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Question #44515

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The Question

The acid-catalyzed hydrolysis of ethanoic anhydride in a non-ideal dioxane-water mixture follows second-order kinetics (first-order with respect to each reactant):

$\ce{(CH3CO)2O + H2O ->[H^+] 2CH3COOH}$

At $300\text{ K}$ , a reaction mixture is prepared with initial concentrations $[\ce{(CH3CO)2O}]_0 = 0.12\text{ M}$ and $[\ce{H2O}]_0 = 1.2\text{ M}$ . The initial rate law is expressed as $-\frac{d[\ce{(CH3CO)2O}]}{dt} = k_{\text{obs}}[\ce{(CH3CO)2O}]$ , where $k_{\text{obs}} = 3.6 \times 10^{-4}\text{ s}^{-1}$ .

An identical mixture (containing the same initial moles of all components) is reacted at $330\text{ K}$ . Due to the non-ideal nature of the solvent, heating from $300\text{ K}$ to $330\text{ K}$ causes a $20\%$ increase in the total volume of the solution.

Given that the activation energy for the true second-order rate constant is $E_a = 3300 R \ln(3)\text{ J mol}^{-1}$ (where $R$ is the universal gas constant), what is the initial rate of appearance of ethanoic acid at $330\text{ K}$ ?

Options

A.
$1.80 \times 10^{-4}\text{ M s}^{-1}$
B.
$9.00 \times 10^{-5}\text{ M s}^{-1}$
C.
$4.50 \times 10^{-5}\text{ M s}^{-1}$
D.
$2.59 \times 10^{-4}\text{ M s}^{-1}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Mechanism_Trap

Don't get tricked by the process! Learn the mechanical traps used in competitive exam questions.

Concepts Behind This Question

Concentration Units Dependency|Pseudo-First Order Kinetics|Stoichiometric Coefficient Division

Why This Question Is Tricky

Common Mistakes

This problem tests two major traps in chemical kinetics.

First, the 'Solvent Effect' trap: students often assume that the concentration of the solvent (water) remains constant across temperatures, failing to account for thermal volume expansion which dilutes all species and alters the effective molarity.

Second, the 'Stoichiometric Coefficient' trap: students frequently confuse the rate of reaction with the rate of appearance/disappearance, either forgetting to multiply by the stoichiometric coefficient of the product (yielding Option B) or erroneously dividing by it (yielding Option C).

By embedding a pseudo-first-order constant that must be unpacked into a true second-order constant, the problem forces the student to track the exact concentration of water rather than treating it as an immutable constant.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Solutions - Class 12
Concept	Concentration Units Dependency
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free