2.2h. Calculating the lattice enthalpy of a group 2 metal oxide MO or Group 2 metal sulfide MS where M = group 2 alkaline earth metal

• ΔH enthalpy abbreviations used for the Born-Haber Cycle of group 2 metal oxides & sulfides

  • 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)	+	1/2O2(g)	ΔHθf(MO)	M2+O2–(s)
ΔHθatom(M)		ΔHθatom(O2)			ΔHθLE(MO)
		O(g) +  2e-	ΔH1st+2nd elec. affin.(O)	O2–(g) +
M(g)	ΔHθ1st + 2nd IE(M)				M2+(g) +  2e-
The Born–Haber Cycle for the formation of an MO ionic oxide

From Hess's Law

ΔH^θ_f(MO) =

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

Watch out for the different enthalpy sign of the two electron affinities and watch the signs in the calculation of the lattice enthalpy - both for the algebra and enthalpy values.

After substitution, rearrange to calculate the lattice enthalpy of the group 2 metal oxide M²⁺O^2–

- ΔH^θ_LE(MO) =

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

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The general enthalpy level diagram of the Born-Haber Cycle for the formation of a Group 2 alkaline earth metal oxide

ΔH_f^θ(MO) = standard enthalpy of formation of group 2 metal oxide (↓ exothermic)

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

From Hess's Law: route B = route A

ΔH^θ_f(MO) + ΔH^θ_LE(MO) =

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

Therefore rearranging to get the lattice enthalpy of a group 2 metal oxide

ΔH^θ_LE(MO) =

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

and watch out for the signs in the algebra as well as the enthalpy values!

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The Born-Haber Cycle to calculate the lattice enthalpy of any Group 2 metal sulfide MS

It would be a similar cycle to calculate the lattice enthalpy of a group II metal sulfide, just replace O with S and the appropriate enthalpy values e.g. for group 2 metal sulfide M²⁺S^2–

M(s)	+	S(s)	ΔHθf(MS)	MS(s)
ΔHθatom(M)		ΔHθatom(S)			ΔHθLE(MS)
		S(g) +  2e-	ΔH1st+2nd elec. affin.(S)	S2–(g) +
M(g)	ΔHθ1st + 2nd IE(M)				M2+(g) +  2e-
The Born–Haber Cycle for the formation of an MS ionic sulfide

For M = Be, Mg, Ca etc.

ΔH^θ_f(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_LE(MS)

Therefore to calculate the lattice enthalpy of a group 2 metal sulfide

-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)

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

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The general enthalpy level diagram of the Born-Haber Cycle for the formation of a Group 2 alkaline earth 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 2 metal sulfide (↑ endothermic)

From Hess's Law: route B = route A

ΔH^θ_f(MS) + 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)

Therefore rearranging to get the lattice enthalpy of a group 2 metal sulfide

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)

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

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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 oxides & group 2 metal sulfides, how to calculate the lattice enthalpy for group 2 metal oxides & group 2 metal sulfides from a Born-Haber Cycle, a full explanation of the terms and enthalpy values of the Born-Haber Cycle for group 2 metal oxides & group 2 metal sulfides, what do I need to know about the Born-Haber Cycle of group 2 metal oxides & group 2 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 2 metal oxides & group 2 metal sulfides.