Problem 25 - Chemistry The Central Science

Question

Consider the ionic compounds KF, NaCl, NaBr, and LiCl. (a) Use ionic radil (Figure 7.8) to estimate the cation-anion distance for each compound. (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?

Step-by-Step Solution

Answer

The cation-anion distances for KF, NaCl, NaBr, and LiCl are 252 pm, 264 pm, 279 pm, and 227 pm respectively. Based on these distances, the order of decreasing lattice energy is LiCl, KF, NaCl, and NaBr. This order is confirmed by the experimental lattice energy values from Table 8.1: LiCl (853 kJ/mol), KF (821 kJ/mol), NaCl (787 kJ/mol), and NaBr (747 kJ/mol). Thus, the predictions based on ionic radii are correct.

Step 1: Calculate the cation-anion distances for each compound

For each compound, add the ionic radii of the cation and anion to find the cation-anion distance. Use Figure 7.8 to find the ionic radii. For KF: - K⁺ radius: 133 pm - F⁻ radius: 119 pm Cation-anion distance = 133 pm + 119 pm = 252 pm For NaCl: - Na⁺ radius: 97 pm - Cl⁻ radius: 167 pm Cation-anion distance = 97 pm + 167 pm = 264 pm For NaBr: - Na⁺ radius: 97 pm - Br⁻ radius: 182 pm Cation-anion distance = 97 pm + 182 pm = 279 pm For LiCl: - Li⁺ radius: 60 pm - Cl⁻ radius: 167 pm Cation-anion distance = 60 pm + 167 pm = 227 pm

Step 2: Arrange compounds in order of decreasing lattice energy

Lattice energy is inversely proportional to the distance between the cation and anion. Smaller cation-anion distance results in stronger attractive forces and thus higher lattice energy. Using the cation-anion distance found above, we can arrange the compounds in order of decreasing lattice energy: 1. LiCl (227 pm) 2. KF (252 pm) 3. NaCl (264 pm) 4. NaBr (279 pm)

Step 3: Compare the predicted order with experimental values

Now, let's compare our prediction with the experimental values of lattice energy from Table 8.1. The lattice energies (in kJ/mol) for the compounds are: - KF: 821 kJ/mol - NaCl: 787 kJ/mol - NaBr: 747 kJ/mol - LiCl: 853 kJ/mol Based on the experimental values, the order of decreasing lattice energy is: 1. LiCl (853 kJ/mol) 2. KF (821 kJ/mol) 3. NaCl (787 kJ/mol) 4. NaBr (747 kJ/mol) This confirms that our predictions based on ionic radii are indeed correct.

Key Concepts

Cation-Anion Distance

The cation-anion distance is crucial in ionic compounds. It refers to the distance between the positively charged cation and the negatively charged anion. This distance is determined by adding the ionic radii of the cation and anion involved. For example:

• KF: The distance is calculated by adding the radius of K⁺, 133 pm, and F⁻, 119 pm, resulting in 252 pm.
• NaCl: The distance is the sum of Na⁺, 97 pm, and Cl⁻, 167 pm, totaling 264 pm.
• NaBr: Here, we add Na⁺, 97 pm, and Br⁻, 182 pm, making 279 pm.
• LiCl: It combines Li⁺, 60 pm, and Cl⁻, 167 pm, totaling 227 pm.

Understanding this distance is key because it influences the strength of the ionic bond. The shorter the distance, the stronger the electrostatic forces of attraction between ions.

Lattice Energy

Lattice energy represents the energy required to separate one mole of an ionic solid into its gaseous ions. This concept plays a significant role in understanding the stability and properties of ionic compounds. The smaller the cation-anion distance, the greater the lattice energy due to stronger attractions between ions.

• LiCl: With the shortest distance of 227 pm, has the highest lattice energy and is more stable.
• KF: Follows with a slightly larger distance of 252 pm.
• NaCl: Comes next with a distance of 264 pm.
• NaBr: Has the longest distance, 279 pm, resulting in the lowest lattice energy.

By comparing experimental lattice energies, predictions based on cation-anion distances confirm the inverse relationship between distance and lattice energy.

Ionic Radii

The ionic radii is the measure of an ion's size and plays a pivotal role in determining the distance between ions in an ionic lattice. Ionic radii enable us to predict and calculate the cation-anion distances, influencing both lattice energy and ionic bonding strength.
For instance, an element like lithium (Li⁺) has a smaller ionic radius (60 pm) compared to sodium (Na⁺, 97 pm), making LiCl have a shorter cation-anion distance than NaCl. Similarly, comparing halides, the fluoride ion (F⁻, 119 pm) is smaller than the bromide ion (Br⁻, 182 pm), resulting in variations in bond strength and lattice stability. Recognizing these radii helps in forming robust predictions in chemical behavior.

Ionic Bonds

Ionic bonds form when electrons transfer from one atom to another, especially between metals and nonmetals, leading to the formation of cations and anions. These bonds create the framework of ionic compounds.
The bond strength is governed mainly by the electrostatic forces between the differently charged ions. Key factors affecting ionic bonds include:

• Charge Magnitude: Higher charges result in stronger bonds due to stronger attractions.
• Distance Between Ions: As seen with cation-anion distance, shorter distances enhance bond strength.

Ionic bonds yield compounds like NaCl or KF with distinctive properties, such as high melting points and electrical conductivity in molten form. Understanding the nature of these bonds allows insights into the physical and chemical characteristics of ionic compounds.