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Question #100394

Difficulty: 8/10 | 🟢 Free

The Question

A $1.00$ L aqueous solution at $298$ K initially contains $0.200$ M of \ce{Fe^{3+}} and $0.050$ M of \ce{Fe^{2+}}, along with a high concentration of \ce{HClO4} to maintain a constant high ionic strength. A constant current of $1.93$ A is passed through the solution for $5000$ seconds, selectively reducing \ce{Fe^{3+}} to \ce{Fe^{2+}} at the cathode with $100\%$ current efficiency. After the electrolysis, the potential of a Platinum electrode dipped in this solution is measured against a Standard Hydrogen Electrode (SHE).

Given: $E^\circ_{\ce{Fe^{3+}/Fe^{2+}}} = 0.770$ V $\frac{2.303 RT}{F} = 0.059$ V Activity coefficients in the final medium: $\gamma_{\ce{Fe^{3+}}} = 0.15$ , $\gamma_{\ce{Fe^{2+}}} = 0.40$ $\log 2 = 0.301$ , $\log 3 = 0.477$ Assume no change in the volume of the solution.

What is the measured potential of the electrode?

Options

A.
$0.734$ V
B.
$0.760$ V
C.
$0.745$ V
D.
$0.780$ 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

Equivalent Concept in Redox|Oxidation State Traps

Why This Question Is Tricky

Examiner Levers

Approximation Bait

Options are extremely close; tests precision vs. early rounding.

Difficulty Boost : +3

Dimensional Analysis

Tests if the student verifies units/dimensions before selecting.

Difficulty Boost : +2

Assumed Constant Trap

Requires a constant not explicitly given (e.g., specific heat of water).

Difficulty Boost : +3

Common Mistakes

The problem tests the intersection of Faraday's laws of electrolysis and the thermodynamic formulation of the Nernst equation.

The 'Hidden Variable' is the non-ideality of the solution due to high ionic strength.

Students commonly default to using analytical concentrations ( $c$ ) in the Nernst equation ( $E = E^\circ - \frac{0.059}{n} \log Q_c$ ).

However, rigorous electrochemistry requires the reaction quotient to be expressed in terms of thermodynamic activities ( $a = \gamma c$ ).

Failing to apply the activity coefficient correction leads to the trap answer $0.760$ V.

Additionally, the problem tests careful stoichiometric accounting by including an initial concentration of the product (\ce{Fe^{2+}}).

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	8
Target Solve Time	180 sec
Access	Free