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Question #44885

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The Question

Consider the following thermodynamic data at 298 K: (i) $\ce{Cr2O7^{2-} + 14H+ + 6e- -> 2Cr^{3+} + 7H2O} \quad E^\circ = 1.33 \text{ V}$ (ii) $\ce{2CrO4^{2-} + 2H+ <=> Cr2O7^{2-} + H2O} \quad K = 1.0 \times 10^{14}$ (iii) Solubility product of $\ce{Cr(OH)3(s)}$ , $K_{sp} = 1.0 \times 10^{-30}$ (iv) Ionic product of water, $K_w = 1.0 \times 10^{-14}$

Assuming $\frac{2.303 RT}{F} = 0.06 \text{ V}$ , calculate the standard reduction potential ( $E^\circ_{\text{basic}}$ ) for the following half-reaction in basic medium: $\ce{CrO4^{2-} + 4H2O + 3e- -> Cr(OH)3(s) + 5OH-}$

Options

A.
$-0.17 \text{ V}$
B.
$-0.31 \text{ V}$
C.
$+0.65 \text{ V}$
D.
$-0.45 \text{ V}$

Check Your Answer

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

KMnO₄ Redox pH Dependency|Dichromate-Chromate Equilibrium|Electrode Potential Dependencies

Why This Question Is Tricky

Common Mistakes

The problem tests the thermodynamic relationship between standard reduction potentials, complexation/dimerization equilibria, and solubility products.

The 'Hidden Variable' is the realization that the standard reduction potential of chromate ( $E^\circ_{\text{CrO}_4^{2-}}$ ) is not the same as dichromate ( $E^\circ_{\text{Cr}_2\text{O}_7^{2-}}$ ), despite both containing Cr(VI).

Students often erroneously use 1.33 V directly for the basic medium calculation, ignoring the $\ce{Cr2O7^{2-} <=> CrO4^{2-}}$ equilibrium which shifts the free energy by $0.84 F$ .

Furthermore, converting from acidic to basic medium requires accounting for both the $K_{sp}$ of $\ce{Cr(OH)3}$ and the autoionization of water ( $K_w$ ) to the 8th power, testing rigorous application of Hess's Law to free energies rather than blindly adding potentials.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	D and F Block Elements - Class 12
Concept	KMnO₄ Redox pH Dependency
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free