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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 [tex]$LiF$[/tex] & [tex]$-1,036$[/tex] \\
\hline [tex]$LiCl$[/tex] & -853 \\
\hline [tex]$NaF$[/tex] & -923 \\
\hline [tex]$KF$[/tex] & -821 \\
\hline [tex]$NaCl$[/tex] & -786 \\
\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 [tex]$NaCl$[/tex] and [tex]$NaF$[/tex].
D. The lattice energy decreases as the cations get smaller, as shown by [tex]$NaF$[/tex] and [tex]$KF$[/tex].

Sagot :

GinnyAnswer
Let's analyze the given table of lattice energies and link them to the properties of cations and anions.

The lattice energies for the given compounds are as follows:
[tex]\[ \begin{array}{|l|l|} \hline \text{Compound} & \text{Lattice Energy (kJ/mol)} \\ \hline LiF & -1036 \\ \hline LiCl & -853 \\ \hline NaF & -923 \\ \hline KF & -821 \\ \hline NaCl & -786 \\ \hline \end{array} \][/tex]

### Step-by-Step Analysis:

#### 1. Cation and Anion Sizes:
- Cations: Li+, Na+, K+
- Li+ is the smallest.
- Na+ is larger than Li+.
- K+ is larger than Na+.

- Anions: F-, Cl-
- F- is smaller than Cl-.

#### 2. How Lattice Energy Relates to Ion Sizes:
- Lattice energy increases as the size of the cations or anions decreases. Smaller ions lead to stronger electrostatic attractions within the crystal lattice, thus higher lattice energy.

#### 3. Comparing Lattice Energies Based on Ion Sizes:
- LiF vs KF:
- Both have the F- anion.
- Li+ (small) vs K+ (large).
- Lattice energy of LiF (-1036 kJ/mol) is higher than KF (-821 kJ/mol).
- Therefore, lattice energy is higher with the smaller cation (Li+).

- LiF vs LiCl:
- Both have Li+ cation.
- F- (small) vs Cl- (large).
- Lattice energy of LiF (-1036 kJ/mol) is higher than LiCl (-853 kJ/mol).
- Supports the notion that lattice energy increases with a smaller anion.

- NaF vs NaCl:
- Both have Na+ cation.
- F- (small) vs Cl- (large).
- Lattice energy of NaF (-923 kJ/mol) is higher than NaCl (-786 kJ/mol).
- Supports the idea that a smaller anion (F-) increases lattice energy.

- NaF vs KF:
- Both have the F- anion.
- Na+ (smaller) vs K+ (larger).
- Lattice energy of NaF (-923 kJ/mol) is higher than KF (-821 kJ/mol).
- Supports the idea that a smaller cation (Na+) increases lattice energy.

### Conclusion:
By examining the lattice energies given, the statement "The lattice energy increases as cations get smaller, as shown by LiF and KF." is best supported. This is evident from the comparison where LiF, with the smaller cation Li+, has a higher lattice energy than KF, which has the larger cation K+.

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