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Lattice Energy Calculator

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.

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.

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