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# The Born-Lande' equation

The Born-Lande equation is a concept originally formulated in 1918 by the scientists Born and Lande and is used to calculate the lattice energy (measure of the strength of bonds) of a compound. This expression takes into account both the Born interactions as well as the Coulombe attractions.

### Introduction

Due to its high simplicity and ease, the Born-Lande equation is commonly used by chemists when solving for lattice energy. This equation proposed by Max Born and Alfred Lande states that lattice energy can be derived friom ionic lattice based on electrostatic potential and the potential energy due to repulsions. To solve for the Born-Lande equation, you must have a basic understanding of lattice energy:

• Lattice energy decreases as you go down a group (as atomic radii goes up, lattice energy goes down).
• Going across the periodic table, atomic radii decreases, therefore lattice energy increases.

### Equation

The Born-Lande equation was derived from these two following equations:

The above two equations combine to form:

$\Delta U (0K) = \dfrac{LA\left | Z_+ \right | \left | Z_- \right |e^2}{4\pi\epsilon_or_o} + \left ( 1- \dfrac{1}{n} \right)$

• Z+    = Cation charge
• Z-     = Anion charge
• e       = 1.6022 x 10-19 C
• 8.85 x 10-12 c2/m

• r0    = closest ion distance
• n     = Born Exponent (typically ranges between 5-12) - used to measure how much a solid compresses

### Calculate Lattice Energy

Lattice energy, based on the equation from above, is dependent on multiple factors. We see that the charge of ions is proportional to the increase in lattice energy. In addition, as ions come into closer contact, lattice energy also increases.

### References

1. Johnson, D. A. Metals and Chemical Change. Cambridge: Royal Society of Chemistry, 2002.
2. Cotton, F. Albert, and F. Albert Cotton. Advanced Inorganic Chemistry. New York: Wiley, 1999.

### Problems

1. Which compound has the greatest lattice energy?

• AlF3 **
• NACl
• LiF
• CaCl2

This question requires basic knowledge of lattice energy. Since F3 gives the compound a +3 positive charge and the Al gives the compound a -1 negative charge, the compound has large electrostatic attraction. The bigger the electrostatic attraction, the greater the lattice energy.

2. What is the lattice energy of NaCl? (Hint: you must look up the values for the constants for this compound )

-756 kJ/mol (again, this value is found in a table of constants)

3. Calculate the lattice energy of NaCl.

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