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Question #44088

Difficulty: 8/10 | 🟢 Free

The Question

A galvanic cell at 298 K is constructed with a Standard Hydrogen Electrode (SHE) as the anode and a silver electrode as the cathode. The cathode compartment contains a saturated aqueous solution of a sparingly soluble silver salt, $\ce{AgA}$ ( $K_{sp} = 10^{-14}$ ), and is maintained at a constant $pH = 4.0$ using a buffer. The conjugate acid $\ce{HA}$ is a weak acid with $K_a = 10^{-8}$ .

Solid $\ce{NaA}$ is then dissolved in the cathode compartment such that the total analytical concentration of the added $\ce{A}$ species is $0.1 \text{ M}$ . Assuming no change in the volume of the solution and that the buffer perfectly maintains $pH = 4.0$ , calculate the shift in the electromotive force ( $\Delta E_{cell}$ ) of the cell.

(Given: $\frac{2.303 RT}{F} = 0.06 \text{ V}$ at 298 K)

Options

A.
$-0.24 \text{ V}$
B.
$-0.36 \text{ V}$
C.
$-0.48 \text{ V}$
D.
$-0.12 \text{ V}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Mechanism_Trap

Don't get tricked by the process! Learn the mechanical traps used in competitive exam questions.

Concepts Behind This Question

Common Ion Effect on Solubility|Nernst Equation Concentration Dependence|Standard Electrode Potential Sign Conventions

Why This Question Is Tricky

Common Mistakes

This problem tests the integration of the Nernst equation with simultaneous heterogeneous (solubility) and homogeneous (acid-base) equilibria.

The 'hidden variable' is the actual concentration of the common ion $\ce{A^-}$ .

Students often fall into the trap of assuming the added analytical concentration of the salt directly equals the common ion concentration ( $[\ce{A^-}] = 0.1 \text{ M}$ ), ignoring the profound effect of the buffer ( $pH = 4.0$ ) which protonates $99.99\%$ of the added $\ce{A^-}$ into $\ce{HA}$ .

Furthermore, they may fail to account for this same hydrolysis effect during the initial dissolution of the sparingly soluble salt.

Distractor B ignores hydrolysis entirely, Distractor C accounts for initial hydrolysis but ignores it for the added salt, and Distractor D ignores initial hydrolysis but accounts for it finally.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Equilibrium - Class 11 Part 1
Concept	Common Ion Effect on Solubility
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free