Science & Lab Tools
Lattice Energy Calculator
Calculate the lattice energy of ionic compounds using the Born-Landé equation
Enter values to calculate lattice energy
Related to Lattice Energy Calculator
The Lattice Energy Calculator uses the Born-Landé equation to calculate the lattice energy of ionic compounds. Lattice energy is the energy required to separate one mole of a solid ionic compound into gaseous ions. This calculator implements the complete Born-Landé equation, which takes into account the electrostatic attraction between ions and repulsion forces that occur at small interionic distances.
The Born-Landé Equation
U = -[(N_A * z+ * z- * e² * k)/(4πε₀r)] * (1 - 1/n)
Where:
U = Lattice energy
N_A = Avogadro's constant (6.022 × 10²³ mol⁻¹)
z+ = Cation charge
z- = Anion charge
e = Elementary charge (1.602 × 10⁻¹⁹ C)
k = Coulomb's constant (8.988 × 10⁹ N⋅m²/C²)
r = Interionic distance (in meters)
n = Born exponent
The calculator takes into account four key parameters: the charges of both the cation and anion, the interionic distance (in picometers), and the Born exponent. The Born exponent typically ranges from 5 to 12 and accounts for the repulsive forces between ions.
The lattice energy is expressed in kilojoules per mole (kJ/mol) and is always reported as a positive value by convention, although the actual process is energetically favorable (negative). A higher lattice energy indicates a stronger ionic bond and greater stability of the crystal structure.
Interpreting Lattice Energy Values
• 250-4000 kJ/mol: Typical range for most ionic compounds
• Higher values (>4000 kJ/mol): Very stable compounds with multiple charges
• Lower values (<250 kJ/mol): Less stable ionic compounds
The magnitude of lattice energy depends primarily on:
1. Ion charges (higher charges = higher energy)
2. Ion size (smaller ions = higher energy)
3. Packing efficiency (better packing = higher energy)
1. What is lattice energy and why is it important?
Lattice energy is the energy required to separate one mole of a solid ionic compound into its constituent gaseous ions. It's crucial in understanding the stability of ionic compounds, their solubility, and their melting points. Higher lattice energy generally indicates stronger ionic bonds and greater stability.
2. What factors affect lattice energy?
The main factors affecting lattice energy are: ionic charges (higher charges lead to stronger attractions), ionic size (smaller ions create stronger attractions), and the arrangement of ions in the crystal structure. The Born exponent accounts for the repulsive forces between electron clouds of adjacent ions.
3. Why is the Born exponent important?
The Born exponent (n) accounts for the repulsive forces between ions when they get too close together. It typically ranges from 5 to 12, with higher values indicating stronger repulsion. The value depends on the electronic configuration of the ions and their arrangement in the crystal structure.
4. How accurate is the Born-Landé equation?
The Born-Landé equation provides a good approximation of lattice energy for many ionic compounds, typically within 5-15% of experimental values. The accuracy depends on the quality of input data (especially the interionic distance) and how well the Born exponent represents the actual repulsive forces in the crystal.
5. What is the scientific source for this calculator?
This calculator is based on the Born-Landé equation, developed by Max Born and Alfred Landé in 1918 as part of the Born-Haber cycle. The equation is derived from quantum mechanical principles and is documented in standard physical chemistry textbooks such as Atkins' Physical Chemistry and Chemical Principles by Steven S. Zumdahl. The constants used (Avogadro's constant, elementary charge, and Coulomb's constant) are from the National Institute of Standards and Technology (NIST). The implementation follows the theoretical framework presented in the Journal of Chemical Education (2015) article "Understanding the Born-Landé Equation" which provides a comprehensive analysis of the equation's application in calculating lattice energies.