• ΔH enthalpy abbreviations used for the Born-Haber Cycle of magnesium chloride

  • 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)	+	Cl2(g)	ΔHθf(MCl2)	Mg2+(Cl–)2(s)
ΔHθatom(Mg)		2xΔHθatom(Cl2)			ΔHθLE(MgCl2)
		2Cl(g) +  2e-	2 x ΔHelec. affin.(Cl)	2X–(g) +
Mg(g)	ΔHθ1st+2nd IE(Mg)				Mg2+(g) + 2 e-
The Born–Haber Cycle for the formation of an MX2 ionic halide salt

From Hess's Law:

ΔH^θ_f(MgCl₂) =

ΔH^θ_atom(Mg) + {2 x ΔH^θ_atom(Cl₂)} + ΔH^θ_{1st IE}(Mg) + ΔH^θ_{2nd IE}(Mg) + {2 x ΔH^θ_{elec. affin.}(Cl)}  + ΔH^θ_LE(MgCl₂)

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(MgCl₂) =

ΔH^θ_atom(Mg) + {2 x ΔH^θ_atom(Cl₂)} + ΔH^θ_{1st IE}(Mg) + ΔH^θ_{2nd IE}(Mg) + {2 x ΔH^θ_{elec. affin.}(Cl)}  - ΔH^θ_f(MgCl₂)

Watch out for the state of the halogen: F₂(g), Cl₂(g), Br₂(l) and I₂(s).

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The full enthalpy level diagram for the Born-Haber Cycle for the formation of magnesium chloride

From Hess's Law: route B = route A

• route A = route B = +1883 kJ mol^–1  (but watch the signs!)

• ΔH^θ_atom(Mg) + {2 x ΔH^θ_atom(Cl₂)} + ΔH^θ_{1st IE}(Mg) + ΔH^θ_{2nd IE}(Mg) + {2 x ΔH^θ_el.affin.(Cl)} = ΔH^θ_f(MgCl₂) + ΔH^θ_LE(MgCl₂)

• So to calculate the lattice enthalpy of magnesium chloride

• ΔH^θ_LE(MgCl₂) = ΔH^θ_atom(Mg) + {2 x ΔH^θ_atom(Cl₂)} + ΔH^θ_{1st IE}(Mg) + ΔH^θ_{2nd IE}(Mg) + {2 x ΔH^θ_el.affin.(Cl)} - ΔH^θ_f(MgCl₂)

• This Born–Haber cycle can be adapted for any Group 2 Alkaline Earth Halide MX₂ e.g. MgF₂, CaCl₂, CaBr₂ etc.

• Why not MgCl? The Born–Haber Cycle for M⁺Cl^– (very similar to NaCl)

• The full enthalpy level diagram for the Born-Haber Cycle for the formation of magnesium monochloride MgCl

From Hess's Law: route B = route A

• route A = route B = +659 kJ mol^–1  (but watch the signs!)

• ΔH^θ_atom(Mg) + ΔH^θ_atom(Cl₂) + ΔH^θ_{1st IE}(Mg) + ΔH^θ_el.affin.(Cl) 

• = ΔH^θ_f(MgCl) + ΔH^θ_LE(MgCl)

• The lattice enthalpy for MgCl can be theoretically calculated (its similar to NaCl, and so with known values for the rest of the cycle, you can then calculate the enthalpy of formation for MgCl.

• ΔH^θ_f(MgCl) turns out to –94 kJ mol^–1, which is much less exothermic than the energy released when the favoured MgCl₂ is formed.

• You should also note with lower charge of on the Mg+ ion, the lattice enthalpy is also much lower, so both factors contribute to the thermodynamically less favourable formation of Mg+Cl^-.

• This is just the same sort of Born-Haber cycle calculations explained, but this time with a different unknown {ΔH^θ_f(MgCl)} versus five known enthalpy values including the theoretically calculated lattice enthalpy {ΔH^θ_LE(MgCl)} - whose calculated value can be very accurate compared to experiment values.

  See section 2.2k Data table of lattice enthalpies, ionic radii (nm) for group 1/2 metal halides, oxides and sulfides and more discussion of trends and comparing theoretical/experiment lattice enthalpies

• Why not MgCl₃?

  • I've found one quoted value of +3949 kJ mol^–1 for the enthalpy of formation of MgCl₃.

  • I think one could reasonably deduce that this highly endothermic compound is hardly likely to exist!

  • Although the more highly charged Mg³⁺ ion would increase the lattice enthalpy, favouring MgCl₃ formation, the formation of Mg³⁺ requires far more energy because the 3rd ionisation requires the removal of an electron from an inner less shielded shell.

  • The 3rd ionisation energy of magnesium is +7740 kJ mol^–1, which completely outweighs any increase in lattice enthalpy due to the more highly charged Mg³⁺ ion, and accounts for such an endothermic enthalpy of formation of MgCl₃.

• Extension of these three calculations

  • You can apply the same arguments for calcium or any other group 2 metal i.e. why CaCl₂ is favoured thermodynamically in preference to CaCl or CaCl₃

• AND, the same arguments for the different halogens for a given group 2 metal

How to draw the Born-Haber Cycle for magnesium chloride MgCl2, MgCl & MgCl3, how to calculate the lattice enthalpy for magnesium chloride MgCl2, MgCl & MgCl3 from a Born-Haber Cycle, a full explanation of the terms and enthalpy values of the Born-Haber Cycle for magnesium chloride MgCl2, MgCl & MgCl3, what do I need to know about the Born-Haber Cycle of magnesium chloride MgCl2, MgCl & MgCl3 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 chloride MgCl2, MgCl & MgCl3.