(a) Does the lattice energy of an ionic solid increase or decrease (i) as the charges of the ions increase, (ii) as the sizes of the ions increase?

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Understand that lattice energy is the energy required to separate one mole of an ionic solid into its gaseous ions.

Recall that lattice energy is directly proportional to the product of the charges of the ions. Therefore, as the charges of the ions increase, the lattice energy increases.

Remember that lattice energy is inversely proportional to the distance between the ions, which is related to the size of the ions. As the sizes of the ions increase, the distance between them increases, leading to a decrease in lattice energy.

Consider the formula for lattice energy: \( U = \frac{k \cdot Q_1 \cdot Q_2}{r} \), where \( U \) is the lattice energy, \( k \) is a constant, \( Q_1 \) and \( Q_2 \) are the charges of the ions, and \( r \) is the distance between the centers of the ions.

Summarize: (i) Lattice energy increases with increasing ion charges, and (ii) lattice energy decreases with increasing ion sizes.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Lattice Energy

Lattice energy is the energy released when gaseous ions combine to form an ionic solid. It is a measure of the strength of the forces between the ions in an ionic compound. Higher lattice energy indicates a more stable ionic solid, as it reflects stronger ionic bonds resulting from the electrostatic attraction between oppositely charged ions.

Charge of Ions

The charge of ions significantly affects lattice energy. As the charges of the ions increase, the electrostatic attraction between them becomes stronger, leading to a higher lattice energy. For example, a compound formed from divalent ions (e.g., Mg²⁺ and O²⁻) will have a greater lattice energy than one formed from monovalent ions (e.g., Na⁺ and Cl⁻) due to the increased charge.

Size of Ions

The size of the ions also influences lattice energy. As the size of the ions increases, the distance between the centers of the ions increases, which weakens the electrostatic attraction and results in lower lattice energy. Therefore, larger ions lead to a decrease in lattice energy, as seen when comparing NaCl to KCl, where K⁺ is larger than Na⁺.

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The substances NaF and CaO are isoelectronic (have the same number of valence electrons). (b) What are the charges of each of the anions in each compound?

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(b) Arrange the following substances not listed in Table 8.1 according to their expected lattice energies, listing them from lowest lattice energy to the highest: MgS, KI, GaN, LiBr.

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Consider the ionic compounds KF, NaCl, NaBr, and LiCl. (b) Based on your answer to part (a), arrange these four compounds in order of decreasing lattice energy. (c) Check your predictions in part (b) with the experimental values of lattice energy from Table 8.1. Are the predictions from ionic radii correct?