# 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.

### 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. Lattice Energy is equal to the change in enthalpy that converts one mole of solid crystal into gaseous ions.

#### Experimental Value

Application of the Born-Mayer equation represents the experimental value because the data is derived from experiment. It gives:

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

aH˚(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 Born-Haber cycle. Rearrangement of the equation gives:                                                                       ΔU(0K)≈ΔfH˚(MX,s)-ΔaH˚(M,s)-nΔaH˚(X,g)-ΣIE(M,g)-nΔEA H˚(X,g)

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/BornHaber2.GIF
4. Housecroft, Catherine E. and Alan G. Sharpe. Inorganic Chemistry. 3rd ed. England: Pearson Education Limited, 2008.174-175.

### 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.

## Tags

Module Vet Level:
Module Target Level:

### Wikitexts

An NSF funded Project