Question

What is the expected value of \(\Delta \text{T}_f\) for \(0.2 \text{ m}\) aqueous \(\text{CaCl}_2\) solution if \(\Delta \text{T}_f\) for \(0.2 \text{ m}\) sucrose solution is \(x \text{ K}\) ?

• A. x
• B. 2x
• C. 3x
• D. \(\frac{x}{2}\)

Hint:

Electrolyte: more ions → higher \(\Delta T_f\).

Answer 1

The Correct Option is C

Concept:
\[ \Delta T_f = i K_f m \] where \(i\) = van’t Hoff factor.

Step 1: For sucrose.
• Non-electrolyte → \(i = 1\)
• \(\Delta T_f = x\)

Step 2: For CaCl$_2$. \[ \text{CaCl}_2 \rightarrow \text{Ca}^{2+} + 2\text{Cl}^- \Rightarrow i = 3 \]

Step 3: Relation. \[ \Delta T_f \propto i \] \[ \Rightarrow \Delta T_f = 3x \] Conclusion: \[ \text{Answer = (C)} \]