Question

Find the expected value of \(\Delta \mathrm{T}_{\mathrm{b}}\) for \(1 \mathrm{~m} \mathrm{AlCl}{ }_3\) solution in water if solution of nonelectrolyte of same concentration has \(\Delta \mathrm{T}_{\mathrm{b}}\) value ' \(x\) ' K .

• A. \(x\text{ }\mathrm{K}\)
• B. \(2x\text{ }\mathrm{K}\)
• C. \(3x\text{ }\mathrm{K}\)
• D. \(4x\text{ }\mathrm{K}\)

Hint:

Use the van't Hoff factor for complete dissociation of AlCl3.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
\( \Delta T_b=i\,K_b\,m \). For the same molality, the elevation is \( i \) times that of a non-electrolyte.

Step 2: Van't Hoff Factor
\( \text{AlCl}_3\rightarrow\text{Al}^{3+}+3\text{Cl}^- \) gives 4 ions, so \( i=4 \).

Step 3: Result
\( \Delta T_b=4x \text{ K} \), option (D).

Final Answer:
The expected elevation is 4x K. \[ \boxed{\text{(D) }4x\text{ K}} \]