Question

Identify the order of reaction if its rate constant is $x\ \mathrm{sec}^{-1}$.

• A. 3
• B. 2
• C. 0
• D. 1

Hint:

Whenever a rate constant is purely a function of time inverse ($\mathrm{s}^{-1}$ or $\mathrm{min}^{-1}$) with no concentration units present, it is always a first-order reaction. This is because the concentration units in the rate and the reactant concentration cancel out perfectly.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The problem asks to determine the overall kinetic order of a chemical reaction given that the unit of its rate constant ($k$) is expressed as $\mathrm{sec}^{-1}$ (or $\mathrm{s}^{-1}$).

Step 2: Key Formula or Approach:
The general mathematical formula for the units of a rate constant $k$ for an $n^{\text{th}}$-order reaction is given by: $$\text{Unit of } k = (\mathrm{mol\ dm}^{-3})^{1-n}\ \mathrm{s}^{-1}$$ Alternatively, this can be stated using molarity ($\mathrm{M}$): $$\text{Unit of } k = \mathrm{M}^{1-n}\ \mathrm{s}^{-1}$$ Where $n$ represents the overall order of the reaction.

Step 3: Detailed Explanation:
We are given that the unit of the rate constant is $\mathrm{sec}^{-1}$. Let's equate this to our general unit formula to solve for the parameter $n$: $$\mathrm{M}^{1-n}\ \mathrm{s}^{-1} = \mathrm{M}^0\ \mathrm{s}^{-1}$$ By comparing the exponents of the concentration term ($\mathrm{M}$): $$1 - n = 0$$ $$n = 1$$ Since $n = 1$, the reaction must follow first-order kinetics.

Step 4: Final Answer:
The order of the reaction is 1, which perfectly maps to option (D).