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Question #44847

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The Question

An aqueous solution of benzenediazonium sulfate, $\ce{(C6H5N2)2SO4}$ , has an initial concentration of $0.05 \text{ M}$ . In the presence of a specific catalyst at $300 \text{ K}$ , it undergoes a zero-order decomposition:

$\ce{(C6H5N2)2SO4 (aq) + 2 H2O (l) \rightarrow 2 C6H5OH (aq) + 2 N2 (g) ^ + 2 H+ (aq) + SO4^{2-} (aq)}$

Assume phenol ( $\ce{C6H5OH}$ ) remains completely unionized, $\ce{N2}$ gas escapes completely, and all strong electrolytes are completely dissociated. The osmotic pressure of the solution is observed to increase at a constant rate of $0.1476 \text{ atm min}^{-1}$ . Calculate the zero-order rate constant $k$ for the decomposition of benzenediazonium sulfate.

(Given: $R = 0.082 \text{ L atm K}^{-1} \text{ mol}^{-1}$ )

Options

A.
$3.0 \times 10^{-3} \text{ mol L}^{-1} \text{ min}^{-1}$
B.
$6.0 \times 10^{-3} \text{ mol L}^{-1} \text{ min}^{-1}$
C.
$2.0 \times 10^{-3} \text{ mol L}^{-1} \text{ min}^{-1}$
D.
$1.2 \times 10^{-3} \text{ mol L}^{-1} \text{ min}^{-1}$

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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

Units of Rate Constant (k)|Zero Order Rate Integration|Molecular Mass Abnormalities

Why This Question Is Tricky

Common Mistakes

This problem tests the intersection of colligative properties and chemical kinetics.

The core trap involves how students handle the rate of change of a colligative property when the number of particles changes during a zero-order reaction.

Students typically memorize $\pi = iCRT$ and might erroneously apply $\frac{d\pi}{dt} = i_{initial}RTk$ (leading to Option C) or ignore the van't Hoff factor entirely $\frac{d\pi}{dt} = RTk$ (leading to Option B).

The hidden variable is the 'differential particle flux' ( $\Delta n$ ).

Because the reaction is zero-order, the rate of change of osmotic pressure depends strictly on the net difference in the number of dissolved particles between products and reactants ( $\Delta n = +2$ ), not the absolute initial or final van't Hoff factors.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Chemical Kinetics - Class 12
Concept	Units of Rate Constant (k)
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free