To determine which statement about crystal lattice energy is best supported by the information in the table, we need to analyze the trend in lattice energy with respect to cation size.
Here is the provided table:
[tex]\[
\begin{array}{|l|c|}
\hline \text{Compound} & \text{Lattice Energy} ( \text{kJ/mol} ) \\
\hline \text{LiF} & -1036 \\
\hline \text{LiCl} & -853 \\
\hline \text{NaF} & -923 \\
\hline \text{KF} & -821 \\
\hline \text{NaCl} & -786 \\
\hline
\end{array}
\][/tex]
Let's consider each provided statement and compare the relevant compounds:
1. The lattice energy increases as cations get smaller, as shown by LiF and KF.
- LiF: Lattice energy = -1036 kJ/mol
- KF: Lattice energy = -821 kJ/mol
- Note that Li is smaller than K. The lattice energy of LiF (-1036 kJ/mol) is more negative (which means higher magnitude) than that of KF (-821 kJ/mol).
- This statement correctly indicates that the lattice energy increases (more negative) as cations get smaller.
2. The lattice energy increases as the cations get larger, as shown by LiF and LiCl.
- LiF: Lattice energy = -1036 kJ/mol
- LiCl: Lattice energy = -853 kJ/mol
- Li is the cation in both compounds. Comparing LiF with LiCl suggests that LiF has higher lattice energy, but this statement implies that larger cations increase lattice energy. Since the anion changes, this comparison isn’t strictly about cation size effects.
3. The lattice energy decreases as cations get smaller, as shown by NaCl and NaF.
- NaCl: Lattice energy = -786 kJ/mol
- NaF: Lattice energy = -923 kJ/mol
- Here, Na is the cation in both compounds. Lattice energy of NaF (-923 kJ/mol) is more negative than NaCl (-786 kJ/mol). This actually supports that lattice energy increases (more negative) as cations get smaller.
4. The lattice energy decreases as the cations get smaller, as shown by NaF and KF.
- NaF: Lattice energy = -923 kJ/mol
- KF: Lattice energy = -821 kJ/mol
- Na is smaller than K. The lattice energy of NaF (-923 kJ/mol) is more negative than that of KF (-821 kJ/mol), showing higher energy for the smaller cation (Na). Therefore, this statement is incorrect because it actually demonstrates an increase in lattice energy (more negative value) as cation size decreases.
Based on the above analysis, the best-supported statement by the information in the table is:
The lattice energy increases as cations get smaller, as shown by LiF and KF.
