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Question #44677

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The Question

A $100 \text{ mL}$ solution initially containing $1.0 \times 10^{-3} \text{ M}$ $\ce{Fe(ClO4)3}$ is subjected to electrolysis at a constant current of $9.65 \text{ mA}$ for $500 \text{ s}$ . The solution also contains inert $\ce{NaClO4}$ such that the total ionic strength ( $I$ ) of the medium is maintained constant at $0.04 \text{ M}$ . After the electrolysis is stopped, the potential of a Platinum electrode dipped in this solution is measured against a Standard Hydrogen Electrode (SHE) at $298 \text{ K}$ .

Assuming the only reaction during electrolysis is the reduction of $\ce{Fe^{3+}}$ to $\ce{Fe^{2+}}$ , calculate the measured cell potential.

[Given: $E^\circ_{\ce{Fe^{3+}/Fe^{2+}}} = 0.770 \text{ V}$ ; Faraday's constant $F = 96500 \text{ C mol}^{-1}$ ; $\frac{2.303 RT}{F} = 0.060 \text{ V}$ at $298 \text{ K}$ . Debye-Hückel Limiting Law: $\log \gamma_i = -A z_i^2 \sqrt{I}$ , where $A = 0.50 \text{ M}^{-1/2}$ for water at $298 \text{ K}$ .]

Options

A.
0.740 V
B.
0.770 V
C.
0.800 V
D.
0.764 V

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Numerical_Precision

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Concepts Behind This Question

Equivalent Concept in Redox|Nernst Equation Concentration Dependence

Why This Question Is Tricky

Common Mistakes

The problem tests the intersection of Faraday's laws of electrolysis and thermodynamic non-ideality in electrochemistry.

Students typically apply the Nernst equation using analytical concentrations ( $E = E^\circ - \frac{RT}{nF}\ln\frac{[\text{Products}]}{[\text{Reactants}]}$ ).

Here, the electrolysis yields $[\ce{Fe^{3+}}] = [\ce{Fe^{2+}}]$ , which would erroneously lead to $E = E^\circ = 0.770 \text{ V}$ (Option B).

The 'Hidden Variable' is the Activity Coefficient ( $\gamma$ ).

In a medium with defined ionic strength, multivalent ions like $\ce{Fe^{3+}}$ and $\ce{Fe^{2+}}$ experience significantly different electrostatic shielding.

The Debye-Hückel Limiting Law must be invoked to find the true thermodynamic activities.

Failing to account for the $z^2$ dependence of the activity coefficient leads to a lethal collision between idealized stoichiometry and real chemical potential.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Some Basic Concepts of Chemistry - Class 11 Part 1
Concept	Equivalent Concept in Redox
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free