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Question #44544

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The Question

A $1.0\text{ kg}$ aqueous solution contains a total of $0.10\text{ moles}$ of a mixture of two octahedral \ce{Co(III)} ammine complexes: a yellow complex $P$ and a green complex $Q$ . Both complexes are synthesized exclusively from anhydrous \ce{CoCl3} and \ce{NH3}. The boiling point of this solution is $100.1352^\circ\text{C}$ at $1\text{ atm}$ .

When excess \ce{AgNO3(aq)} is added to this solution, $W$ grams of \ce{AgCl(s)} precipitate is formed. Assuming $100\%$ ionization of the complexes and ideal behavior, what is the value of $W$ ?

(Given: $K_b$ for water = $0.52\text{ K kg mol}^{-1}$ , Molar mass of \ce{AgCl} = $143.5\text{ g mol}^{-1}$ , Boiling point of pure water = $100.0000^\circ\text{C}$ )

Options

A.
$22.96\text{ g}$
B.
$34.44\text{ g}$
C.
$37.31\text{ g}$
D.
$43.05\text{ g}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Exception_Exposure

Learn to identify edge cases and boundary exceptions that JEE examiners hide in math problems.

Concepts Behind This Question

Van’t Hoff Factor (i) Application|Ammonolysis Complexity|Werner’s Theory Postulates

Why This Question Is Tricky

Common Mistakes

This problem tests the intersection of Werner's Coordination Theory and Colligative Properties.

The 'Hidden Variable' is the mathematical relationship between the Van't Hoff factor and the number of ionizable counter-ions.

Students often get bogged down trying to identify the exact formulas of the yellow (luteo) and green (praseo) complexes and solving simultaneous equations.

The elegant exception/shortcut is realizing that for any mononuclear complex, the total moles of particles in solution is simply the sum of the moles of the complex itself and the moles of its dissociated counter-ions ( $n_{particles} = n_{complex} + n_{counter-ions}$ ).

Distractors trap students who confuse total chlorine atoms with ionizable chloride ions, or who miscalculate the Van't Hoff factor.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Solutions - Class 12
Concept	Van’t Hoff Factor (i) Application
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free