Lattice Energy Calculator Formula

Understand the math behind the lattice energy calculator. Each variable explained with a worked example.

Use the Lattice Energy Calculator

Formulas Used

Lattice Energy (U)

lattice_energy = -(madelung * 1389.4 * z_cation * z_anion / (distance_pm / 100)) * (1 - 1 / born_exp)

Variables

VariableDescriptionDefault
z_cationCation Charge (z⁺)1
z_anionAnion Charge (z⁻)1
distance_pmInterionic Distance (r₀)(pm)281
madelungMadelung Constant (A)1.748
born_expBorn Exponent (n)8

How It Works

Born-Landé Equation for Lattice Energy

Formula

U = −(A × N_A × e² × z⁺ × z⁻) / (4πε₀ × r₀) × (1 − 1/n)

Simplified with constants combined: U = −(A × 1389.4 × z⁺ × z⁻ / r₀) × (1 − 1/n)

Where r₀ is in angstroms (pm/100), and 1389.4 kJ·Å/mol combines N_A, e², and 4πε₀.

Where:

  • A = Madelung constant (depends on crystal structure)
  • z⁺, z⁻ = ion charges
  • r₀ = interionic distance
  • n = Born exponent (5-12 depending on electron configuration)

    • Worked Example

    NaCl: z⁺ = 1, z⁻ = 1, r₀ = 281 pm, A = 1.748, n = 8.

    z_cation = 1z_anion = 1distance_pm = 281madelung = 1.748born_exp = 8
    1. 01U = -(A × 1389.4 × z⁺ × z⁻ / r₀) × (1 - 1/n)
    2. 02r₀ = 281 pm = 2.81 Å
    3. 03U = -(1.748 × 1389.4 × 1 × 1 / 2.81) × (1 - 1/8)
    4. 04U = -(864.2) × (0.875)
    5. 05U = -756 kJ/mol

    Frequently Asked Questions

    What is lattice energy?

    Lattice energy is the energy released when gaseous ions combine to form one mole of an ionic solid. Higher lattice energy means a more stable crystal.

    What is the Madelung constant?

    The Madelung constant accounts for the geometry of the crystal. For NaCl structure it is 1.748, for CsCl it is 1.763, for ZnS (zinc blende) it is 1.638.

    What factors increase lattice energy?

    Higher ion charges and shorter interionic distances increase lattice energy. MgO (2+, 2-) has much higher lattice energy than NaCl (1+, 1-).

    Ready to run the numbers?

    Open Lattice Energy Calculator