Lattice Energy Calculator
Born-Haber cycle, for the one term nobody can measure.
Work out Lattice Energy. Born-Haber cycle, for the one term nobody can measure. Shows the working, not just the answer.
ΔH°f of the ionic solid. NaCl is −411.
Turning the solid metal into gaseous atoms. Sodium is +107.
Removing the electron from the gaseous metal atom. Sodium is +496.
Per mole of atoms, so half the bond enthalpy for a diatomic. Cl₂ gives +122.
Adding the electron to the gaseous non-metal atom. Chlorine is −349.
Lattice energy
-787 kJ/mol
Exothermic — forming the lattice releases energy
The Born-Haber cycle is Hess's law applied to a specific loop, and it exists because lattice energy is the one term in it that cannot be measured directly. Every other step — sublimation, ionisation, dissociation, electron affinity, formation — is measurable, so the lattice energy comes out by difference. Sign convention matters here. This reports the enthalpy of FORMING the lattice from gaseous ions, which is negative. Many tables quote the energy required to break it apart instead, giving the same magnitude with the opposite sign, so a figure of −787 and one of +787 for sodium chloride are the same fact stated two ways. Lattice energy rises steeply with ionic charge and falls with ionic radius, which is why magnesium oxide melts at 2,852 °C and sodium chloride at 801 °C.
How the Lattice Energy Calculator works
Enter the five measurable enthalpies from a Born-Haber cycle and this returns the lattice energy by difference. That is the whole reason the cycle exists — lattice energy is the only term in it that cannot be measured directly.
Also known as: born haber cycle calculator · lattice enthalpy calculator · how to calculate lattice energy · born haber cycle for nacl
Frequently asked questions
What is lattice energy?
The enthalpy change when gaseous ions come together to form one mole of an ionic solid. For sodium chloride it is about −787 kJ/mol, and the large negative value is why ionic solids are so stable.
How does a Born-Haber cycle work?
It is Hess's law applied to a loop: form the salt directly, or take the long route through sublimation, ionisation, dissociation and electron affinity. Both must give the same total, so the unmeasurable step comes out by difference.
Why do some tables give a positive lattice energy?
Because they quote the energy needed to break the lattice apart rather than to form it. Same magnitude, opposite sign — −787 and +787 kJ/mol for sodium chloride are the same fact stated two ways.
What makes lattice energy large?
High ionic charge and small ionic radius. Magnesium oxide with 2+ and 2− ions has a lattice energy around −3,795 kJ/mol against sodium chloride's −787, which is why it melts at 2,852 °C rather than 801.
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