Lattice energy formula & Solved Examples

Education Journalist | Study Abroad Lead

Lattice energy is the energy released when two oppositely charged gaseous ions are attracted to each other forming an ionic solid. The process is endothermic due to the fact that the attraction of two ions causes the release of energy. The lattice energy can be found using Coulomb’s law, LE = kQ₁Q₂/r, Where LE is the lattice energy, K has a value of 2.31 x 10^-19, Q1 and Q2 are the numerical ion charge, and R = the distance between the ion centres.

Table of Content

Ionic Lattice Energy Formula
Formula for Crystalline Lattice Energy
Lattice Energy Concept
Things to Remember
Solved Examples

Ionic Lattice Energy Formula

[Click Here for Sample Questions]

The lattice energy for all solids can be found using the modified Coulomb’s law formula.

LE = kQ₁Q₂/r

In this equation, Q1 and Q2 are the charges on the ion and r is the inter-nuclear distance. The lattice energy is directly proportional to the ion products and inversely related to the inter-nuclear distance.

K is a proportionality constant with the value of 2.31 x 10^-19

The Lattice Energy is always positive and it represents the amount of energy required to dissociate 1 mole of an ionic solid into gaseous ions.

Read More: Crystal Lattice

Formula for Crystalline Lattice Energy

[Click Here for Sample Questions]

The formula for lattice energy of a mole of crystalline solid, given by Max Born and Alfred Landé is as given below:

Na= Avogadro constant

M = Madelung constant for the lattice

Z+ = charge number of cation

Z- = charge number of anion

E = elementary charge, 1.6022×10−19C

ε= Permittivity of free space

r= distance to closest ion

n= value between 5 to 12 and is related to the electronic configuration of the ions involved

The positive ion faces both attraction from the negative ion and repulsion from the positive one.

Lattice Energy Concept

[Click Here for Sample Questions]

We have noticed that a reaction between a metal and a non-metal usually produces an ionic compound. This is because there is an electron transfer from metal to Non-metal and hence they become more rigid in structure. Lattice energy is the result of two oppositely charged gaseous ions attracting each other and forming an ionic bond. It is a complicated process and is endothermic in nature. They usually have a brittle characteristic with a Crystalline flat surface in lattice form. Due to the strong electronic bond, they can not be deformed easily. They melt at relatively high temperatures due to the regular arrangement of ion structure.

Read More: Endothermic Reaction

Things To Remember

[Click Here for Sample Questions]

Lattice Energy Formula is a modified Coulomb’s law formula that is (LE = kQ₁Q₂/r)
Lattice energy refers to the energy released when two oppositely charged gaseous ions are attracted to each other thus forming an ionic bond.
Lattice Energy is always positive and generally have a brittle crystalline structure due to the compact bonding of ionic bond.
Due to the presence of a strong electronic bond, they are not deformed easily and hence melt at a very high temperature due to the arrangement of ions.

Solved Examples

Ques. The lattice energy of AgBr is 895 KJ mol^-1. Predict what will be the Lattice energy of the isomorphous AgI using the Born-Lande equation. The numerics of rc + ra is 321 pm for AgBr and 342 pm for AgI.

Ans. If the variance between AgBr and AGL were in the size of anion we could have expected the lattice energies to be related to the inverse ratio of rc +ra.

Henceforth we expect the Lattice energy of AgI to be = (895)(321/342)= 840 J MOLE⁻¹

Ques. Determine the lattice energy for NaCl.

Ans. Using the above formula and known values, we have:

NaCl = (6.022×10²³mol^-1).(1.74756)(1.6022×10⁻¹⁹)2(1.747558)4π(8.854×10⁻¹²C²/m)(282×10⁻¹²m)(1^–19.1)

= – 756kJ permol

Therefore lattice energy for NaCl is 756 KJ per mol.

Ques. The lattice energy of four ionic compounds W, X, Y and Z are measured. The energies are found to be −922 kJ/mol,−769 kJ/mol,−718 kJ/mol and −688 kJ/mol respectively. The four ionic compounds are NaCl, LiF, KBr, and KCl.
a) Which of these ionic compounds can be identified as X compound on the basis of the lattice energy?
b) Why do they have a strong electronic bond?

Ans. The correct answer is NaCl

Lattice Energy is lowest in

LiF, NaCl, KBr, KCl

Ans. KCl

This is because they have a very low solubility in water

They have a strong electronic bond because they are made of two oppositely charged ions and as a result, they have a good strong bonding between them which requires a lot of energy to break. Thus the reaction is also endothermic.

Ques. What are some characteristics of lattice energy?

Ans. Lattice Energy has the following characteristics:

They are brittle in character and flat crystalline structure in lattice form.
The reaction is endothermic and has strong electronic bonds.
The lattice energy is always positive as energy is not consumed but released.
They melt at a higher relative temperature.

Ques. Why is lattice enthalpy positive?

Ans. The lattice enthalpy is always positive because lattice enthalpy refers to the energy required to break up an ionic solid and convert it into gaseous ions and in doing so, the value always remains positive since this is an endothermic reaction.

Ques. The lattice energy of an ionic compound depends upon: Charge only, size only, charge and size both, or packing of ion only?

Ans. charge and size both

This is because as the ion and ion radius increase, the energy of the lattice increases along with it and vice-versa. Hence, lattice energy is dependent both on charge and size.

Ques. Which of the following will decrease lattice strain?
Line defects, point defects, dislocation, heating the material

Ans. heating the material

When heating is done, the size of the ions increases and as a result, the distance between their nucleus increase. Thus, attraction decreases and less energy is released.

Ques. The lattice energy is inversely proportional to:
the sum of the radii of the Cation only, anion only, both cation and anion

Ans. Both cation and anion

According to the Born-Lande equation, the lattice energy is directly proportional to the cation’s and anion’s charge and inversely proportional to the interatomic distance.

Ques. Why lattice energy of NaCl is greater than KCl?

Ans. The lattice energy of NaCl is greater than KCl because K+ is larger than Na+ so NaCl has relatively higher lattice energy and a higher Melting point than KCl. Due to the relative electronegativity, the bonding is predominantly ionic.

Read More:

Born-Haber Cycle	Lattice Enthalpy
Ionic Bond	Thermochemistry
Work Energy Theorem	Chemical Bonding and Structure
Helmholtz Free Energy	Close Packing Structure

Lattice energy formula & Solved Examples

Ionic Lattice Energy Formula

Formula for Crystalline Lattice Energy

Lattice Energy Concept

Things To Remember

Solved Examples

CBSE CLASS XII Related Questions

1.
What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?

2.
A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.

3.
Write any two features of nuclear forces.

4.
Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

5.
If Bohr’s quantization postulate (angular momentum \( = \frac{nh}{2\pi} \)) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.

Comments

SUBSCRIBE TO OUR NEWS LETTER

Lattice energy formula & Solved Examples

Ionic Lattice Energy Formula

Formula for Crystalline Lattice Energy

Lattice Energy Concept

Things To Remember

Solved Examples

CBSE CLASS XII Related Questions

1.What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?

2.A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.

3. Write any two features of nuclear forces.

4.Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

5. If Bohr’s quantization postulate (angular momentum \( = \frac{nh}{2\pi} \)) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?

2.
A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.

3.
Write any two features of nuclear forces.

4.
Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

5.
If Bohr’s quantization postulate (angular momentum \( = \frac{nh}{2\pi} \)) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.