To determine which statement about crystal lattice energy is best supported by the given table of lattice energies, we'll analyze the relationships between the compounds provided. Specifically, these relationships will clarify whether lattice energy increases or decreases with the size of the cations.
First, let’s recap the given lattice energies:
- LiF: -1036 kJ/mol
- LiCl: -853 kJ/mol
- NaF: -923 kJ/mol
- KF: -821 kJ/mol
- NaCl: -786 kJ/mol
Now, let's evaluate each statement:
1. The lattice energy increases as cations get smaller, as shown by LiF and KF.
- LiF: -1036 kJ/mol
- KF: -821 kJ/mol
- Here, we are comparing Li+ and K+. Li+ is a smaller cation than K+.
- The lattice energy of LiF is higher (more negative) than that of KF.
- This supports the statement that lattice energy increases (becomes more negative) as cations get smaller.
2. The lattice energy increases as the cations get larger, as shown by LiF and LiCl.
- LiF: -1036 kJ/mol
- LiCl: -853 kJ/mol
- With Li+ as the constant cation, we cannot make a meaningful comparison about the effect of cation size since the anion changes (F- vs. Cl-).
3. The lattice energy decreases as cations get smaller, as shown by NaCl and NaF.
- NaCl: -786 kJ/mol
- NaF: -923 kJ/mol
- Na+ is the constant cation, and we are now comparing different anions (Cl- and F-). Thus, this statement about cation size is not relevant based on these compounds.
4. The lattice energy decreases as the cations get smaller, as shown by NaF and KF.
- NaF: -923 kJ/mol
- KF: -821 kJ/mol
- We are comparing Na+ and K+. Na+ is smaller than K+.
- The lattice energy of NaF is higher (more negative) than that of KF.
- This statement is incorrect because the lattice energy does not decrease with smaller cations; it actually increases (becomes more negative).
After examining the lattice energy values and considering the above analyses, the best-supported statement is:
The lattice energy increases as cations get smaller, as shown by LiF and KF.
Hence, the most supported statement is the first one.
