Chapter 7, Problem 101A

Interpretation Introduction

Interpretation:

Ionic compounds among $\text{NaCl}$, $\text{KCl}$ or ${\text{MgCl}}_{\text{2}}$ which have the greatest lattice energy needs to be explained.

Concept introduction:

Ions are arranged in a crystal lattice in ionic compound. Therefore, the energy needed to separate 1 mol of the ions of an ionic compound is known as the lattice energy. The magnitude of the forces keeping ions is expressed by the lattice energy.

Answer to Problem 101A

${\text{MgCl}}_{\text{2}}$ has the highest lattice energy compared to $\text{NaCl}$ and $\text{KCl}$.

Explanation of Solution

First consider $\text{NaCl}$ and $\text{KCl}$. Both sodium and potassium are group 1 metals and they produce only +1 cation. Since, lattice energy increases with the magnitude of the charge on the metal cation with decreasing atomic size. In a group, atomic size increases down the group. Therefore, atomic size of sodium is smaller than potassium hence; it has greater lattice energy than potassium. Again compare $\text{NaCl}$ and ${\text{MgCl}}_{\text{2}}$. Sodium is a group 1 metal and its charge is +1 whereas magnesium is a group 2 metal and its charge is +2. As lattice energy increases with increase in charge. Therefore, ${\text{MgCl}}_{\text{2}}$ has highest lattice energy.

Conclusion

Lattice energy is directly related to the size of the ions bonded. The compound formed by the smaller ions have more closely spaced ionic charges. The electrostatic force of gravity between opposite charges raises as the length between the charges decreases; smaller ions produce more powerful interionic attractions and greater lattice energies.