Lattice enthalpy — OCR A-Level Chemistry

Lattice enthalpy, ΔLEH, is the enthalpy change when one mole of an ionic lattice forms from its gaseous ions, and it is exothermic, so a stable lattice has a negative value. Its magnitude measures the strength of ionic bonding in a giant ionic lattice: the more negative ΔLEH, the stronger the electrostatic attraction holding the oppositely charged ions together. Strength increases with higher ionic charges and smaller ionic radii, because these raise the attraction between ions. For example, MgO has a much more negative lattice enthalpy than NaCl since Mg²⁺ and O²⁻ are doubly charged and smaller than Na⁺ and Cl⁻. This links back to the ionic bonding ideas in 2.2.2 b–c.

A Born–Haber cycle applies Hess's law to build an ionic solid from its elements through gaseous ions, so the lattice enthalpy is obtained indirectly because it cannot be measured directly. Starting from the elements in their standard states, you atomise each element (using enthalpy of atomisation, and bond enthalpy for a diatomic such as Cl₂), then ionise the metal (first and, for Mg, second ionisation enthalpy), add the electron affinity terms for the non-metal, and finally apply the lattice enthalpy to form the solid. For NaCl the cycle links Na(s) + ½Cl₂(g) → NaCl(s) to the sum of atomisation, ionisation, electron affinity and lattice terms. For MgCl₂ you must include two Cl atoms and the second ionisation enthalpy of Mg.

This criterion asks you to use the lattice enthalpy of a simple ionic solid, such as NaCl or MgCl₂, together with the relevant energy terms, in calculations and explanations. The relevant terms are the enthalpy of formation, the enthalpy of atomisation of the metal, the bond dissociation enthalpy of the non-metal, the ionisation enthalpy or enthalpies of the metal, and the electron affinity of the non-metal. You combine them through a Born–Haber cycle so that the lattice enthalpy, which cannot be measured directly, is found from measurable quantities. You also use these terms to explain trends, for example why MgCl₂ has a more exothermic lattice enthalpy than NaCl because of the 2⁺ charge on Mg²⁺ and the smaller ionic radius, giving stronger electrostatic attraction.

A Born–Haber cycle is an enthalpy-level (Hess's law) diagram that connects the elements in their standard states to a solid ionic lattice through a sequence of defined steps, so that lattice enthalpy can be found indirectly. Start from the elements in their standard states and apply, in a consistent order, the enthalpy change of formation of the compound, the atomisation of the metal, the atomisation of the non-metal, the ionisation energy or energies of the metal, the electron affinity or affinities of the non-metal, and finally the lattice enthalpy. For a diatomic non-metal such as chlorine, atomisation of ½Cl₂(g) to Cl(g) is the single step that represents breaking the bond and forming gaseous atoms; do not add a separate bond-dissociation step as well. Apply Hess's law so the sum of the steps round the cycle equals the direct formation route, and solve for the unknown.

Related calculations use the Born–Haber cycle to find an unknown enthalpy term, most often lattice enthalpy, from the other steps. Set the enthalpy of formation equal to the sum of the steps on the indirect route: atomisation of the metal, atomisation of the non-metal (including bond dissociation for a diatomic), ionisation enthalpy of the metal, electron affinity of the non-metal and lattice enthalpy. Rearrange for the unknown and substitute values with correct signs. For example, for an MX compound the formation enthalpy equals the sum of these steps, so lattice enthalpy is found by subtracting the other terms. Watch for multiples when two ions form, and keep units consistent in kJ mol⁻¹. A multiple-choice item may test the sign, the rearrangement or the effect of a doubled formula.

This item tests precise definitions and correct use of three terms. Lattice enthalpy is the enthalpy change when one mole of an ionic lattice forms from its gaseous ions, for example Na⁺(g) + Cl⁻(g) → NaCl(s); the value is exothermic and the reverse process is lattice dissociation enthalpy, a separate term. First ionisation energy is the energy needed to remove one mole of electrons from one mole of gaseous atoms, forming one mole of gaseous 1⁺ ions, for example Na(g) → Na⁺(g) + e⁻. First electron affinity is the enthalpy change when one mole of gaseous atoms each gain one electron to form one mole of gaseous 1⁻ ions, for example Cl(g) + e⁻ → Cl⁻(g). Read each option against these wordings, checking state symbols, the one-mole quantity and the direction of change.

Here you must explain and use enthalpy change of solution, defined as the enthalpy change when one mole of a solute dissolves in a solvent, written ∆solH. The key features are the amount (one mole of solute), the process (dissolving, not reacting) and the direction of the change. In a Born–Haber style cycle you break the ionic lattice into gaseous ions (endothermic, the reverse of lattice enthalpy) and then hydrate those ions (exothermic), and the sum gives ∆solH. For an ionic solid such as sodium chloride, ∆solH is the net result of these two steps, so it can be positive or negative depending on which term dominates. Use the term only for the dissolving step and keep it distinct from hydration enthalpy, which applies to one mole of gaseous ions.

The enthalpy change of hydration, ∆hydH, is the enthalpy change when 1 mol of gaseous ions dissolves in water to form a dilute aqueous solution of ions. The ions start as free gaseous ions and end surrounded by water molecules, so the process is always exothermic for a single ion type: energy is released as ion–dipole attractions form between the ion and the δ⁻ oxygen or δ⁺ hydrogen ends of water. Because the definition fixes the amount at 1 mol of gaseous ions, ∆hydH is quoted per mole of that ion, so a compound such as MgCl₂ involves two separate hydration values, one for Mg²⁺ and one for Cl⁻. A larger charge and a smaller ionic radius give a more exothermic ∆hydH, so Mg²⁺ releases more energy than Na⁺.

Enthalpy change of solution, ΔsolH, is the enthalpy change when one mole of an ionic solid dissolves in water to form a very dilute solution. It can be broken into two energy terms. Breaking the lattice is endothermic: the reverse of lattice enthalpy, so +ΔlattH (lattice enthalpy is defined as exothermic for formation). Hydrating the separated gaseous ions is exothermic: ΔhydH for each ion. So ΔsolH = ΔlattH(formation, negative) reversed to positive, plus the hydration enthalpies. For NaCl the lattice term is large and positive and the two hydration terms are negative; the sum is small and slightly endothermic, yet NaCl still dissolves because entropy increases. Never claim dissolving requires hydration to outweigh lattice energy.

An enthalpy cycle is a Born–Haber style diagram that applies Hess's law: the total enthalpy change is independent of route. To construct one, place the elements in their standard states at the bottom and the ionic solid at the top, then build two routes between them. The direct route is the enthalpy of formation of the solid. The indirect route steps through atomisation of the metal, atomisation of the non-metal, first and successive ionisation energies of the metal, electron affinity (or affinities) of the non-metal, and finally lattice enthalpy. Label every arrow with its sign and species, and check that the arrows form a closed loop. For example, for sodium chloride the indirect route runs Na(s) → Na(g) → Na⁺(g) and ½Cl₂(g) → Cl(g) → Cl⁻(g), then gaseous ions → NaCl(s). Apply Hess's law to solve for the unknown, usually lattice enthalpy.

Explain qualitatively how ionic charge and ionic radius affect two exothermic quantities. Lattice enthalpy becomes more exothermic when ionic charge increases and when ionic radius decreases, because the electrostatic attraction between oppositely charged ions in the lattice is stronger; for example, MgO has a more exothermic lattice enthalpy than NaCl. Enthalpy change of hydration becomes more exothermic when ionic charge increases and when ionic radius decreases, because the attraction between each gaseous ion and the polar water molecules (ion–dipole attraction) is stronger; for example, the Mg²⁺ ion is hydrated more exothermically than the Na⁺ ion. Link each trend to the strength of attraction and to the energy released, and compare ions of the same charge before changing charge.

Lattice enthalpy is the enthalpy change when one mole of an ionic lattice forms from its gaseous ions, given the symbol ΔLEH and usually a large negative value for a stable lattice. Because energy is released as oppositely charged ions pack together, the magnitude of ΔLEH measures how strongly the ions are held in the giant ionic lattice: a more negative value means stronger ionic bonding. Magnitude rises with higher ionic charges and with smaller ionic radii, since the electrostatic attraction between ions increases. For example, magnesium oxide has a far more negative lattice enthalpy than sodium chloride because Mg²⁺ and O²⁻ carry double charges and are smaller than Na⁺ and Cl⁻.