• ΔH enthalpy abbreviations used for the Born-Haber Cycle of magnesium oxide and magnesium sulfide

  • 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.

Mg(s)	+	1/2O2(g)	ΔHθf(MgO)	Mg2+O2-(s)
ΔHθatom(Mg)		ΔHθatom(O2)			ΔHθLE(MgO)
		O(g) +  2e-	ΔH1st+2nd elec. affin.(O)	O2–(g) +
Mg(g)	ΔHθ1st + 2nd IE(Mg)				Mg2+(g) +  2e-
The Born–Haber Cycle for the formation of an MgO ionic oxide

ΔH^θ_f(MgO) =

ΔH^θ_atom(Mg) + ΔH^θ_atom(O₂) + ΔH^θ_{1st IE}(Mg) + ΔH^θ_{2nd IE}(Mg) + ΔH^θ_{1st elec. affin.}(O) + ΔH^θ_{2nd elec. affin.}(O) + ΔH^θ_LE(MgO)

Watch out for the different enthalpy signs of the two electron affinities of oxygen atoms.

Rearrangement gives the lattice enthalpy of magnesium oxide and be very careful of the signs in the algebra as well as the enthalpy values!

-ΔH^θ_LE(MgO) = ΔH^θ_atom(Mg) + ΔH^θ_atom(O₂) + ΔH^θ_{1st IE}(Mg) + ΔH^θ_{2nd IE}(Mg) + ΔH^θ_{1st elec. affin.}(O) + ΔH^θ_{2nd elec. affin.}(O) - ΔH^θ_f(MgO)

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A Born-Haber Cycle for magnesium oxide expressed as an enthalpy level diagram to calculate its lattice enthalpy

ΔH_f^θ(MgO) = standard enthalpy of formation of magnesium oxide (↓ exothermic)

ΔH^θ_at(Mg) = standard enthalpy of atomisation of magnesium (↑ endothermic)

 ΔH^θ_atom(O₂) = standard enthalpy of atomisation of oxygen (↑ endothermic)

 ΔH^θ_1stea.(O) = standard enthalpy of the 1st electron affinity of oxygen (↓ exothermic)

 ΔH^θ_2ndea.(O^-) = standard enthalpy of the 2nd electron affinity of oxygen (↑ endothermic)

ΔH^θ_{1st IE}(Mg) = standard enthalpy of the 1st ionisation energy of magnesium (↑ endothermic)

ΔH^θ_{2nd IE}(Mg) = standard enthalpy of the 2nd ionisation energy of magnesium (↑ endothermic)

ΔH^θ_LE(MgO) = lattice enthalpy of magnesium oxide (↑ endothermic)

From Hess's Law: route A = route B

route A = route B = +3845 kJ mol^–1  (but watch the signs!)

ΔH^θ_atom(Mg) + ΔH^θ_atom(O₂) + ΔH^θ_{1st IE}(Mg) + ΔH^θ_{2nd IE}(Mg) + ΔH^θ_{1st elec. affin.}(O) + ΔH^θ_{2nd elec. affin.}(O)  = ΔH^θ_f(MgO) + ΔH^θ_LE(MgO)

and be very careful of the signs in the algebra as well as the enthalpy values!

Rearrangement gives the expression to calculate the lattice enthalpy of magnesium oxide.

ΔH^θ_LE(MgO) = ΔH^θ_atom(Mg) + ΔH^θ_atom(O₂) + ΔH^θ_{1st IE}(Mg) + ΔH^θ_{2nd IE}(Mg) + ΔH^θ_{1st elec. affin.}(O) + ΔH^θ_{2nd elec. affin.}(O) - ΔH^θ_f(MgO)

Using this data gives a lattice energy of 3845 kJ mol^–1, but one of my data books quotes 3889 kJ mol^–1.

This Born–Haber cycle can be adapted for any Group 2 Alkaline Earth metal oxide MO e.g. CaO, BaO etc.

Born-Haber Cycle for magnesium sulfide and calculation of its lattice enthalpy

Mg(s)	+	S(s)	ΔHθf(MgS)	Mg2+S2-(s)
ΔHθatom(Mg)		ΔHθatom(S)			ΔHθLE(MgS)
		S(g) +  2e-	ΔH1st+2nd elec. affin.(S)	S2–(g) +
Mg(g)	ΔHθ1st + 2nd IE(Mg)				Mg2+(g) +  2e-
The Born–Haber Cycle for the formation of an MO ionic oxide

ΔH^θ_f(MgS) =

ΔH^θ_atom(Mg) + ΔH^θ_atom(S) + ΔH^θ_{1st IE}(Mg) + ΔH^θ_{2nd IE}(Mg) + ΔH^θ_{1st elec.affin.}(S) + ΔH^θ_{2nd elec. affin.}(S) + ΔH^θ_LE(MgS)

Rearrange the expression to calculate the lattice enthalpy of magnesium oxide, and watch out for the different enthalpy sign of the two electron affinities of gaseous sulfur atoms AND watch out for the different enthalpy sign of the two electron affinities of oxygen atoms.

- ΔH^θ_LE(MgS) = ΔH^θ_atom(Mg) + ΔH^θ_atom(S) + ΔH^θ_{1st IE}(Mg) + ΔH^θ_{2nd IE}(Mg) + ΔH^θ_{1st elec.affin.}(S) + ΔH^θ_{2nd elec. affin.}(S) - ΔH^θ_f(MgS)

This Born–Haber cycle can be adapted for any Group 2 Alkaline Earth metal sulfide MS e.g. CaS, BaS etc.

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A general Born-Haber Cycle for magnesium sulfide expressed as a general enthalpy level diagram to calculate the lattice enthalpy of any Group 2 metal sulfide

ΔH_f^θ(MS) = standard enthalpy of formation of group 2 metal sulfide (↓ exothermic)

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

 ΔH^θ_atom(S) = standard enthalpy of atomisation of sulfur (↑ endothermic)

 ΔH^θ_1stea.(S) = standard enthalpy of the 1st electron affinity of sulfur (↓ exothermic)

 ΔH^θ_2ndea.(S^-) = standard enthalpy of the 2nd electron affinity of sulfur (↑ endothermic)

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

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

ΔH^θ_LE(MS) = lattice enthalpy of the group sulfide (↑ endothermic)

From Hess's Law: route B = route A

ΔH^θ_atom(M) + ΔH^θ_atom(S) + ΔH^θ_{1st IE}(M) + ΔH^θ_{2nd IE}(M) + ΔH^θ_{1st elec. affin.}(S) + ΔH^θ_{2nd elec. affin.}(S)  = ΔH^θ_f(MS) + ΔH^θ_LE(MS)

and be very careful of the signs in the algebra as well as the enthalpy values!

Rearrangement gives the expression to calculate the lattice enthalpy of magnesium oxide.

- ΔH^θ_LE(MS) = ΔH^θ_atom(M) + ΔH^θ_atom(S) + ΔH^θ_{1st IE}(M) + ΔH^θ_{2nd IE}(M) + ΔH^θ_{1st elec. affin.}(S) + ΔH^θ_{2nd elec. affin.}(S) - ΔH^θ_f(MS)

How to draw the Born-Haber Cycle for magnesium oxide & magnesium sulfide, how to calculate the lattice enthalpy for magnesium oxide & magnesium sulfide from a Born-Haber Cycle, a full explanation of the terms and enthalpy values of the Born-Haber Cycle for magnesium oxide & magnesium sulfide, what do I need to know about the Born-Haber Cycle of magnesium oxide & magnesium sulfide 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 magnesium oxide & magnesium sulfide.