Born-Haber Cycle Calculator

Calculate ionic compound lattice energy using the Born-Haber cycle and Hess's law.

Enthalpy of formation delta-Hf (kJ/mol) (kJ/mol)

e.g. NaCl: -411 kJ/mol

Sublimation energy of metal (kJ/mol) (kJ/mol)

Na: 108, K: 89, Ca: 178

First ionization energy IE1 (kJ/mol) (kJ/mol)

Na: 496, K: 419, Ca: 590

Dissociation energy of nonmetal (kJ/mol) (kJ/mol)

Cl2: 244 (1/2 bond energy)

Electron affinity EA (kJ/mol, negative) (kJ/mol)

Cl: -349, Br: -325, O: -141

Second IE or EA (if 2+ or 2- ion) (kJ/mol)

Ca2+ needs IE2=1145

Please check your inputs and try again.

Why Lattice Energy Is Measured Indirectly

Lattice energy cannot be measured directly — you cannot take a mole of gaseous Na⁺ and Cl⁻ and watch them assemble. The Born–Haber cycle obtains it by applying Hess's law: build the compound by two different routes and equate them.

Step	Process	Sign
Sublimation	Metal solid → gas	Endothermic (+)
Ionisation	Metal atom → cation + e⁻	Endothermic (+)
Dissociation	Half X₂ → X atom	Endothermic (+)
Electron affinity	X atom + e⁻ → X⁻	Usually exothermic (−)
Lattice formation	Gaseous ions → solid	Strongly exothermic

The cycle also explains a subtlety about second electron affinities. Adding a second electron to an already-negative ion is endothermic — you are forcing an electron onto a negative species. Oxide formation is only favourable because the resulting O²⁻ gives a much larger lattice energy.

What Controls Lattice Energy

U ∝ (z⁺ × z⁻) / (r⁺ + r⁻)

Compound	Charges	U (kJ/mol)	Melting point
NaCl	1×1	−787	801°C
CaO	2×2	−3,414	2,572°C
MgO	2×2	−3,795	2,852°C
AlN	3×3	−13,800	2,200°C (subl.)

Charge dominates. Going from 1:1 to 2:2 roughly quadruples lattice energy, which is why MgO melts at 2,852°C against NaCl's 801°C. Ionic radius matters too but far less, since it enters as a sum in the denominator rather than a product.

This also explains solubility patterns: dissolving requires overcoming lattice energy with hydration energy. High-charge salts have lattice energies too large for hydration to compensate, which is why MgO and CaO are essentially insoluble while NaCl is not.

Worked Examples

Example 1: NaCl: Hf=-411, sub=108, IE1=496, dis=244(Cl-Cl/2), EA=-349

U=-411-108-496-244-(-349)

Result: U=-910 kJ/mol

Literature: -788 kJ/mol (Kapustinskii estimate)

Example 2: MgO: Hf=-601, sub=148, IE1=738, IE2=1451, dis=249, EA=-141

U=-601-148-738-1451-249-(-141)

Result: U=-3046 kJ/mol

Very high lattice energy - hard refractory material

Example 3: Why MgO is so refractory

2×2 charges versus NaCl's 1×1

Result: U roughly 4.8× larger

Charge product quadruples the electrostatic attraction. The melting point rises from 801°C to 2,852°C as a direct consequence.

Example 4: The second electron affinity

O + e⁻ → O⁻ is exothermic; O⁻ + e⁻ → O²⁻ is endothermic

Result: Net EA for O²⁻ is positive

Oxide formation is favourable only because the doubly charged ion produces a vastly larger lattice energy that more than repays the cost.

Common Mistakes

⚠️

Getting a sign wrong in the cycle

Sublimation, ionisation and dissociation are endothermic; electron affinity and lattice formation are usually exothermic. One sign error inverts the answer.

⚠️

Forgetting to halve diatomic dissociation

Forming one mole of Cl atoms requires half a mole of Cl₂, so use half the bond dissociation energy.

⚠️

Assuming all electron affinities are exothermic

The first is usually exothermic, but the second is strongly endothermic because an electron is being forced onto an already-negative ion.

⚠️

Overlooking that charge dominates radius

Lattice energy scales with the product of charges but only inversely with the sum of radii. Charge effects are far larger.

Frequently Asked Questions

Why lattice energy trends?

Lattice energy increases with: smaller ions (closer approach), higher charge (stronger electrostatic attraction). MgO (2+/2-) has much higher lattice energy than NaCl (1+/1-), making MgO harder with much higher mp.

Lattice energy and solubility?

High lattice energy generally means less soluble (stronger crystal to break up). But hydration energy also matters. Solubility depends on delta-H_dissolution = U + hydration energies - can be +/- .

Why can't lattice energy be measured directly?

Because you cannot experimentally assemble a lattice from separated gaseous ions. The Born–Haber cycle obtains it from measurable quantities using Hess's law.

Why is the second electron affinity endothermic?

Because an electron is being added to an already-negative ion, against electrostatic repulsion. Energy must be supplied.

What makes MgO melt so much higher than NaCl?

Charge. Both ions are doubly charged, so the charge product is four times larger, giving a lattice energy roughly 4.8 times greater.

How does lattice energy relate to solubility?

Dissolving requires hydration energy to overcome lattice energy. High-charge salts have lattice energies too large for hydration to compensate, so they are insoluble.

Formula Explorer connections

Interpretation: This relationship tracks energy transfer, state-function change or the balance between enthalpy and entropy in a chemical process. Assumption: Keep energy units compatible, use kelvin for absolute temperature, and match standard states and reaction stoichiometry. Thermodynamic favorability does not determine reaction speed.

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