Lattice Energy Calculator
Estimate the lattice energy of an ionic solid from its crystal structure, ion charges, interionic distance, and Born exponent using the Born-Lande equation.
🧂 What is Lattice Energy?
Lattice energy is the energy released when gaseous cations and anions come together to form one mole of an ionic solid, or the energy required to reverse that process and break the crystal back into gaseous ions. It is the single number that best measures how strongly an ionic compound's ions hold onto each other, and this calculator estimates it with the Born-Lande equation, the standard electrostatic model taught in general chemistry.
This calculation matters across chemistry: predicting relative melting and boiling points of ionic compounds, explaining solubility trends (a very high lattice energy can make a compound resist dissolving even when hydration would otherwise be favourable), building complete Born-Haber cycles to find experimental lattice energies indirectly, and comparing the stability of different possible crystal structures for the same compound.
A common misconception is that lattice energy depends mainly on the identity of the elements involved. In the Born-Lande model, it actually depends only on four purely geometric and electrostatic quantities: the Madelung constant of the crystal structure, the magnitudes of the two ion charges, the interionic distance, and the Born exponent describing short-range repulsion, none of which reference the elements by name once those four numbers are known.
This calculator applies the Born-Lande equation directly with presets for six common crystal structures, so you can estimate lattice energy for any ionic compound once you know its structure type, ion charges, and interionic distance.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Sodium chloride
Rock salt structure (M = 1.748), |z⁺| = 1, |z⁻| = 1, r₀ = 282 pm, n = 8.
Example 2 — Potassium chloride
Rock salt structure (M = 1.748), |z⁺| = 1, |z⁻| = 1, r₀ = 314 pm, n = 9.
Example 3 — Potassium bromide
Rock salt structure (M = 1.748), |z⁺| = 1, |z⁻| = 1, r₀ = 330 pm, n = 9.5.
❓ Frequently Asked Questions
🔗 Related Calculators
What is lattice energy?
Lattice energy is the energy released when gaseous cations and anions come together to form one mole of a solid ionic crystal (by convention, a negative value), or equivalently the energy required to break that crystal apart into gaseous ions (a positive magnitude). It is a direct measure of how strongly an ionic solid's ions attract each other.
What is the Born-Lande equation?
The Born-Lande equation estimates lattice energy from pure electrostatics (Coulomb's law) between point-charge ions arranged in a crystal lattice, corrected by a repulsion term for the Born exponent n, which accounts for short-range electron cloud repulsion once ions get very close together.
What is the Madelung constant?
The Madelung constant M is a dimensionless geometric factor that sums the electrostatic interactions of one ion with every other ion in the infinite crystal lattice, both attractive and repulsive. It depends only on the crystal's geometric arrangement, common values are 1.748 for rock salt (NaCl-type), 1.763 for caesium chloride type, and 5.039 for fluorite type.
What is the Born exponent and how do I choose it?
The Born exponent n accounts for the repulsion between electron clouds as ions approach each other closely, larger n means the ions resist compression more strongly. Linus Pauling tabulated typical values by electron configuration: 5 for helium-type ions, 7 for neon-type, 9 for argon-type, 10 for krypton-type, and 12 for xenon-type, with mixed-ion compounds commonly using the average of the two ions' values.
Why is lattice energy usually shown as a negative number?
By the common thermodynamic convention, lattice energy is defined as the energy change for forming the solid from gaseous ions, an exothermic (energy-releasing) process, so it is negative. Some textbooks instead define lattice energy (or lattice enthalpy) as the energy needed to break the solid apart, which flips the sign to positive, always check which convention a source is using.
How does ion charge affect lattice energy?
Lattice energy magnitude is directly proportional to the product of the ion charge magnitudes, |z+| times |z-|. This is why compounds with 2+ and 2- ions, like magnesium oxide, have far larger lattice energies than 1+ and 1- compounds like sodium chloride, even with similar interionic distances.
How does interionic distance affect lattice energy?
Lattice energy magnitude is inversely proportional to the interionic distance r0, smaller ions that pack closer together produce stronger electrostatic attraction and larger lattice energy magnitude. This is a direct consequence of Coulomb's law, where force and potential energy both scale as 1 divided by distance.
Is the Born-Lande equation exact?
No, it is a useful approximation that treats ions as point charges and ignores effects like covalent character in the bond, van der Waals forces, and zero-point energy. More refined models like the Born-Mayer equation or a full Born-Haber cycle calculation from experimental thermodynamic data give more accurate results, but the Born-Lande equation is the standard first approximation taught in introductory chemistry.
What units does lattice energy use?
This calculator reports lattice energy in kilojoules per mole (kJ/mol), the standard unit for molar energies in chemistry. Typical magnitudes range from a few hundred kJ/mol for singly-charged ion pairs like sodium chloride to several thousand kJ/mol for highly charged small ions like aluminium oxide.
Why do smaller, more highly charged ions form harder, higher-melting solids?
Higher lattice energy directly correlates with stronger ionic bonding throughout the crystal, which requires more thermal energy to disrupt. This is why magnesium oxide (2+ and 2- ions, small radii) melts at roughly 2852°C while sodium chloride (1+ and 1- ions, larger radii) melts at only about 801°C, both consequences of the same lattice energy relationship.