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Introduction
The lattice energy of an ionic compound is a measure of the strength of the ionic bonds within the compound.
It provides information on a variety of properties of ionic solids, including their volatility, solubility, and hardness, among others.
It is not possible to directly measure the lattice energy of an ionic solid.
Nevertheless, it is possible to estimate it with the help of the Born-Haber cycle.
A common way of expressing the magnitude of this quantity is in terms of kilojoules per mole (kJ/mol).
Alternatively, it can be defined as the amount of energy that must be supplied to one mole of an ionic crystal in order for it to be separated into gaseous ions in a vacuum through an endothermic process.
Example
The crystal structure of a sodium chloride molecule is depicted in the diagram below.
With respect to this ionic molecule, the lattice energy is defined as the amount of energy required for the subsequent reaction to take place.
786 kilojoules is the amount of energy that must be supplied to one mole of sodium chloride in order for it to be separated into gaseous Na+ and Cl– ions in this example.
Difference between Lattice energy and Lattice Enthalpy
This equation can be used to express the molar lattice energy of an ionic crystal in terms of molar lattice enthalpy, pressure, and change in volume in terms of the following variables:
∆GU = GH – p∆Vm
Where:
The molar lattice energy is denoted by the symbol GU.
The molar lattice enthalpy is denoted by the symbol GH.
The change in volume is represented by the symbol Vm (per mole).
Letter p denotes pressure.
As a result, when calculating the lattice energies of ionic solids, the outer pressure must also be taken into account.
Factors that influence the amount of lattice energy available
The magnitude of charge associated with the constituent ions and the distance between the constituent ions are the two primary factors that influence the lattice energy of an ionic compound, and they are as follows:
The Born-Haber Cycle
The Born-Haber cycle is based on Hess’ law of constant heat of summation, which can be found in the textbooks.
If a chemical reaction occurs in one step or several steps, the total heat of reaction remains constant, according to Hess’ laws.
For example, in the case of a chemical reaction A B, the heat of reaction (H) equals +Q.
Alternatively, if the reaction occurs in a series of steps, as follows:
A → C ΔH1 = q1
C → D ΔH2 = q2
D → B ΔH3 = q3
In this case, according to Hess’s law, plus Q equals q1 plus q2 plus q3.
It should be noted that this law holds true for both cyclic and non-cyclic processes.
Lattice energy is represented by the expression
We use the Born-Lande equation to calculate the Lattice energy of NaCl.
The Born-Lande equation has a radius of 2.81 x 10-10 m, which is the sum of the radii. The average of the values for Na+ and Cl– is given by n = 8.
The Lattice Energy Formula per mole is represented by the symbol
Avogadro’s constant (6.022 1022) is denoted by the letter NA.
Madelung’s constant is denoted by α
e = Electron charge (1.6022* 10-19C)
Z+ is the charge of the cation and Z- is for anion.
ϵo= Permittivity of unoccupied free space
n is the exponent of the Born exponent.
r0 is the distance between the closest ions.
UL denotes the equilibrium value of lattice energy.
The equation for lattice energy
∆ U=∆ H-p∆ Vm
∆ U = molar lattice energy molar lattice energy
∆ H is the molar lattice enthalpy divided by the number of molecules in the lattice.
∆ Vm = change in volume per mole of molar pressure
p = outer pressure
Charge of Constituent Ions
Individual ions in an ionic lattice are attracted to one another as a result of the electrostatic forces that exist between them.
It is known that the strength of the electrostatic force of attraction is directly proportional to the amount of charge that the constituent ions hold, i.e., the greater the charge, the stronger the force of attraction, and the more rigid the lattice is.
The lattice energy of calcium chloride, for example, is greater than that of potassium chloride in spite of the fact that the crystal arrangements of these two compounds are nearly identical.
Due to the fact that the positive charge held by the calcium cation (+2) is significantly larger than the positive charge held by the potassium cation (+1), this is true.
As a result, the electrostatic forces of attraction in calcium chloride are stronger as a result of this phenomenon (than those in potassium chloride).
Therefore, the lattice energy of CaCl2 is greater than the lattice energy of potassium chloride.
Distance Between Ions
An ionic compound has a lattice energy that is inversely proportional to the distance between the ions in the compound.
Ion lattice energy decreases with increasing distance between ions.
This is due to weaker electrostatic forces holding the ions together as well as a decrease in lattice energy.
Because they are smaller, smaller atoms have smaller interatomic distances in the ionic lattice and stronger binding forces than larger atoms.
So the smaller the size of the constituent ions is, the greater the amount of lattice energy that the ionic solid has in its structure.
Conclusion
The energy required to convert one mole of an ionic solid into gaseous ionic constituents can be defined as the amount of energy required to form the lattice structure.
It is possible to determine the net enthalpy of formation and the first four of the five energies through experimentation, but it is not possible to measure the lattice energy directly.
It is instead calculated by subtracting the net enthalpy of formation from the net enthalpy of formation and then subtracting the other four energies in the Born–Haber cycle.
