Question

A \(0.1\) molal aqueous solution of \(\text{K}_{3}[\text{Fe(CN)}_{6}]\) freezes at \(-0.85{}^{\circ }\)C. If \(K_{f}\) for water is \(1.86\) K kg mol\({}^{-1}\), what is the van't Hoff factor for this solution?

• A. \(3.0\)
• B. \(3.5\)
• C. \(4.0\)
• D. \(4.57\)

Hint:

Use the freezing point depression formula with the van't Hoff factor, i = delta Tf / (Kf m).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
For an electrolyte, the observed depression in freezing point is \(\Delta T_f = i\,K_f\,m\).

Step 2: Find the Depression
\(\Delta T_f = 0 - (-0.85) = 0.85\) K

Step 3: Calculation
\(i = \dfrac{\Delta T_f}{K_f m} = \dfrac{0.85}{1.86 \times 0.1} = \dfrac{0.85}{0.186} = 4.57\)

Step 4: Compare the options
The van't Hoff factor is \(4.57\), option (D).

Final Answer:
The van't Hoff factor of the solution is 4.57. \[ \boxed{\text{(D) }4.57} \]