Question

The SI unit of rate constant for a first order reaction is:

• A. \(mol\,L^{-1}s^{-1}\)
• B. \(s^{-1}\)
• C. \(L\,mol^{-1}s^{-1}\)
• D. \(mol^{-1}L\,s^{-1}\)

Hint:

For a first order reaction: \[ k = s^{-1} \] The unit depends only on reaction order, not on reaction mechanism.

Answer 1

The Correct Option is B

Concept: For a first order reaction: \[ \text{Rate} = k[A] \] The unit of rate constant depends on reaction order.

Step 1: Write units of rate and concentration. Units of rate: \[ mol\,L^{-1}s^{-1} \] Units of concentration: \[ mol\,L^{-1} \]

Step 2: Substitute into rate law. For first order: \[ k = \frac{\text{Rate}}{[A]} \] Thus: \[ k = \frac{mol\,L^{-1}s^{-1}} {mol\,L^{-1}} \] Cancelling concentration units: \[ k = s^{-1} \]

Step 3: Write final answer. Hence SI unit of first order rate constant is: \[ \boxed{s^{-1}} \] Therefore correct option is: \[ \boxed{(B)} \]