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Question #45014

Difficulty: 8/10 | 🟢 Free

The Question

A galvanic cell is constructed at $298\text{ K}$ with the following representation:

$\ce{Co}(s) | \ce{Co^{2+}}(10^{-3}\text{ M}) || \ce{[Co(NH_3)_6]^{3+}}(0.1\text{ M}), \ce{[Co(NH_3)_6]^{2+}}(0.01\text{ M}), \ce{NH_3}(1\text{ M}) | Pt(s)$

Given the following standard thermodynamic and electrochemical data at $298\text{ K}$ : $E^\circ_{\ce{Co^{2+}/Co}} = -0.28\text{ V}$ $E^\circ_{\ce{Co^{3+}/Co^{2+}}} = +1.81\text{ V}$ Overall formation constant ( $\beta_6$ ) for $\ce{[Co(NH_3)_6]^{3+}} = 10^{35}$ Overall formation constant ( $\beta_6$ ) for $\ce{[Co(NH_3)_6]^{2+}} = 10^5$

Assuming $\frac{2.303RT}{F} = 0.06\text{ V}$ , calculate the electromotive force ( $E_{\text{cell}}$ ) of the cell.

Options

A.
+0.44 V
B.
+0.41 V
C.
+0.59 V
D.
+2.24 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

Half-Reaction Media Sensitivity|Nernstian Redox Equilibrium|E° (M²⁺/M) Anomalies

Why This Question Is Tricky

Common Mistakes

This problem tests the 'Coordination Equilibrium + Electrochemistry' trap.

Students often blindly use standard reduction potentials from tables ( $+1.81\text{ V}$ ) without accounting for how ligand coordination alters the free energy of the oxidized and reduced states differently.

The massive Crystal Field Stabilization Energy (CFSE) of the $d^6$ low-spin $\ce{Co^{3+}}$ complex makes its formation constant ( $10^{35}$ ) vastly larger than that of $\ce{Co^{2+}}$ ( $10^5$ ), drastically lowering the reduction potential from $+1.81\text{ V}$ to $+0.01\text{ V}$ .

Distractors target failures to square the complex concentrations in the reaction quotient $Q$ (Option B), forgetting the $n=2$ electron transfer in the Nernst equation (Option C), or completely ignoring the complexation thermodynamics (Option D).

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Redox Reactions - Class 11 Part 2
Concept	Half-Reaction Media Sensitivity
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free