To determine which statement about crystal lattice energy is best supported by the information in the table, we need to analyze the differences in lattice energies between different pairs of compounds.
Here's the information given in the table:
- [tex]\( \text{LiF} = -1036 \, \text{kJ/mol} \)[/tex]
- [tex]\( \text{LiCl} = -853 \, \text{kJ/mol} \)[/tex]
- [tex]\( \text{NaF} = -923 \, \text{kJ/mol} \)[/tex]
- [tex]\( \text{KF} = -821 \, \text{kJ/mol} \)[/tex]
- [tex]\( \text{NaCl} = -786 \, \text{kJ/mol} \)[/tex]
Now, we will calculate the differences in lattice energies for the given pairs:
1. LiF and KF: To see how lattice energy changes as cations get smaller (LiF and KF):
[tex]\[
\Delta E_{1} = \text{LiF} - \text{KF} = -1036 - (-821) = -215 \, \text{kJ/mol}
\][/tex]
The lattice energy increases when moving from KF to LiF, suggesting that as cations get smaller, the lattice energy increases.
2. LiCl and LiF: To see how lattice energy changes as cations get larger (LiF and LiCl):
[tex]\[
\Delta E_{2} = \text{LiCl} - \text{LiF} = -853 - (-1036) = 183 \, \text{kJ/mol}
\][/tex]
The lattice energy decreases when moving from LiF to LiCl, suggesting that as cations get larger, the lattice energy decreases.
3. NaCl and NaF: To see how lattice energy changes with the same cation but different anions (NaCl and NaF):
[tex]\[
\Delta E_{3} = \text{NaCl} - \text{NaF} = -786 - (-923) = 137 \, \text{kJ/mol}
\][/tex]
This suggests that the lattice energy decreases slightly when moving from NaF to NaCl.
4. NaF and KF: To see how lattice energy changes as cations get smaller (NaF and KF):
[tex]\[
\Delta E_{4} = \text{NaF} - \text{KF} = -923 - (-821) = -102 \, \text{kJ/mol}
\][/tex]
The lattice energy increases when moving from KF to NaF, suggesting that as cations get smaller, the lattice energy increases.
Therefore, the statement that is best supported by the information in the table is:
The lattice energy increases as cations get smaller, as shown by LiF and KF.
This is because the calculated difference ([tex]\( \Delta E_1 = -215 \, \text{kJ/mol} \)[/tex]) indicates an increase in lattice energy when moving from a larger cation (KF) to a smaller cation (LiF). This analysis supports statement 1.
