Lattice Energy: Experimental vs. Calculated values
Lattice energy is the amount of energy required to break an ionic solid into
its ions in their gas phase. It is difficult to determine lattice energy directly
through experimentation. Therefore, several methods have been developed
in order to estimate values for lattice energy.
1. Introduction
2. Trends
3. Calculating Lattice Energy
4. References
5. Outside Links
6. Problems
7. Contributors
Introduction
Lattice energy is usually estimated by using the Born-Fajans-Haber cycle, an
application of Hess' Law. It is important to be able to calculate lattice energy
because it can be used as a way to predict the melting points and solubilities
of ionic compounds.
Trends


Lattice energy decreases as ionic radii increases
Lattice energy increases as charges on the ions increases
Lattice energy gives an idea of how strongly ions in an ionic solid are
interacting. This is why these values can be used to predict properties such
as the melting point of the substance.
Calculating Lattice Energy
Lattice Energy is equal to the change in enthalpy that converts one mole of
solid crystal into gaseous ions.
Experimental Value (Born-Fajans-Haber cycle)
Application of the Born-Mayer equation represents the experimental value
because the data is derived from experiment. It gives:
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ΔfH˚(MX,s)=ΔaH˚(M,s)+nΔaH˚(X,g)+ΣIE(M,g)+nΔEA
H(X,g)+Δlattice H˚(MX,s)
ΔfH˚(MX,s)=standard enthalpy of formation
ΔaH˚(M,s)=enthalpy of atomization of metal M
nΔaH˚(X,g)=enthalpy of atomization of X
ΣIE(M,g)=sum of the ioninzation energies for the processes (M(g) --> M+(g) +
e- --> M2+(g) + 2e-...)
ΔEA H(X,g)=enthalpy change associated with the attachment of an electron
Δlattice H˚(MX,s)=Lattice enthalpy change
*See Reference 3
Calculated Value
The calculated value is an approximation determined by using the BornHaber cycle. Rearrangement of the equation gives:
ΔU(0K)≈ΔfH˚(MX,s)-ΔaH˚(M,s)-nΔaH˚(X,g)ΣIE(M,g)-nΔEA H˚(X,g)
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For example:
NaCl: ΔU(0K)≈ -411-108-496-(244/2)-(-349)≈ -788 kJ/mol
References
1. Ralph, William, F.Geoffrey, and Jeffry. General Chemistry. Ninth ed. New
Jersey:Pearson Education, Inc. 2007. p500;513-515.
2. Combs, Leon. "Lattice Energy". Dr. Leon L. Combs.
1999. http://erkki.kennesaw.edu/genchem8/ge00002.htm
3. Picture of NaCl
diagram http://intro.chem.okstate.edu/1314f00/lecture/chapter7/BornHa
ber2.GIF
4. Housecroft, Catherine E. and Alan G. Sharpe. Inorganic Chemistry. 3rd
ed. England: Pearson Education Limited, 2008.174-175.
Outside Links
Problems
1. Which one of the following has the greatest lattice energy?
A) MgO
B) NaCl
C) LiCl
D) MgCl2
Answer: A)MgO. It has ions with the largest charge.
2. Which one of the following has the greatest Lattice Energy?
A) NaCl
B) CaCl2
C) AlCl3
D) KCl
Answer: C)AlCl3. According to the periodic trends, as the radius of the ion
increases, lattice energy decreases.
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