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Question #44107

Difficulty: 8/10 | 🟢 Free

The Question

A concentration cell is constructed at $298\text{ K}$ using two zinc electrodes. Compartment A contains a saturated solution of $\ce{Zn(OH)2}$ in an aqueous medium maintained at $\text{pH} = 14.0$ . Compartment B contains a saturated solution of $\ce{Zn(OH)2}$ in an aqueous buffer maintained at $\text{pH} = 10.0$ .

Given: $K_{sp}(\ce{Zn(OH)2}) = 1.0 \times 10^{-16}$ $\beta_4$ for $\ce{[Zn(OH)4]^{2-}} = 1.0 \times 10^{15}$ $\frac{2.303 RT}{F} = 0.06\text{ V}$ Assume $\ce{[Zn(OH)4]^{2-}}$ is the only hydroxo-complex formed.

Calculate the EMF of the cell: $\ce{Zn(s) | Compartment A || Compartment B | Zn(s)}$ .

Options

A.
$+0.24\text{ V}$
B.
$-0.21\text{ V}$
C.
$+0.48\text{ V}$
D.
$+0.12\text{ V}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Numerical_Precision

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

Concepts Behind This Question

Amphiprotic Ion pH|Nernstian Redox Equilibrium|Concentration Cells

Why This Question Is Tricky

Common Mistakes

This problem tests the 'Hidden Variable' of effective concentration (activity) versus analytical concentration in Nernstian Equilibrium.

Students often fall into the trap of calculating the total dissolved zinc using the formation constant $\beta_4$ of the amphoteric complex $\ce{[Zn(OH)4]^{2-}}$ .

However, the electrode potential is thermodynamically coupled only to the free $\ce{Zn^{2+}}$ ion concentration, which is strictly constrained by the $K_{sp}$ and the pH of the saturated solution.

The $\beta_4$ value is a deliberate distractor to bait the calculation of total molarity.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Equilibrium - Class 11 Part 1
Concept	Amphiprotic Ion pH
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free