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.