Question

(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? (b) Using a periodic table, arrange the following substances according to their expected lattice energies, listing them from lowest lattice energy to the highest: \(\mathrm{ScN}, \mathrm{KBr}, \mathrm{MgO}\), NaF. Compare your list with the data in Table \(8.2\).

Short answer

(a) (i) Lattice energy increases as the charges of the ions increase. (ii) Lattice energy decreases as the sizes of the ions increase. (b) The order of the compounds according to their expected lattice energies, from lowest to highest, is \(\mathrm{KBr} < \mathrm{NaF} < \mathrm{MgO} < \mathrm{ScN}\).

Step-by-step solution

Answer (a)

(i) As the charges of the ions increase, the electrostatic attraction between them becomes stronger, leading to an increase in the lattice energy. (ii) As the sizes of the ions increase, the distances between them increase, thus decreasing the electrostatic attraction between the ions. This results in a decrease in the lattice energy.

Answer (b)

In order to list the given substances according to their expected lattice energies, we need to consider the charges and sizes of the constituent ions. To do this, we should first determine the ionic charges of each compound. Upon examining the periodic table, we find the following charges: - \(\mathrm{ScN}\): Sc\(^{3+}\) and N\(^{3-}\) - \(\mathrm{KBr}\): K\(^{1+}\) and Br\(^{1-}\) - \(\mathrm{MgO}\): Mg\(^{2+}\) and O\(^{2-}\) - \(\mathrm{NaF}\): Na\(^{1+}\) and F\(^{1-}\) Now, considering these charges, we can use the general trend that lattice energy increases with increasing charge of the ions and decreases with increasing ion size: 1. Low lattice energy: \(\mathrm{KBr}\). It has ions with the lowest charges (1+ and 1-), and both ions are quite large. 2. Higher lattice energy: \(\mathrm{NaF}\). The ions have the same charges as KBr (1+ and 1-), but the ions are smaller, leading to stronger electrostatic attraction. 3. Even higher lattice energy: \(\mathrm{MgO}\). It has ions with higher charges (2+ and 2-), and the ions are of moderate size compared to the other compounds. 4. Highest lattice energy: \(\mathrm{ScN}\). It has ions with the highest charges (3+ and 3-) among all the compounds, leading to the strongest electrostatic attraction. Therefore, the compounds can be ordered according to their lattice energies, from lowest to highest, as follows: \(\mathrm{KBr} < \mathrm{NaF} < \mathrm{MgO} < \mathrm{ScN}\). Comparing this list with the data given in Table 8.2, it should be consistent with the experimental values.

Key concepts

Electrostatic Attraction

Electrostatic attraction is a fundamental concept for understanding lattice energy in ionic solids. It refers to the force that draws positively and negatively charged ions together. This force is governed by Coulomb's Law, which indicates that the electrostatic attraction between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

In the context of ionic solids, the electrostatic attraction is crucial because it stabilizes the crystal structure. The ions are arranged in a fixed, repeating pattern to maximize these attractive forces. Stronger electrostatic attraction leads to higher lattice energy because more energy is required to break apart the ionic solid into its constituent ions.

Understanding the nature of electrostatic attraction helps explain why certain ionic substances have higher lattice energies than others. For instance, compounds with higher ionic charges experience greater electrostatic forces and thus higher lattice energies. At the same time, smaller ions can pack more closely together, increasing these forces and further elevating the lattice energy.

Ionic Charges

Ionic charges significantly impact the lattice energy of a compound. Essentially, ionic charges refer to the magnitude of positive or negative charge held by an ion. This charge is often a result of an atom losing or gaining electrons during chemical bonding.

When considering lattice energy, the general rule is: the greater the ionic charges, the stronger the electrostatic attraction between the ions. Hence, compounds with higher charges will typically exhibit higher lattice energies. This is well demonstrated by comparing compounds like KBr and MgO.

• KBr has ions with charges of +1 and -1.
• MgO has ions with charges of +2 and -2.

Due to these differences, MgO will have a significantly higher lattice energy than KBr. Understanding the effect of ionic charges enables predictions regarding the relative size of lattice energies in different compounds.

Ion Size

Ion size plays a pivotal role in determining the lattice energy of ionic compounds. This is because the distance between ions affects the strength of their electrostatic interactions. Larger ions have greater distances between their centers, which weakens the electrostatic attraction and thus reduces the lattice energy.

To illustrate, compare compounds like NaF and KBr. Although both have ions with charges of +1 and -1, the differing sizes of their ions leads to varying lattice energies.

• NaF consists of relatively small ions, which can pack close together, resulting in a stronger attraction and, therefore, higher lattice energy.
• KBr contains larger ions, causing a weaker electrostatic attraction and lower lattice energy.

When small ions can closely pack, they strengthen electrostatic interactions, increasing the compound's lattice energy. This underscores how important ion size is when analyzing lattice energies.