Born‑Haber cycles are one of those A2 topics that look terrifying on first sight — a ladder of arrows, half a dozen enthalpy terms with intimidating names, and a lattice enthalpy you can’t measure directly. But underneath the jargon, a Born‑Haber cycle is just Hess’s law drawn as a staircase. Learn the steps once and it becomes one of the most methodical, mark‑friendly topics on the paper.
Why we need Born‑Haber cycles
We can’t measure lattice enthalpy — the energy change when gaseous ions come together to form one mole of a solid ionic lattice — directly in the lab. So we find it indirectly, by building a cycle of steps we can measure and applying Hess’s law: the total enthalpy change is the same whichever route you take.
That’s the whole idea. Everything else is just knowing the individual steps.
The enthalpy terms you need to know
Each term is one “step” on the cycle. Learn what each one means:
| Term | What it is | Sign | |—|—|—| | Enthalpy of formation (ΔHf) | Forming 1 mol of the compound from its elements in standard states | usually − | | Enthalpy of atomisation (ΔHat) | Forming 1 mol of gaseous atoms from an element | + (endothermic) | | First ionisation energy (IE) | Removing 1 electron from each gaseous atom to form + ions | + | | Electron affinity (EA) | Adding 1 electron to each gaseous atom to form − ions | 1st is usually − | | Lattice enthalpy (ΔHlatt) | Gaseous ions → 1 mol solid lattice | − (formation) |
A few watch‑points that examiners love to test:
- Atomisation of a diatomic element (like Cl₂): atomising gives you one mole of atoms, so you take half the bond dissociation energy per mole of atoms — mind the factor of 2.
- Second ionisation / second electron affinity appear for Group 2 metals (form 2+ ions) and Group 6 non‑metals (form 2− ions). The second electron affinity is endothermic (+) because you’re forcing a second electron onto an already‑negative ion.
Building the cycle step by step
Think of it as a staircase between two points: the elements at the bottom and the ionic solid, with the gaseous ions at the top.
Take sodium chloride (NaCl) as the classic example:
- Start with the elements in standard states: Na(s) + ½Cl₂(g).
- Atomise the sodium: Na(s) → Na(g). (+ΔHat)
- Atomise the chlorine: ½Cl₂(g) → Cl(g). (+ΔHat)
- Ionise the sodium: Na(g) → Na⁺(g) + e⁻. (+ first IE)
- Electron affinity of chlorine: Cl(g) + e⁻ → Cl⁻(g). (− EA)
- You’re now at the top with gaseous ions: Na⁺(g) + Cl⁻(g).
- Lattice enthalpy brings them down to the solid: Na⁺(g) + Cl⁻(g) → NaCl(s). (−ΔHlatt)
- The direct route from elements straight to the solid is the enthalpy of formation (ΔHf).
Hess’s law says both routes have the same total. So:
$$Delta H_f = Delta H_{at}(text{Na}) + Delta H_{at}(text{Cl}) + IE(text{Na}) + EA(text{Cl}) + Delta H_{latt}$$
Rearrange to find whichever term the question asks for — usually the lattice enthalpy.
How to actually answer the exam question
- Draw the cycle — even a rough energy‑level diagram earns marks and stops you making sign errors.
- Label every arrow with its enthalpy term and value.
- Apply Hess’s law: the direct route (ΔHf) equals the sum of the indirect route.
- Substitute and solve for the unknown, watching every sign.
Examiner’s tip
The number‑one cause of lost marks here is sign errors. Endothermic steps (atomisation, ionisation, 2nd electron affinity) are positive; exothermic steps (lattice formation, 1st electron affinity, formation) are usually negative. Draw the diagram — going up the staircase is +, coming down is −. It’s far harder to get a sign wrong when you can see the direction of the arrow. And don’t forget the ½ for diatomic elements.
A useful follow‑on: theoretical vs experimental lattice enthalpy
A common extension asks you to compare the experimental lattice enthalpy (from the Born‑Haber cycle) with a theoretical value (from a perfect‑ionic‑model calculation). If they differ significantly, it suggests the compound has covalent character — the ionic model isn’t perfect. That comparison is a favourite higher‑mark question, so be ready to explain it.
The bottom line
A Born‑Haber cycle is just Hess’s law as a staircase:
- Know each enthalpy term and its usual sign.
- Build from elements → gaseous ions → solid lattice.
- Watch the ½ for diatomics and the endothermic 2nd electron affinity.
- Draw the diagram and let it protect you from sign errors.
Work through three or four cycles and the method locks in — it’s the same staircase every time.
If Born‑Haber cycles (or any A2 energetics) still feel like a tangle of arrows, we can build them together, step by step, until the logic is obvious.
👉 Book a free intro call and let’s make energetics straightforward.