average bond enthalpies in kJ mol⁻¹ (IB data booklet).

Bonds broken (reactants) — endothermic +

Bonds formed (products) — exothermic −

ΔH = Σ(bonds broken) − Σ(bonds formed). A negative answer means the reaction is exothermic.

3. Hess's law R1.2.2

Hess's law: the enthalpy change of a reaction is independent of the route taken — it depends only on the initial and final states. This is a direct consequence of energy conservation: if two routes went from the same start to the same finish with different ΔH, you could build a perpetual energy machine by going round the cycle.

So if a reaction is hard to measure directly, we find an alternative route whose steps we do know, and add them up. Reverse a step and you reverse the sign of its ΔH. Below, the combustion of carbon to CO₂ is shown directly and via carbon monoxide — reveal route 2 and check that the two routes agree.

Doing Higher Level? HL extends R1.2 with standard enthalpies of formation and combustion, lattice enthalpy, Born–Haber cycles and enthalpies of solution & hydration. → Open the HL lesson

Common mistakes examiners see

Is breaking a bond exothermic or endothermic?✗ Exothermic — bonds release energy when they break. ✓ Endothermic — breaking a bond always absorbs energy (ΔH positive). Energy is released when bonds form.

Which way round is the bond-enthalpy formula?✗ ΔH = Σ(formed) − Σ(broken). ✓ ΔH = Σ(bonds broken) − Σ(bonds formed). Broken first (energy in), then subtract formed (energy out).

Why is a bond-enthalpy answer only approximate?✗ Because you rounded the numbers. ✓ Bond enthalpies are averages over many molecules, and the method assumes all species are gaseous — so it ignores the exact molecular environment and any intermolecular forces.

What happens to ΔH when you reverse a reaction in a Hess cycle?✗ It stays the same. ✓ Its sign flips — the magnitude is unchanged but ΔH becomes its negative.

Does the route change the overall ΔH?✗ Yes — a longer route releases more energy. ✓ No — Hess's law says ΔH depends only on the initial and final states, never on the path between them.

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Energy Cycles in Reactions