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The table lists the lattice energies of some compounds.

\begin{tabular}{|l|l|}
\hline
\multicolumn{1}{|c|}{Compound} & Lattice Energy (kJ/mol) \\
\hline
LiF & [tex]$-1,036$[/tex] \\
\hline
LiCl & [tex]$-853$[/tex] \\
\hline
NaF & [tex]$-923$[/tex] \\
\hline
KF & [tex]$-821$[/tex] \\
\hline
NaCl & [tex]$-786$[/tex] \\
\hline
\end{tabular}

Which statement about crystal lattice energy is best supported by the information in the table?

A. The lattice energy increases as cations get smaller, as shown by LiF and KF.
B. The lattice energy increases as the cations get larger, as shown by LiF and LiCl.
C. The lattice energy decreases as cations get smaller, as shown by NaCl and NaF.
D. The lattice energy decreases as the cations get smaller, as shown by NaF and KF.

Sagot :

GinnyAnsweridn
To determine which statement about crystal lattice energy is best supported by the information in the table, let's analyze the given lattice energies in relation to cation size:

### Given Lattice Energies:
- LiF: -1036 kJ/mol
- LiCl: -853 kJ/mol
- NaF: -923 kJ/mol
- KF: -821 kJ/mol
- NaCl: -786 kJ/mol

### Analysis of Relationships:

1. LiF vs. KF:
- Cations: Li[tex]\(^+\)[/tex] vs. K[tex]\(^+\)[/tex]
- Lattice Energies: LiF (-1036 kJ/mol) vs. KF (-821 kJ/mol)
- Observation: Li[tex]\(^+\)[/tex] is smaller than K[tex]\(^+\)[/tex], and LiF has a more negative (higher) lattice energy than KF.

2. LiF vs. LiCl:
- Anions: F[tex]\(^-\)[/tex] vs. Cl[tex]\(^-\)[/tex]
- Cations: Li[tex]\(^+\)[/tex]
- Lattice Energies: LiF (-1036 kJ/mol) vs. LiCl (-853 kJ/mol)
- Observation: Since F[tex]\(^-\)[/tex] is smaller than Cl[tex]\(^-\)[/tex], comparing these does not directly relate to cation size changes.

3. NaCl vs. NaF:
- Anions: Cl[tex]\(^-\)[/tex] vs. F[tex]\(^-\)[/tex]
- Cations: Na[tex]\(^+\)[/tex]
- Lattice Energies: NaCl (-786 kJ/mol) vs. NaF (-923 kJ/mol)
- Observation: Since F[tex]\(^-\)[/tex] is smaller than Cl[tex]\(^-\)[/tex], comparing these does not directly relate to cation size changes.

4. NaF vs. KF:
- Cations: Na[tex]\(^+\)[/tex] vs. K[tex]\(^+\)[/tex]
- Anions: F[tex]\(^-\)[/tex]
- Lattice Energies: NaF (-923 kJ/mol) vs. KF (-821 kJ/mol)
- Observation: Na[tex]\(^+\)[/tex] is smaller than K[tex]\(^+\)[/tex], and NaF has a more negative (higher) lattice energy than KF.

### Conclusion:

From the comparisons:

- LiF vs. KF:
- Li[tex]\(^+\)[/tex] is smaller than K[tex]\(^+\)[/tex].
- LiF with Li[tex]\(^+\)[/tex] has a higher lattice energy (-1036 kJ/mol) than KF with K[tex]\(^+\)[/tex] (-821 kJ/mol).

- NaF vs. KF:
- Na[tex]\(^+\)[/tex] is smaller than K[tex]\(^+\)[/tex].
- NaF with Na[tex]\(^+\)[/tex] has a higher lattice energy (-923 kJ/mol) than KF with K[tex]\(^+\)[/tex] (-821 kJ/mol).

Both sets of comparisons clearly support the statement: "The lattice energy increases as cations get smaller."

Thus, the statement best supported by the data is:
"The lattice energy increases as cations get smaller, as shown by LiF and KF."
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