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Question #44803

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The Question

The pseudo-first order hydrolysis of di-tert-butyl oxalate (DTBO) is carried out in an aqueous solution containing $0.25 \text{ M } \ce{HClO4}$ at $298 \text{ K}$ :

$\ce{(COOC(CH3)3)2 + 2H2O -> H2C2O4 + 2(CH3)3COH}$

The initial concentration of DTBO is $0.25 \text{ M}$ and its half-life is $20 \text{ min}$ . At $t = 20 \text{ min}$ , an aliquot of the reaction mixture is taken and titrated \textit{in situ} (without adding external acid) with a highly concentrated $\ce{KMnO4}$ solution. Assume the volume change during titration is negligible and tert-butanol is resistant to oxidation.

At the equivalence point, a faint pink color persists due to an unreacted $\ce{MnO4-}$ concentration of $5.0 \times 10^{-6} \text{ M}$ . Calculate the reduction potential of the $\ce{MnO4- / Mn^2+}$ half-cell in the titration flask at this equivalence point.

(Given: $E^\circ_{\ce{MnO4- / Mn^2+}} = 1.51 \text{ V}$ , $\frac{2.303 RT}{F} = 0.06 \text{ V}$ . Assume $\ce{H2C2O4}$ acts as a weak acid whose dissociation is completely suppressed by $\ce{HClO4}$ .)

Options

A.
$1.366 \text{ V}$
B.
$1.462 \text{ V}$
C.
$1.433 \text{ V}$
D.
$1.404 \text{ V}$

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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

Pseudo-First Order Kinetics|KMnO₄ Redox pH Dependency|Degree of Dissociation (Alpha)

Why This Question Is Tricky

Common Mistakes

This problem tests the intersection of chemical kinetics, redox stoichiometry, and electrochemistry.

The core trap lies in the Nernstian dependency of the $\ce{KMnO4}$ reduction potential on $[\ce{H+}]$ .

Students typically treat titrations as idealized processes where the indicator's environment remains constant (Option D assumes $[\ce{H+}]$ remains $0.25 \text{ M}$ ).

However, the oxidation of oxalic acid by permanganate actively consumes protons ( $\ce{6H+}$ per $\ce{5H2C2O4}$ ).

Failing to subtract the consumed $\ce{H+}$ from the $\ce{HClO4}$ -derived proton pool leads to an incorrect pH at the equivalence point.

Because $[\ce{H+}]$ is raised to the 8th power in the Nernst equation, overlooking this stoichiometric consumption drastically skews the calculated reduction potential.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Chemical Kinetics - Class 12
Concept	Pseudo-First Order Kinetics
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free