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Born-Haber Cycles

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.

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Born-Haber Cycles

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  1. 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= -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

  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

  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, 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>.

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