# What is the lattice energy?

Finds the lattice energy of an ionic compound with the Born–Haber cycle from the enthalpy of formation, sublimation, ionization, bond dissociation and electron affinity, solves the cycle for ΔH°f or the electron affinity, or estimates a lattice energy from a salt of the same structure.

- Page: https://www.acalculator.org/chemistry/lattice-energy-calculator
- JSON spec: https://www.acalculator.org/chemistry/lattice-energy-calculator.json
- Version: b7246e1659d7

## Default answer

Example with the default inputs (Find Lattice energy, Metal atoms per formula unit (a) 1, Nonmetal atoms per formula unit (b) 1, ΔH°f of the compound (kJ/mol) −553.5, ΔH°s of the metal (kJ/mol) 76.5, Ionization energy (kJ/mol) 375.7, ½D: atomize the nonmetal (kJ/mol) 79.4, Electron affinity (kJ/mol) −328.2): ΔH_lattice = 756.9 kJ/mol.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| find | Find | The lattice energy by the Born–Haber cycle, ΔH°f or the electron affinity from it, or an estimate from a known salt. |
| a | Metal atoms per formula unit (a) | How many metal ions one formula unit holds: 1 in CsF, 2 in Na₂O. |
| b | Nonmetal atoms per formula unit (b) | How many nonmetal ions one formula unit holds: 1 in CsF, 2 in MgCl₂. |
| hf | ΔH°f of the compound (kJ/mol) | The standard enthalpy of formation of the solid, usually negative. |
| hs | ΔH°s of the metal (kJ/mol) | The enthalpy to turn the metal into gaseous atoms (sublimation), per mole of atoms. |
| ie | Ionization energy (kJ/mol) | The energy to remove the cation’s electrons from a mole of gaseous metal atoms (IE₁ + IE₂ + …). |
| hd | ½D: atomize the nonmetal (kJ/mol) | The enthalpy to make a mole of gaseous nonmetal atoms: half the X₂ bond energy for a gas such as F₂. |
| ea | Electron affinity (kJ/mol) | The energy change when a mole of gaseous nonmetal atoms gains the anion’s electrons; negative when energy is released (F: −328.2). |
| u | Lattice energy (kJ/mol) | The energy to separate a mole of the solid into gaseous ions: positive. |
| u1 | Known lattice energy (kJ/mol) | The lattice energy of a salt with the same crystal structure, such as 1,023 kJ/mol for LiF. |
| z1c | Known salt: cation charge | The size of the known salt’s cation charge: 1 for Li⁺. |
| z1a | Known salt: anion charge | The size of the known salt’s anion charge: 1 for F⁻. |
| r1 | Known salt: interionic distance (pm) | The known salt’s cation–anion distance in pm, such as 200.8 for LiF. |
| z2c | New salt: cation charge | The size of the new salt’s cation charge: 2 for Mg²⁺. |
| z2a | New salt: anion charge | The size of the new salt’s anion charge: 2 for O²⁻. |
| r2 | New salt: interionic distance (pm) | The new salt’s cation–anion distance in pm, such as 231 for NaF. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| result | Answer | The lattice energy, ΔH°f or the electron affinity, in kJ/mol. |
| lattice | Lattice energy (kJ/mol) | The energy to separate a mole of the solid into gaseous ions. |
| formation | ΔH°f (kJ/mol) | The standard enthalpy of formation of the compound. |
| affinity | Electron affinity (kJ/mol) | The energy change per mole of nonmetal atoms gaining the anion’s electrons. |
| metal | Metal steps (kJ/mol) | a × (ΔH°s + IE): making the gaseous cations. |
| nonmetal | Nonmetal steps (kJ/mol) | b × (½D + EA): making the gaseous anions. |

## Method

ΔH_lattice = a × (ΔH°s + IE) + b × (½D + EA) − ΔH°f; ΔH°f = a × (ΔH°s + IE) + b × (½D + EA) − ΔH_lattice; EA = (ΔH_lattice + ΔH°f − a × (ΔH°s + IE)) ÷ b − ½D; U₂ = U₁ × (Z₂⁺Z₂⁻ ÷ Z₁⁺Z₁⁻) × (R₁ ÷ R₂).

## Assumptions

- Lattice energy is positive: the energy to separate the solid into gaseous ions (OpenStax’s sign). Some books use the negative of it.
- ΔH°s, IE, ½D and EA are per mole of atoms; IE is the sum of the ionization energies the cation needs, and EA the sum of the electron affinities the anion needs.
- The estimate from a known salt holds only for the same crystal structure, where the constant C is the same.

## Worked examples

1. find = u, a = 1, b = 1, hf = -553.5, hs = 76.5, ie = 375.7, hd = 79.4, ea = -328.2 gives lattice = 756.9, metal = 452.2, nonmetal = −248.8, result = ΔH_lattice = 756.9 kJ/mol. Source: OpenStax, Chemistry 2e, §7.5 Strengths of Ionic and Covalent Bonds (Born–Haber cycle for CsF: 756.9 kJ/mol; ΔH_lattice = C(Z⁺)(Z⁻) ÷ R₀), https://openstax.org/books/chemistry-2e/pages/7-5-strengths-of-ionic-and-covalent-bonds, the Born–Haber cycle for CsF (Table 7.4): 756.9 kJ/mol.
2. find = f, a = 1, b = 1, u = 756.9, hs = 76.5, ie = 375.7, hd = 79.4, ea = -328.2 gives formation = −553.5, result = ΔH°f = −553.5 kJ/mol. Source: OpenStax, Chemistry 2e, §7.5 Strengths of Ionic and Covalent Bonds (Born–Haber cycle for CsF: 756.9 kJ/mol; ΔH_lattice = C(Z⁺)(Z⁻) ÷ R₀), https://openstax.org/books/chemistry-2e/pages/7-5-strengths-of-ionic-and-covalent-bonds: the CsF cycle solved for ΔH°f.
3. find = ea, a = 1, b = 1, u = 756.9, hf = -553.5, hs = 76.5, ie = 375.7, hd = 79.4 gives affinity = −328.2, result = EA = −328.2 kJ/mol. Source: OpenStax, Chemistry 2e, §7.5 Strengths of Ionic and Covalent Bonds (Born–Haber cycle for CsF: 756.9 kJ/mol; ΔH_lattice = C(Z⁺)(Z⁻) ÷ R₀), https://openstax.org/books/chemistry-2e/pages/7-5-strengths-of-ionic-and-covalent-bonds: the CsF cycle solved for the electron affinity of F.
4. find = scale, u1 = 1,023, z1c = 1, z1a = 1, r1 = 200.8, z2c = 1, z2a = 1, r2 = 231 gives lattice = 889.257, result = ΔH_lattice ≈ 889.257 kJ/mol. Source: OpenStax, Chemistry 2e, Chapter 7 Exercises, §7.5, https://openstax.org/books/chemistry-2e/pages/7-exercises, Exercise 76: the closest choice is 890 kJ/mol.
5. find = scale, u1 = 1,023, z1c = 1, z1a = 1, r1 = 201, z2c = 2, z2a = 2, r2 = 205 gives lattice = 4,012.16, result = ΔH_lattice ≈ 4,012.16 kJ/mol. Source: OpenStax, Chemistry 2e, Chapter 7 Exercises, §7.5, https://openstax.org/books/chemistry-2e/pages/7-exercises, Exercise 79: the closest choice is 4,008 kJ/mol.
6. find = scale, u1 = 794, z1c = 1, z1a = 1, r1 = 269, z2c = 1, z2a = 1, r2 = 231 gives lattice = 924.615. Source: OpenStax, Chemistry 2e, Chapter 7 Exercises, §7.5, https://openstax.org/books/chemistry-2e/pages/7-exercises, Exercise 84: the closest choice is 924 kJ/mol.

## FAQ

### How do I calculate lattice energy with the Born–Haber cycle?

Add the energies to make the gaseous ions from the elements, then subtract the enthalpy of formation: ΔH_lattice = ΔH°s + IE + ½D + EA − ΔH°f. For CsF (OpenStax): 76.5 + 375.7 + 79.4 + (−328.2) − (−553.5) = 756.9 kJ/mol.

### What sign does lattice energy have?

OpenStax defines it as the energy to separate a mole of the solid into gaseous ions, which is positive (endothermic). Some books use the reverse step, forming the solid from the ions, and give a negative number of the same size.

### What do I enter for a compound such as MgCl₂ or Na₂O?

Set a and b to the numbers of metal and nonmetal ions per formula unit (MgCl₂: a = 1, b = 2). Enter IE as the total to make the cation (IE₁ + IE₂ for Mg²⁺) and EA as the total to make the anion (EA₁ + EA₂ for O²⁻), each per mole of atoms; the page multiplies the metal steps by a and the nonmetal steps by b.

### Why does lattice energy depend on ion charge and size?

It follows Coulomb’s law: ΔH_lattice = C × Z⁺ × Z⁻ ÷ R₀, with Z the ion charges and R₀ the distance between ion centers. Doubling both charges makes it about four times as large: LiF is 1,023 kJ/mol and MgO, with nearly the same distance, 3,900 kJ/mol.

### How can I estimate a lattice energy without the full cycle?

Scale from a salt with the same crystal structure: U₂ = U₁ × (Z₂⁺Z₂⁻ ÷ Z₁⁺Z₁⁻) × (R₁ ÷ R₂). NaF from LiF: 1,023 × 200.8 ÷ 231 = 889 kJ/mol, near OpenStax’s answer of 890 kJ/mol. The structures must match, because the constant C depends on it.

### How do I find the electron affinity from the lattice energy?

Solve the cycle for EA: EA = (ΔH_lattice + ΔH°f − ΔH°s − IE) ÷ b − ½D. With CsF’s values and a lattice energy of 756.9 kJ/mol, fluorine’s electron affinity comes out at −328.2 kJ/mol.

## Sources

- OpenStax, Chemistry 2e, §7.5 Strengths of Ionic and Covalent Bonds: lattice energy (positive, for MX(s) → M⁺(g) + X⁻(g)), ΔH_lattice = C(Z⁺)(Z⁻) ÷ R₀, the Born–Haber cycle for CsF in Table 7.4 (ΔH°s = 76.5, ½D = 79.4, IE = 375.7, EA = −328.2, ΔH°f = −553.5, ΔH_lattice = 756.9 kJ/mol), LiF 1,023 and MgO 3,900 kJ/mol. https://openstax.org/books/chemistry-2e/pages/7-5-strengths-of-ionic-and-covalent-bonds (retrieved 2026-10-19)
- OpenStax, Chemistry 2e, Chapter 7 Exercises, §7.5: Exercise 76 (NaF from LiF, choose 890 kJ/mol), Exercise 79 (MgO from LiF, choose 4,008 kJ/mol), Exercise 84 (NaF from KF, choose 924 kJ/mol). https://openstax.org/books/chemistry-2e/pages/7-exercises (retrieved 2026-10-19)