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# Lattice Energy

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 Sub Topics Lattice energy of an Ionic crystal is the energy released when the required number of gaseous cations and anions are brought together from an infinite distance to form one gm mole of the solid crystal. The energy required to separate ions of one gm mole of solid ionic crystal from their equilibrium position in the crystal to infinity is also known as lattice energy.

## Definition

"The lattice energy of an Ionic crystal is the heat energy evolved when one mole of crystalline solid is formed from its separate gaseous ions under standard conditions."

All lattice energies are negative because heat energy is evolved when the ions come together to form electrovalent bonds.

Lattice energies provide a measure of the strength of the electrovalent bonds holding the ions together in a crystal lattice.

## Equation

The lattice energy is denoted by $U_{c}$, it is the amount of energy released when one mole of Ionic crystals is formed from gaseous ions which are at infinite separations. Thus,

$U_{c}$ = -(P.E)o $\times$ N

$U_{c}$ = - $\frac{NAe^{2}Z_{1}Z_{2}}{r_{o}}(\frac{1}{n}-1)$

$U_{c}$ = - $\frac{NAe^{2}Z_{1}Z_{2}}{r_{o}}(1 - \frac{n}{1})$

where, N is the Avogadro's number. Equation is known as Born's equation.

The lattice energy $U_{c}$ depends upon the charges of the ions, multiple charged ions giving more lattice energy than singly charged ions.

## Trend

Let us consider the lattice energy of the following two compounds.

 Compound Lattice energy (KJ/mol) NaF -910 CaO -3414

The magnitude of lattice energy of CaO is greater than the lattice energy of NaF. Even though the separation between the calcium and oxygen is slightly greater (which would tend to lower the lattice energy), the lattice energy for CaO is almost four times greater.

By summarizing the trend in lattice energies, the following point is observed.
• Lattice energies become less exothermic (less negative) with increasing Ionic radius.
• Lattice energies become more exothermic (more negative) with increasing magnitude of Ionic charge.

## Chart

Lattice energy involves the following terms.
• the heat of vaporization of the metal.
• the ionization energy of the vaporized metal.
• the heat of dissociation and electron affinity of the halogen.
Lattice energy for some of the metal halides are tabulated below.

 Compound Lattice energy NaCl 183.5 KI 152.4 RbI 156.1 CaI 142.5 TiCl 167 TiBr 164 TiI 159 CaF2 617.7 SrF2 587.5 BaF2 556.4

## Determination

Born-Haber cycles allow values for lattice enthalpies to be determined from experimental data. It is also useful to be able to calculate lattice enthalpies without needing to know other thermodynamic data. In the Ionic model, the energy change when the gaseous ions come together to form an ionic solid comes from the electrostatic interactions between the ions. By considering all the electrostatic interactions presentation an ionic solid a theoretical value for the lattice energy can be obtained.

The lattice energy is the difference in potential energy between the ions in the solid lattice and the ions widely separated as a gas. The change in internal energy when two ions of charges +z and -z are brought from an infinite distance to distance r is given by the equation.

## Problems

Some of the problems of lattice energy are given below.

### Solved Examples

Question 1: Calculate the lattice energy of KCl
given that,
$\Delta H_{f}$ = -438KJ/mol-1; $\Delta H_{1}$ = 89KJ/mol-1; $\Delta H_{2}$ = 244KJ/mol-1; $\Delta H_{3}$ = 425KJ/mol-1; $\Delta H_{4}$ = -355KJ/mol-1.
Solution:

$\Delta H_{f}$ = $\Delta H_{1}$ + $\Delta H_{2}$ + $\Delta H_{3}$ + $\Delta H_{4}$ + $\Delta H_{5}$

-438 = 89 +$\frac{1}{2}$ (244) + 425 + (-355) + $\Delta H_{5}$

$\Delta H_{5}$ = -719 kJ mol-1

Hence, the lattice energy of KCl is -719kJ mol-1

Question 2: Out of NaCl and MgO which has the higher value of lattice energy and why?
Solution:
MgO has higher lattice energy than NaCl because of small size and high charge.