Calculate lattice energy using the Born-Landé equation. Compare ionic compounds, explore Madelung constants, and understand crystal energetics with the Born-Haber cycle.
Lattice energy is the energy released when gaseous ions combine to form one mole of an ionic solid. It is a key measure of ionic bond strength and directly influences the melting point, solubility, and hardness of ionic compounds. Higher lattice energy means a more stable crystal.
The Born-Landé equation calculates lattice energy from the Madelung constant (which depends on crystal structure), ion charges, interionic distance, and the Born exponent (which accounts for short-range repulsion). For quick estimates without knowing the crystal structure, the Kapustinskii equation uses only ion charges and radii.
This calculator supports both the Born-Landé and Kapustinskii approaches. Enter ion charges, radii, and crystal structure (or use presets for common ionic compounds) to compute lattice energy, compare compounds, and explore how lattice energy correlates with physical properties. A Born-Haber cycle breakdown shows how lattice energy fits into the overall thermodynamic formation of ionic compounds.
For best results, combine calculator output with direct observation and periodic check-ins with a veterinarian or qualified advisor. Small adjustments made early usually improve comfort, safety, and long-term outcomes more than large corrective changes made later.
Calculate and compare lattice energies of ionic compounds. Understand crystal stability, predict physical properties, and learn the Born-Haber cycle. Essential for inorganic chemistry and materials science. This lattice energy calculator helps you compare outcomes quickly and reduce avoidable mistakes when making day-to-day care decisions. Use the estimate as a planning baseline and confirm final decisions with a qualified professional when risk is high.
Born-Landé: U = -(Nₐ × M × z⁺ × z⁻ × e²) / (4πε₀ × r₀) × (1 - 1/n) Kapustinskii: U = (1202.5 × ν × z⁺ × z⁻) / (r⁺ + r⁻) × (1 - 34.5/(r⁺ + r⁻)) where: M = Madelung constant n = Born exponent (6-12) ν = number of ions per formula r₀ = r⁺ + r⁻ (interionic distance)
Result: U ≈ 786 kJ/mol
NaCl has the rock salt structure (Madelung constant 1.7476). With Na⁺ (116 pm) and Cl⁻ (167 pm), r₀ = 283 pm. Born-Landé gives U ≈ 786 kJ/mol, close to the experimental value of 787 kJ/mol.
The Madelung constant accounts for the infinite sum of Coulomb interactions in a crystal. Different crystal structures have different constants: rock salt (NaCl) = 1.7476, cesium chloride (CsCl) = 1.7627, zinc blende (ZnS) = 1.6381, fluorite (CaF₂) = 2.5194, rutile (TiO₂) = 2.408. The Madelung constant is difficult to compute because the alternating series converges slowly.
To find the lattice energy of NaCl: start with Na(s) + ½Cl₂(g) → NaCl(s), ΔHf = -411 kJ/mol. Then trace through sublimation of Na (+107), ionization of Na (+496), dissociation of Cl₂ (+122), electron affinity of Cl (-349), and lattice energy (U). Solving: U = -411 - 107 - 496 - 122 + 349 = -787 kJ/mol.
Real lattice energies deviate from Born-Landé predictions for compounds with significant covalent character (like AgI), polarizable ions (large anions), or transition metals with crystal field stabilization energy. The Born-Mayer equation improves on Born-Landé by using an exponential repulsion term.
A dimensionless number that represents the geometric arrangement of ions in a crystal lattice. It depends only on the crystal structure, not the specific ions. NaCl-type = 1.7476, CsCl-type = 1.7627, ZnS-type = 1.6381.
MgO has doubly-charged ions (Mg²⁺, O²⁻) and smaller ionic radii. Since lattice energy is proportional to the product of charges and inversely proportional to distance, MgO (3850 kJ/mol) far exceeds NaCl (787 kJ/mol).
A thermodynamic cycle that breaks the formation of an ionic compound into steps: sublimation, ionization, electron affinity, dissociation, and lattice energy. Hess's law lets you calculate any one step if the others are known.
Solubility depends on the balance between lattice energy (keeping ions in the crystal) and hydration energy (pulling ions into solution). If hydration energy exceeds lattice energy, the compound dissolves.
A number (typically 5-12) that accounts for the repulsive force when electron clouds overlap at short distances. It depends on the electron configuration of the ions: He-type ≈ 5, Ne-type ≈ 7, Ar-type ≈ 9.
Not directly. It is calculated from the Born-Haber cycle using measurable quantities (ΔHf°, IE, EA, sublimation energy, bond dissociation energy) or estimated from equations like Born-Landé.