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Question #44817

Difficulty: 8/10 | 🟢 Free

The Question

The acid-catalyzed hydrolysis of an ester is a pseudo-first-order reaction in dilute aqueous solutions. In a highly dilute aqueous buffer, the pseudo-first-order rate constant is $k_0 = 6.0 \times 10^{-4} \text{ s}^{-1}$ at $298 \text{ K}$ . The same reaction is carried out at $298 \text{ K}$ in an aqueous solution containing $\frac{125}{9} \text{ mol kg}^{-1}$ of \ce{LiCl} (assuming complete dissociation). Assuming that the activity of water is equal to its mole fraction and the catalytic activity of the acid remains unchanged, what is the new pseudo-first-order rate constant, $k_{obs}$ ? (Molar mass of water = $18 \text{ g mol}^{-1}$ )

Options

A.
$4.0 \times 10^{-4} \text{ s}^{-1}$
B.
$4.8 \times 10^{-4} \text{ s}^{-1}$
C.
$2.0 \times 10^{-4} \text{ s}^{-1}$
D.
$6.0 \times 10^{-4} \text{ s}^{-1}$

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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

Rate Law Derivation from Mechanism|Pseudo-First Order Kinetics|Van’t Hoff Factor (i) Application

Why This Question Is Tricky

Common Mistakes

This problem tests the thermodynamic reality of pseudo-first-order kinetics.

Students often memorize that water concentration is constant and its activity is unity.

However, in highly concentrated solutions, the solvent's activity drops significantly.

Students must apply Raoult's Law (ideal solvent behavior) and the Van't Hoff factor ( $i=2$ for LiCl) to find the true mole fraction of water, which directly scales the pseudo-first-order rate constant.

The primary trap is forgetting the Van't Hoff factor when calculating the mole fraction of the solvent, leading to an incorrect activity of 0.8 instead of 0.667.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Chemical Kinetics - Class 12
Concept	Rate Law Derivation from Mechanism
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free