- Identify the trend: Lattice energy magnitude increases as ionic radii decrease, due to stronger electrostatic attraction.
- Evaluate the data: Compare compounds where only the cation or only the anion changes to isolate the effect of size.
- Validate: The statement "The lattice energy increases as cations get smaller, as shown by LiF and KF" matches the data, as \(Li^+\) is smaller than \(K^+\) and \(|LiF| > |KF|\).
- Conclusion: The first statement is correct. \(\boxed{\text{The lattice energy increases as cations get smaller, as shown by LiF and KF.}}\)
Explanation
- Analyzing Data and Trends
To determine which statement is supported by the provided lattice energy data, we first need to understand the relationship between ionic size and lattice energy. Lattice energy is defined as the energy released when gaseous ions form a crystal lattice, and its magnitude is greater (more negative) when ions are smaller and have higher charges, as the electrostatic attraction is stronger. From the periodic table, we know the trends for ionic radii: for the cations \(Li^+ < Na^+ < K^+\) and for the anions \(F^- < Cl^-\). A higher magnitude of lattice energy indicates a stronger crystal lattice.
The magnitudes are:
- \(|LiF| = 1036 \text{ kJ/mol}\)
- \(|NaF| = 923 \text{ kJ/mol}\)
- \(|KF| = 821 \text{ kJ/mol}\)
- \(|LiCl| = 853 \text{ kJ/mol}\)
- \(|NaCl| = 786 \text{ kJ/mol}\)
- Evaluating Statements
Let's evaluate each statement:
- "The lattice energy increases as cations get smaller, as shown by LiF and KF": Comparing LiF (\(Li^+\)) and KF (\(K^+\)), the cation \(Li^+\) is smaller than \(K^+\). The magnitude of the lattice energy for LiF (1036) is greater than for KF (821). This correctly shows that as the cation gets smaller, the lattice energy increases.
- "The lattice energy increases as the cations get larger, as shown by LiF and LiCl": This compares LiF and LiCl, where the cation is the same (\(Li^+\)). The lattice energy change is due to the anion, not the cation size. This statement is incorrect.
- "The lattice energy decreases as cations get smaller, as shown by NaCl and NaF": This compares NaCl and NaF, where the cation is the same (\(Na^+\)). The lattice energy change is due to the anion. This statement is incorrect.
- "The lattice energy decreases as the cations get smaller, as shown by NaF and KF": Comparing NaF (\(Na^+\)) and KF (\(K^+\)), the cation \(Na^+\) is smaller than \(K^+\). As we go from NaF to KF, the cation actually gets larger. This statement is therefore incorrect.
- Conclusion
Based on our evaluation, the only statement consistent with both the periodic trends and the provided table is the first one. The data for LiF and KF shows that replacing a larger cation (\(K^+\)) with a smaller one (\(Li^+\)) while keeping the same anion (\(F^-\)) results in an increase in the magnitude of the lattice energy. Thus, the statement "The lattice energy increases as cations get smaller, as shown by LiF and KF" is the best supported.
The final answer is: \(\boxed{\text{The lattice energy increases as cations get smaller, as shown by LiF and KF.}}\)
Examples
Lattice energy is a fundamental concept in material science, crucial for understanding the properties of solid materials. For instance, engineers use this knowledge to predict the melting points and solubilities of ionic compounds. A substance with a very high lattice energy, like LiF, will generally have a higher melting point, making it more stable under extreme heat. This is important in designing electrolytes for advanced batteries, where thermal stability and ion mobility are key performance factors.