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Question #44364

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The Question

An aqueous solution of D-glucose at $298\text{ K}$ is at mutarotation equilibrium, consisting of $36\%$ $\alpha$ -D-glucopyranose and $64\%$ $\beta$ -D-glucopyranose (open-chain form $\approx 0.02\%$ ). At $t=0$ , a large excess of a trapping reagent is added. This reagent reacts instantaneously and irreversibly \textit{exclusively} with the open-chain aldehyde form of D-glucose. Let $k_\alpha$ and $k_\beta$ be the first-order rate constants for the ring-opening of the $\alpha$ and $\beta$ anomers, respectively, where $k_\alpha \neq k_\beta$ . Which of the following statements correctly describes the kinetic decay of the total unreacted cyclic glucose concentration, $[G]_{total}$ , and the evolution of the $\alpha/\beta$ ratio during the reaction?

Options

A.
$[G]_{total}$ decays as a biphasic function $[\alpha]_0 e^{-k_\alpha t} + [\beta]_0 e^{-k_\beta t}$ , and the $\alpha/\beta$ ratio changes continuously over time.
B.
$[G]_{total}$ decays as a single exponential function $([\alpha]_0 + [\beta]_0) e^{-k_{obs} t}$ where $k_{obs} = 0.36 k_\alpha + 0.64 k_\beta$ , maintaining a constant $\alpha/\beta$ ratio.
C.
$[G]_{total}$ decays following pseudo-zero-order kinetics because the concentration of the reactive open-chain intermediate is thermodynamically buffered at $0.02\%$ .
D.
$[G]_{total}$ decays as a single exponential function $([\alpha]_0 + [\beta]_0) e^{-(k_\alpha + k_\beta) t}$ , and the $\alpha/\beta$ ratio rapidly shifts to $1:1$ .

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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

Optical Activity and Enantiomers|D-Glucose Anomeric Equilibrium|Reducing Sugar Criteria

Why This Question Is Tricky

Common Mistakes

This question tests the 'Hidden Variable' of kinetic decoupling in a classic thermodynamic equilibrium.

Students memorize that mutarotation maintains an equilibrium ratio via Le Chatelier's principle and exhibits first-order kinetics.

The trap is assuming that the $\alpha$ and $\beta$ anomers remain in rapid pre-equilibrium when a reagent consumes the intermediate.

By irreversibly scavenging the open-chain form, the interconversion pathway is severed.

The anomers are forced into independent, parallel kinetic pathways, changing the macroscopic decay from a single exponential to a biphasic function and continuously altering the anomeric ratio.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Haloalkanes and Haloarenes - Class 12
Concept	Optical Activity and Enantiomers
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free