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Question #44798

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The Question

The acid-catalyzed hydrolysis of ethyl ethanoate is studied in a mixed aqueous solvent system at $298 \text{ K}$ :

$\ce{CH3COOC2H5 (aq) + H2O (l) ->[H^+] CH3COOH (aq) + C2H5OH (aq)}$

The true rate law for the reaction is given by $\text{Rate} = k[\ce{CH3COOC2H5}][\ce{H2O}][\ce{H+}]$ .

The reaction is carried out with an initial ester concentration of $0.20 \text{ M}$ , a constant water concentration of $50 \text{ M}$ , and a constant $\text{pH}$ of $1.0$ . Under these conditions, the half-life of the reaction is found to be $693 \text{ s}$ ( $\ln 2 = 0.693$ ).

A student incorrectly assumes that because water is a reactant, its rate of disappearance follows the pseudo-first-order relation $-\frac{d[\ce{H2O}]}{dt} = k_{obs}[\ce{H2O}]$ .

Determine the true third-order rate constant $k$ and the actual rate of disappearance of water at $t = 1386 \text{ s}$ .

Options

A.
$2.0 \times 10^{-4} \text{ M}^{-2}\text{s}^{-1}$ and $5.0 \times 10^{-5} \text{ M s}^{-1}$
B.
$2.0 \times 10^{-5} \text{ M}^{-2}\text{s}^{-1}$ and $5.0 \times 10^{-2} \text{ M s}^{-1}$
C.
$2.0 \times 10^{-4} \text{ M}^{-2}\text{s}^{-1}$ and $2.0 \times 10^{-4} \text{ M s}^{-1}$
D.
$1.0 \times 10^{-3} \text{ M}^{-2}\text{s}^{-1}$ and $0 \text{ M s}^{-1}$

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Explanation

How the Examiner Thinks

Exception_Exposure

Learn to identify edge cases and boundary exceptions that JEE examiners hide in math problems.

Concepts Behind This Question

Stoichiometric Coefficient Division|Pseudo-First Order Kinetics

Why This Question Is Tricky

Common Mistakes

The question targets a profound misconception in pseudo-first-order kinetics: confusing the macroscopic constancy of a solvent's concentration with a zero rate of disappearance, or erroneously applying the pseudo-first-order rate constant to the solvent itself ( $-\frac{d[\ce{H2O}]}{dt} = k_{obs}[\ce{H2O}]$ ).

Because water is in large excess, its concentration is treated as constant for rate law integration, but it still strictly obeys the stoichiometric rate of disappearance dictated by the limiting reagent (the ester).

Additionally, it tests the ability to extract the true third-order rate constant by accounting for the hidden variable of catalyst concentration ( $[\ce{H+}]$ derived from pH).

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Chemical Kinetics - Class 12
Concept	Stoichiometric Coefficient Division
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free