Before You Begin

Question #44654

Difficulty: 8/10 | 🟢 Free

The Question

A zero-order reaction $\ce{A(aq) -> Products(aq)}$ occurs in a liquid solvent at $298 \text{ K}$ . The initial molality of reactant A is $2.5 \text{ m}$ . After $60 \text{ min}$ , the molality of A decreases to $0.7 \text{ m}$ . The density of the solution remains constant at $1.25 \text{ g mL}^{-1}$ throughout the reaction, and all products remain dissolved in the solution. Given that the molar mass of A is $200 \text{ g mol}^{-1}$ , calculate the rate constant $k$ of the reaction.

Options

A.
$0.025 \text{ mol L}^{-1} \text{ min}^{-1}$
B.
$0.030 \text{ mol L}^{-1} \text{ min}^{-1}$
C.
$0.022 \text{ mol L}^{-1} \text{ min}^{-1}$
D.
$0.038 \text{ mol L}^{-1} \text{ min}^{-1}$

Check Your Answer

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

Dimensional Consistency of Constants|Zero Order Rate Integration|Concentration Units Dependency

Why This Question Is Tricky

Common Mistakes

The problem tests the dimensional consistency of the zero-order rate constant and the physical meaning of concentration units.

Students often memorize the molality-to-molarity conversion formula $C = \frac{1000 \cdot m \cdot \rho}{1000 + m \cdot M_A}$ and apply it blindly at time $t$ .

However, this formula assumes a binary solution (only solvent and solute A).

As the reaction progresses, products form and contribute to the total mass of the solution.

Because the reaction occurs in a closed system, the total mass and volume of the solution remain constant.

The correct approach requires normalizing the moles of A against the constant initial total volume, rather than the hypothetical volume of a solution containing only the remaining A.

Failing to account for this 'hidden variable' (the mass of the products) leads to an incorrect final molarity and rate constant.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Some Basic Concepts of Chemistry - Class 11 Part 1
Concept	Dimensional Consistency of Constants
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free