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Born-Haber Cycle Calculator

Calculate lattice enthalpy using Hess's Law.

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Lattice Enthalpy

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Overview

The Born-Haber cycle is a thermochemical application of Hess's Law used to calculate the lattice energy of ionic crystalline solids. It relates the standard enthalpy of formation of an ionic compound to the energy required to atomize and ionize the constituent elements.

Symbols

Variables

= Enthalpy of Formation, (M) = Atomization (Metal), (X) = Atomization (Non-metal), IE = Ionization Energy, EA = Electron Affinity

Enthalpy of Formation
kJ/mol
Atomization (Metal)
kJ/mol
Atomization (Non-metal)
kJ/mol
IE
Ionization Energy
kJ/mol
EA
Electron Affinity
kJ/mol
Lattice Enthalpy
kJ/mol

Apply it well

When To Use

When to use: Use this cycle when direct experimental measurement of lattice enthalpy is not feasible. It is applicable for calculating any missing energetic component of an ionic compound's formation when the other thermodynamic values are known.

Why it matters: This cycle allows scientists to evaluate the strength of ionic bonds and the stability of crystals. Discrepancies between theoretical lattice energy and values derived from the cycle often reveal the degree of covalent character in a bond.

Avoid these traps

Common Mistakes

  • Sign errors (endo vs exo).
  • Forgetting atomization of diatomic elements.
  • Wrong electron affinity values.

One free problem

Practice Problem

Calculate the lattice enthalpy (LE) for Sodium Chloride (NaCl) using the following thermochemical data: enthalpy of formation (Hf) = -411 kJ/mol, enthalpy of atomization of Na (HatM) = 107 kJ/mol, enthalpy of atomization of Cl (HatX) = 121 kJ/mol, first ionization energy of Na (IE) = 496 kJ/mol, and electron affinity of Cl (EA) = -349 kJ/mol.

Enthalpy of Formation-411 kJ/mol
Atomization (Metal)107 kJ/mol
Atomization (Non-metal)121 kJ/mol
Ionization Energy496 kJ/mol
Electron Affinity-349 kJ/mol

Solve for: LE

Hint: Rearrange the equation to LE = Hf - (HatM + HatX + IE + EA).

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Atkins' Physical Chemistry
  2. IUPAC Gold Book
  3. Wikipedia: Born-Haber cycle
  4. P. W. Atkins, J. de Paula, J. Keeler, Atkins' Physical Chemistry, 11th ed., Oxford University Press, 2018
  5. Atkins' Physical Chemistry, 11th Edition
  6. IUPAC Gold Book (Compendium of Chemical Terminology)
  7. OCR A-Level Chemistry A — Energetics (Born–Haber cycles)