Transcript 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.
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
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
Example of Born-Haber Cycle in Energy
Level Diagram
• Animation
Using Born-Haber Cycles to Find the
Stability of Ionic Compounds
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
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. 17984. 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>.