Question

Write the unit of (i) second order reaction and (ii) zero order reaction.

Hint:

Master formula for $k$ units: $M^{1-n} \cdot Time^{-1}$ where M is Molarity ($mol~L^{-1}$) and $n$ is the order.

Answer 1

Step 1: Concept
Dimensional analysis of the rate constant ($k$) for different orders of reaction.

Step 2: Meaning
The general formula for the unit of a rate constant for an $n^{th}$ order reaction is $(mol~L^{-1})^{1-n} s^{-1}$.

Step 3: Analysis
(i) For a second order reaction, $n = 2$. Substituting this into the formula gives: $(mol~L^{-1})^{1-2} s^{-1} = (mol~L^{-1})^{-1} s^{-1} = L~mol^{-1}~s^{-1}$.
(ii) For a zero order reaction, $n = 0$. Substituting this into the formula gives: $(mol~L^{-1})^{1-0} s^{-1} = mol~L^{-1}~s^{-1}$.

Step 4: Conclusion
The units dynamically scale based on the concentration dependence of the rate law.

Final Answer:
(i) Second order reaction unit: $L~mol^{-1}~s^{-1}$
(ii) Zero order reaction unit: $mol~L^{-1}~s^{-1}$