When should I use the Born–Landé equation vs a Born–Haber cycle?

Use Born–Landé when you have approximate ionic radii, charges, and the Madelung constant and want a model-based prediction. Use a Born–Haber cycle when you have tabulated enthalpy data (sublimation, ionization energies, electron affinities, bond dissociation, and formation enthalpy) and want a value consistent with experimental thermochemistry.

How accurate are lattice energy calculations from this tool?

Born–Landé is a simplified electrostatic model that ignores covalency and polarization, while Born–Haber results depend on the quality of enthalpy data. Values are usually best for comparing trends and magnitudes across ionic compounds rather than as exact experimental values.

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Lattice Energy Calculator

Q: Why is lattice energy often quoted as a positive number?

Many textbooks define lattice energy as the energy required to separate the ions to infinity, which is endothermic and therefore positive. In thermochemical cycles, the lattice enthalpy for forming MX(s) from gaseous ions is exothermic and negative. This calculator reports U with sign but also shows the magnitude |U|.

Estimate ionic lattice energy using the Born–Landé equation or a Born–Haber cycle. See step-by-step workings, a contribution mini chart, and a lattice strength gauge. Designed for General Chemistry and Inorganic Chemistry courses.

Background

Lattice energy (or lattice enthalpy) measures how strongly ions are held together in an ionic solid. It can be estimated either from a model (Born–Landé) using ionic charges, distance, and the Madelung constant, or from experimental enthalpies in a Born–Haber cycle (using sublimation, ionization energy, electron affinity, bond dissociation, and formation enthalpy).

Choose a mode and enter values

Born–Landé mode: good for model-based estimates using ionic radii, charges, and Madelung constant.

Mode:

Born–Landé equation (model)

Born–Haber cycle (enthalpy data)

Show:

Step-by-step working

Mini chart: energy contributions

Lattice strength gauge

Round to sensible significant figures

Born–Landé inputs:

Example: NaCl → M ≈ 1.7476, |z₊| = 1, |z₋| = 1. CaO → charges 2⁺, 2⁻.

Closest approach distance r₀ (cation–anion, center-to-center):

Typical n values: 7–10. For NaCl, r₀ ≈ 283 pm, n ≈ 9.

We use the Born–Landé form: U = − (N_A M z₊ z₋ e² / (4π ε₀ r₀)) (1 − 1/n), reported in kJ·mol⁻¹.

Quick picks:

Chips prefill typical textbook data and auto-calculate; you can tweak values and recalculate.

Result:

No results yet. Choose a mode, enter values, and click Calculate or use a quick pick.

How to use this calculator

Born–Landé mode: supply Madelung constant M, ionic charges |z₊| and |z₋|, the closest approach distance r₀, and the Born exponent n. Use quick picks for NaCl or CaO if you’re unsure of starting values.
Born–Haber mode: enter tabulated enthalpies in kJ·mol⁻¹: formation ΔH°f of MX(s), sublimation ΔHsub, ΣIE, bond dissociation D(X₂), ΣEA, and any other terms required by your specific cycle.
Use the steps to see how each term contributes, the mini-chart to compare magnitudes, and the gauge to judge whether your lattice energy is small, moderate, or very high in magnitude.

How this calculator works

In Born–Landé mode, the calculator treats the ionic solid as a regular array of point charges. From your inputs (M, |z₊|, |z₋|, r₀, and n) it first converts the distance r₀ into meters, then builds the electrostatic term (N_A M z₊ z₋ e² / 4π ε₀ r₀) and finally applies the repulsion correction (1 − 1/n) to obtain U in kJ·mol⁻¹.

In Born–Haber mode, the calculator follows a thermochemical cycle: it starts from elements in their standard states, adds your sublimation, ionization, bond dissociation, electron affinity, and “other” terms, and uses the tabulated formation enthalpy ΔH°f to solve the cycle equation for the unknown lattice enthalpy U.

In both modes, the tool reports U with its thermochemical sign and also shows the magnitude |U|, along with a mini chart and gauge so you can quickly compare how strong different ionic lattices are.

Formula & Equation Used

1. Born–Landé equation (model):

U = - \frac{N_{A} M z_{+} z_{-} e^{2}}{4 π ε_{0} r_{0}} (1 - \frac{1}{n})

We report U in kJ·mol⁻¹. Many textbooks quote the magnitude |U| as “lattice energy” (energy to separate the ions).

2. Born–Haber cycle (one common convention):

{ΔH}^{°} [M X (s)] = ΔH sub + Σ IE + \frac{1}{2} D (X_{2}) + Σ EA + other + U

U = {ΔH}^{°} [M X (s)] - ΔH sub - Σ IE - \frac{1}{2} D (X_{2}) - Σ EA - other

Signs matter: formation enthalpy is often negative, sublimation and ionization are positive, electron affinities are often negative.

Example Problems & Step-by-Step Solutions

Example 1 — Born–Landé estimate for NaCl

Suppose NaCl has M = 1.7476, |z₊| = 1, |z₋| = 1, r₀ = 283 pm, and n = 9.
Convert r₀ to meters: 283 pm = 2.83×10⁻¹⁰ m. Insert into the Born–Landé expression with ionic constants:
U ≈ −7.9×10² kJ·mol⁻¹ (magnitude |U| ≈ 790 kJ·mol⁻¹), close to experimental values.

Example 2 — Born–Haber cycle for NaCl(s)

Use approximate data (kJ·mol⁻¹): ΔH°f[NaCl(s)] = −411, ΔHsub(Na) = +108, IE(Na) = +496, ½D(Cl₂) = 122 (so D(Cl₂) = 244), EA(Cl) = −349.
U = ΔH°f − ΔHsub − IE − ½D − EA = −411 − 108 − 496 − 122 − (−349) ≈ −7.9×10² kJ·mol⁻¹.

Frequently Asked Questions

Q: Why is lattice energy often quoted as a positive number?

Many textbooks define “lattice energy” as the energy required to separate the ions to infinity, which is endothermic and therefore positive. In thermochemical cycles, the lattice enthalpy for forming MX(s) from gaseous ions is exothermic and negative. This calculator reports U with sign but also shows the magnitude |U|.

Q: When should I use Born–Landé vs Born–Haber?

Use Born–Landé when you have approximate ionic radii, charges, and the Madelung constant and want a model-based prediction. Use Born–Haber when you have tabulated enthalpy data and want a value consistent with experimental thermochemistry.

Q: How accurate are these lattice energy estimates?

Born–Landé is a simplified electrostatic model that ignores covalency and polarization. Born–Haber results depend on the quality and consistency of enthalpy data. Values are usually good for trends and order-of-magnitude comparisons rather than exact predictions.

Ions