Step 1: Understanding the Concept:
For an electrolyte solution, the depression in freezing point (\(\Delta T_f\)) depends on the number of particles in solution, which is accounted for by the van 't Hoff factor (\(i\)). The degree of dissociation (\(\alpha\)) relates to this factor.
Step 2: Key Formula or Approach:
The formulas required are:
\[ \Delta T_f = i \cdot K_f \cdot m \]
\[ \alpha = \frac{i - 1}{n - 1} \]
where \(n\) is the number of ions produced per formula unit.
Step 3: Detailed Explanation:
Given values:
\(\Delta T_f = 0.046\text{ K}\)
\(K_f = 1.86\text{ K kg mol}^{-1}\)
\(m = 0.02\text{ m}\)
\(n = 2\)
First, calculate the van 't Hoff factor (\(i\)):
\[ 0.046 = i \times 1.86 \times 0.02 \]
\[ 0.046 = i \times 0.0372 \]
\[ i = \frac{0.046}{0.0372} \approx 1.2365 \]
Now, calculate the degree of dissociation (\(\alpha\)):
\[ \alpha = \frac{i - 1}{n - 1} = \frac{1.2365 - 1}{2 - 1} = 0.2365 \]
Convert this to a percentage:
\[ \text{Percent dissociation} = \alpha \times 100% = 0.2365 \times 100% = 23.65% \]
Rounding to one decimal place gives \(23.6%\).
Step 4: Final Answer:
The calculated percent dissociation is approximately \(23.6%\), matching option (B).