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Question #44830

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The Question

The acid-catalyzed hydrolysis of methyl acetate in a dilute aqueous buffer at $300\text{ K}$ follows pseudo-first order kinetics with an observed rate constant $k_{obs} = 5.55 \times 10^{-4}\text{ s}^{-1}$ . The activation energy for the reaction is $E_a = 45.92\text{ kJ mol}^{-1}$ . Assuming the concentration of water remains constant at $55.5\text{ M}$ and the true rate law is $\text{Rate} = k_{true}[\ce{Ester}][\ce{H2O}]$ , calculate the true Arrhenius pre-exponential factor ( $A_{true}$ ) for the bimolecular reaction in SI units ( $\text{m}^3\text{ mol}^{-1}\text{ s}^{-1}$ ). (Given: $2.303 RT = 5.74\text{ kJ mol}^{-1}$ at $300\text{ K}$ )

Options

A.
$1\text{ m}^3\text{ mol}^{-1}\text{ s}^{-1}$
B.
$10^3\text{ m}^3\text{ mol}^{-1}\text{ s}^{-1}$
C.
$5.55 \times 10^4\text{ m}^3\text{ mol}^{-1}\text{ s}^{-1}$
D.
$10^6\text{ m}^3\text{ mol}^{-1}\text{ s}^{-1}$

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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

Arrhenius Pre-exponential Factor|Pseudo-First Order Kinetics

Why This Question Is Tricky

Common Mistakes

This problem tests two critical traps in chemical kinetics.

First, the 'Hidden Variable' trap: Students often treat the observed pre-exponential factor ( $A_{obs}$ ) in pseudo-first order reactions as an absolute constant, failing to realize that $A_{obs} = A_{true}[\ce{H2O}]$ .

Second, the 'Unit Conversion' trap: The requirement to convert the bimolecular rate constant from Molarity ( $\text{mol L}^{-1}$ ) to SI units ( $\text{mol m}^{-3}$ ) before extracting the pre-exponential factor.

A common error is using $1\text{ L} = 10^3\text{ m}^3$ or ignoring the conversion entirely, leading to incorrect orders of magnitude (Options B and D).

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Chemical Kinetics - Class 12
Concept	Arrhenius Pre-exponential Factor
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free