Lattice Energy Calculator
Calculate the lattice energy of any ionic compound using three methods: the Born-Lande equation (for precise crystallographic data), the Kapustinskii approximation (for quick ionic-radii estimates), or the Born-Haber thermochemical cycle (from experimental formation enthalpies). Switch between methods with the mode selector, results appear instantly in kJ/mol.
Formula
Worked example
For NaCl using the Kapustinskii equation: v = 2, |z+| = 1, |z-| = 1, r(Na+) = 102 pm, r(Cl-) = 181 pm, r_sum = 283 pm. U = 120.2 * 2 * 1 * 1 / 283 * (1 - 34.5/283) = 0.8502 * 0.8781 = 0.747 kJ/mol per pm... scaled: U approx 769 kJ/mol, close to the experimental 787 kJ/mol. With Born-Lande (M = 1.74756, n = 7, r0 = 281 pm): U = (6.022e23 * 1.74756 * 1 * (1.602e-19)^2) / (4*pi * 8.854e-12 * 2.81e-10) * (1 - 1/7) = 757 kJ/mol.
What is lattice energy?
Lattice energy is the amount of energy released when one mole of an ionic solid is formed from its constituent gaseous ions. Because the ions have opposite charges, they attract each other strongly, and a large amount of energy is liberated as they condense into the ordered crystal lattice. By convention, lattice energy is reported as a positive value (the magnitude of the exothermic energy release), though in the Born-Haber cycle it appears as a large negative enthalpy term. The higher the lattice energy, the more stable the ionic compound: it takes that much energy to break the lattice apart again into free ions.
The three calculation methods
This calculator supports three levels of rigor. The Kapustinskii approximation is the quickest: it needs only the ionic charges and the crystal-ionic radii of the cation and anion, which are tabulated for nearly every common ion. It is accurate to within about 5-10 percent of the experimental value for most compounds and requires no knowledge of the crystal structure. The Born-Lande equation is more precise: it uses the Madelung constant (a geometric factor that depends on the exact crystal structure) and the closest interionic distance r0, which is ideally measured by X-ray crystallography. The repulsion correction term (1 - 1/n), where n is the Born exponent, accounts for the overlap of electron clouds at short range. The Born-Haber cycle takes a purely thermochemical approach: using Hess's law, it constructs a closed energy cycle from the standard enthalpy of formation, the sublimation enthalpy of the metal, ionization energies, bond dissociation energies, and electron affinities. Because all of these quantities can be measured independently, the lattice energy derived from this cycle is considered the most reliable benchmark and often serves as the experimental reference against which the model equations are tested.
What affects lattice energy? Trends across the periodic table
Two factors dominate: ionic charge and interionic distance. The electrostatic attraction is proportional to the product |z+||z-|, so doubling both charges multiplies the lattice energy by four. This explains why MgO (charges 2 and 2) has a lattice energy of about 3795 kJ/mol compared to only 787 kJ/mol for NaCl (charges 1 and 1). Interionic distance is inversely proportional to lattice energy: smaller ions pack closer together, increasing the attraction. Down any group the ions get larger, so lattice energy falls: LiF (1037 kJ/mol) > NaF (923) > KF (821) > CsF (740). Across a period the ion radii shrink as nuclear charge rises without adding a new electron shell, so lattice energies generally increase. Crystal structure also matters because the Madelung constant varies between structural types, though this effect is smaller than the charge and distance effects.
Practical significance of lattice energy
Lattice energy governs the physical and chemical properties of ionic compounds. High-lattice-energy compounds such as Al2O3 (corundum) and MgO are refractory ceramics with very high melting points (over 2000 degrees C) and are used as high-temperature insulators and abrasives. Solubility in water depends on the competition between lattice energy (which must be overcome to dissolve the compound) and the hydration enthalpy (energy released when the freed ions interact with water molecules). When the hydration enthalpy exceeds the lattice energy, the compound dissolves; when it does not, the compound is insoluble. This balance also explains why salts with small, highly charged ions can be either very soluble or very insoluble depending on the relative magnitudes of both terms.
Lattice energies of common ionic compounds
| Compound | Formula | Lattice energy (kJ/mol) | Structure |
|---|---|---|---|
| Lithium fluoride | LiF | 1037 | Rock-salt |
| Lithium chloride | LiCl | 853 | Rock-salt |
| Sodium fluoride | NaF | 923 | Rock-salt |
| Sodium chloride | NaCl | 787 | Rock-salt |
| Sodium bromide | NaBr | 747 | Rock-salt |
| Sodium iodide | NaI | 704 | Rock-salt |
| Potassium chloride | KCl | 717 | Rock-salt |
| Potassium bromide | KBr | 689 | Rock-salt |
| Caesium chloride | CsCl | 657 | CsCl-type |
| Magnesium oxide | MgO | 3795 | Rock-salt |
| Calcium oxide | CaO | 3460 | Rock-salt |
| Calcium fluoride | CaF2 | 2651 | Fluorite |
| Barium oxide | BaO | 3054 | Rock-salt |
| Aluminium oxide | Al2O3 | 15916 | Corundum |
| Zinc sulfide | ZnS | 3615 | Zinc blende |
Experimental (Born-Haber) lattice energies in kJ/mol. Values are for standard conditions and reported as positive magnitudes.
Frequently asked questions
Why is lattice energy always reported as a positive number?
By convention, lattice energy is the energy released when the crystalline solid is formed from gaseous ions. Since energy is released (exothermic), the process has a negative enthalpy, but the lattice energy magnitude is quoted as a positive number for convenience. In Born-Haber cycle equations, the lattice energy term appears with a negative sign because it represents energy given off, not absorbed. Some textbooks define it the opposite way (as the energy required to break the lattice apart), which gives the same magnitude but a different sign convention - always check which definition a source is using.
What is the Madelung constant and where do I find it?
The Madelung constant (M) is a dimensionless number that accounts for the geometry of the crystal lattice - specifically, the sum of electrostatic interactions between one reference ion and all other ions in the infinite crystal. It depends only on the structure type, not on the specific ions. Rock-salt (NaCl-type) structures have M = 1.74756, caesium chloride has 1.76267, fluorite (CaF2-type) has 2.51939, and so on. The value is built into this calculator for common structure types. If you know your compound's crystal structure from the literature, select it from the dropdown and the correct M is applied automatically.
How do I pick the right Born exponent n?
The Born exponent n accounts for the short-range electron-cloud repulsion that prevents ions from collapsing into each other. It depends on the outermost electron configuration: ions with a helium-like shell use n = 5, neon-like use 7, argon-like 9, krypton-like 10, and xenon-like 12. For a compound where the cation and anion have different configurations, use the arithmetic average. For example, NaCl has Na+ (Ne-like, n = 7) and Cl- (Ar-like, n = 9), giving an average of 8. The Born exponent has only a modest effect on the result - changing it by 1 typically shifts the lattice energy by 1-2 percent.
What is the difference between the Kapustinskii and Born-Lande equations?
The Born-Lande equation is more fundamental: it uses the exact Madelung constant for the specific crystal structure plus the measured interionic distance. The Kapustinskii approximation trades accuracy for convenience by replacing M with an average value and using the sum of tabulated ionic radii instead of a measured r0. Kapustinskii is often more practical for comparing trends or estimating the lattice energy of a hypothetical compound because it only needs the ion identities. Born-Lande is preferred when the crystal structure is known and precision matters.
Why does doubling the ionic charges have such a large effect?
Lattice energy is proportional to the product |z+||z-|. If you go from a 1+/1- salt (like NaCl) to a 2+/2- oxide (like MgO), the charge product jumps from 1 to 4 - a four-fold increase before accounting for the smaller ionic radii. In practice, MgO has a lattice energy about 4.8 times larger than NaCl, because the Mg2+ and O2- ions are also smaller than Na+ and Cl-, which further increases the electrostatic energy by reducing r0. This charge amplification is why magnesium oxide is refractory while sodium chloride dissolves easily in water.
Can I use the Born-Haber cycle for compounds with more than one anion?
Yes, but you need to include all the relevant enthalpy steps. For CaF2, you add the first and second ionization energies of Ca (not just the first), and you use the electron affinity of fluorine multiplied by two (for two F atoms gaining electrons). The bond dissociation step uses the full F2 bond energy, not half (since two F atoms are needed). Enter the sum of all ionization energies in the SigmaIE field and the total electron affinity contribution in the EA field, and adjust the stoichiometry of the dissociation term manually in the half-D field. The cycle still closes to give you the lattice energy through Hess's law.