**Calculating the Lattice Energy of KCl**

The lattice energy of an ionic compound is the energy required to separate one mole of the solid into its constituent ions in the gas phase. It is a measure of the strength of the ionic bonds in the compound.

To calculate the lattice energy of KCl, we need to consider the various factors that contribute to the overall energy.

**Coulomb's Law**
Coulomb's law states that the energy of interaction between two charged particles is directly proportional to the product of their charges and inversely proportional to the distance between them.

Mathematically, Coulomb's law can be written as:
E = k * (Q1 * Q2) / r

Where E is the energy of interaction, k is a proportionality constant, Q1 and Q2 are the charges of the particles, and r is the distance between them.

In the case of KCl, we have K+ and Cl- ions. The lattice energy can be calculated by summing up the energies of interaction between all the ions in the crystal lattice.

**Lattice Energy Calculation**

1. Calculate the distance between the ions:
The distance between the ions, denoted as r, can be determined using the ionic radii of K+ and Cl- ions. Given that a = 628 pm, which is the sum of the ionic radii, we can calculate the distance between the ions as follows:
r = a / 2 = 314 pm = 3.14 Å

2. Calculate the energy of interaction between the ions:
Using Coulomb's law, we can calculate the energy of interaction between the K+ and Cl- ions:
E = k * (Q1 * Q2) / r

Given that k is a constant and Q1 = +1 for K+ and Q2 = -1 for Cl-, the equation simplifies to:
E = k / r

3. Calculate the lattice energy:
The lattice energy is the sum of the energies of interaction between all the ions in the crystal lattice. Since KCl has a 1:1 ratio of K+ and Cl- ions, the lattice energy can be written as:
Lattice energy = n * E

Where n is the number of ions in the formula unit of the compound.

4. Substitute the values and calculate:
Given that n = 9 and A = 1.746, we can substitute the values into the equation:
Lattice energy = 9 * (1.746 / 3.14)

Calculating the above expression gives us the lattice energy of KCl.

**Conclusion**

In conclusion, the lattice energy of KCl can be calculated using Coulomb's law and considering the distance between the ions and their charges. By summing up the energies of interaction between all the ions in the crystal lattice, we can determine the strength of the ionic bonds in the compound.