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Question #45022

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The Question

The standard electrode potentials ( $E^\circ_{\ce{M^{3+}/M^{2+}}}$ ) for the first-row transition metals exhibit significant deviations from a smooth periodic trend. Notably, $E^\circ_{\ce{Cr^{3+}/Cr^{2+}}} = -0.41\text{ V}$ while $E^\circ_{\ce{V^{3+}/V^{2+}}} = -0.26\text{ V}$ , and $E^\circ_{\ce{Mn^{3+}/Mn^{2+}}} = +1.57\text{ V}$ . Consider a redox titration in an acidic aqueous medium (pH = 0) at 298 K, where a deep purple oxoanion $P$ of a 3d metal is reduced by the aqua complex of $\ce{Cr^{2+}}$ . Based on Crystal Field Theory (CFT) and thermodynamic principles, which of the following statements is CORRECT?

Options

A.
The intense color of $P$ is due to a Laporte-forbidden $d-d$ transition, and $\ce{Cr^{2+}}$ is a stronger reducing agent than $\ce{V^{2+}}$ because the oxidation to $\ce{Cr^{3+}}$ maximizes exchange energy.
B.
The high positive $E^\circ_{\ce{Mn^{3+}/Mn^{2+}}}$ is primarily driven by the high Crystal Field Stabilization Energy (CFSE) of the resulting $\ce{Mn^{2+}}$ aqua complex, while $P$ exhibits Metal-to-Ligand Charge Transfer (MLCT).
C.
The anomalous reducing power of $\ce{Cr^{2+}}$ over $\ce{V^{2+}}$ is driven by the high CFSE ( $-1.2 \Delta_o$ ) of the $t_{2g}^3$ configuration of $\ce{Cr^{3+}}$ , while the color of $P$ originates from an allowed $\ce{O}(2p) \rightarrow \ce{Mn}(3d)$ Ligand-to-Metal Charge Transfer (LMCT).
D.
The reduction of $P$ yields a $d^5$ complex with a CFSE of $-2.0 \Delta_o$ , and the $E^\circ_{\ce{Cr^{3+}/Cr^{2+}}}$ is negative because the third ionization enthalpy of $\ce{Cr}$ is lower than that of $\ce{V}$ .

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How the Examiner Thinks

Mechanism_Trap

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Concepts Behind This Question

Electrode Potential Sign Conventions|Variable Oxidation State Stability|Color and Charge Transfer

Why This Question Is Tricky

Common Mistakes

This question tests the intersection of thermodynamic cycles, Crystal Field Theory (CFT), and spectroscopy.

The primary trap is the assumption that periodic trends in electrode potentials strictly follow ionization energies or simple exchange energy rules.

Students often incorrectly assume $\ce{Cr^{2+}}$ oxidizes to $\ce{Cr^{3+}}$ to gain exchange energy (it actually loses exchange energy: $d^4$ has 6 pairs, $d^3$ has 3 pairs).

The 'Hidden Variable' is that the exceptional stability of $\ce{Cr^{3+}}$ in aqueous solution is dictated by the CFSE of the $t_{2g}^3$ configuration ( $-1.2 \Delta_o$ ), which overrides its higher third ionization energy compared to Vanadium.

Additionally, it tests the common misconception that all transition metal colors are $d-d$ transitions, requiring the identification of LMCT in the $d^0$ $\ce{MnO4^-}$ complex.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Redox Reactions - Class 11 Part 2
Concept	Electrode Potential Sign Conventions
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free