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Question #44811

Difficulty: 8/10 | 🟢 Free

The Question

The gas-phase decomposition of a volatile compound $\ce{A}$ follows first-order kinetics according to the balanced stoichiometric equation: $3 \ce{A}(g) \rightarrow 4 \ce{B}(g) + \ce{C}(g)$ The reaction is initiated at $400\text{ K}$ in a rigid, closed vessel containing pure $\ce{A}(g)$ at an initial pressure of $120\text{ torr}$ . After exactly $30\text{ minutes}$ , the total pressure inside the vessel is measured to be $160\text{ torr}$ . Assuming ideal gas behavior and that the rate of the reaction is defined as $r = -\frac{1}{3}\frac{d[\ce{A}]}{dt} = k[\ce{A}]$ , what is the rate constant of the reaction ( $k$ )?

Options

A.
$\frac{\ln 2}{90} \text{ min}^{-1}$
B.
$\frac{\ln 2}{30} \text{ min}^{-1}$
C.
$\frac{\ln 2}{10} \text{ min}^{-1}$
D.
$\frac{\ln (4/3)}{30} \text{ min}^{-1}$

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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

First Order Half-Life Independence|Stoichiometric Coefficient Division

Why This Question Is Tricky

Common Mistakes

This problem tests the rigid interpretation of the 'Rate of Reaction' versus the 'Rate of Disappearance'.

Students frequently calculate the observed rate constant ( $k_{obs}$ ) from the half-life of the reactant's decay ( $k_{obs} = \ln 2 / t_{1/2}$ ) but forget to divide by the stoichiometric coefficient ( $a=3$ ) to find the true rate constant of the reaction ( $k$ ).

This factor-of- $a$ error is a classic trap in advanced chemical kinetics, exploiting the difference between $-d[A]/dt$ and $-(1/a)d[A]/dt$ .

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Chemical Kinetics - Class 12
Concept	First Order Half-Life Independence
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free