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Question #44649

Difficulty: 8/10 | 🟢 Free

The Question

An aqueous solution is prepared by dissolving $25$ g of \ce{K3[Fe(CN)6]} (Molar mass $= 329$ g mol $^{-1}$ ) in $1.0 \times 10^2$ g of water. The experimental freezing point of this solution is measured to be $-3.6^\circ\text{C}$ .

Assuming the Van't Hoff factor ( $i$ ) remains constant over the temperature range, calculate the experimental Van't Hoff factor ( $i$ ) to the correct number of significant figures, and the expected boiling point of the solution at $1$ atm.

(Given: $K_f = 1.86$ K kg mol $^{-1}$ , $K_b = 0.512$ K kg mol $^{-1}$ , normal boiling point of water is exactly $100^\circ\text{C}$ )

Options

A.
$i = 2.5$ , $T_b = 100.99^\circ\text{C}$
B.
$i = 2.5$ , $T_b = 100.97^\circ\text{C}$
C.
$i = 4.0$ , $T_b = 101.6^\circ\text{C}$
D.
$i = 2.6$ , $T_b = 101.0^\circ\text{C}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Numerical_Precision

Improve calculation stamina and avoid rounding errors in high-stakes competitive examinations.

Concepts Behind This Question

Significant Figures in Arithmetic|Van’t Hoff Factor (i) Application

Why This Question Is Tricky

Common Mistakes

The problem tests two critical concepts: 1) High Concentration Non-Ideality: At high concentrations, strong electrolytes like \ce{K3[Fe(CN)6]} deviate significantly from their ideal Van't Hoff factor ( $i=4$ ) due to ion pairing. 2) Significant Figures and Premature Rounding: Students must report the final value of $i$ to 2 significant figures ( $2.5$ ).

However, a common trap is using this rounded value in subsequent calculations.

According to strict significant figure rules, intermediate values must not be rounded.

Using the exact $i$ (or the direct ratio $\Delta T_b / \Delta T_f$ ) yields a boiling point of $100.99^\circ\text{C}$ , whereas using the rounded $i$ yields $100.97^\circ\text{C}$ .

Additionally, it traps students who perform incorrect sequential rounding ( $2.547 \rightarrow 2.55 \rightarrow 2.6$ ).

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Some Basic Concepts of Chemistry - Class 11 Part 1
Concept	Significant Figures in Arithmetic
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free