Born-Haber Cycle Calculator

Last updated: April 5, 2026

The Born-Haber Cycle Calculator applies Hess's law to ionic compounds, combining ionization energies, electron affinities, lattice energies, and atomization enthalpies to compute any unknown thermochemical value — most commonly lattice energy, which cannot be measured directly in the lab.

Calculator

Metal Sublimation EnthalpykJ/mol

Total Ionization Enthalpy of MetalkJ/mol

Bond Dissociation Enthalpy of X2kJ/mol

Number of X Atoms in Product Formula

Electron Affinity per X AtomkJ/mol

Standard Enthalpy of FormationkJ/mol

Results

X2 Dissociation Contribution

121.3

kJ/mol

Total Electron Affinity Contribution

-348.6

kJ/mol

Cycle Sum Before Lattice Step

375.8

kJ/mol

Lattice Enthalpy

-787

kJ/mol

Lattice Enthalpy Magnitude

787

kJ/mol

Results

X2 Dissociation Contribution

121.3

kJ/mol

Total Electron Affinity Contribution

-348.6

kJ/mol

Cycle Sum Before Lattice Step

375.8

kJ/mol

Lattice Enthalpy

-787

kJ/mol

Lattice Enthalpy Magnitude

787

kJ/mol

How stable is sodium chloride? Lattice energy — the enthalpy released when gaseous ions combine to form the ionic solid — is the answer. But lattice energy cannot be measured directly in the lab. The Born-Haber cycle solves this by applying Hess's law: the enthalpy change for forming an ionic solid from its elements must equal the sum of all individual steps, regardless of the path. The Born-Haber cycle calculator computes any missing thermochemical quantity in the cycle.

Born-Haber Cycle for NaCl: Step by Step

The cycle from Na(s) + ½Cl₂(g) → NaCl(s):

Sublimation of Na(s) → Na(g): +108 kJ/mol (endothermic)
Dissociation of ½Cl₂(g) → Cl(g): +122 kJ/mol (½ × bond dissociation energy)
First ionization energy of Na(g) → Na⁺(g) + e⁻: +496 kJ/mol (endothermic)
Electron affinity of Cl(g) + e⁻ → Cl⁻(g): −349 kJ/mol (exothermic)
Lattice energy Na⁺(g) + Cl⁻(g) → NaCl(s): −788 kJ/mol (exothermic; this is what we solve for)

By Hess's law: ΔHf = +108 + 122 + 496 − 349 + LE. Standard enthalpy of formation of NaCl(s) = −411 kJ/mol. Therefore: LE = −411 − 108 − 122 − 496 + 349 = −788 kJ/mol. Use this online calculator to solve for any step.

Factors Affecting Lattice Energy

Lattice energy is determined by the Kapustinskii equation approximation and is strongly affected by: ionic charge — lattice energy scales as the product of ion charges (q₁ × q₂); MgO (2+ and 2−) has a much larger lattice energy (−3,791 kJ/mol) than NaCl (1+ and 1−) (−788 kJ/mol); ionic radius — smaller ions pack more closely, increasing electrostatic attraction; LiF (−1,037 kJ/mol) has higher lattice energy than CsI (−604 kJ/mol) due to smaller ionic radii. These trends govern ionic compound solubility, melting points, and hardness.

Experimental vs. Theoretical Lattice Energy

When the experimental (Born-Haber) lattice energy differs significantly from the theoretical (Born-Landé) lattice energy, the compound has substantial covalent character. Example: AgCl — Born-Haber LE = −905 kJ/mol vs. Born-Landé = −770 kJ/mol. The 135 kJ/mol difference indicates significant covalent contribution to bonding in AgCl — consistent with silver halides' low water solubility and photosensitivity. The bond dissociation energy calculator and chemical bonding calculators complement this tool.

Visual Analysis

How It Works

Enter any five of the six thermochemical values: enthalpy of formation, sublimation enthalpy, bond dissociation energy (½ for diatomic), first ionization energy, electron affinity, and lattice energy. The calculator uses Hess's law: ΔHf = ΔH_sub + ½BDE + IE + EA + LE to solve for the missing quantity. Sign conventions: endothermic positive, exothermic negative.

Understanding Your Results

The calculated lattice energy is typically a large negative number (exothermic), indicating that forming the crystal from gaseous ions releases significant energy. The magnitude tells you how stable the ionic crystal is. Values around -700 to -800 kJ/mol are typical for alkali halides (NaCl ~ -787 kJ/mol), while divalent compounds like MgO give values around -3800 kJ/mol. If the result differs significantly from the Born-Lande calculated value, it suggests additional bonding contributions (covalent character).

Worked Examples

Lattice Energy of NaCl via Born-Haber Cycle

Inputs

sublimation107.3

ionization495.8

dissociation242.6

electron affinity-348.6

formation enthalpy-411.2

Results

lattice energy-786.8

sum steps375.8

U = -411.2 - 107.3 - 495.8 - 121.3 - (-348.6) = -411.2 - 375.8 = -786.8 kJ/mol. This matches the well-known experimental lattice energy of NaCl.

Lattice Energy of KBr via Born-Haber Cycle

Inputs

sublimation89

ionization418.8

dissociation193.9

electron affinity-324.6

formation enthalpy-393.8

Results

lattice energy-674

sum steps280.2

U = -393.8 - 89.0 - 418.8 - 96.95 - (-324.6) = -393.8 - 280.15 = -674.0 kJ/mol. The literature value for KBr lattice energy is approximately -672 kJ/mol.

Frequently Asked Questions

The Born-Haber cycle is a thermochemical cycle that applies Hess's law to the formation of an ionic compound from its elements. It breaks the formation process into individual measurable steps — sublimation, bond dissociation, ionization, electron affinity, and lattice energy — and uses the fact that the sum of all enthalpy changes around any closed cycle must equal zero. The cycle is named after Max Born and Fritz Haber, who developed it in 1919. Its primary use is calculating lattice energy — the enthalpy of forming an ionic crystal from its gaseous ions — which cannot be measured directly by calorimetry but can be precisely calculated by closing the cycle with all other experimentally known values.

Lattice energy (LE) is found by rearranging Hess's law: LE = ΔHf − ΔH_sublimation − ½ΔH_bond dissociation − First IE − Electron affinity. For NaCl: LE = −411 − (+108) − (+122) − (+496) − (−349) = −411 − 108 − 122 − 496 + 349 = −788 kJ/mol. Sign conventions: endothermic processes (sublimation, ionization, bond breaking) are positive; exothermic processes (electron affinity for most nonmetals, lattice energy, formation of most ionic compounds) are negative. The large negative lattice energy (−788 kJ/mol for NaCl) reflects the strong electrostatic attraction in the ionic crystal and explains why NaCl has a high melting point (801°C) and is a hard crystalline solid.

Lattice energy is the enthalpy change when one mole of ionic solid forms from its gaseous ions: Na⁺(g) + Cl⁻(g) → NaCl(s); LE = −788 kJ/mol. It is always exothermic (negative) because forming a crystal from isolated ions releases energy. Lattice energy is important because it determines: melting point — compounds with higher lattice energy melt at higher temperatures (MgO mp 2852°C vs. NaCl mp 801°C); solubility — ionic compounds with very high lattice energies resist dissolution (LE must be overcome by solvation enthalpy); hardness — higher lattice energy correlates with harder crystals; compound stability — the Born-Haber cycle shows whether a compound is thermodynamically stable overall. Lattice energy increases with higher ionic charges and smaller ionic radii.

Ionization energy (IE) is the energy required to remove an electron from a neutral gaseous atom: Na(g) → Na⁺(g) + e⁻; ΔH = +496 kJ/mol (always endothermic for first IE). Electron affinity (EA) is the energy change when a neutral gaseous atom gains an electron: Cl(g) + e⁻ → Cl⁻(g); ΔH = −349 kJ/mol (exothermic for most nonmetals, meaning the anion is more stable). In a Born-Haber cycle: the ionization energy step costs energy (positive); the electron affinity step (for typical halogens and chalcogens) releases energy (negative). Note: some elements have positive (endothermic) electron affinities — noble gases, group 2 metals, and nitrogen have positive or near-zero EAs because their electron configurations make them resistant to gaining an extra electron.

The Born-Haber (experimental) lattice energy can be compared to the theoretical lattice energy calculated from the Born-Landé equation, which assumes purely ionic bonding. When the Born-Haber lattice energy is significantly larger (more negative) than the Born-Landé value, the extra stabilization indicates covalent character — the bonding has a partial covalent contribution beyond the pure ionic model. This is Fajans' rules in quantitative form: compounds with small, highly charged cations (high polarizing power) and large, polarizable anions show the most covalent character. Examples: AgCl — excess LE ~135 kJ/mol; AlCl₃ — very large excess, predominantly covalent character. By contrast, NaF — Born-Haber and Born-Landé values agree closely, confirming predominantly ionic bonding.

Lattice energy is defined as the enthalpy change for: Ionic crystal(s) → Gaseous cations(g) + Gaseous anions(g). This process would require completely vaporizing the ionic compound into separated gas-phase ions — an experiment that is practically impossible to perform calorimetrically because: ionic solids decompose, melt, or react with container materials before reaching the extreme temperatures needed; maintaining stoichiometric gaseous ion populations without recombination or ionization is not experimentally feasible; the process is highly endothermic, requiring temperatures that make precision calorimetry very difficult. Instead, the Born-Haber cycle provides an elegant indirect route: measure all the other steps in the cycle (sublimation, ionization, electron affinity, bond dissociation, formation enthalpy) and calculate lattice energy by subtraction using Hess's law.

Sources & Methodology

Atkins, P., de Paula, J. (2014). Atkins' Physical Chemistry, 10th ed. Oxford. Housecroft, C.E., Sharpe, A.G. (2018). Inorganic Chemistry, 5th ed. Pearson. NIST Chemistry WebBook (2023). Thermochemical Data.

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How It Works

Understanding Your Results

Worked Examples

Lattice Energy of NaCl via Born-Haber Cycle

Inputs

sublimation107.3

ionization495.8

dissociation242.6

electron affinity-348.6

formation enthalpy-411.2

Results

lattice energy-786.8

sum steps375.8

U = -411.2 - 107.3 - 495.8 - 121.3 - (-348.6) = -411.2 - 375.8 = -786.8 kJ/mol. This matches the well-known experimental lattice energy of NaCl.

Lattice Energy of KBr via Born-Haber Cycle

Inputs

sublimation89

ionization418.8

dissociation193.9

electron affinity-324.6

formation enthalpy-393.8

Results

lattice energy-674

sum steps280.2

U = -393.8 - 89.0 - 418.8 - 96.95 - (-324.6) = -393.8 - 280.15 = -674.0 kJ/mol. The literature value for KBr lattice energy is approximately -672 kJ/mol.

Frequently Asked Questions