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: Use the general formula for the unit of a rate constant, \( (concentration)^{1-n}(time)^{-1} \), where \(n\) is the order.
Step 2: Put \(n = 1\) for a first order reaction: \( (mol\ L^{-1})^{1-1}(s)^{-1} = (mol\ L^{-1})^{0}\,s^{-1} \).
Step 3: Anything raised to power zero equals 1, so the concentration term disappears completely and only the time term survives.
Step 4: Hence the unit is simply \( s^{-1} \) (or \( min^{-1} \)), which is why the half-life of a first order reaction is independent of the starting concentration.
\[\boxed{k_{first\ order}=s^{-1}}\]