Lattice Energy Calculator

Calculate the lattice energy of an ionic crystal using the Born-Landé equation.

Crystal Parameters

Madelung Constant (M)

Cation Charge (z+)

Anion Charge (z-)

Interionic Distance (r₀)

Born Exponent (n)

Calculation Results

Enter crystal parameters to calculate lattice energy

Overview

Lattice energy quantifies the electrostatic forces holding ionic crystals together. It's the energy released when gaseous ions combine to form a solid crystal lattice. Higher lattice energies indicate stronger ionic bonds and correlate with higher melting points, lower solubility in polar solvents, and greater stability. The Born-Landé equation calculates this energy from fundamental electrostatic principles.

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Pro Tips

Use the Born-Landé equation: U = -[ (Nₐ · M · z⁺ · z⁻ · e²) / (4πε₀ · r₀) ] · (1 - 1/n).
z⁺ and z⁻ are the numerical charges of the ions (e.g., +1, -1).
r₀ is the equilibrium interionic distance (sum of the ionic radii).
n is the Born exponent, which depends on the electron configuration of the ions (typical values are 5 to 12).
Remember that lattice energy cannot be measured directly; it's calculated using the Born-Haber cycle from other measurable properties.
Higher charges and smaller ionic radii lead to much stronger lattice energies.

Fun Facts

"The stronger the lattice energy, the higher the melting point of the crystal. This is why NaCl melts at 801°C, but Al₂O₃ melts at over 2,000°C!"
"Lattice energy is always a negative value because energy is released when gaseous ions come together to form a solid (exothermic process)."
"The Born-Landé equation was developed in 1918 by Max Born and Alfred Landé to estimate these energies from crystal structure data."
"The Madelung constant (M) accounts for the geometry of the crystal—different constants apply to NaCl, CsCl, or Zinc Blende structures."
"Lattice energy is the reason why ionic compounds don't exist as isolated gas-phase molecules under normal conditions."
"The strength of the ionic bond is almost entirely electrostatic, determined by the distance between nuclei and the charge of the ions."

Formula: U = - (N·M·z⁺·z⁻·e²) / (4πε₀r₀) · (1 - 1/n)

Comparative Lattice Energies

Visualizing the strength of attraction in various ionic crystals (Absolute Values in kJ/mol).

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