2.2f. Calculating the lattice enthalpy of a group 2 metal halide using the Born–Haber cycle diagram

• ΔH enthalpy abbreviations used for the Born-Haber Cycle of group 2 metal halides

  • f = enthalpy of formation

  • atom = atomisation energy

  • BE = bond enthalpy

  • IE = ionisation energy

  • LE = lattice enthalpy expressed exothermically i.e. from free gaseous ions to ionic crystals.

  • elec.affin = electron affinity

• Each cycle involves 6–8 enthalpy values, of which you must know all of them except one!

• You can then calculate the unknown enthalpy value by substitution and simple algebraic rearrangement.

• No numerical values are shown on all Born–Haber cycle diagrams, but some are shown on selected enthalpy level diagrams.

M(s)	+	X2(g/l/s)	ΔHθf(MX2)	M2+(X–)2(s)
ΔHθatom(M)		2xΔHθatom(X2)			ΔHθLE(MX2)
		2X(g) +  2e-	2 x ΔHelec. affin.(X)	2X–(g) +
M(g)	ΔHθ1st+2nd IE(M)				M2+(g) +  e-
The Born–Haber Cycle for the formation of an MX2 ionic halide salt

For X = halogen and M = group 2 metal

From Hess's Law:

ΔH^θ_f(MX₂) =

ΔH^θ_atom(M) + {2 x ΔH^θ_atom(X₂)} + ΔH^θ_{1st IE}(M) + ΔH^θ_{2nd IE}(M) + {2 x ΔH^θ_{elec. affin.}(X)}  + ΔH^θ_LE(MX₂)

After substitution, rearrange to calculate the lattice enthalpy of the group 2 metal halide and watch out for the signs in the algebra as well as the enthalpy values!

-ΔH^θ_LE(MX₂) =

ΔH^θ_atom(M) + {2 x ΔH^θ_atom(X₂)} + ΔH^θ_{1st IE}(M) + ΔH^θ_{2nd IE}(M) + {2 x ΔH^θ_{elec. affin.}(X)}  - ΔH^θ_f(MX₂)

Watch out for the state of the halogen: F₂(g), Cl₂(g), Br₂(l) and I₂(s) and watch out for the signs in the algebra as well as the enthalpy values!

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Other lattice enthalpies that can be calculated with the magnesium chloride Born-Haber Cycle for any Group 2 metal oxide using an enthalpy level diagram

A general scheme is set out below of a general Born-Haber Cycle for a group 2 metal halide salt using an enthalpy level diagram.

ΔH_f^θ(MX₂) = standard enthalpy of formation of group 2 halide salt e.g. iodide  (↓ exothermic)

ΔH^θ_at(M) = standard enthalpy of atomisation of the group 2 metal (↑ endothermic)

 ΔH^θ_atom(X₂) = standard enthalpy of atomisation of the halogen X₂ (↑ endothermic)

 ΔH^θ_ea.(X) = standard enthalpy of the electron affinity of the halogen (↓ exothermic)

ΔH^θ_{1st IE}(M) = standard enthalpy of the 1st ionisation of the group 2 metal (↑ endothermic)

ΔH^θ_{2ndt IE}(M) = standard enthalpy of the 2nd ionisation of the group 2 metal (↑ endothermic)

ΔH^θ_LE(MX) = lattice enthalpy of the group 2 metal halide salt (↑ endothermic)

From Hess's Law: route B = route A

ΔH_f^θ(MX) + ΔH^θ_LE(MX) =

ΔH^θ_at(M) + 2 x ΔH^θ_atom(X) + ΔH^θ_{1st IE}(M) + ΔH^θ_2ndIE(M) + {2 x ΔH^θ_ea.(X)}

rearranging to get the lattice enthalpy of a group 2 metal halide salt and watch out for the signs in the algebra as well as the enthalpy values!

 ΔH^θ_LE(MX) =

ΔH^θ_at(M) + 2 x ΔH^θ_atom(X) + ΔH^θ_{1st IE}(M) + ΔH^θ_2ndIE(M) + {2 x ΔH^θ_ea.(X)} - ΔH_f^θ(MX)

Hence you can calculate the lattice enthalpy of any group 2 metal halide assuming it is a purely ionic compound e.g. magnesium bromide, calcium fluoride, strontium iodide, barium chloride etc.

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Born-Haber Cycle and Lattice Enthalpy INDEX

Energetics–Thermochemistry–Thermodynamics Notes INDEX

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How to draw the Born-Haber Cycle for group 2 metal halides, how to calculate the lattice enthalpy for group 2 metal halides from a Born-Haber Cycle, a full explanation of the terms and enthalpy values of the Born-Haber Cycle for group 2 metal halides, what do I need to know about the Born-Haber Cycle of group 2 metal halides for AQA, Edexcel, OCR, Salters, CIE, WJEC Eduqas & CCEA  A-level chemistry, US grades 11-12 K12 AP Honors chemistry courses, how to use enthalpies of formation, ionisation, atomisation, electron affinity and lattice enthalpy to problem solve the Born-Haber Cycle for group 2 metal halides.