23.1 Lattice energy and Born-Haber cycles

Enthalpy of atomisation is the enthalpy change when one mole of gaseous atoms forms from an element in its standard state. Lattice energy here is the enthalpy change when gaseous ions form one mole of an ionic solid lattice.

State the direction and physical states before using a value in a cycle. Reversing a step changes its sign; lattice energy of dissociation is the opposite direction to lattice formation.

Na(s) → Na(g) contributes atomisation, while Na⁺(g) + Cl⁻(g) → NaCl(s) is lattice formation. Both are different from sublimation or hydration.

Do not call any solid-to-gas process atomisation, and do not mix lattice formation and separation conventions in one calculation.

First electron affinity is the enthalpy change for X(g) + e⁻ → X⁻(g). It is usually exothermic when the incoming electron is attracted to the nucleus, but the numerical sign depends on the convention used.

Across a period, nuclear attraction generally increases; down a group, distance and shielding increase. Filled or half-filled subshell effects can create small deviations, so explain trends rather than drawing a perfect line.

Halogens have strongly favourable first electron affinities because gaining one electron completes the p subshell. Group 16 values differ from Group 17 because electron pairing and nuclear attraction compete.

Electron affinity is not ionisation energy in reverse, and the second electron affinity is a different process involving an anion.

A Born–Haber cycle applies Hess’s law to an ionic solid. Typical steps are atomisation, ionisation energies, electron affinities, bond dissociation for a non-metal, and lattice formation, linked to the standard enthalpy of formation.

Write every species and state on the energy path. For +2 cations include two successive ionisation energies; for −2 anions include the second electron affinity with its correct sign.

For MgO(s), the cycle includes Mg atomisation, IE₁ + IE₂, oxygen atomisation, EA₁ + EA₂ and lattice formation, summing to ΔHf°.

A cycle is not a list of numbers: omitting a gaseous atom or using the wrong electron-affinity direction invalidates the result.

Use Hess’s law: the algebraic sum of the enthalpy changes around the cycle equals the standard enthalpy of formation. Rearrange only after deciding whether each step forms or separates a species.

Keep a sign table and isolate the unknown lattice energy or electron affinity. Check units and compare the magnitude with the expected ionic attraction.

If all steps except lattice formation are known, ΔHlatt = ΔHf° − (atomisation + ionisation + electron-affinity terms). A negative formation lattice energy is expected in the formation direction.

Do not change signs because a value “looks too large”, and do not use lattice dissociation data as formation data without reversal.

Lattice energy reflects electrostatic attraction between oppositely charged ions. Greater ionic charge strengthens attraction, while a smaller internuclear distance also increases the magnitude.

Compare like structures and state what is held constant. Charge effects are often larger than radius effects, but both act through Coulombic attraction and lattice packing.

MgO has a more negative lattice-formation enthalpy than NaCl because Mg²⁺/O²⁻ charges are larger, despite the ions not being identical in size.

Do not claim that radius alone determines lattice energy or compare compounds with different structures without qualification.