How To Calculate the Lattice Energy?

In Chemistry, Lattice energy and Lattice enthalpy are the two most commonly used terminologies. Some students might consider it; they have the same meaning. Another way round, some Students Consider it, they have a different meaning. Both are used to calculate bond strength in an ionic or Covalent bond that ultimately elaborates the attractive forces in ions, so these terms are problematic.

The fact is that Lattice energy and Lattice Enthalpy has a different meaning. These terms are differentiated based on their mode of calculation. However, the difference between them is negligible. Lattice energy is the amount of energy that is required to break a solid bond into gaseous elements. On the other hand, Lattice Enthalpy is considered the change in enthalpy whenever the bond is formed or broken. 

This article will elaborate only on lattice Energy, Lattice Energy definition, Lattice energy formulas, Lattice Energy equation, and some practical examples to understand Lattice Energy’s concepts.

What is Lattice Energy

Lattice energy is a calculation of ionic bond strength in an ionic compound. Also, it can be described as a method of measuring cohesive forces that bind ions.  It gives insights into various characteristics, including its volatility, solubility, and durability of ionic solids. In an Ionic solid, lattice energy cannot be directly measured. Even so, it can be calculated with the help of the Born-Haber cycle. Generally, it is expressed as kilojoules per mole (kJ/mol).

Lattice Energy Definition 

Lattice Energy definition can be explained in two distinct ways by a sort of potential energy. One is the energy necessary for breaking an ionic solid as its atoms are converted to ions (gaseous). This description gives meaning to the lattice energy, which is always positive because the reaction is endothermic. Second, this energy is used in the reverse phase in which gaseous ions bond to form the atoms of an ionic solid.

While we expect a systematic system to be less unchanging since its entropy is limited, the situation is not the same. Since the reaction is exothermic in certain conditions, the value of the lattice energy is always negative. As gaseous ions combine to form atoms, the energy required for the conversion value is expressed as a kJ/mol unit. Keeping in mind that the association between a metal and a non-metal usually results in developing an ionic compound. 

We can also notice a transfer of negative charge particles called an electron from metal to non-metal. Such ionic compounds are typically crystalline, stiff, and breakable substances with smooth lattice planes. Deformation does not happen quickly. Also, at higher temperatures, they tend to melt. 

For instance, NaCl melts at 801 degrees Celsius. Such characteristics help ions maintain their consistent form in the crystalline lattice. As a result, ions with different opposite charges tend to have energy because of electrostatic solid force. A sodium chloride molecule’s crystal lattice is depicted below the structure in the crystalline lattice. 

 The crystal lattice structure of a NaCl

In the given ionic molecule below, the energy needed for the following reaction is the lattice energy.

NaCls→Na+g+Cl-(g)

Here, the energy that is provided to 1 mole of NaCl to isolate it into gaseous Na⁺ and Cl^– ions is 786.0 kJ.

This article will show you the lattice energy equation, lattice energy formula, how to calculate it step by step, and give you examples of how the equation & formula can be utilized. 

Lattice Energy Equation

We have some theories that the lattice energy can be calculated by adding positive and negative ions for forming an ionic solid.  But, the estimated number of ions will never be assembled under the circumstances for determining heat transfer rate. Instead, lattice energies are determined through experimentally specific enthalpy shifts from a cycle called Born–Haber cycle.

The Born-Haber cycle representation in a single equation is given below:

The heat of formation=Heat of atomization+Dissociation energy of Ionization energies+ 

Sum of Electron affinities+ Lattice energy)

Arranging the above equation to find lattice energy, we get;

Lattice energy=Heat of formation-Heat of atomization- Dissociation energy-

(Sum of Ionization energies)-Sum of Electron affinities 

Also, the molar lattice energy of an ionic crystal can be presented as molar lattice enthalpy, pressure, and change in volume via the given equation below;

∆GU=∆GH-p∆Vm

Where:

• ∆GU=Molar lattice energy
• ∆GH=Molar lattice enthalpy
• ∆Vm=Change in volume(per mole)
• p=The outer pressure

Lattice Energy Formula

a) For ionic lattice energy

The lattice energy formula of an equivalent ionic solid could be determined with the help of a revised formula of Coulomb’s law. The formula is as given below;

U=-k’Q1Q2r0

Where: 

• Q1& Q2=Charges on the ions
• r0=Internuclear distance
• k=Proportionality constant
• U=Lattice energy

b) For crystalline lattice energy

Lattice energy, as we say, is the energy generated when two different charged ions called cation and anion are mixed for forming an ionic solid. On the other hand, lattice energy is often used to describe the overall potential energy of ionic compounds. This Born-Lande equation is that equation that helps to determine the crystalline lattice energy.

Its formula is given by;

UL=NAMz+z-e24π0r01-1n

Where: 

• NA=Avogadro constant (6.022*1023
• M=Madelung constant
• z+=Charge of cation
• z-=Charge of anion
• 0=Permittivity of free space
• n=Born Exponent
• r0=Closest ion distance
• UL=Equilibrium value of lattice energy

How to calculate Lattice Energy

The steps to calculate lattice energy based on the Born-Haber Cycle are given below;

1. Firstly, determine the heat of formation.
2. Then, find the heat of atomization and dissociation energy
3. Thirdly, find the ionization energies and electron affinities
4. Finally, determine the lattice energy by subtracting steps 2 & 3 from step 1.

Factor affecting Lattice Energy

There are two significant factors that affect lattice energy. They are given below.

a. Charge related with constituent ions

The attractive or repulsive forces known as electrostatic forces among ions in an ionic lattice made them attract one another. Also, the energy of the electrostatic force of attraction is directly related to the charge distance detained together by means of integral ions. This means that the higher the charge tougher the attraction force and the stronger the lattice energy.

b. distance between the ions

On the other hand, the lattice energy of ions is inversely related to the distance between ions. The bigger the difference between the ions in a lattice, the smaller their electrostatic forces and ultimately lower the lattice energy. The atoms that are smaller have shorter interatomic distances in the ionic lattice but higher binding forces. As a result, the higher the lattice energy of ionic solid, the smaller the size of the integral ions.

Example 1. Find the Lattice Energy of NaCl(s) by the Born-Haber cycle method. 

It seems complicated to quantify the enthalpy shift from a solid crystal and convert it into its dispersed gas ions.  It’s much more difficult to consider doing the opposite: starting from scattered gas ions and measuring the enthalpy change as they solidify. Instead, lattice enthalpies should always be measured, which can be done in the Born-Haber cycle.

Let’s consider the Born-Haber cycle for sodium chloride (NaCl)

Step 1. Firstly, determine the heat of formation.

So, from the Born-Haber cycle, we could see that the heat of the formation of NaCl(s) is -411 kJ/mol. 

Step 2. Then, find the heat of atomization and dissociation energy

The 107.00 kJ/mol is the atomization enthalpy of sodium in the given figure above. The 122.00 kJ/mol is the atomization enthalpy of chlorine.

Step 3. Thirdly, find the ionization energies and electron affinities

The 496 kJ/mol is called the first ionization energy of sodium. The -349 kJ/mol is called the first electron affinity of chlorine.

Step 4. Determine the lattice energy by subtracting steps 2 & 3 from step 1.

Using the equation of lattice energy, we get

Lattice energy=Heat of formation-Heat of atomization-                                     Dissociation energy-(Sum of Ionization energies)-                                     Sum of Electron affinities

Or Lattice Energy (LE)= -411- 107 – 122 – 496 + 349 = -787 kJ/mol

Example 2. Determine the lattice energy for NaCl by using the Born-Lande formula. 

Given, 

NA=6.022*1023/mol

M=1.74756

z+=+1

z-=-1

0=8.854185×10-12 C²Jm 

n=9.1

r0=2.82 × 10-10 m

Now, using the formula from above, we get.

UL=NAMz+z-e24π0r01-1n

UNaCl=6.022*1023×1.74756×1×-11.602*10-1924π×8.854185×10-12×2.82 × 10-101-19.1=-756kJmol

Hence, the lattice energy for NaCl is 756 kJ per mole.

FAQ’s

Sr.	Questions	Answers
1	Is Lattice Energy always positive, or could it be negative?	Lattice is the amount of energy required to break the ionic bond, so it means the energy will be absorbed, so that’s why it is always positive. It is always considered an endothermic reaction
2	Which Ionic Bond has Highest Lattice Energy?	Sodium Fluoride (NaF) has the highest lattice energy due to the smaller size of the cation. The smaller the size of ions, the more will be the force of attraction and vice versa.
3	Does Lattice Energy always increase across the period?	Yes, Lattice Energy always increases across the period. Because across the period, size will decrease. So, stronger will be the ionic bond, and more energy will require to break the bond.
4	What is Lattice Energy used for?	Lattice Energy Indirectly tells us about the Stability of the Ionic bond. If lattice energy is more, then the bond would be stable and vice versa.