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Question #44860

Difficulty: 8/10 | 🟢 Free

The Question

Consider the hexaaqua complexes of \ce{Cr^{3+}}, \ce{Cr^{2+}}, \ce{Mn^{3+}}, and \ce{Mn^{2+}} in an aqueous medium at 298 K298\text{ K}. The standard reduction potentials are E∘(\ceCr3+/\ceCr2+)=−0.41 VE^\circ(\ce{Cr^{3+}}/\ce{Cr^{2+}}) = -0.41\text{ V} and E∘(\ceMn3+/\ceMn2+)=+1.57 VE^\circ(\ce{Mn^{3+}}/\ce{Mn^{2+}}) = +1.57\text{ V}.

Let PP = Magnitude of the Crystal Field Stabilization Energy (CFSE) in units of Δo\Delta_o (ignoring pairing energy) for the +3+3 hexaaqua complex that corresponds to the more negative E∘(M3+/M2+)E^\circ(M^{3+}/M^{2+}) value. Let QQ = Total number of unpaired electrons in the ground state of the +3+3 hexaaqua complex that corresponds to the highly positive E∘(M3+/M2+)E^\circ(M^{3+}/M^{2+}) value. Let RR = Number of complexes among the four mentioned above that experience strong Jahn-Teller distortion. Let SS = Number of dd-electrons in the metal ion of the complex that acts as the strongest reducing agent among the four. Let TT = Number of dd-electrons in the metal ion of the complex that acts as the strongest oxidizing agent among the four.

Calculate the value of the expression: (P×10)+(Q×R)+(S×T)(P \times 10) + (Q \times R) + (S \times T).

Options

  • A.

    36

  • B.

    30

  • C.

    32

  • D.

    35

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Exception_Exposure

Learn to identify edge cases and boundary exceptions that JEE examiners hide in math problems.

Concepts Behind This Question

E° (M³⁺/M²⁺) Redox Potential|Magnetic Moment Quenching|Color and d-d Transitions

Why This Question Is Tricky

Common Mistakes

The question tests the thermodynamic drivers behind the anomalous E∘(M3+/M2+)E^\circ(M^{3+}/M^{2+}) values for Cr and Mn.

Students often fall into the 'Magnetic Quenching Trap', assuming that the high reduction potential of \ce{Mn^{3+}} implies a low-spin state (t2g4t_{2g}^4) to justify its instability.

In reality, \ce{[Mn(H2O)6]^{3+}} is high-spin (t2g3eg1t_{2g}^3 e_g^1) and its high E∘E^\circ is driven by the massive 3rd ionization energy required to break the d5d^5 exchange energy of \ce{Mn^{2+}}.

Furthermore, the question rigorously tests the conditions for strong Jahn-Teller distortion (asymmetric ege_g filling) and the identification of redox agents based on dd-electron configurations.

Quick Facts About This Question

Question Information

SubjectChemistry
ChapterD and F Block Elements - Class 12
ConceptE° (M³⁺/M²⁺) Redox Potential
Difficulty8
Cognitive Load7
Target Solve Time160 sec
AccessFree