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Question #44536

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The Question

Pentaamminechloridocobalt(III) chloride, \ce{[Co(NH3)5Cl]Cl2}, undergoes a pseudo-first-order aquation reaction in water to form pentaammineaquacobalt(III) chloride, \ce{[Co(NH3)5(H2O)]Cl3}. A solution is prepared by dissolving $0.10 \text{ mol}$ of \ce{[Co(NH3)5Cl]Cl2} and $0.05 \text{ mol}$ of \ce{NaCl} in $1.0 \text{ kg}$ of water at $298 \text{ K}$ . The half-life of the aquation reaction at this temperature is $69.3 \text{ min}$ . Assuming ideal behavior and complete ionization of all ionic species, what is the theoretical freezing point of the solution corresponding to its composition after $138.6 \text{ min}$ ? (Given: $K_f$ for water is $1.86 \text{ K kg mol}^{-1}$ )

Options

A.
$-0.8835 ^\circ\text{C}$
B.
$-0.7440 ^\circ\text{C}$
C.
$-0.9300 ^\circ\text{C}$
D.
$-0.7905 ^\circ\text{C}$

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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

Freezing Point Depression (Pure Solvent)|Pseudo-First Order Kinetics|Stoichiometric Coefficient Division

Why This Question Is Tricky

Common Mistakes

This problem tests the integration of chemical kinetics with colligative properties.

The 'Hidden Variable' is the time-dependent van't Hoff factor $i(t)$ .

Students often calculate the concentration of the remaining reactant but fail to account for the fact that the stoichiometry of the aquation reaction increases the total number of ions in solution (from $i=3$ to $i=4$ ).

The trap is assuming the total molality of particles remains constant (Option B) or forgetting to include the spectator ions from the added NaCl correctly (Option D).

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Solutions - Class 12
Concept	Freezing Point Depression (Pure Solvent)
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free