Question

The rate constant for the reaction, $2\text{N}_2\text{O}_{5(\text{g})} \longrightarrow 2\text{N}_2\text{O}_{4(\text{g})} + \text{O}_{2(\text{g})}$ is $4.98 \times 10^{-4} \text{ s}^{-1}$ . What is the order of reaction?

• A. 2
• B. 1
• C. Zero
• D. 3

Hint:

Unit of $k$ is $s^{-1}$? It's ALWAYS first order. Unit is $M^{-1}s^{-1}$? It's second order.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The kinetic order of a chemical reaction can be unequivocally determined solely by inspecting the units of its rate constant ($k$).
Step 2: Key Formula or Approach:
The general unit for the rate constant of an $n$-th order reaction is mathematically given by: \[ \text{Unit of } k = \left(\text{mol L}^{-1}\right)^{1-n} \text{s}^{-1} \] where $n$ represents the overall order of the reaction.
Step 3: Detailed Explanation:
The problem explicitly states that the rate constant is $k = 4.98 \times 10^{-4} \text{ s}^{-1}$. Notice carefully that the unit is simply $\text{s}^{-1}$ (inverse seconds), and it contains no concentration terms (neither $\text{mol}$ nor $\text{L}$). Let's logically equate the general unit formula to the given unit: \[ \left(\text{mol L}^{-1}\right)^{1-n} \text{s}^{-1} = \text{s}^{-1} \] For this equation to hold true algebraically, the exponent of the concentration term must be exactly zero, because any non-zero value raised to the power of 0 equals 1. \[ 1 - n = 0 \] Solving for $n$: \[ n = 1 \] Therefore, the reaction is a first-order reaction. The stoichiometry of the balanced equation ($2\text{N}_2\text{O}_5$) does not dictate the order, which is a purely experimentally determined quantity reflected accurately in the units of $k$.
Step 4: Final Answer:
The order of the reaction is 1.