Born–Haber cycles (A-level only) — AQA A-Level Chemistry
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Born–Haber cycles (A-level only) explained
Lattice enthalpy can be quoted in either direction, and the sign follows from the direction chosen.
Read the full explanation
Lattice formation enthalpy is the enthalpy change when one mole of a solid ionic compound is formed from its constituent gaseous ions, for example Ca²⁺(g) + 2Cl⁻(g) → CaCl₂(s), ∆H = −2237 kJ mol⁻¹; it is always negative, because strong electrostatic attractions are being made. Lattice dissociation enthalpy is the exact reverse, one mole of the solid dissociating fully into gaseous ions, and is always positive and numerically equal. The one mole refers to the compound, not to the ions, so a definition that says one mole of gaseous ions is refused. Gaseous state symbols on the ions are essential.
Born–Haber cycles are used to calculate lattice enthalpies using the following data: enthalpy of formation ionisation energy enthalpy of atomisation bond enthalpy electron affinity.
Lattice enthalpy cannot be measured directly, so a Born–Haber cycle reaches it indirectly from values that can be measured. The route runs from the elements in their standard states down to the compound by two paths. One path is the enthalpy of formation. The other builds gaseous ions step by step: atomise the metal, atomise the non metal or break its bond, remove electrons from the metal atoms as successive ionisation energies, add electrons to the non metal atoms as electron affinities, then bring the gaseous ions together by the lattice formation enthalpy. Because both paths start and finish at the same places, ∆fH equals the sum of the steps, and any one unknown can be found by rearrangement.
Students should be able to: define each of the above terms and lattice enthalpy construct Born–Haber cycles to calculate lattice enthalpies using these enthalpy changes construct Born–Haber cycles to calculate one of the other enthalpy changes compare lattice enthalpies from Born–Haber cycles with those from calculations based on a perfect ionic model to provide evidence for covalent character in ionic compounds.
Born-Haber cycles use Hess's Law to calculate lattice enthalpy (enthalpy change when one mole of solid ionic lattice forms from gaseous ions). The cycle links standard enthalpy of formation (one mole of compound formed from elements in standard states) to atomisation (one mole of gaseous atoms formed from an element), ionisation (one mole of electrons removed from gaseous atoms), electron affinity (one mole of electrons added to gaseous atoms), and lattice enthalpy. Example: For NaCl, formation enthalpy equals the sum of the other steps. A theoretical lattice enthalpy assumes a perfect ionic model with undistorted spherical ions. If the experimental value is significantly more exothermic, the extra strength indicates covalent character: the cation polarises the anion's electron cloud.
Cycles are used to calculate enthalpies of solution for ionic compounds from lattice enthalpies and enthalpies of hydration.
Dissolving an ionic solid is modelled as two steps. First the lattice is pulled apart into gaseous ions, which costs the lattice dissociation enthalpy and is strongly endothermic. Then each gaseous ion is surrounded by water molecules attracted to its charge, releasing the enthalpy of hydration, which is negative and larger in magnitude for small, highly charged ions. The enthalpy of solution is the sum: ∆solH = ∆latH(dissociation) + Σ∆hydH. For calcium chloride, +2237 for the lattice, −1650 for the calcium ion and two lots of −364 for the chloride ions give −141 kJ mol⁻¹, so the solution warms. Remember to count one hydration enthalpy for every ion in the formula, and to use the dissociation value, not the formation value, in this cycle.
Your focus
- Define lattice dissociation enthalpy and lattice formation enthalpy so that the two differ only in direction and sign.
- Write an equation with state symbols corresponding to the lattice enthalpy of a stated ionic compound.
- Deduce the sign of a lattice enthalpy from the direction of the equation supplied.
Show all 15 objectives
- Explain why a definition referring to one mole of gaseous ions does not describe lattice enthalpy.
- Construct a Born–Haber cycle for a named ionic compound with every level labelled with formulae, charges and state symbols.
- Calculate a lattice enthalpy from tabulated data by summing the indirect route and reversing the sign of every step travelled against its arrow, then check that lattice formation comes out negative and lattice dissociation positive.
- Select the correct number of moles for each step from the formula of the compound.
- Explain why the second electron affinity of oxygen is endothermic while the first is exothermic.
- Define lattice enthalpy, enthalpy of formation, atomisation, ionisation energy, and electron affinity.
- Construct Born-Haber cycles to calculate lattice enthalpies or other enthalpy changes.
- Compare experimental and theoretical lattice enthalpies to deduce covalent character.
- Calculate an enthalpy of solution from a lattice enthalpy and the hydration enthalpies of each ion present.
- Define enthalpy of hydration with reference to one mole of gaseous ions and an aqueous solution.
- Deduce from a calculated enthalpy of solution whether the temperature of the water rises or falls.
- Explain why the hydration enthalpy of a small, highly charged ion is more exothermic than that of a large singly charged ion.
Born–Haber cycles (A-level only) exam tips
Marking Points
- one mark for one mole of a solid ionic compound, formed from or dissociating into its constituent ions
- one mark for specifying that the ions are gaseous
- one mark for the sign that matches the direction defined, negative for formation and positive for dissociation
- one mark for a supporting equation with state symbols, such as Na⁺(g) + Cl⁻(g) → NaCl(s)
- one mark for each enthalpy term placed on the correct level of the cycle with the correct direction of arrow
- one mark for using two ionisation energies for a 2⁺ ion, or two electron affinities where a 2⁻ ion is formed
- one mark for doubling the atomisation or the electron affinity where two moles of the non metal atoms are needed
- one mark for the correct arithmetic with signs, giving the lattice enthalpy with units kJ mol⁻¹
- Define lattice enthalpy as the enthalpy change when one mole of a solid ionic compound is formed from its gaseous ions.
- Define standard enthalpy of formation, atomisation, ionisation energy, and electron affinity, specifying one mole and correct state symbols.
- Construct a Born-Haber cycle to calculate lattice enthalpy by applying Hess's Law to sum the constituent enthalpy changes.
- Compare experimental and theoretical lattice enthalpies, stating that a more exothermic experimental value indicates covalent character due to anion polarisation.
- one mark for a cycle or expression combining the lattice dissociation enthalpy with the hydration enthalpies
- one mark for multiplying the hydration enthalpy by the number of that ion in the formula
- one mark for using the correct sign for each term, positive for dissociation and negative for hydration
- one mark for the final enthalpy of solution with sign and units, and for deducing the temperature change it implies
Examiner Tips
- 💡Read the question for which direction is wanted; formation and dissociation differ only in sign.
- 💡Write the equation with state symbols beneath your definition; it often carries a mark and settles the direction.
- 💡For a compound such as CaCl₂, put two chloride ions in the equation so it makes exactly one mole of compound.
- 💡Write the state symbols and charges on every level of the cycle; most sign errors are really level errors.
- 💡Check the number of moles at each step against the formula of the compound before you substitute.
- 💡Set the arithmetic out as one line of substitution so process marks survive an error in a single term.
- 💡When constructing cycles, ensure arrows for endothermic processes point up and exothermic point down.
- 💡State which value is more exothermic before interpreting covalent character.
- 💡Write the cycle with gaseous ions at the top, solid at one corner and aqueous ions at the other, then follow the arrows.
- 💡Count the ions from the formula before substituting; the doubling mark is the one most often lost.
- 💡A negative enthalpy of solution means heat is released, so the temperature of the water rises.
Common Mistakes
- defining it as one mole of gaseous ions rather than one mole of the compound
- omitting the gaseous state of the ions, which leaves the definition ambiguous
- quoting a lattice formation enthalpy as positive
- writing the ions as aqueous, which describes hydration instead
- using the same sign for both the formation and the dissociation value
- using the bond enthalpy of Cl₂ where the cycle needs the atomisation enthalpy, which is half that value per mole of atoms
- forgetting to double the electron affinity when two halide ions are formed
- using only the first ionisation energy for a Group 2 metal
- treating the second electron affinity of oxygen as negative, when it is positive
- adding all the values without regard to the direction of the arrows
- Failing to construct the cycle correctly using Hess's Law; correct by ensuring the sum of clockwise enthalpy changes equals the anticlockwise changes.
- Concluding covalent character from a theoretical value being more exothermic; correct by checking that the experimental value is more exothermic.
- Describing polarisation backwards; correct by stating the cation polarises the anion.
- using the lattice formation enthalpy without reversing its sign for the dissolving step
- counting only one chloride hydration enthalpy for a compound of formula CaCl₂
- assuming dissolving must be endothermic because the lattice has to be broken
- predicting the temperature falls when the calculated enthalpy of solution is negative
- defining enthalpy of hydration without specifying that the ions start as gaseous