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Question #44801

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The Question

Consider the acid-catalyzed hydrolysis of a Schiff base ( $\ce{S}$ ) in an aqueous buffer at 298 K, which proceeds via the following mechanism: $\ce{S + H+ <=>[K_a] SH+} \quad \text{(Fast equilibrium)}$ $\ce{SH+ + H2O ->[k_2] Products} \quad \text{(Slow, rate-determining)}$ where $K_a$ is the acid dissociation constant of the protonated imine ( $\ce{SH+}$ ), given as $1.0 \times 10^{-5} \text{ M}$ . The reaction follows pseudo-first order kinetics with respect to the total substrate concentration $[\ce{S}]_{total}$ , with an observed rate constant $k_{obs}$ . At a buffer pH of 5.0, $k_{obs} = 6.0 \times 10^{-4} \text{ s}^{-1}$ . Assuming the mechanism remains unchanged, what is the value of $k_{obs}$ at a buffer pH of 4.30? (Given: $\log 2 = 0.30$ )

Options

A.
$1.0 \times 10^{-3} \text{ s}^{-1}$
B.
$3.0 \times 10^{-3} \text{ s}^{-1}$
C.
$2.0 \times 10^{-4} \text{ s}^{-1}$
D.
$8.0 \times 10^{-4} \text{ s}^{-1}$

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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

Pseudo-First Order Kinetics|Schiff Base pH Dependence|Steady State Approximation

Why This Question Is Tricky

Common Mistakes

This problem tests the student's ability to move beyond the rote assumption that acid-catalyzed pseudo-first order rate constants ( $k_{obs}$ ) are directly proportional to $[\ce{H+}]$ .

In the hydrolysis of Schiff bases, the substrate itself acts as a weak base.

The active reacting species is the protonated imine ( $\ce{SH+}$ ).

As pH drops, the equilibrium shifts, and the concentration of $\ce{SH+}$ saturates as it approaches $[\ce{S}]_{total}$ .

Failing to account for this equilibrium partitioning leads to the erroneous assumption of a linear dependence of rate on $[\ce{H+}]$ , trapping students into simply multiplying the rate by the factor of $[\ce{H+}]$ increase (Option B), or incorrectly assuming the unprotonated species is the reactive one (Option C).

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