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Question #44212

Difficulty: 8/10 | 🟢 Free

The Question

An electrochemical cell is constructed at 298 K:

\ce{Pt(s) | I^- (0.1 M) | I_2(s) || Fe^{2+} (0.1 M), Fe(OH)_3(s) | Pt(s)}

The right half-cell is buffered at $\text{pH} = 3.0$ .

Given: $E^\circ_{\ce{Fe^{3+}/Fe^{2+}}} = 0.77\text{ V}$ $E^\circ_{\ce{I_2/I^-}} = 0.53\text{ V}$ $K_{sp}(\ce{Fe(OH)_3}) = 10^{-38}$ $\frac{2.303 RT}{F} = 0.06\text{ V}$ $1\text{ F} = 96500\text{ C/mol}$

Calculate the cell potential ( $E_{cell}$ ) and the Gibbs free energy change ( $\Delta G$ ) for the cell reaction as written: \ce{2 Fe^{3+}(aq) + 2 I^-(aq) -> 2 Fe^{2+}(aq) + I_2(s)}

Options

A.
$E_{cell} = -0.06\text{ V}, \Delta G = +11.58\text{ kJ/mol}$
B.
$E_{cell} = +0.06\text{ V}, \Delta G = -11.58\text{ kJ/mol}$
C.
$E_{cell} = +0.54\text{ V}, \Delta G = -104.22\text{ kJ/mol}$
D.
$E_{cell} = -0.06\text{ V}, \Delta G = +5.79\text{ kJ/mol}$

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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

IUPAC Sign Convention|Reaction Quotient vs. Equilibrium Constant|Nernstian Redox Equilibrium

Why This Question Is Tricky

Common Mistakes

This problem tests the integration of solubility equilibria with Nernstian redox systems and the IUPAC sign convention.

The primary trap is the cognitive dissonance of a negative cell potential: students often assume galvanic cells must have $E_{cell} > 0$ and artificially invert the sign (Option B).

Furthermore, the reaction quotient $Q$ ( $10^{10}$ ) heavily exceeds the equilibrium constant $K$ ( $10^8$ ), driving the reaction non-spontaneously in the forward direction.

A secondary trap involves the stoichiometry of the free energy calculation: failing to recognize that the balanced equation provided requires $n=2$ electrons leads to a halved $\Delta G$ value (Option D).

Finally, incorrectly formulating the reaction quotient leads to Option C.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Thermodynamics - Class 11 Part 1
Concept	IUPAC Sign Convention
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free