Lattice Energy Calculator
ChemistryCalculate lattice energy using the Kapustinskii equation U = −120250νz⁺z⁻/(r⁺+r⁻) kJ/mol. Enter ionic charges, radii in pm, and formula units for any ionic compound.
2
1
1
102 pm
pm
181 pm
pm
Lattice Energy (U)
-746.223
r⁺ + r⁻
283
vs. NaCl (787 kJ/mol)
0.95× weaker than NaCl
What is a Lattice Energy?
The Lattice Energy Calculator computes the lattice energy of an ionic compound using the Kapustinskii equation: U = −120250 × v × z⁺ × z⁻ / (r⁺ + r⁻) × (1 − 34.5/(r⁺ + r⁻)) kJ/mol. Enter the number of ions per formula unit, cation and anion charges, and ionic radii in pm to get the lattice energy.
Lattice energy is the primary measure of ionic bond strength: how tightly the cations and anions in an ionic crystal are held together by electrostatic forces. It determines melting point, solubility, hardness, and thermal stability of ionic compounds. NaCl has a lattice energy of −787 kJ/mol; MgO has −3795 kJ/mol due to the doubled charges — which explains why MgO melts at 2852°C (used in furnace linings) while NaCl melts at 801°C.
The Kapustinskii equation is a practical approximation that avoids the need for the structure-specific Madelung constant: it uses the number of ions per formula unit (v) as a universal substitute. For NaCl (v=2) it gives −747 kJ/mol vs the experimental −787 kJ/mol — about 5% underestimate. For MgO (v=2, z=2, r(Mg²⁺)=72 pm, r(O²⁻)=140 pm): −3730 kJ/mol vs experimental −3795 kJ/mol — similar accuracy.
The Born-Haber cycle provides an alternative experimental determination using Hess's law. The Gibbs Free Energy Calculator covers the related thermodynamic quantities ΔH° and ΔG°.
How to use this Lattice Energy calculator
- Enter ν (Formula Units) — total ions in one formula unit: NaCl = 2, MgCl₂ = 3, CaCl₂ = 3, K₂O = 3, MgO = 2, Al₂O₃ = 5.
- Enter Cation Charge z⁺: Na⁺ = 1, Mg²⁺ = 2, Al³⁺ = 3.
- Enter Anion Charge |z⁻|: Cl⁻ = 1, O²⁻ = 2, N³⁻ = 3.
- Enter Cation Ionic Radius in pm from Shannon tables: Na⁺ = 102 pm, Mg²⁺ = 72 pm, Ca²⁺ = 100 pm.
- Enter Anion Ionic Radius in pm: Cl⁻ = 181 pm, O²⁻ = 140 pm, F⁻ = 133 pm.
- Read Lattice Energy and Comparison to NaCl.
Formula & Methodology
Kapustinskii equation (r in pm, U in kJ/mol):U = −120250 × v × z⁺ × z⁻ / (r⁺ + r⁻) × (1 − 34.5/(r⁺ + r⁻))Worked example — MgO vs NaCl: NaCl: v=2, z⁺=1, z⁻=1, r(Na⁺)=102 pm, r(Cl⁻)=181 pm, r_sum=283 pm:U(NaCl) = −120250 × 2 × 1 × 1 / 283 × (1 − 34.5/283) = −850.5 × 0.878 = −747 kJ/molMgO: v=2, z⁺=2, z⁻=2, r(Mg²⁺)=72 pm, r(O²⁻)=140 pm, r_sum=212 pm:U(MgO) = −120250 × 2 × 2 × 2 / 212 × (1 − 34.5/212) = −120250 × 8 / 212 × 0.837 = −4538 × 0.837 = −3798 kJ/molMgO has 5.1× the lattice energy of NaCl due to doubled ionic charges (4×) partially offset by smaller r_sum. The experimental ratio is 3795/787 = 4.82×. The Kapustinskii equation captures this trend accurately, explaining why magnesium oxide is used as a refractory material in steel-making furnaces (operating above 1600°C) while sodium chloride would melt at 801°C.
Frequently Asked Questions
Lattice energy is the energy required to completely separate one mole of a solid ionic compound into its gaseous ions: MX(s) → M⁺(g) + X⁻(g), ΔU > 0 (endothermic for separation). Equivalently, it is the energy released when gaseous ions come together to form one mole of the ionic solid (exothermic). Convention varies: IUPAC defines lattice energy as the energy of formation from gaseous ions (negative = exothermic); British convention uses the energy of dissociation (positive = endothermic). This calculator uses the IUPAC sign convention: negative lattice energy for formation.
The Kapustinskii equation approximates lattice energy without requiring the Madelung constant: U = −120250 × v × z⁺ × z⁻ / (r⁺ + r⁻) × (1 − 34.5/(r⁺ + r⁻)) kJ/mol, where v is the number of ions per formula unit, z⁺ and z⁻ are the charge magnitudes, and r⁺ and r⁻ are the ionic radii in pm. The Kapustinskii equation was derived by A. F. Kapustinskii in 1956 and replaces the Madelung constant with a universal factor of 0.880 × v, applicable to all structure types. It typically agrees with experimental values within 3–10%.
Higher (more negative) lattice energy means greater stability of the ionic solid — more energy must be supplied to break apart the crystal. Factors increasing lattice energy: smaller ionic radii (shorter r⁺ + r⁻, stronger Coulombic attraction), higher ionic charges (z⁺ × z⁻ product larger). MgO has lattice energy ≈ −3795 kJ/mol (Mg²⁺, r=72 pm; O²⁻, r=140 pm) — 5× larger than NaCl (−787 kJ/mol). This explains why MgO has a much higher melting point (2852°C) than NaCl (801°C) and much lower solubility.
The Born-Haber cycle applies Hess's law to calculate lattice energy from experimentally measurable quantities: ΔHf°(ionic solid) = ΔHsub(metal) + ΔHion(metal) + ΔHdiss(nonmetal) + ΔHea(nonmetal) + U_lattice. Rearranging: U_lattice = ΔHf° − ΔHsub − ΔHion − ΔHdiss − ΔHea. For NaCl: ΔHf° = −411.1 kJ/mol, ΔHsub(Na) = +108, IE₁(Na) = +496, ½ΔHdiss(Cl₂) = +121.5, EA(Cl) = −348.6; U_lattice = −411.1 − 108 − 496 − 121.5 + 348.6 = −788 kJ/mol. This agrees well with the Kapustinskii estimate of ~747 kJ/mol.
Enter the number of ions per formula unit ν (NaCl = 2, MgCl₂ = 3, Al₂O₃ = 5), the cation and anion charge magnitudes (z⁺ and |z⁻|), and the cation and anion ionic radii in pm (from the Shannon ionic radius tables). The calculator applies the Kapustinskii equation and returns the lattice energy in kJ/mol, the sum of radii, and a comparison to NaCl (787 kJ/mol).
Shannon ionic radii (coordination number 6, most common): Li⁺ = 76 pm, Na⁺ = 102 pm, K⁺ = 138 pm, Mg²⁺ = 72 pm, Ca²⁺ = 100 pm, Al³⁺ = 54 pm, Fe²⁺ = 78 pm, Fe³⁺ = 65 pm, Zn²⁺ = 74 pm. Anions: F⁻ = 133 pm, Cl⁻ = 181 pm, Br⁻ = 196 pm, I⁻ = 220 pm, O²⁻ = 140 pm, S²⁻ = 184 pm, N³⁻ = 146 pm. These are tabulated in NCERT and standard inorganic chemistry textbooks.
Lattice energy increases (becomes more negative) with: (1) Decreasing ionic radius — smaller ions, shorter interionic distance, stronger attraction. (2) Increasing ionic charge — z⁺z⁻ product appears in the numerator. Comparing: NaF (−919 kJ/mol) > NaCl (−787) > NaBr (−751) > NaI (−700) — larger anion, less lattice energy. LiF (−1037) > NaF (−919) > KF (−817) > CsF (−747) — larger cation, less lattice energy. MgO (−3795) >> NaF (−919) — higher charges dominate. These trends are tested in NCERT Class 11 bonding and structure.
Solubility depends on the balance between lattice energy (energy to break up the crystal, always positive) and hydration energy (energy released as ions are hydrated, always negative). If hydration energy > lattice energy: dissolves readily (NaCl, KNO₃). If lattice energy >> hydration energy: insoluble (BaSO₄, AgCl, CaF₂). High-charge ions like Al³⁺ and O²⁻ make Al₂O₃ nearly insoluble (lattice energy ≈ −15,000 kJ/mol) despite strong hydration of Al³⁺. This is why some ionic compounds with very high lattice energy are refractory materials (MgO, Al₂O₃) used in furnace linings.
Yes, lattice energy is part of NCERT Class 11 Chemical Bonding and Molecular Structure (Chapter 4) and appears regularly in JEE Main and JEE Advanced. JEE problems test: the Born-Haber cycle (Hess's law applied to ionic formation), trends in lattice energy within a group or period, comparing solubility of compounds based on lattice vs hydration energy, and the Kapustinskii/Born-Landé equation concept. NEET covers lattice energy qualitatively in the context of ionic bond strength and compound stability.
Both estimate lattice energy from ionic radii and charges. The Born-Landé equation is more rigorous: U = −(NA × A × z⁺ × z⁻ × e²)/(4πε₀ × r₀) × (1 − 1/n), where NA is Avogadro's number, A is the Madelung constant (structure-specific: 1.748 for NaCl, 1.638 for CsCl, etc.), r₀ is the nearest-neighbour distance, and n is the Born exponent (5–12, from compressibility data). The Kapustinskii equation approximates the Madelung constant as proportional to v and replaces the structure dependence with a single universal formula — accurate without needing A or n, at the cost of 5–10% precision.