Lattice Energy Calculator

What is Lattice Energy?

Lattice energy is a measure of the strength of the forces between the ions in an ionic solid. It is defined as the energy released when one mole of an ionic compound is formed from its gaseous ions. A higher (more negative) lattice energy corresponds to a more stable crystal lattice and stronger ionic bonds.

The Born-Landé Equation

The Born-Landé equation is a theoretical model used to estimate the lattice energy (U) of a crystalline ionic compound. It considers the electrostatic attraction between ions and a repulsive term that accounts for electron cloud overlap. The equation is:

U = - (Nₐ · M · |Z⁺| · |Z⁻| · e²) / (4πε₀r₀) · (1 - 1/n)

• U: The lattice energy in Joules per mole.
• Nₐ: Avogadro's constant (6.022 x 10²³ mol⁻¹).
• M: The Madelung constant, which depends on the geometry of the crystal lattice.
• Z⁺ and Z⁻: The integer charges of the cation and anion (e.g., +1, -2).
• e: The elementary charge (1.602 x 10⁻¹⁹ C).
• ε₀: The permittivity of free space (8.854 x 10⁻¹² F/m).
• r₀: The shortest inter-ionic distance between cation and anion in meters.
• n: The Born exponent, a number related to the compressibility of the solid.

How to Use the Lattice Energy Calculator

1. Madelung Constant (M): Enter the Madelung constant for your crystal structure. For example, NaCl (rock salt structure) has M ≈ 1.748. CsCl has M ≈ 1.763.
2. Born Exponent (n): Enter the Born exponent. This value typically ranges from 5 to 12 and can be estimated based on the electron configurations of the ions.
3. Ion Charges (Z⁺, Z⁻): Input the integer charges of your cation and anion. For example, for MgCl₂, Z⁺ is 2 and Z⁻ is 1. Enter them as positive numbers.
4. Inter-ionic Distance (r₀): Enter the distance between the centers of the cation and anion in picometers (pm). This is often the sum of the ionic radii.
5. Calculate: The calculator will compute the lattice energy in kJ/mol.

Factors Affecting Lattice Energy

The Born-Landé equation highlights the two main factors influencing lattice energy:

• Ionic Charge: Lattice energy increases significantly with higher ionic charges. For example, MgO (Mg²⁺, O²⁻) has a much higher lattice energy than NaCl (Na⁺, Cl⁻).
• Inter-ionic Distance (Ionic Radii): Lattice energy decreases as the distance between ions increases (i.e., as ions get larger). Smaller ions can get closer together, resulting in stronger electrostatic attraction and higher lattice energy.

Frequently Asked Questions (FAQ)

Why is lattice energy a negative value?

By convention, lattice energy is the energy *released* when the lattice is formed from gaseous ions. The formation of a stable bond releases energy, so the value is exothermic and therefore negative.

What is the difference between the Born-Landé and Born-Haber cycle?

The Born-Landé equation is a theoretical calculation based on a physical model of the crystal. The Born-Haber cycle, on the other hand, determines the lattice energy experimentally by applying Hess's Law to a series of measurable enthalpy changes (like ionization energy, electron affinity, and enthalpy of formation).