Born-Haber Cycles

A method to calculate Lattice Enthalpies

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

Lattice Enthalpies• Adding the two previous reactions

Na(g) + Cl(g) Na+(g) + Cl-

(g) ΔHᶿ= -349 + 496 = +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

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

Born-Haber Cycle Steps

1. Atomize Solid SodiumNa(s) Na(g); ΔHᶿe = +108 mol-1

2. Atomize chlorine gasCl2 (g) Cl(g); ΔHᶿe = +121 mol-1

3. Form sodium ions from the sodium atomsNa(g) Na+

(g) + e-; ΔHᶿi.e = +498 mol-1

4. Form chloride ions from the chlorine atomsCl(g) + e- Cl-

(g); ΔHᶿe.g. = -351 mol-1

5. Pack the sodium and chloride ions together to make solid sodium chlorideNa(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

The indirect route of reaction For Sodium Chloride

Example of Born-Haber Cycle in Energy Level Diagram

• Animation

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

Theoretical Lattice EnthalpiesCalculating 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

Comparison of Theoretical and Experimental Lattice Enthalpies

Compound Theoretical value/kJ mol-1

Experimental Value/kJ mol-1

NaCl -769 -732

NaBr -732 -747

NaI -682 -704

AgCl -864 -915

AgBr -830 -904

AgI -808 -889

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.

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

Bibliography• Clugston, M. J., and Rosalind Flemming. "Chapter 10."

Advanced Chemistry. Oxford: Oxford UP, 2000. 156-57. Print.

• Ford, Mike. "5." Higher Level Chemistry. By Catrin Brown. Harlow: Pearson Education Limited, 2009. 179-84. Print.

• Neuss, Geoffrey. "5." Chemistry: Course Companion. Oxford: Oxford UP, 2007. 103-05. Print.

• Population, General. "Energetics (hl)." IB Chemistry Higher Level Revision Notes: Energetics. Isis, 1 Jan. 2011. Web. 29 Feb. 2012. <http://ibchem.com/IB/ibnotes/brief/ene-hl.htm>.