# Lattice Energy Calculator

Estimate lattice energy of ionic compounds using the Born-Lande equation. Enter ion charges, interionic distance, Madelung constant, and Born exponent.

## What this calculates

Estimate the lattice energy of an ionic compound using the Born-Lande equation. Enter the ion charges, interionic distance, Madelung constant, and Born exponent to calculate how much energy holds the crystal together.

## Inputs

- **Cation Charge** — min 1, max 6 — Magnitude of the positive ion charge (e.g. 1 for Na+, 2 for Mg2+).
- **Anion Charge** — min 1, max 4 — Magnitude of the negative ion charge (e.g. 1 for Cl-, 2 for O2-).
- **Interionic Distance (r₀)** (pm) — min 50, max 1000 — Distance between ion centers, usually the sum of ionic radii. 281 pm for NaCl.
- **Madelung Constant (A)** — min 0.1 — Geometry-dependent constant. NaCl = 1.7476, CsCl = 1.7627, ZnS (zinc blende) = 1.6381.
- **Born Exponent (n)** — min 5, max 12 — Depends on electron configuration: He=5, Ne=7, Ar=9, Kr=10, Xe=12. Use average for mixed pairs.

## Outputs

- **Lattice Energy** (kJ/mol) — Estimated lattice energy (negative = exothermic).
- **Coulombic Energy** (kJ/mol) — The pure electrostatic attraction term.
- **Repulsion Factor (1 - 1/n)** — Born repulsion correction factor.
- **Calculation Steps** — formatted as text — Born-Lande equation breakdown.

## Details

Lattice energy is the energy released when gaseous ions come together to form a solid ionic crystal. It is a direct measure of how strongly the ions attract each other in the lattice.

**The Born-Lande Equation**

U = -(N_A x A x z+ x z- x e^2) / (4 pi epsilon_0 x r_0) x (1 - 1/n)

- **N_A** = Avogadro's number (6.022 x 10^23)
- **A** = Madelung constant (depends on crystal structure)
- **z+, z-** = magnitudes of ion charges
- **e** = elementary charge
- **r_0** = interionic distance (sum of ionic radii)
- **n** = Born exponent (related to compressibility)

**NaCl Example**

For NaCl: z+ = 1, z- = 1, r_0 = 281 pm, A = 1.7476, n = 8

The calculated lattice energy is about -756 kJ/mol, close to the experimental value of -787 kJ/mol.

**Common Madelung Constants**

| Structure | Madelung Constant |
|-----------|------------------|
| NaCl (rock salt) | 1.7476 |
| CsCl | 1.7627 |
| ZnS (zinc blende) | 1.6381 |
| ZnS (wurtzite) | 1.6413 |
| CaF2 (fluorite) | 2.5194 |

**Trends**

Lattice energy increases with higher ion charges and smaller ionic radii. MgO (-3850 kJ/mol) has a much higher lattice energy than NaCl (-787 kJ/mol) because Mg2+ and O2- have double the charges.

## Frequently Asked Questions

**Q: What is lattice energy?**

A: Lattice energy is the energy released when isolated gaseous ions form a solid ionic crystal. It is always negative (exothermic) and reflects the strength of the ionic bonds in the crystal. Higher lattice energy means a more stable, harder-to-melt compound.

**Q: What is the Madelung constant?**

A: The Madelung constant accounts for the geometry of the crystal lattice. Each ion interacts with all other ions in the crystal, not just its nearest neighbor. The Madelung constant sums up all these attractive and repulsive contributions for a given structure type.

**Q: What is the Born exponent?**

A: The Born exponent n accounts for the short-range repulsion between electron clouds when ions get very close. Its value depends on the electron configurations of the ions: helium-like = 5, neon-like = 7, argon-like = 9, krypton-like = 10, xenon-like = 12.

**Q: Why does the calculated value differ from experimental data?**

A: The Born-Lande equation is an estimate. It assumes a purely ionic model and uses approximate repulsion terms. Real crystals have some covalent character, zero-point energy, and other effects not captured by this equation. For more accuracy, the Born-Mayer equation uses an exponential repulsion term.

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Source: https://vastcalc.com/calculators/chemistry/lattice-energy
Category: Chemistry
Last updated: 2026-04-08