Before You Begin

Question #44132

Difficulty: 8/10 | 🟢 Free

The Question

An electrochemical cell is constructed at $298 \text{ K}$ by coupling a Standard Hydrogen Electrode (SHE) as the anode with a cathode half-cell. The cathode half-cell consists of a platinum wire dipped into a $1.0 \text{ L}$ aqueous solution prepared by completely dissolving $0.05 \text{ moles}$ of pure magnetite ( $\ce{Fe3O4(s)}$ ) in excess dilute $\ce{HClO4(aq)}$ under an inert atmosphere. The final concentration of $\ce{H+(aq)}$ in the solution is adjusted to $1.0 \text{ M}$ .

Given: Standard reduction potential $E^\circ_{\ce{Fe^{3+}/Fe^{2+}}} = 0.770 \text{ V}$ $\frac{2.303RT}{F} = 0.060 \text{ V}$ $\log 2 = 0.30$

Assuming ideal behavior and no hydrolysis of metal ions, what is the electromotive force (EMF) of the cell?

Options

A.
$0.788 \text{ V}$
B.
$0.752 \text{ V}$
C.
$0.770 \text{ V}$
D.
$0.844 \text{ V}$

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

Average vs. Actual Oxidation State|Nernstian Redox Equilibrium|Electrode Potential Sign Conventions

Why This Question Is Tricky

Common Mistakes

The problem tests the conceptual boundary between solid-state average oxidation states and aqueous redox equilibria.

A common 'Lethal Collision' occurs when students treat $\ce{Fe3O4}$ as having an average $+8/3$ oxidation state, leading them to construct a fictitious Nernstian equation for the overall dissolution (yielding $0.844 \text{ V}$ ).

Another frequent trap is confusing the stoichiometry of the inverse spinel structure, mistakenly assuming a 2:1 ratio of $\ce{Fe^{2+}}$ to $\ce{Fe^{3+}}$ , which inverts the reaction quotient $Q$ and results in $0.752 \text{ V}$ .

The core principle is that electrochemical potential is strictly governed by the specific active redox sites ( $\ce{Fe^{3+}/Fe^{2+}}$ ) present in the solution.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Redox Reactions - Class 11 Part 2
Concept	Average vs. Actual Oxidation State
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free