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Question #45031

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The Question

The standard reduction potential of the aqueous $Co^{3+}/Co^{2+}$ couple is $+1.81\text{ V}$ at $298\text{ K}$ . Upon the addition of excess aqueous ammonia, the complexes $[Co(NH_3)_6]^{3+}$ and $[Co(NH_3)_6]^{2+}$ are formed, with overall formation constants $\beta_6^{III} = 10^{34}$ and $\beta_6^{II} = 10^5$ , respectively. The dramatic difference in formation constants is primarily driven by Ligand Field Stabilization Energy (LFSE) compensation. Calculate the standard reduction potential ( $E^\circ$ ) for the $[Co(NH_3)_6]^{3+}/[Co(NH_3)_6]^{2+}$ half-cell. Additionally, identify the spin-only magnetic moments ( $\mu_{eff}$ ) of the oxidized and reduced ammine complexes, respectively. (Given: $\frac{2.303RT}{F} = 0.059\text{ V}$ )

Options

A.
$+0.10\text{ V};\ 0\text{ BM},\ 3.87\text{ BM}$
B.
$+3.52\text{ V};\ 0\text{ BM},\ 1.73\text{ BM}$
C.
$+0.10\text{ V};\ 0\text{ BM},\ 1.73\text{ BM}$
D.
$+3.52\text{ V};\ 4.90\text{ BM},\ 3.87\text{ BM}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Mechanism_Trap

Don't get tricked by the process! Learn the mechanical traps used in competitive exam questions.

Concepts Behind This Question

Complex Ion Oxidation States|Electrode Potential Dependencies

Why This Question Is Tricky

Common Mistakes

This problem tests the intersection of Electrochemistry and Coordination Chemistry.

The 'Hidden Variable' is the oxidation-state dependence of the spectrochemical series.

Students often memorize $NH_3$ as a strong-field ligand, erroneously assigning a low-spin state to $Co^{2+}$ ( $d^7$ , $\mu = 1.73\text{ BM}$ ).

However, $NH_3$ only provides sufficient crystal field splitting ( $\Delta_o > P$ ) for the higher-charged $Co^{3+}$ ion.

Furthermore, the problem traps students who fail to recognize that the massive LFSE gain in forming the low-spin $d^6$ complex thermodynamically stabilizes the $+3$ state, drastically lowering the reduction potential from $+1.81\text{ V}$ to $+0.10\text{ V}$ .

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Redox Reactions - Class 11 Part 2
Concept	Complex Ion Oxidation States
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free