Lattice Energy
Calculate lattice energy of any ionic compound using the Kapustinskii equation. Enter charges and ionic radii, or use compound presets for instant results. Free chemistry calculator.
About This Calculator
The Lattice Energy Calculator computes the lattice energy of any ionic compound using the Kapustinskii equation, a widely used approximation that requires only the ionic charges and ionic radii as inputs. Lattice energy is defined as the energy released when one mole of an ionic solid is formed from its constituent gaseous ions, and it is a key measure of ionic bond strength and crystal stability.
The Kapustinskii equation is given by U = 120200 · ν · |z⁺| · |z⁻| / (r⁺ + r⁻) · (1 − 34.5 / (r⁺ + r⁻)), where U is the lattice energy in kJ/mol, ν is the number of ions per formula unit, z⁺ and z⁻ are the charges of the cation and anion respectively, and r⁺ and r⁻ are their ionic radii in picometers. The constant 120200 kJ·pm/mol combines fundamental constants including Avogadro's number, electronic charge, and vacuum permittivity, while 34.5 pm represents the repulsive Born-Mayer term.
This calculator includes preset values for seven common ionic compounds (NaCl, KCl, MgO, CaO, NaF, KBr, CsCl) with their known ionic radii from Shannon's compilation. Simply click a compound button to populate all parameters, or enter custom values manually. The results display the computed lattice energy along with intermediate values including the charge product, sum of radii, and the repulsion term. Bar and pie charts provide visual comparison of ionic radii and charge distribution.
How the Kapustinskii Equation Works
The Kapustinskii equation builds on the Born-Landé equation but simplifies it by replacing the Madelung constant and Born exponent with universal constants. The numerator represents the electrostatic attraction between oppositely charged ions, scaled by the number of ions in the formula unit. The denominator accounts for the distance between ion centers, and the repulsion term (1 − 34.5/(r⁺+r⁻)) corrects for the short-range repulsion between electron clouds. This approximation works well for most ionic compounds, giving results within ±5% of experimental values from Born-Haber cycles.
Applications of Lattice Energy
Lattice energy is fundamental to understanding ionic compound properties: it explains trends in melting points (higher lattice energy = higher melting point), hardness, solubility in water, and thermal stability. In materials science, lattice energy calculations help predict the stability of novel ionic compounds. In geology and mineralogy, lattice energy correlates with mineral hardness and cleavage. In environmental chemistry, lattice energy affects the dissolution rates of ionic minerals and compounds in natural waters.
Frequently Asked Questions
What is lattice energy and how is it defined?
Lattice energy is the energy released when one mole of an ionic compound is formed from its constituent gaseous ions. It is also defined as the energy required to completely separate one mole of an ionic solid into its gaseous ions. Lattice energy is always an exothermic process (negative value) when forming the lattice, but is conventionally reported as a positive value representing the strength of the ionic bond. Higher lattice energy indicates a stronger ionic bond and a more stable crystal structure.
What is the Kapustinskii equation for lattice energy?
The Kapustinskii equation is an approximation for calculating lattice energy without detailed knowledge of the crystal structure. It is given by U = 120200 · ν · |z⁺| · |z⁻| / (r⁺ + r⁻) · (1 − 34.5 / (r⁺ + r⁻)), where U is the lattice energy in kJ/mol, ν is the number of ions per formula unit, z⁺ and z⁻ are the charges of the cation and anion, and r⁺ and r⁻ are the ionic radii in picometers. The constant 34.5 pm accounts for the repulsive Born-Mayer term, and 120200 kJ·pm/mol combines Avogadro's number, the electronic charge, and vacuum permittivity.
How does ionic charge affect lattice energy?
Ionic charge has a dramatic effect on lattice energy because it appears as the product |z⁺|·|z⁻| in the Kapustinskii equation. Doubling the charge on both ions quadruples the lattice energy. For example, NaCl with monovalent ions (z⁺=z⁻=1) has a lattice energy of about 746 kJ/mol, while CaO with divalent ions (z⁺=z⁻=2) has a lattice energy of about 3430 kJ/mol — roughly 4.6 times larger. This is why compounds with highly charged ions (like MgO, Al₂O₃) have very high melting points and hardness.
How do ionic radii affect lattice energy?
Lattice energy decreases as ionic radii increase because the sum of radii r⁺+r⁻ appears in the denominator of the Kapustinskii equation. Larger ions mean greater distance between the nuclei of cations and anions, which weakens the electrostatic attraction. For example, NaCl (r⁺+r⁻ = 283 pm) has a lattice energy of 746 kJ/mol, while KI with larger ions (r⁺+r⁻ = 353 pm) has a lower lattice energy of about 632 kJ/mol. This trend explains why melting points decrease when going down a group in the periodic table.
What is the difference between Kapustinskii and Born-Landé equations?
The Born-Landé equation is more accurate but requires knowing the Madelung constant (which depends on the specific crystal structure like NaCl-type, CsCl-type, or zinc blende) and the Born exponent (a measure of lattice compressibility). The Kapustinskii equation simplifies this by using a constant value of 34.5 pm for the repulsion term and approximating the Madelung constant divided by the number of ions as roughly 0.85 for all structures. While less precise for individual compounds, the Kapustinskii equation gives good estimates (±5%) and only requires ionic radii and charges as inputs.
What is the lattice energy of NaCl?
The lattice energy of NaCl (sodium chloride, common table salt) is approximately 746 kJ/mol using the Kapustinskii equation. The Born-Haber cycle gives a more accurate value of about 788 kJ/mol. The difference arises because the Kapustinskii equation is an approximation that averages over all crystal structures. Inputs for NaCl: ν = 2, z⁺ = 1 (Na⁺), z⁻ = 1 (Cl⁻), r⁺ = 102 pm (Na⁺), r⁻ = 181 pm (Cl⁻).
What is the lattice energy of common compounds?
Common lattice energies (Kapustinskii approximation): NaCl = 746 kJ/mol, KCl = 673 kJ/mol, KBr = 638 kJ/mol, NaF = 894 kJ/mol, MgO = 3795 kJ/mol, CaO = 3430 kJ/mol, CsCl = 605 kJ/mol, LiF = 1012 kJ/mol. In general, compounds with smaller ions and higher charges have larger lattice energies, resulting in higher melting points, greater hardness, and lower solubility in water.
How is lattice energy used in the Born-Haber cycle?
The Born-Haber cycle is a thermochemical cycle that uses Hess's law to calculate the lattice energy of an ionic compound indirectly. It sums the enthalpies of formation, sublimation, ionization energy, dissociation energy, and electron affinity to determine the lattice energy. This experimental method is considered more accurate than theoretical approximations. The Born-Haber cycle is commonly taught in undergraduate chemistry courses and demonstrates the relationship between lattice energy and other thermodynamic quantities like the standard enthalpy of formation of the ionic solid.