Question

Unit of rate constant of a first order reaction is —

• A. \( mol\ L^{-1}\ s^{-1} \)
• B. \( s^{-1} \)
• C. \( mol^{-1}\ L\ s^{-1} \)
• D. None of these

Hint:

Use unit = (mol L-1)^(1-n) s^-1 with n = 1; the concentration term cancels out.

Answer 1

The Correct Option is B

Step 1: For a reaction of order \(n\), the unit of the rate constant is \( (mol\ L^{-1})^{1-n}\ s^{-1} \).
Step 2: For a first order reaction, rate \(= k[A]\). Rearranging, \( k = \dfrac{\text{rate}}{[A]} \).
Step 3: Substitute the units: rate has units \( mol\ L^{-1}\ s^{-1} \) and concentration \([A]\) has units \( mol\ L^{-1} \).
\[ k = \frac{mol\ L^{-1}\ s^{-1}}{mol\ L^{-1}} = s^{-1} \]
Step 4: The concentration units cancel, leaving \( s^{-1} \).
Correct answer: (ii) \( s^{-1} \). Options (i) and (iii) are the units for zero and second order respectively.