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Question #45068

Difficulty: 8/10 | 🟢 Free

The Question

The base-catalyzed hydrolysis of an ester $\ce{RCOOR'}$ is carried out in an aqueous buffer solution containing a weak acid $\ce{HA}$ ( $pK_a = 9.00$ ) and its sodium salt $\ce{NaA}$ at $298\text{ K}$ . The initial concentrations are $[\ce{Ester}]_0 = 0.10\text{ M}$ , $[\ce{HA}]_0 = 0.10\text{ M}$ , and $[\ce{NaA}]_0 = 0.10\text{ M}$ . The true second-order rate constant for the hydroxide-catalyzed hydrolysis is $k_{\ce{OH}} = 1.0 \times 10^2\text{ M}^{-1}\text{s}^{-1}$ .

Assume the hydrolysis goes to completion and the only base present in significant amount to catalyze the reaction is $\ce{OH-}$ . The carboxylic acid formed ( $\ce{RCOOH}$ , $pK_a \approx 4.8$ ) immediately and completely reacts with $\ce{A-}$ to form $\ce{HA}$ .

Calculate the time required for 50% hydrolysis of the ester. (Given: $\ln 2 = 0.693$ , $K_w = 1.0 \times 10^{-14}$ )

Options

A.
1307 s
B.
693 s
C.
1000 s
D.
886 s

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Numerical_Precision

Improve calculation stamina and avoid rounding errors in high-stakes competitive examinations.

Concepts Behind This Question

Acidity and Basicity (pKa/pKb)|Pseudo-First Order Kinetics

Why This Question Is Tricky

Common Mistakes

This problem tests the boundary of the pseudo-first-order approximation.

Students typically assume that in a buffered solution, the pH remains constant, leading to a constant $k_{obs}$ and a simple exponential decay ( $t_{1/2} = \ln 2 / k_{obs} = 693\text{ s}$ , which is a trap).

However, when the reactant concentration is comparable to the buffer capacity, the buffer is progressively exhausted.

The 'hidden variable' is the instantaneous $[\ce{OH-}]$ , which must be expressed as a function of the reaction progress variable $x$ .

This requires setting up a differential equation that couples chemical kinetics with dynamic buffer equilibrium.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Organic Chemistry – Some Basic Principles and Techniques - Class 11 Part 2
Concept	Acidity and Basicity (pKa/pKb)
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free