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Question #44818

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The Question

The electrophilic nitrosation of 4-pyridone ( $K$ ) at 298 K in an aqueous buffer proceeds exclusively via its minor enol tautomer, 4-hydroxypyridine ( $E$ ). The elementary steps are:

Step 1: $K \xrightarrow{k_1} E$ Step 2: $E \xrightarrow{k_{-1}} K$ Step 3: $E + NO^+ \xrightarrow{k_2} P + H^+$

The rate constants are given as: $k_1 = 1.0 \times 10^{-5} \text{ s}^{-1}$ $k_{-1} = 1.0 \times 10^2 \text{ s}^{-1}$ $k_2 = 5.0 \times 10^4 \text{ M}^{-1}\text{s}^{-1}$

Assuming the Steady-State Approximation (SSA) is applicable to the enol intermediate, calculate the initial rate of formation of product $P$ when the initial concentrations are $[K]_0 = 0.1 \text{ M}$ and $[NO^+]_0 = 2.0 \times 10^{-3} \text{ M}$ . Additionally, determine the limiting kinetic order of the reaction with respect to $[NO^+]$ at extremely high concentrations of $NO^+$ .

Options

A.
$5.0 \times 10^{-7} \text{ M s}^{-1}$ ; Zero order
B.
$1.0 \times 10^{-6} \text{ M s}^{-1}$ ; First order
C.
$5.0 \times 10^{-7} \text{ M s}^{-1}$ ; First order
D.
$1.0 \times 10^{-6} \text{ M s}^{-1}$ ; Zero order

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Mechanism_Trap

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Concepts Behind This Question

Steady State Approximation|Nitrogenous Base Keto-Enol Tautomerism|Chemical Kinetics

Why This Question Is Tricky

Common Mistakes

This problem tests the application of the Steady-State Approximation (SSA) to a tautomeric pre-equilibrium that is not strictly 'fast'.

Students often fall into the trap of assuming tautomerism is an instantaneous dynamic equilibrium ( $K_{eq} = [E]/[K]$ ), which leads to the incorrect rate law $v = K_{eq} k_2 [K][NO^+]$ (yielding $1.0 \times 10^{-6} \text{ M s}^{-1}$ , Option B).

By forcing the use of SSA, the student must recognize that the rate of the second step ( $k_2[NO^+]$ ) is comparable to the reverse tautomerization ( $k_{-1}$ ), causing a deviation from pure pre-equilibrium kinetics.

Furthermore, it tests the conceptual understanding of kinetic shifts: at high electrophile concentrations, the rate-determining step shifts entirely to the enolization process, resulting in zero-order dependence on the electrophile.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Chemical Kinetics - Class 12
Concept	Steady State Approximation
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free