2.2j Born–Haber cycle energy level diagrams for a group 1 metal 'normal' oxide M₂O and Group 1 metal sulfide M₂S

• ΔH enthalpy abbreviations used for the Born-Haber Cycle of group 1 oxides and sulfides

  • f = enthalpy of formation

  • atom = atomisation energy

  • BE = bond enthalpy = tom

  • 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.

e.g. the cycle for group 1 alkali metal oxide where M = Li, Na, K etc.

2M(s)	+	1/2O2(g)	ΔHθf(M2O)	(M+)2O2–(s)
2 x ΔHθatom(M)		ΔHθatom(O2)			ΔHθLE(M2O)
		O(g) +  2e-	ΔH1st+2nd elec. affin.(O)	O2–(g) +
2M(g)	2 x {ΔHθ1st (M)}				2M+(g) +  2e-
The Born–Haber Cycle for the formation of an MO ionic oxide

e.g. for sodium oxide M = Na

from Hess's Law

ΔH^θ_f(M₂O) = {2 x ΔH^θ_atom(M)} + ΔH^θ_atom(O₂) + {2 x ΔH^θ_{1st IE}(M)} + ΔH^θ_{1st elec. affin.}(O) + ΔH^θ_{2nd elec. affin.}(O)  + ΔH^θ_LE(M₂O)

Watch out for the different enthalpy sign of the two electron affinities.

Rearranging gives the lattice enthalpy of a group 1 oxide ('normal' not peroxides)

- ΔH^θ_LE(M₂O) = {2 x ΔH^θ_atom(M)} + ΔH^θ_atom(O₂) + {2 x ΔH^θ_{1st IE}(M)} + ΔH^θ_{1st elec. affin.}(O) + ΔH^θ_{2nd elec. affin.}(O) - ΔH^θ_f(M₂O)

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The Born-Haber cycle for sodium oxide shown as an enthalpy level diagram for sodium oxide.

From Hess's Law: route B = route A

route A = route B = +2114 kJ mol^–1  for sodium oxide and be very careful of the signs in the algebra as well as the enthalpy values!

{2 x ΔH^θ_atom(Na)} + ΔH^θ_atom(O₂) + {2 x ΔH^θ_{1st IE}(Na)} + ΔH^θ_{1st elec. affin.}(O) + ΔH^θ_{2nd elec. affin.}(O)

 = ΔH^θ_f(Na₂O) + ΔH^θ_LE(Na₂O)

ΔH^θ_LE(Na₂O) = {2 x ΔH^θ_atom(Na)} + ΔH^θ_atom(O₂) + {2 x ΔH^θ_{1st IE}(Na)} + ΔH^θ_{1st elec. affin.}(O) + ΔH^θ_{2nd elec. affin.}(O) - ΔH^θ_f(Na₂O)

2nd electron affinity of oxygen is the same as the 1st electron affinity of the O^– ion, but you may think of these as the 1st and 2nd electron affinities of oxygen atoms themselves, in the same way that you refer to the 1st and 2nd ionisation energies of gaseous sodium atoms.

This Born–Haber cycle can be adapted for any Group 1 Alkali Metal oxide M₂O e.g. Li₂O, K₂O etc.

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A general Born-Haber Cycle for a group 1 metal oxide expressed as an enthalpy level diagram

ΔH_f^θ(M₂O) = standard enthalpy of formation of group 1 oxide (↓ exothermic)

ΔH^θ_at(M) = standard enthalpy of atomisation of the group 1 metal (↑ 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}(M) = standard enthalpy of the 1st ionisation of the group 1 metal (↑ endothermic)

ΔH^θ_LE(M₂O) = lattice enthalpy of the group 1 metal oxide (↑ endothermic)

From Hess's Law: route B = route A

{2 x ΔH^θ_atom(M)} + ΔH^θ_atom(O₂) + {2 x ΔH^θ_{1st IE}(M)} + ΔH^θ_{1st elec. affin.}(O) + ΔH^θ_{2nd elec. affin.}(O)

 = ΔH^θ_f(M₂O) + ΔH^θ_LE(M₂O)

Rearrange to obtain the lattice enthalpy of a Group 1 metal oxide and be very careful of the signs in the algebra as well as the enthalpy values!

ΔH^θ_LE(M₂O) = {2 x ΔH^θ_atom(M)} + ΔH^θ_atom(O₂) + {2 x ΔH^θ_{1st IE}(M)} + ΔH^θ_{1st elec. affin.}(O) + ΔH^θ_{2nd elec. affin.}(O) - ΔH^θ_f(M₂O)

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Born-Haber Cycle for a Group 1 alkali metal sulfide to compute its lattice enthalpy

2M(s)	+	S(s)	ΔHθf(M2S)	(M+)2S2–(s)
2 x ΔHθatom(M)		ΔHθatom(S)			ΔHθLE(M2S)
		S(g) +  2e-	ΔH1st+2nd elec. affin.(S)	S2–(g) +
2M(g)	2 x {ΔHθ1st (M)}				2M+(g) +  2e-
The Born–Haber Cycle for the formation of an MO ionic oxide

e.g. for M = Li, Na and K etc.

From Hess's Law

ΔH^θ_f(M₂S) = {2 x ΔH^θ_atom(M)} + ΔH^θ_atom(S) + {2 x ΔH^θ_{1st IE}(M)} + ΔH^θ_{1st elec. affin.}(S) + ΔH^θ_{2nd elec. affin.}(S)  + ΔH^θ_LE(M₂S)

Watch out for the different enthalpy sign of the two electron affinities of gaseous sulfur atoms.

Rearrange to obtain the lattice enthalpy of any Group 1 metal sulfide and be very careful of the signs in the algebra as well as the enthalpy values!

- ΔH^θ_LE(M₂S) = {2 x ΔH^θ_atom(M)} + ΔH^θ_atom(S) + {2 x ΔH^θ_{1st IE}(M)} + ΔH^θ_{1st elec. affin.}(S) + ΔH^θ_{2nd elec. affin.}(S) - ΔH^θ_f(M₂S)

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A general Born-Haber Cycle for a group 1 metal sulfide expressed as an enthalpy level diagram to calculate lattice enthalpy

ΔH_f^θ(M₂S) = standard enthalpy of formation of group 1 sulfide (↓ exothermic)

ΔH^θ_at(M) = standard enthalpy of atomisation of the group 1 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 of the group 1 metal (↑ endothermic)

ΔH^θ_LE(M₂S) = lattice enthalpy of the group 2 metal oxide (↑ endothermic)

From Hess's Law: route A = route B

{2 x ΔH^θ_atom(M)} + ΔH^θ_atom(S) + {2 x ΔH^θ_{1st IE}(M)} + ΔH^θ_{1st elec. affin.}(S) + ΔH^θ_{2nd elec. affin.}(S)

 = ΔH^θ_f(M₂S) + ΔH^θ_LE(M₂S)

Rearrange to obtain the lattice enthalpy of any Group 1 metal sulfide and be very careful of the signs in the algebra as well as the enthalpy values!

ΔH^θ_LE(M₂S) = {2 x ΔH^θ_atom(M)} + ΔH^θ_atom(S) + {2 x ΔH^θ_{1st IE}(M)} + ΔH^θ_{1st elec. affin.}(S) + ΔH^θ_{2nd elec. affin.}(S) - ΔH^θ_f(M₂S)

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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 1 metal oxides and group 1 metal sulfides, how to calculate the lattice enthalpy for Group 1 metal oxides and group 1 metal sulfides from a Born-Haber Cycle, a full explanation of the terms and enthalpy values of the Born-Haber Cycle for Group 1 metal oxides and group 1 metal sulfides, what do I need to know about the Born-Haber Cycle of Group 1 metal oxides and group 1 metal sulfides 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 1 metal oxides and group 1 metal sulfides.