Question

Given that the nearest neighbor distance (Ro) and the Madelung constant for the potassium chloride crystal are 3.14 and 1.64 respectively, calculate the binding energy per mole for the solid.(charge on an ion in a KCl lattice = 1.6 x 10⁻¹⁹C).

Answer 1

The binding energy per mole for the solid KCl is approximately 8.396 x 10^(-38) C^2/m.

Step-by-step explanation:

The binding energy per mole for a solid can be calculated using the formula:

Binding Energy = Madelung Constant * Lattice Energy

Given that the Madelung constant for the potassium chloride (KCl) crystal is 1.64 and the nearest neighbor distance (Ro) is 3.14, we can calculate the lattice energy using the formula:

Lattice Energy = k' * (Q1 * Q2) / Ro

Where

Q1 and Q2 are the charges on the ions

k' is a constant that depends on the specific arrangement of ions in the solid lattice and their valence electron configurations.

The charge on an ion in a KCl lattice is given as 1.6 x 10^(-19) C.

Substituting the given values into the equations, we can calculate the binding energy per mole for the solid KCl:

Lattice Energy = (1.6 x 10^(-19) C * 1.6 x 10^(-19) C) / 3.14 = 5.1142 x 10^(-38) C^2/m

Binding Energy = 1.64 * 5.1142 x 10^(-38) C^2/m = 8.396 x 10^(-38) C^2/m

Therefore, the binding energy per mole for the KCl solid is approximately 8.396 x 10^(-38) C^2/m.