Problem 24 - Chemistry The Central Science In Si Units

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) 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: \(\mathrm{MgS},\) KI, GaN, LiBr.

Step-by-Step Solution

Answer

(a) Lattice energy increases with higher charges and decreases with larger ion sizes. (b) The order is KI < LiBr < MgS < GaN.

Step 1: Understanding Lattice Energy

Lattice energy is the energy required to separate one mole of an ionic solid into its gaseous ions or the energy released when gaseous ions combine to form an ionic solid. It is influenced by the charges on the ions and the sizes of the ions.

Step 2: Effect of Ion Charges

The lattice energy increases with an increase in the charges of the ions. This is because greater charge results in a stronger electrostatic attraction between the ions.

Step 3: Effect of Ion Sizes

Lattice energy decreases as the sizes of the ions increase. Larger ions result in a smaller electrostatic attraction due to increased distances between ions.

Step 4: Analyzing Ion Charges and Sizes for Compounds

- **MgS**: Mg has a charge of +2, and S has a charge of -2. - **KI**: K has a charge of +1, and I has a charge of -1. - **GaN**: Ga has a charge of +3, and N has a charge of -3. - **LiBr**: Li has a charge of +1, and Br has a charge of -1. GaN has the largest ion charges, followed by MgS, then KI and LiBr, which have the same ion charges.

Step 5: Considering Ion Sizes

Smaller ions result in higher lattice energy. Among the halide ions, I⁻ is the largest, and Br⁻ is smaller. For cations, generally, the order of increasing size is Li⁺ < Mg²⁺ < Ga³⁺ (though cation sizes vary more within groups and charges). In GaN and MgS, expect the effective distance between ions to be small due to overall less electron shielding and higher charge.

Step 6: Arranging by Lattice Energies

From the previous steps, compounds with higher ion charges will generally have higher lattice energy, and smaller ion sizes will also increase lattice energy. Thus, ordering from lowest to highest lattice energy should take into account both these aspects: - KI (lowest charge and larger ion size) - LiBr (lower charge than GaN and larger size influence) - MgS (higher charge than the previous but less than GaN) - GaN (highest charge and small ions)

Key Concepts

Ionic Solids

Ionic solids are a fascinating type of chemical compound. They form when oppositely charged ions cluster together in a repeating pattern, held in place by strong forces. These forces result from the attraction between the positive and negative charges of the ions.
Take a solid like sodium chloride (table salt), for example. It consists of sodium (\( ext{Na}^+ \)) and chloride (\( ext{Cl}^- \)) ions tightly packed together. The whole structure is like a 3D jigsaw puzzle, with ions fitting perfectly into a regular arrangement.
Ionic solids have unique properties. They tend to have high melting and boiling points because of the strong bonds between the ions. When you heat these salts, you need a lot of energy to break apart the tight framework of ions. Generally, these solids are also good insulators of electricity in solid form but become conductive when molten or dissolved in water.

Electrostatic Attraction

Electrostatic attraction is the force that pulls objects with opposite charges towards each other. In the world of ionic compounds, this is the force that keeps the ions locked in their solid arrangement.
Imagine two magnets pulling each other due to their opposite poles. That's similar to how ionic bonds work, but instead of magnets, we have ions with positive and negative charges. These forces are at the heart of what makes ionic solids strong and high in lattice energy.
Factors like ion charge and distance between ions affect electrostatic attraction. Stronger charges mean stronger attraction. Similarly, when ions are closer together, the attraction also increases. Basically, anything that increases this pull between ions boosts the lattice energy, making the ionic solid more stable and harder to break apart.

Ion Charges

Ion charges play a critical role in determining the lattice energy of an ionic solid. Simply put, the higher the positive or negative charge, the stronger the force keeping the ions together.
For example, compare \( ext{MgS} \) and \( ext{KI} \). In \( ext{MgS} \), the magnesium ion has a charge of \( +2 \) and sulfur \( -2 \), resulting in a total charge product of 4, which marks strong attractions. On the other hand, in \( ext{KI} \), both ions have charges of \( +1 \) and \( -1 \) respectively, with a charge product of just 1.
Thus, higher charges lead to significantly more lattice energy, translating to more robust and more stable solids. If you're looking at numerous ionic compounds, those with the highest ion charges often possess the greatest lattice energy.

Ion Sizes

Ion size is another key factor affecting lattice energy. The size of an ion determines the distance between its nucleus and that of the adjacent ion. When ions are smaller, they can pack more closely together, increasing the electrostatic attraction between them. This boosts the lattice energy.
For instance, if you were to compare \( ext{LiBr} \) to \( ext{KI} \), the smaller lithium ion means its ions are closer together, which tends to increase the lattice energy compared to larger ions like potassium.
However, there are scenarios where ion size alone doesn't tell the full story since larger ions often result in less lattice energy. Hence, the interplay between ion sizes and charges must be considered when pondering an ionic compound's structural strength. Studying these aspects helps in predicting properties like solubility and reactivity, vital in chemistry and material sciences.