Atom Calculator
Explore atomic structure: find protons, neutrons, electrons, mass number, and isotope notation for any element. Includes ion charges, isotope data, and periodic table reference.
Lattice Energy Calculator
Calculate lattice energy using the Born-Landé equation. Compare ionic compounds, explore Madelung constants, and understand crystal energetics with the Born-Haber cycle.
Common Compounds
pm
pm
He-type≈5, Ne≈7, Ar≈9, Kr≈10, Xe≈12
Born-Landé⧉
751 kJ/mol
Full crystal lattice calculation
Kapustinskii⧉
7 kJ/mol
Quick estimate (structure-independent)
Coulomb (pair)⧉
491 kJ/mol
Single ion pair only (no Madelung)
Interionic Distance⧉
283 pm
r⁺ (116) + r⁻ (167)
Madelung Constant⧉
1.7476
Rock Salt (NaCl)
Radius Ratio⧉
0.695
CN = 6 expected
Lattice Energy vs. Melting Point
NaCl801°C
787
KCl770°C
715
LiF870°C
1037
MgO2852°C
3850
CaO2614°C
3401
NaF993°C
923
CsCl645°C
657
BaO1923°C
3054
Compound Comparison Table
| Compound | Charges | r₀ (pm) | U exp (kJ/mol) | M.P. (°C) |
|---|---|---|---|---|
| NaCl — Sodium Chloride | 1+/1− | 283 | 787 | 801 |
| KCl — Potassium Chloride | 1+/1− | 319 | 715 | 770 |
| LiF — Lithium Fluoride | 1+/1− | 209 | 1037 | 870 |
| MgO — Magnesium Oxide | 2+/2− | 212 | 3850 | 2852 |
| CaO — Calcium Oxide | 2+/2− | 240 | 3401 | 2614 |
| NaF — Sodium Fluoride | 1+/1− | 235 | 923 | 993 |
| CsCl — Cesium Chloride | 1+/1− | 348 | 657 | 645 |
| BaO — Barium Oxide | 2+/2− | 275 | 3054 | 1923 |
Planning notes, formulas, and examples
About the Lattice Energy Calculator
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.
When This Page Helps
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.
How to Use the Inputs
- Select a preset ionic compound or enter custom ion data.
- Specify cation and anion charges and radii.
- Choose the crystal structure for the Madelung constant.
- View lattice energy from both Born-Landé and Kapustinskii equations.
- Compare lattice energies across common ionic compounds.
- Explore the relationship between lattice energy and melting point.
- Check the Born-Haber cycle energy terms.
Formula used
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)Example Calculation
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.
Tips & Best Practices
- Lattice energy increases with higher ion charges and smaller ionic radii.
- Doubly-charged ions (e.g., Mg²⁺, O²⁻) give roughly 4× the lattice energy of singly-charged ions at the same distance.
- The Kapustinskii equation is accurate to ~5% without knowing the crystal structure.
- Fluorides and oxides have the highest lattice energies in their respective groups.
- When lattice energy > hydration energy, the compound is typically insoluble in water.
- Transition metal compounds may have additional stabilization from crystal field effects.
Crystal Structures and Madelung Constants
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.
Born-Haber Cycle in Practice
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.
Beyond Simple Ionic Models
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.
Sources & Methodology
Last updated:
Frequently Asked Questions
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.
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