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Question #44887

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The Question

Unlike Tollens' reagent (which oxidizes both aldoses and ketoses) and Fehling's solution (which requires isomerizable sugars in alkaline media), Cr(VI) in an acidic buffer (pH = 3.0) at 298 K selectively oxidizes the $\beta$ -pyranose anomer of D-glucose to D-glucono- $\delta$ -lactone. The active oxidant is exclusively the monomeric acid chromate ion, \ce{HCrO4-}.

In a kinetic experiment, D-glucose is dissolved to a total concentration of $0.10 \text{ M}$ . It undergoes rapid mutarotation to reach an equilibrium between $\alpha$ and $\beta$ anomers with $K_{eq} = \frac{[\beta]}{[\alpha]} = 4.0$ .

The total analytical concentration of Cr(VI) added is $0.30 \text{ M}$ . The dimerization constant for the equilibrium $2\ce{HCrO4-} \rightleftharpoons \ce{Cr2O7^{2-}} + \ce{H2O}$ is $K_d = 50 \text{ M}^{-1}$ .

The rate law for the consumption of the active oxidant is given by: $-\frac{d[\ce{HCrO4-}]}{dt} = k[\beta\text{-anomer}][\ce{HCrO4-}]$ where $k = 1.2 \times 10^{-2} \text{ M}^{-1}\text{s}^{-1}$ .

Assuming the mutarotation equilibrium is maintained, what is the initial rate of formation of D-glucono- $\delta$ -lactone?

Options

A.
$7.2 \times 10^{-5} \text{ M s}^{-1}$
B.
$4.8 \times 10^{-5} \text{ M s}^{-1}$
C.
$2.88 \times 10^{-4} \text{ M s}^{-1}$
D.
$5.4 \times 10^{-4} \text{ M s}^{-1}$

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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

Dichromate-Chromate Equilibrium|Tollens vs. Fehling Specificity|Graphical Slopes Analysis

Why This Question Is Tricky

Common Mistakes

This problem tests three critical 'hidden variables' often overlooked by students: 1) The Speciation Kinetics Trap: Blindly using the total analytical concentration of a reagent ( $0.30$ M) instead of calculating the specific active species ( $\ce{HCrO4-}$ at $0.05$ M) via the dimerization equilibrium. 2) The Tautomeric Shift Trap: Failing to account for mutarotation and using the total sugar concentration instead of the specific reactive $\beta$ -anomer. 3) The Stoichiometric Rate Trap: Overlooking the stoichiometric coefficients linking the rate of disappearance of the oxidant (3-electron change per Cr) to the rate of appearance of the product (2-electron change per aldose).

Option B is the trap for forgetting stoichiometry, Option C ignores speciation, and Option D ignores both speciation and mutarotation.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	D and F Block Elements - Class 12
Concept	Dichromate-Chromate Equilibrium
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free