756
kJ/mol
7.84
eV/pair
864
kJ/mol
0.875
756
kJ/mol
7.84
eV/pair
864
kJ/mol
0.875
The Lattice Energy Calculator computes the electrostatic energy released when gaseous ions combine to form an ionic crystal, using the Born-Lande equation. Lattice energy is one of the most important thermodynamic quantities in ionic chemistry, directly influencing a compound's melting point, solubility, and hardness. Higher lattice energies correspond to more stable crystal structures. For example, NaCl has a lattice energy of approximately 787 kJ/mol, while MgO, with its doubly-charged ions, has a much higher value of about 3850 kJ/mol. This calculator uses the Madelung constant for the crystal structure and the Born exponent to account for short-range repulsion. By entering the ion charges, interionic distance, and crystal parameters, you obtain a reliable estimate of the lattice energy.
The Born-Lande equation calculates lattice energy as:
U = -(NA x M x z+ x z- x e2) / (4 x pi x epsilon0 x r0) x (1 - 1/n)
Where:
The equation combines the long-range Coulombic attraction (represented by the Madelung constant) with the short-range Pauli repulsion (represented by the Born exponent). The result is a negative energy value (exothermic), but lattice energy is conventionally reported as a positive number representing the energy required to separate the crystal into gaseous ions.
Lattice energy values typically range from 600-1000 kJ/mol for singly-charged ion pairs (NaCl ~787, KBr ~672) to 3000-4000+ kJ/mol for doubly-charged pairs (MgO ~3850, CaO ~3461). Higher lattice energies indicate greater crystal stability, higher melting points, lower solubility in water (generally), and greater hardness. The value is always positive when expressed as the energy to dissociate the lattice.
Inputs
Results
Using the Born-Lande equation with NaCl crystal parameters (M = 1.7476, r0 = 2.81 A, n = 8), the calculated lattice energy is approximately 756 kJ/mol. The experimental value is 787 kJ/mol.
Inputs
Results
MgO has doubly charged ions and a short interionic distance. With z+ = z- = 2, r0 = 2.10 A, and n = 7, the lattice energy is approximately 3935 kJ/mol, close to the experimental value of 3850 kJ/mol.
The Madelung constant accounts for the long-range electrostatic interactions in an ionic crystal. It depends on the crystal geometry: NaCl-type = 1.7476, CsCl-type = 1.6381, zinc blende = 1.6381, wurtzite = 1.6413, fluorite = 5.0388, rutile = 4.770.
The Born exponent (n) accounts for the short-range repulsion between electron clouds when ions approach each other. It depends on the electron configuration: He-type ~5, Ne-type ~7, Ar-type ~9, Kr-type ~10, Xe-type ~12. For mixed ion pairs, use the average.
The Born-Lande equation shows that U is proportional to z+ times z-. Doubling both charges quadruples the lattice energy. This is why MgO (2+, 2-) has roughly 4-5 times the lattice energy of NaCl (1+, 1-).
Higher lattice energy generally decreases solubility because more energy is needed to break apart the crystal. However, the hydration energy of the ions also matters. A substance dissolves when hydration energy exceeds lattice energy.
No, it is an approximation. More accurate models include the Born-Mayer equation (exponential repulsion term) and the Kapustinskii equation (simplified, no Madelung constant needed). Experimental values from Born-Haber cycles are the most accurate.
Interionic distances can be found in crystallographic databases (ICSD), textbook tables, or estimated by adding ionic radii (Shannon radii). For NaCl: r(Na+) = 1.02 A + r(Cl-) = 1.81 A = 2.83 A.
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