Chapter 9: Problem 9

Why is the equilibrium separation distance between \(\mathrm{K}^{+}\) and \(\mathrm{Cl}^{-}\) different for a diatomic molecule than for solid KCl?

Short Answer

Expert verified

The equilibrium separation distance between K+ and Cl- ions is different in diatomic molecules and solid KCl due to the differences in their electrostatic interactions. In diatomic KCl, the equilibrium separation distance depends solely on the forces between the individual K+ and Cl- ions, while in the solid KCl lattice, the equilibrium separation distance depends on the summed forces of neighboring ion pairs in the lattice structure. The different forces acting upon the ions in these two arrangements result in distinct equilibrium separation distances.

Step by step solution

1. Understand the properties of diatomic molecules and solid lattices

Diatomic molecules refer to those compounds which consist of two atoms bonded together. In diatomic KCl, it is formed by a K+ and Cl- ion bonding together. On the other hand, solid KCl is an ionic compound that consists of K+ and Cl- ions arranged in a regular 3-dimensional lattice.

2. Explain the bonding in diatomic KCl

In diatomic KCl, there is an electrostatic attraction between the positive ion, K+, and the negative ion, Cl-. When the K+ and Cl- ions get close enough, they will attract each other which results in the formation of an ionic bond due to the forces of attraction and repulsion. The equilibrium separation distance between the ions is found to be the distance at which the attractive forces balance the repulsive forces. At this distance, the energy of the system is at its lowest.

3. Describe the forces in the solid KCl lattice

In a solid KCl lattice, the attractive forces between the ions are influenced not just by one nearest neighboring ion pair, but by all neighboring ions in the lattice structure. The K+ and Cl- ions are surrounded by numerous neighboring ions in a repeating pattern, which results in a sum of electrostatic interaction energies that must be considered. The equilibrium separation distance in the lattice depends on the balance of these attractive forces and the repulsive forces acting upon the ions.

4. Compare the forces in diatomic KCl and solid KCl lattice

In diatomic KCl, the equilibrium separation distance depends solely on the forces between the individual K+ and Cl- ions, while in the solid KCl lattice, the equilibrium separation distance depends on the summed forces of neighboring ion pairs in the lattice structure. The summed forces in the solid KCl lattice are different from the forces in the diatomic molecule, which leads to a different equilibrium separation distance.

5. Conclusion

The equilibrium separation distance between K+ and Cl- ions is different for diatomic molecules and solid KCl because of the differences in the electrostatic interactions between the ions. In diatomic KCl, the forces acting between a single ion pair are considered, whereas, in a solid KCl lattice, the summed forces of all the neighboring ion pairs influence the equilibrium separation distance. This results in differing behavior and properties in the diatomic molecule compared to the solid lattice structure.

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Why is the equilibrium separation distance between \(\mathrm{K}^{+}\) and \(\mathrm{Cl}^{-}\) different for a diatomic molecule than for solid KCl?

Short Answer

Step by step solution

1. Understand the properties of diatomic molecules and solid lattices

2. Explain the bonding in diatomic KCl

3. Describe the forces in the solid KCl lattice

4. Compare the forces in diatomic KCl and solid KCl lattice

5. Conclusion

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