Problem

For a K+—Cl− ion pair, attractive and repulsive energies EA and ER, respectively, depend o...

For a K+—Cl− ion pair, attractive and repulsive energies EA and ER, respectively, depend on the distance between the ions r, according to

For these expressions, energies are expressed in electron volts per K+—Cl− pair, and r is the distance in nanometers.The net energy EN is just the sum of the preceding two expressions.

(a) Superimpose on a single plot EN, ER, and EA versus r up to 1.0 nm.
(b) On the basis of this plot, determine (i) the equilibrium spacing r0 between the K+ and Cl− ions, and (ii) the magnitude of the bonding energy E0 between the two ions.
(c) Mathematically determine the r0 and E0 values using the solutions to Problem 2.14, and compare these with the graphical results from part (b).

Problem 2.14

The net potential energy between two adjacent ions, EN, may be represented by the sum of Equations 2.8 and 2.9; that is,

Calculate the bonding energy E0 in terms of the parameters A, B, and n using the following procedure:

1. Differentiate EN with respect to r, and then set the resulting expression equal to zero, because the curve of EN versus r is a minimum at E0.
2. Solve for r in terms of A, B, and n, which yields r0, the equilibrium interionic spacing.
3. Determine the expression for E0 by substituting r0 into Equation.