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Lattice Energy Calculator

Chemistry

Calculate lattice energy using the Kapustinskii equation U = −120250νz⁺z⁻/(r⁺+r⁻) kJ/mol. Enter ionic charges and formula units for any ionic compound.

Reviewed by the thecalcu.com team · Last updated December 7, 2025

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

This calculator computes your Lattice Energy (U), r⁺ + r⁻, vs. NaCl (787 kJ/mol) from the values you enter.

Inputs
Formula Units (ν — total ions per formula unit)Cation Charge (z⁺)Anion Charge (|z⁻|)Cation Ionic RadiusAnion Ionic Radius
Outputs
Lattice Energy (U)r⁺ + r⁻vs. NaCl (787 kJ/mol)

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°.

Why Use a Lattice Energy Calculator?

The Kapustinskii equation multiplies and divides several constants with ionic radii and charges, and both the correction factor (1 − 34.5/(r⁺+r⁻)) and the unit handling (result in kJ/mol with r in pm) require care. This calculator applies the equation directly.

For NCERT Class 11 problems on ionic bond strength, and JEE problems involving Born-Haber cycle components, knowing the approximate lattice energy from just ionic radii and charges is valuable, the Kapustinskii equation gives chemical intuition about how charge and size control crystal stability.

Who Should Use This Calculator?

Class 11 and 12 chemistry students studying ionic bonding, Born-Haber cycles, and lattice energy trends (NCERT Chapter 4, Chemical Bonding) in preparation for CBSE boards and JEE/NEET.

Inorganic chemistry students and researchers comparing theoretical and experimental lattice energies across ionic compound series, or estimating lattice energies for newly synthesised ionic materials.

Materials scientists assessing the stability and melting points of ionic ceramics (MgO, Al₂O₃, ZrO₂), ionic liquids, and perovskite oxides from their lattice energies.

Pharmaceutical chemists estimating dissolution behaviour of ionic drug salts, compounds with high lattice energy require more energy to dissolve, affecting bioavailability.

What Insights Does the Lattice Energy Calculator Give You?

Lattice Energy U (kJ/mol) is the primary output, the energy of formation of the ionic crystal from gaseous ions (negative = exothermic). More negative U = stronger ionic bonding = higher melting point, lower solubility (when hydration energy is relatively constant), greater hardness.

r⁺ + r⁻ (pm) is the sum of ionic radii, the key distance term in the Kapustinskii denominator. Comparing compounds with the same charges (e.g., NaCl vs KCl), the smaller r_sum gives larger |U|.

Comparison to NaCl puts the result in context, NaCl (787 kJ/mol) is the textbook reference. "2.3× stronger than NaCl" immediately conveys that MgO has more than double the lattice binding energy.

How to use this Lattice Energy calculator

  1. Enter ν (Formula Units), total ions in one formula unit: NaCl = 2, MgCl₂ = 3, CaCl₂ = 3, K₂O = 3, MgO = 2, Al₂O₃ = 5.
  2. Enter Cation Charge z⁺: Na⁺ = 1, Mg²⁺ = 2, Al³⁺ = 3.
  3. Enter Anion Charge |z⁻|: Cl⁻ = 1, O²⁻ = 2, N³⁻ = 3.
  4. Enter Cation Ionic Radius in pm from Shannon tables: Na⁺ = 102 pm, Mg²⁺ = 72 pm, Ca²⁺ = 100 pm.
  5. Enter Anion Ionic Radius in pm: Cl⁻ = 181 pm, O²⁻ = 140 pm, F⁻ = 133 pm.
  6. Read Lattice Energy and Comparison to NaCl.
Show formula & methodology ↓Show less ↑

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/mol

MgO: 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/mol

MgO 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

What is lattice energy?
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.
What is the Kapustinskii equation for lattice energy?
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%.
How does lattice energy relate to the stability of ionic compounds?
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.
What is the Born-Haber cycle and how does it relate to lattice energy?
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.
How do I use the Lattice Energy Calculator?
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).
What are common ionic radii for the Kapustinskii equation?
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.
What is the trend in lattice energy across ionic compounds?
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.
How is lattice energy related to solubility of ionic compounds?
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.
Is lattice energy tested in Indian competitive chemistry examinations?
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.
What is the difference between the Born-Landé and Kapustinskii equations?
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.