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Question #44752

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The Question

A $1.00 \text{ L}$ aqueous solution initially containing $0.10 \text{ M}$ \ce{AgNO3} is electrolyzed using inert Platinum electrodes at $298 \text{ K}$ . A constant current of $9.65 \text{ A}$ is passed through the solution for $510 \text{ s}$ . After the electrolysis is complete, $0.10 \text{ moles}$ of solid \ce{NaCH3COO} is added to the solution. Assume no change in volume occurs upon the addition of the solid and during electrolysis.

Given at $298 \text{ K}$ : $K_{sp}(\ce{AgCH3COO}) = 2.5 \times 10^{-3}$ $K_a(\ce{CH3COOH}) = 2.0 \times 10^{-5}$ Faraday's constant $F = 96500 \text{ C mol}^{-1}$ Molar mass of $\ce{AgCH3COO} = 167 \text{ g mol}^{-1}$ Molar mass of $\ce{Ag} = 108 \text{ g mol}^{-1}$

Calculate the mass of the \ce{AgCH3COO} precipitate formed in the solution.

Options

A.
$0.00 \text{ g}$
B.
$3.07 \text{ g}$
C.
$5.51 \text{ g}$
D.
$8.35 \text{ g}$

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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

Faraday's First and Second Laws|Solubility of Solids in Liquids

Why This Question Is Tricky

Common Mistakes

The problem tests the integration of Faraday's laws of electrolysis with ionic equilibrium (solubility and buffer/weak acid).

The 'hidden variable' is the generation of $\ce{H+}$ ions at the anode during the electrolysis of water (since $\ce{NO3-}$ is inert).

Students often focus only on the metal ion ( $\ce{Ag+}$ ) reduction at the cathode and forget that the anodic oxidation of water produces $\ce{H+}$ , which lowers the pH.

When the weak base anion ( $\ce{CH3COO-}$ ) is added, it is protonated by the electrogenerated $\ce{H+}$ , significantly reducing the free $[\ce{CH3COO-}]$ available for precipitation.

Failing to account for this anodic $\ce{H+}$ generation leads to the false conclusion that $\ce{AgCH3COO}$ will precipitate (Option B).

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Electrochemistry - Class 12
Concept	Faraday's First and Second Laws
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free