What is lattice energy?

Lattice energy is the energy released when one mole of an ionic compound is formed from its constituent gaseous ions at infinite separation. It is always negative (exothermic) by the standard convention used here. A larger magnitude (more negative) indicates a more stable lattice and stronger ionic interactions.

What is the Born-Lande equation?

The Born-Lande equation is E = −(N_A · M · Z⁺ · Z⁻ · e²) / (4πε₀ · r₀) · (1 − 1/n), where N_A is Avogadro's number, M is the Madelung constant, Z⁺ and Z⁻ are the ion charge numbers, e is the elementary charge, ε₀ is the permittivity of free space, r₀ is the equilibrium interionic distance (sum of ionic radii), and n is the Born exponent representing the repulsive term.

What is the Madelung constant?

The Madelung constant (M) accounts for the geometric arrangement of ions in the crystal lattice. Common values: NaCl structure = 1.7476, CsCl structure = 1.7627, ZnS (zinc blende) = 1.6381, ZnS (wurtzite) = 1.6413, CaF₂ (fluorite) = 2.5194, TiO₂ (rutile) = 2.408. You can enter a custom value for other structures.

What is the Born exponent n?

The Born exponent n represents the repulsive interaction between ions at close range. It is estimated from the electron configurations of the ions: He-like ions → n = 5, Ne-like → 7, Ar-like / Cu⁺-like → 9, Kr-like / Ag⁺-like → 10, Xe-like / Au⁺-like → 12. For compounds with mixed configurations, use the average of the two ions.

Why does lattice energy increase with higher ion charge?

The Born-Lande equation shows lattice energy is proportional to the product Z⁺ × Z⁻. Doubling both charges quadruples the electrostatic attraction, so MgO (2+, 2−) has a much larger lattice energy (~3795 kJ/mol) than NaCl (1+, 1−) (~786 kJ/mol).

How accurate is the Born-Lande equation?

For simple ionic compounds, the Born-Lande equation typically agrees with experimental Born-Haber cycle values within 1–3%. Accuracy decreases for compounds with significant covalent character, very soft ions, or complex crystal structures not well described by a single Madelung constant.

Lattice Energy Calculator

Enter ion charges, ionic radii, and the Madelung constant to estimate lattice energy via the Born-Lande equation.

Born-Lande Equation Inputs

E = −(N_A · M · Z⁺ · Z⁻ · e²) / (4πε₀ · r₀) · (1 − 1/n)

Ion Charges

Cation charge (Z⁺)

Enter as positive integer

Anion charge (Z⁻)

Enter as positive integer

Ionic Radii (pm)

Cation radius (pm)

Anion radius (pm)

Madelung Constant (M)

Born Exponent (n)

Typical range: 5 (He-like) to 12 (Xe-like). Use average for mixed configurations.

Load common compound

Born Exponent Reference

He configuration (Li⁺, Be²⁺)n = 5

Ne configuration (Na⁺, Mg²⁺, O²⁻, F⁻)n = 7

Ar / Cu⁺ (K⁺, Ca²⁺, Cl⁻)n = 9

Kr / Ag⁺ (Rb⁺, Br⁻)n = 10

Xe / Au⁺ (Cs⁺, I⁻)n = 12

Enter parameters and click Calculate to see the lattice energy.

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Summary

The Lattice Energy Calculator uses the Born-Lande equation to estimate the lattice energy of an ionic crystal — the energy released when gaseous ions combine to form one mole of a crystalline ionic compound. You supply the charges of the cation and anion, their ionic radii (in picometers), the Madelung constant for the crystal structure, and the Born exponent n. The result is expressed in kJ/mol and indicates how strongly the ions are held together in the lattice.

How it works

Enter the charge numbers of the cation (e.g. +2 for Ca²⁺) and anion (e.g. -1 for F⁻).
Enter the ionic radius of the cation and the ionic radius of the anion in picometers (pm).
Select or enter the Madelung constant for your crystal structure (e.g. 1.7476 for NaCl).
Enter the Born exponent n (typically 5–12, depending on the electron configuration of the ions).
Click Calculate to apply the Born-Lande equation and obtain the lattice energy in kJ/mol.
A negative value confirms the lattice energy is released (exothermic formation); a larger magnitude means a stronger, more stable lattice.

Use cases

Estimate lattice energies for alkali halides, alkaline earth oxides, and other ionic compounds.
Compare lattice stability across a series of ionic compounds in physical chemistry coursework.
Verify textbook Born-Lande calculations for NaCl, MgO, CaF2, and similar compounds.
Understand trends: higher ion charges and smaller ionic radii both increase lattice energy.
Support Born-Haber cycle calculations by providing a computed lattice energy value.
Explore how changing the crystal structure (and thus the Madelung constant) affects stability.
Prepare for university-level inorganic chemistry exams on ionic bonding and crystal energetics.
Cross-check experimental lattice enthalpies against Born-Lande theoretical predictions.

Frequently Asked Questions

Last updated: 2026-09-30 · Reviewed by Nham Vu