• ΔH enthalpy abbreviations used for the Born-Haber Cycle of sodium chloride (298K/101kPa)

  • f = enthalpy of formation

  • atom = atomisation energy (I've seen this notated as enthalpy of sublimation, technically correct for sodium, but they are different general definitions, and I strongly disagree with the use of this term here).

  • BE = bond enthalpy (half of this = enthalpy of atomisation for diatomic gases like fluorine and chlorine, since breaking the bond creates two atoms of chlorine.)

  • 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.

Na(s)	+	1/2Cl2(g)	ΔHθf(NaCl)	Na+Cl–(s)
ΔHθatom(Na)		ΔHθatom(Cl2)			ΔHθLE(NaCl)
		Cl(g) +  e-	ΔHelec.affin(Cl)	Cl–(g) +
Na(g)	ΔHθ1st IE(Na)				Na+(g) +  e-
The Born–Haber Cycle for the formation of a sodium chloride, an ionic halide salt

•  From Hess's Law

• ΔH^θ_f(NaCl) = –411 kJ mol^–1 (then, ready for substitution, but watch the signs!)

• = ΔH^θ_atom(Na) + ΔH^θ_atom(Cl₂) + ΔH^θ_{1st IE}(Na) + ΔH^θ_{elec. affin.}(Cl) + ΔH^θ_LE(NaCl)

• I suggest you substitute all the enthalpy values in before rearranging to calculate the unknown e.g. the lattice enthalpy of sodium chloride can calculated on rearrangement and be very careful of the signs in the algebra as well as the enthalpy values!

• -ΔH^θ_LE(NaCl) =

• ΔH^θ_atom(Na) + ΔH^θ_atom(Cl₂) + ΔH^θ_{1st IE}(Na) + ΔH^θ_{elec. affin.}(Cl) - ΔH^θ_f(NaCl)

• This Born–Haber cycle can be adapted for any Group 1 Alkali Metal Halide MX e.g. LiF, NaBr, KCl, KBr etc.

• 

• In Fig. 1 (above) for sodium chloride ΔH₁ = ΔH₂ + ΔH₃ + ΔH₄ + ΔH₅ + ΔH₆ because all the arrows in the cycle point from the start to the finish

  • This shows how to present and solve a Hess's Law cycle for the formation of an ionic metal chloride and is an example of the so–called Born–Haber Cycle.

  • From Hess's Law and watch the delta H signs!

  • ΔH₁ = ΔH₂ + ΔH₃ + ΔH₄ + ΔH₅ + ΔH₆

  • ΔH^θ_f(NaCl) =

  • ΔH^θ_atom(Na) + ΔH^θ_atom(Cl) + ΔH^θ_{elec. affin.}(Cl) + ΔH^θ_{1st IE}(Na) + ΔH^θ_LE(NaCl)

  • So: –411 = (+107) + (+121) + (–355) + (+502) + (–786)

  • I often work in () at first retaining the original delta H sign, it reduces the risk of 'sign error'!

  • –411 = +107 +121 –355 +502 –786 = –411

  • If you know five of the six values you can theoretically calculate the 6th enthalpy value which is the most important application of this particular Hess's Law cycle.

  • Although I've put in all the numbers, just imagine the lattice enthalpy was the unknown

  • i.e. –ΔH₆ = ΔH₂ + ΔH₃ + ΔH₄ + ΔH₅ – ΔH₁

• Fig 2. shows one how to present a Born–Haber cycle diagram for the formation of an ionic metal chloride by using an enthalpy level diagram.

  • However, in solving problems via enthalpy diagrams you need to define your start and end points and watch the signs!

  • Fig. 3 shows one possible start and end point.

  • The sum of the 'upper loop' enthalpy changes must equal the sum of the 'lower loop' changes, but the signs of the numerical enthalpy values must be appropriate,

  • so ΔH₂ + ΔH₃ + ΔH₅ + ΔH₄ equals the upper loop, and no change in signs required, the arrows point towards the end products,

  • but the sum of the lower loop enthalpies = ΔH₁ + (–ΔH₆) because the arrow must point in the opposite direction to Fig. 2 and the sign of ΔH₆ must therefore be reversed,

  • so ΔH₂ + ΔH₃ + ΔH₅ + ΔH₄ =  ΔH₁ –ΔH₆ to solve a problem.

  • +107 +121 + 502 –355 = –411 – –786 = +375

  • so, +375 = +375, so, if 5 values known, the 6th can be theoretically calculated.

  • Below is a repeat of Fig. 2 with all the enthalpy data marked on, but I have shown the lattice enthalpy as endothermic, whereas in Fig. 2 it is shown as exothermic - remember they are numerically the same!

  • I've used the style below for many of the diagrams on successive pages 2.2d to 2.2j

The full enthalpy level diagram for the Born-Haber Cycle for sodium chloride NaCl (Na⁺Cl^-) to calculate its lattice enthalpy

This is another way of presenting how to calculate the lattice enthalpy of sodium chloride using an enthalpy level diagram (298K/101kPa), all the relevant enthalpy data are included.

ΔH_f^θ(NaCl) = standard enthalpy of formation of sodium chloride (↓ exothermic)

ΔH^θ_at(Na) = standard enthalpy of atomisation of sodium (↑ endothermic)

 ΔH^θ_atom(Cl₂) = standard enthalpy of atomisation of chlorine (↑ endothermic)

 ΔH^θ_ea.(Cl) = standard enthalpy of the electron affinity of chlorine (↓ exothermic)

ΔH^θ_{1st IE}(Na) = standard enthalpy of the 1st ionisation of sodium (↑ endothermic)

ΔH^θ_LE(NaCl) = lattice enthalpy of sodium chloride (↑ endothermic on this diagram)

From Hess's Law: route B = route A

ΔH_f^θ(NaCl) + ΔH^θ_LE(NaCl) = ΔH^θ_at(Na) + ΔH^θ_atom(Cl₂) + ΔH^θ_{1st IE}(Na) +  ΔH^θ_ea.(X)

rearranging gives you the lattice enthalpy of sodium chloride, but be very careful of the signs in the algebra as well as the enthalpy values!

 ΔH^θ_LE(NaCl) = ΔH^θ_at(Na) + ΔH^θ_atom(Cl₂) + ΔH^θ_{1st IE}(Na) +  ΔH^θ_ea.(Cl) - ΔH_f^θ(NaCl)

Other lattice enthalpies of MX that can be calculated with the 'sodium chloride' Born-Haber Cycle expressed in terms of enthalpy level

The full enthalpy level diagram for the Born-Haber Cycle for any group 1 halide salt, assumed to be a pure ionic compound. Key below the diagram.

ΔH_f^θ(MX) = standard enthalpy of formation of group 1 halide salt e.g. fluoride or chloride  (↓ exothermic)

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

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

 ΔH^θ_ea.(X) = standard enthalpy of the electron affinity of the halogen e.g. fluorine or chlorine (↓ exothermic)

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

ΔH^θ_LE(MX) = lattice enthalpy of the halide salt e.g. fluoride or chloride (↑ endothermic)

From Hess's Law: route B = route A

ΔH_f^θ(MX) + ΔH^θ_LE(MX) = ΔH^θ_at(M) + ΔH^θ_atom(X₂) + ΔH^θ_{1st IE}(M) +  ΔH^θ_ea.(X)

ΔH^θ_LE(MX) = ΔH^θ_at(M) + ΔH^θ_atom(X₂) + ΔH^θ_{1st IE}(M) +  ΔH^θ_ea.(X) - ΔH_f^θ(MX)

Solve for unknown e.g. lattice enthalpy of sodium chloride and be very careful of the signs in the algebra as well as the enthalpy values!

The enthalpy level diagram for the Born-Haber Cycle for the formation of a Group 1 metal halide (e.g. fluoride and bromide). M = Li, Na, K, Rb, Cs and Fr, X = F, Cl, Br, I, At

Using F₂(g), all the fluorides from group I metals, lithium fluoride LiF, sodium fluoride NaF, potassium fluoride KF, rubidium fluoride RbF, caesium fluoride CsF and francium fluoride FrF.

Using Cl₂(g), all the chlorides from group I metals, lithium chloride LiCl, potassium chloride KCl, rubidium chloride RbCl, caesium chloride CsCl and francium chloride FrCl.

For fluorides and chlorides the halogen is in the gaseous state at 298K/191kP.

Hence you can calculate the lattice enthalpy of any group 1 metal halide assuming it is a purely ionic compound.

See also the Born-Haber Cycle for Group 1 bromides and Group 1 iodides

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