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Question #44240

Difficulty: 8/10 | 🟢 Free

The Question

Consider the following redox reaction at $298 \text{ K}$ :

$\ce{Ag+(aq) + Fe^{2+}(aq) \rightleftharpoons Ag(s) + Fe^{3+}(aq)}$

Given standard reduction potentials: $E^\circ_{\ce{Ag+/Ag}} = +0.80 \text{ V}$ and $E^\circ_{\ce{Fe^{3+}/Fe^{2+}}} = +0.77 \text{ V}$ . The initial concentrations of the aqueous species are $[\ce{Ag+}] = 10^{-2} \text{ M}$ , $[\ce{Fe^{2+}}] = 10^{-3} \text{ M}$ , and $[\ce{Fe^{3+}}] = 10^{-1} \text{ M}$ .

Assuming $\frac{2.303 RT}{F} = 0.06 \text{ V}$ and $F = 96500 \text{ C/mol}$ , determine the Gibbs free energy change ( $\Delta G$ ) for the reaction under these conditions and predict its spontaneity in the forward direction.

Options

A.
$+20.265 \text{ kJ/mol}$ , Non-spontaneous
B.
$-2.895 \text{ kJ/mol}$ , Spontaneous
C.
$-26.055 \text{ kJ/mol}$ , Spontaneous
D.
$-20.265 \text{ kJ/mol}$ , Spontaneous

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

Spontaneity Criteria|Electrode Potential Sign Conventions|Concentration Units Dependency

Why This Question Is Tricky

Common Mistakes

This problem tests the critical distinction between standard thermodynamic potential ( $E^\circ_{\text{cell}}$ ) and state-dependent potential ( $E_{\text{cell}}$ ).

Students often fall into the trap of predicting spontaneity solely based on a positive $E^\circ_{\text{cell}}$ (calculating $\Delta G^\circ = -2.895 \text{ kJ/mol}$ ).

However, spontaneity under specific conditions is dictated by $\Delta G = \Delta G^\circ + RT \ln Q$ .

When the reaction quotient $Q$ is sufficiently large ( $Q > K$ ), the concentration term dominates, making $E_{\text{cell}}$ negative and $\Delta G$ positive, thus reversing the direction of spontaneity.

Quick Facts About This Question

Question Information

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