1. A method to calculate Lattice Enthalpies
Born-Haber Cycles
A method to calculate Lattice Enthalpies

2. Ionization Energy & Electron Affinity
The first ionization energy of an element is the energy required to remove one mole of electrons from one mole of gaseous atoms.
It is represented by ( H ) and corresponds to the energy needed to form a positive ion
Na(g)  Na+(g) + e- ΔHᶿi = +496kJ mol-1
The first electron affinity is the enthalpy change when one mole of gaseous atoms attracts one mole of electrons.
Cl(g) + e-  Cl-(g) ΔHᶿe = -349 mol-1
It is represented by ( H ) and corresponds to the energy needed to form a negative ion

3. Lattice Enthalpies
Adding the two previous reactions
Na(g) + Cl(g)  Na+(g) + Cl-(g) ΔHᶿ= = +147 mol-1
Endothermic process
The products of this reaction from an ionic lattice
Na+(g) + Cl-(g) NaCl(s) ΔHᶿlat = -790 mol-1
Exothermic process
The lattice enthalpy expresses this enthalpy change in terms of the reverse endothermic process – The formation of gaseous ions from one mole of a solid crystal

4. Experimental Lattice Enthalpies & Born Haber Cycle
Experimental lattice enthalpy cannot be calculated directly
Energy cycle based on elemental form is a method of finding said enthalpy
Born-Haber method related to Hess Law – Expresses reaction from the elemental form in an energy cycle

5. Born-Haber Cycle Steps
The indirect route of reaction For Sodium Chloride
1. Atomize Solid Sodium
Na(s)  Na(g); ΔHᶿe = +108 mol-1
2. Atomize chlorine gas
Cl2 (g)  Cl(g); ΔHᶿe = +121 mol-1
3. Form sodium ions from the sodium atoms
Na(g) Na+(g) + e-; ΔHᶿi.e = +498 mol-1
4. Form chloride ions from the chlorine atoms
Cl(g) + e-  Cl-(g); ΔHᶿe.g. = -351 mol-1
5. Pack the sodium and chloride ions together to make solid sodium chloride
Na(s) + Cl2  NaCl(s); ΔHᶿlat for = -787 mol-1
Sum of the indirect route equals -411 kJ mol-1 hence the standard enthalpy change for the formation of sodium chloride is -411 kJ mol-1

6. Example of Born-Haber Cycle in Energy Level Diagram
Animation

7. Using Born-Haber Cycles to Find the Stability of Ionic Compounds

8. Theoretical Lattice Enthalpies
Calculating lattice enthalpies based on the ionic model
Theoretical lattice enthalpy is calculated based on the ionic model
The ionic model assumes that the ions are perfectly spherical and only electro static interactions play a role
Energy needed to seperate ions (lattice enthalpy) is based upon the following:
An increase in the ionic radius of one of the ions decreases the attraction between ions
An increase in the ionic charge increases the ionic attraction between the ions

9. Comparison of Theoretical and Experimental Lattice Enthalpies
Compound
Theoretical value
/kJ mol-1
Experimental Value
NaCl
-769
-732
NaBr
-747
NaI
-682
-704
AgCl
-864
-915
AgBr
-830
-904
AgI
-808
-889

10. Using The Comparison to Indicate The Ionic Nature of a Compound
The closer the correlation between the ionic model and the Born-Haber model the more electrostatic bonding is occuring
If there is a large discrepancy, it is likely that a degree of covalent bonding is occuring
NaCl has a 2% discrepancy - electro-static bonding between perfect spheres
AgCl has a 6% discrepancy - covalent nature to the bond.
The ionic / covalent nature of the bond is dictated by the difference in electro negativity, the greater this is, the more ionic the bond will be.

11. Summary
Born-Haber cycles are an application of Hess’s law to ionic compounds
Born-Haber cycles may be used to calculate the theoretical standard enthalpy changes of formation of ionic compounds to see how likely they are to exist
A comparison of experimental values and theoretical values for lattice enthalpies indicates the bond character of the ionic lattice

12. Bibliography
Clugston, M. J., and Rosalind Flemming. "Chapter 10." Advanced Chemistry. Oxford: Oxford UP, Print.
Ford, Mike. "5." Higher Level Chemistry. By Catrin Brown. Harlow: Pearson Education Limited, Print.
Neuss, Geoffrey. "5." Chemistry: Course Companion. Oxford: Oxford UP, Print.
Population, General. "Energetics (hl)." IB Chemistry Higher Level Revision Notes: Energetics. Isis, 1 Jan Web. 29 Feb <