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Question #44676

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The Question

A piece of iron (\ce{Fe}) is exposed to a drop of water at $298 \text{ K}$ , initiating a differential aeration corrosion cell. The periphery of the drop acts as the cathode due to high oxygen concentration, while the center acts as the anode. The area of the cathodic region ( $A_c$ ) is $20$ times the area of the anodic region ( $A_a$ ). If the steady-state cathodic current density ( $i_c$ ) is $9.65 \times 10^{-5} \text{ A cm}^{-2}$ , calculate the localized rate of mass loss of iron at the anodic region in $\text{g h}^{-1} \text{ cm}^{-2}$ .

(Given: Molar mass of \ce{Fe} = $56 \text{ g mol}^{-1}$ , $1 \text{ F} = 96500 \text{ C mol}^{-1}$ , assume iron oxidizes to \ce{Fe^{2+}} at the anode)

Options

A.
$2.016 \times 10^{-3}$
B.
$1.008 \times 10^{-4}$
C.
$1.344 \times 10^{-3}$
D.
$5.040 \times 10^{-6}$

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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

Equivalent Concept in Redox|Corrosion as Electrochemical Process

Why This Question Is Tricky

Common Mistakes

The question tests the application of the Law of Equivalence in localized electrochemical processes (Differential Aeration Cell).

Students often mistakenly apply the bulk cathodic current density directly to the anodic mass loss calculation, ignoring the area ratio ( $A_c/A_a$ ).

Because the anodic area is much smaller, the localized current density ( $i_a$ ) is significantly higher, leading to rapid, deep pitting corrosion.

Failing to account for this 'Hidden Variable' (the area ratio) leads to an underestimation of the corrosion rate by a factor of 20 (Option B).

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