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Question #44074

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The Question

A half-cell is constructed at $298 \text{ K}$ by immersing a platinum electrode in a $1.0 \text{ L}$ aqueous solution containing $0.01 \text{ M}$ \ce{K2Cr2O7}, $0.1 \text{ M}$ \ce{CrCl3}, and $0.1 \text{ M}$ of a weak monobasic acid \ce{HA} ( $K_a = 10^{-5}$ ). This half-cell is connected to a Standard Hydrogen Electrode (SHE) to form a galvanic cell.

Assuming the degree of dissociation of \ce{HA} is small ( $\alpha \ll 1$ ) and neglecting any volume changes or complexation, what is the initial electromotive force (EMF) of the cell?

(Given: $E^\circ_{\ce{Cr2O7^{2-}/Cr^{3+}}} = 1.33 \text{ V}$ , $\frac{2.303 RT}{F} = 0.06 \text{ V}$ at $298 \text{ K}$ )

Options

A.
$0.91 \text{ V}$
B.
$1.19 \text{ V}$
C.
$1.30 \text{ V}$
D.
$1.33 \text{ V}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Exception_Exposure

Learn to identify edge cases and boundary exceptions that JEE examiners hide in math problems.

Concepts Behind This Question

Degree of Dissociation (α) approximation|Dichromate-Chromate Equilibrium|Equivalent Concept in Redox

Why This Question Is Tricky

Common Mistakes

This problem tests the thermodynamic coupling between weak acid dissociation (ionic equilibrium) and the Nernstian potential shift of a highly pH-dependent redox couple.

The 'Hidden Variable' is the 14th power dependence on $[\ce{H+}]$ , which drastically shifts the effective oxidizing power of dichromate.

Common traps include: treating the weak acid as a strong acid ( $[\ce{H+}] = 0.1 \text{ M}$ leading to $1.19 \text{ V}$ ), forgetting the stoichiometric coefficient of 14 in the Nernst equation (leading to $1.30 \text{ V}$ ), or ignoring the non-standard pH entirely (leading to $1.33 \text{ V}$ ).

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Equilibrium - Class 11 Part 1
Concept	Degree of Dissociation (α) approximation
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free