Question

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. Determine the equilibrium spacing (also called bonding length, the most stable distance) r0 and the magnitude of the bonding energy E0 between the two ions.

Answer 1

The equilibrium spacing or bonding length, r0, and the magnitude of the bonding energy, E0, can be determined by setting the net energy equal to zero and substituting the equilibrium spacing into the expressions for the attractive and repulsive energies.

Step-by-step explanation:

The equilibrium spacing or bonding length, r0, for a K+−Cl− ion pair is the distance between the ions at which the potential energy of the system is at a minimum. The magnitude of the bonding energy or E0 is the difference in potential energy between the lowest state (at the optimal internuclear distance) and the state where the two ions are completely separated.

The equilibrium spacing can be determined by finding the distance at which the attractive and repulsive energies add up to the greatest overall attractive force. This can be done by setting the net energy EN equal to zero and solving for r.

The bonding energy is equal to the sum of the attractive energy EA and the repulsive energy ER. By substituting the equilibrium spacing into the expressions for EA and ER, we can calculate the magnitude of the bonding energy.