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Lattice Energy

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Lattice Energy is the energy required to break apart an ionic compound into its gaseous ions. We can also define it as the energy released when the gaseous atoms combine to form a crystal lattice. The lattice energy of any compound cannot be directly measured and we use various methods or techniques to find the lattice energy such as the use of the Born Haber cycle to find the lattice energy of any compound. Lattice energy is measured in kJ/mol.

In this article, we will learn about Lattice energy, lattice enthalpy, their difference, and others in detail.

What is  Lattice Energy?

The lattice energy of any compound is the energy given to a solid ionic compound to break into its gaseous state, we can also say that it is the amount of energy released when gaseous ions combine to form a solid lattice. We use various methods, such as the Born-Haber cycle or the Coulombic equation to find the lattice energy of any compound. The value of lattice energy can be used to predict the stability of an ionic compound and to compare the relative stabilities of different ionic compounds. It is also related to the melting and boiling points of ionic compounds. Ionic compounds have high melting and high boiling points due to the strong attractive forces between the ions.

Lattice Energy Definition

The energy required to convert one mole of an ionic solid into its gaseous ionic constituents is called the lattice energy of the ionic compound. It is measured in kJ/mol. As in this case, the lattice energy is the energy given to the ionic compound so this process is an endothermic reaction.

Lattice Energy Examples

We can explain the lattice energy of the ionic compound by explaining their ionic crystals and the lattice energy of the ionic compound NaCl is discussed below,

Lattice Energy of NaCl

The lattice energy of the NaCl is calculated as the crystal lattice of the NaCl is discussed below,

NaCl crystal

 

The reaction of the NaCl lattice is,

NaCl(s)  → Na+(g) + Cl(g)

The energy required to break the 1 mole of the ionic crystal of the NaCl into its gaseous atom is 786 kilojoules.

Factors Affecting  Lattice Energy

Lattice Energy of an ionic compound depends upon various factors that are,

  • Charge of Ions
  • Size of Ions
  • Polarizability of Ions
  • Ionization Energy
  • Electron Affinity

Let’s learn about these factors in detail.

Charge of Ions

Lattice energy generally increases with the magnitude of the charge on the ions. This is because the electrostatic forces holding the ions together are stronger when the charges are larger.

Size of Ions

Lattice energy generally decreases with the size of the ions. This is because larger ions have a greater distance between their centers, which reduces the strength of the electrostatic forces holding them together.

Polarizability of Ions

Lattice energy generally decreases with the polarizability of the ions. This is because polarizable ions can more easily distort their electron clouds in response to the electrostatic forces of the other ions, which reduces the strength of the forces holding them together.

Ionization Energy

Lattice energy generally increases with the ionization energy of the ions. This is because a higher ionization energy means that it takes more energy to remove an electron from an atom, which means that the ion will be more stable and have a higher lattice energy.

Electron Affinity

Lattice energy generally increases with the electron affinity of the ions. This is because a higher electron affinity means that it takes more energy to add an electron to an atom, which means that the ion will be more stable and have higher lattice energy.

The lattice energy of combining two ions A and B is shown in the image added below.

Lattice Energy

 

Lattice Energy Formula

The Coulombic equation is a commonly used formula for calculating the lattice energy of an ionic compound. It is based on Coulomb’s law, which states that the attractive or repulsive force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Lattice Energy (U) is the energy required to completely separate one mole of an ionic solid into its gaseous ions. The Lattice Energy formula is given by:

U = -(Z×e)² / (4πεor)

where 
Z is the Charge of the Ion
e is the Electronic Charge
εo is the Vacuum Permittivity
r is the Distance between the Ionic Centres

We can understand this by the example added below.

Example: Let’s consider the case of NaCl. Na+ and Cl are the ions in this compound and the lattice energy of NaCl

Solution:

Lattice Energy of NaCl is calculated using the formula

U = – (Z×e)² / (4πεor)

Substituing all the value in the formula

U = – (1×1.6 x 10-19C)² / (4Ï€ x 8.854 x 10-12 F/m x 2.82 x 10-10 m)

U = – 7.61 x 105 J/mol

Thus, the lattice energy of the NaCl is  – 7.61 x 105 J/mol.

Note: Lattice energy is highly dependent on ionic radius and charge, thus it is highly exothermic for highly charged ions with small radii and endothermic for low-charged ions with large radii.

Born-Lande Equation

Since, Lattice Energy is determined by a number of factors hence, Max Born and Alfred Lande gave the following formula to calculate Lattice Energy for one mole of Crystalline Solid

U = (NAMz+ze2/4πεoro)/(1-1/n)

Where, 

  • NA is Avogadro Number
  • M is Madelung Constant
  • Z+ and Z is charge for cation and anion
  • e is basic electronic charge = 1.6×10-19 C
  • εo is Absolute Permittivity
  • ro is distance to closest ion
  • n is Born Exponent which is different for Different Molecules

Calculation of Lattice Energy using the Born-Haber Cycle

The Born-Haber cycle is a method used to calculate the lattice energy of an ionic compound from experimentally determined or theoretically predicted quantities. The lattice energy of an ionic compound is the energy required to separate the compound into its gaseous ions. Born-Haber cycle involves several steps, including:

  • Determining the enthalpy of formation of the compound from its elements. This can be done through calorimetry or other methods.
  • Calculating the electron affinity of the negative ion. This is the energy required to add an electron to a neutral atom to form a negative ion.
  • Calculating the ionization energy of the positive ion. This is the energy required to remove an electron from a neutral atom to form a positive ion.
  • Determining the enthalpy of sublimation of the positive ion. This is the energy required to vaporize the positive ion.
  • Calculating the enthalpy of vaporization of the negative ion. This is the energy required to vaporize the negative ion.

Lattice energy can then be calculated using the following equation:

Lattice Energy = Enthalpy of Formation + Electronic Affinity + Ionization Energy – Enthalpy of Sublimation of Positive Ion – Enthalpy of Vaporization of Negative ion

The Born-Haber cycle allows for the prediction of lattice energies for ionic compounds that have not yet been synthesized, as well as the determination of lattice energies for known compounds.

Difference  Between  Lattice Energy and Lattice Enthalpy

Lattice energy and Lattice Enthalpy both are measures to explain the stability of an ionic compound. However, the basic difference between them is how they are calculated and what factors they take into account. The basic difference between the lattice energy and lattice enthalpy is discussed in the table below.

Parameters

Lattice Energy

Lattice Enthalpy

Definition Lattice energy measures the energy required to separate an ionic compound into its component ions. Lattice enthalpy is the measure of the energy change that occurs when an ionic compound is formed from its component ions.
How to Calculate It is calculated using the Born-Haber cycle It is calculated by measuring the energy required to break the bonds in the compound and separate the ions, and then subtracting this value from the energy required to form the bonds in the compound.
Factors Responsible
  • Formation of the gaseous atoms from the element.
  • Ionization of the atoms to form ions.
  • Electron affinity of the ions.
  • The lattice energy of the ionic compound
  • It defines the enthalpy change in a crystal lattice when the structure is formed or broken.
  • It measures the strength of all the forces acting between the ions in the structure of an ionic solution.
Conclusion The lattice energy of an ionic compound is therefore the sum of all these energies, and it reflects the overall stability of the compound. Lattice enthalpy is therefore a measure of the energy required to convert an ionic compound into its component ions, and it reflects the strength of the bonds in the compound.

Comparison Between Lattice Energy and Lattice Enthalpy

We can easily calculate the lattice energy of any crystal by using the lattice enthalpy and pressure applied to the object by using the formula,

ΔLatticeU = ΔLatticeH – pΔVm

where,
ΔLatticeU denotes the molar lattice energy
ΔLatticeH denotes the molar lattice enthalpy
ΔVm is the change in volume (per mole)
p is the pressure

Thus, using the above equation we can easily compare the lattice energy and the lattice enthalpy of the ionic compound.

Also, Check

Examples on Lattice Energy

Example 1: Consider the ionic compound sodium chloride (NaCl). The sodium ion (Na+) has a charge of +1, and the chloride ion (Cl) has a charge of -1. The distance between the ions in the NaCl crystal is about 0.282 nanometers. Find the lattice energy of NaCl.

Solution:

U = (1 + (-1))/(0.282 x 10-9)

    = 2/(0.282 x 10-9)

    = 7.09 x 109 J/mol

This value of lattice energy indicates that a significant amount of energy is required to separate the ions in a crystal of NaCl.

Example 2: How to use the Born-Haber cycle to calculate the lattice energy of an ionic compound: Calcium oxide (CaO)

Solution:

Use the following steps to calculate the lattice energy of CaO using Born-Haber cycle.

  • Determine the enthalpy of the formation of calcium oxide. This can be done by measuring the heat of the reaction when calcium metal reacts with oxygen gas to form calcium oxide.
  • Calculate the electron affinity of the oxide ion (O2-). This is the energy required to add an electron to a neutral oxygen atom to form an oxide ion. The electron affinity of oxygen is -141 kJ/mol.
  • Calculate the ionization energy of the calcium ion (Ca2+). This is the energy required to remove an electron from a neutral calcium atom to form a calcium ion. The first ionization energy of calcium is 590 kJ/mol.
  • Determine the enthalpy of the sublimation of the calcium ion. This is the energy required to vaporize the calcium ion. The enthalpy of the sublimation of calcium is 167 kJ/mol.
  • Calculate the enthalpy of vaporization of the oxide ion. This is the energy required to vaporize the oxide ion. The enthalpy of vaporization of oxygen is 249 kJ/mol.

The lattice energy of calcium oxide can then be calculated using the following equation:

Lattice energy = Enthalpy of formation + Electron affinity + Ionization energy – Enthalpy of sublimation of positive ion – Enthalpy of vaporization of negative ion

Putting all the values

Lattice Energy = -635 kJ/mol + (-141 kJ/mol) + (590 kJ/mol) – (167 kJ/mol) – (249 kJ/mol)

Lattice Energy = -487 kJ/mol

This is the lattice energy of calcium oxide.

Example 3: How to use the Born-Haber cycle to calculate the lattice energy of an ionic compound: Calcium chloride (CaCl2)

Solution:

Use the following steps to calculate the lattice energy of CaCl2 using Born-Haber cycle.

  • Determine the enthalpy of the formation of calcium chloride. This can be done by measuring the heat of the reaction when calcium metal reacts with chlorine gas to form calcium chloride. The enthalpy of the formation of calcium chloride is -786 kJ/mol.
  • Calculate the electron affinity of the chloride ion (Cl-). This is the energy required to add an electron to a neutral chlorine atom to form a chloride ion. The electron affinity of chlorine is -349 kJ/mol.
  • Calculate the ionization energy of the calcium ion (Ca2+). This is the energy required to remove an electron from a neutral calcium atom to form a calcium ion. The first ionization energy of calcium is 590 kJ/mol.
  • Determine the enthalpy of the sublimation of the calcium ion. This is the energy required to vaporize the calcium ion. The enthalpy of the sublimation of calcium is 167 kJ/mol.
  • Calculate the enthalpy of vaporization of the chloride ion. This is the energy required to vaporize the chloride ion. The enthalpy of vaporization of chlorine is 121 kJ/mol.

The lattice energy of calcium chloride can then be calculated using the following equation:

Lattice energy = Enthalpy of formation + Electron affinity + Ionization energy – Enthalpy of sublimation of positive ion – Enthalpy of vaporization of negative ion

Putting all the values

Lattice Energy = (-786 kJ/mol) + (-349 kJ/mol) + (590 kJ/mol) – (167 kJ/mol) – (121 kJ/mol)

Lattice Energy = -823 kJ/mol

This is the lattice energy of Calcium Chloride.

Example 4: Calculate the lattice energy of magnesium oxide (MgO) using the following information:

  • Enthalpy of formation of MgO: -601 kJ/mol
  • Electron affinity of O2-: -141 kJ/mol
  • Ionization energy of Mg2+: 738 kJ/mol
  • Enthalpy of sublimation of Mg2+: 150 kJ/mol
  • Enthalpy of vaporization of O2-: 249 kJ/mol

Solution:

Lattice energy = Enthalpy of formation + Electron affinity + Ionization energy – Enthalpy of sublimation of positive ion – Enthalpy of vaporization of negative ion

Lattice energy = (-601 kJ/mol) + (-141 kJ/mol) + (738 kJ/mol) – (150 kJ/mol) – (249 kJ/mol)

Lattice energy = -454 kJ/mol

This is the lattice energy of magnesium oxide.

Example 5: Calculate the lattice energy of lithium fluoride (LiF) using the following information:

  • Enthalpy of formation of LiF: -567 kJ/mol
  • Electron affinity of F: -328 kJ/mol
  • Ionization energy of Li+: 520 kJ/mol
  • Enthalpy of sublimation of Li+: 78 kJ/mol
  • Enthalpy of vaporization of F: 121 kJ/mol

Solution:

Lattice Energy = Enthalpy of formation + Electron affinity + Ionization energy – Enthalpy of sublimation of positive ion – Enthalpy of vaporization of negative ion

Lattice Energy = (-567 kJ/mol) + (-328 kJ/mol) + (520 kJ/mol) – (78 kJ/mol) – (121 kJ/mol)

Lattice Energy = -524 kJ/mol

This is the lattice energy of lithium fluoride.

Example 6: Calculate the lattice energy of sodium oxide (Na2O) using the following information:

  • Enthalpy of formation of Na2O: -451 kJ/mol
  • Electron affinity of O2-: -141 kJ/mol
  • Ionization energy of Na+: 496 kJ/mol
  • Enthalpy of sublimation of Na+: 109 kJ/mol
  • Enthalpy of vaporization of O2-: 249 kJ/mol

Solution:

Lattice Energy = Enthalpy of formation + Electron affinity + Ionization energy – Enthalpy of sublimation of positive ion – Enthalpy of vaporization of negative ion

Lattice Energy = (-451 kJ/mol) + (-141 kJ/mol) + (496 kJ/mol) – (109 kJ/mol) – (249 kJ/mol)

Lattice Energy = -345 kJ/mol

This is the lattice energy of sodium oxide.

FAQ on Lattice Energy

Q1: What is Lattice Energy?

Answer:

The lattice energy is defined as the energy required by the ionic compound in the crystal lattice to change to the gaseous state. It is measured in kJ/mol.

Q2: What are the Factors on Lattice Energy depends?

Answer:

Lattice energy depends on various factors such as,

  • Charge on the Constituent Ions
  • Distance between the Ions

Q3: How charge of an Ion affect Lattice Energy?

Answer:

The charge on the ions is directly proportional to the lattice energy of the crystal and the higher is the charge on the ion the higher the lattice energy of the crystal, i.e. the higher energy is required to break the ionic compound from its crystal form to gaseous form.

Q4: How temperature affects Lattice Energy?

Answer:

There is no subsequent effect of the temperature on the lattice energy of the crystal, but the temperature effect the lattice enthalpy of the crystal at higher temperature enthalpy of the particle decreases.

Q5: What is Hess law?

Answer:

Hess law is the basic law that tells us that the total change in the enthalpy of a chemical reaction remains constant irrespective of the path taken by the reaction.



Last Updated : 19 Dec, 2023
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