Question

Identify unit of rate constant for first order reaction from the following.

• A. mol dm$^{-3}$ s$^{-1}$
• B. s$^{-1}$
• C. mol$^{-1}$ dm$^{3}$ s$^{-1}$
• D. mol dm$^{-3}$

Hint:

First-order rate constants are independent of concentration units; they only depend on time.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The units of the rate constant (\(k\)) depend on the overall order of the reaction (\(n\)).
The general unit for a reaction of order \(n\) is \((\text{concentration})^{1-n} \times \text{time}^{-1}\).
Step 2: Key Formula or Approach:
For order \(n\):
Unit of \(k = (\text{mol dm}^{-3})^{1-n} \text{ s}^{-1}\)
Step 3: Detailed Explanation:
For a first-order reaction, \(n = 1\).
Substitute \(n = 1\) into the general formula:
Unit of \(k = (\text{mol dm}^{-3})^{1-1} \text{ s}^{-1}\)
Unit of \(k = (\text{mol dm}^{-3})^{0} \text{ s}^{-1}\)
Since any non-zero value raised to the power 0 is 1:
Unit of \(k = 1 \times \text{s}^{-1} = \text{s}^{-1}\)

Let's analyze other options for clarity:
(A) is for zero-order (\(n=0\)).
(C) is for second-order (\(n=2\)).
Step 4: Final Answer:
The unit of the rate constant for a first-order reaction is \(\text{s}^{-1}\).