The following are the rate constants of two different reactions. Determine the overall order of reaction for each case:
$(a)$ $6.66 \times 10^{-3} \, s^{-1}$
$(b)$ $4.5 \times 10^{-2} \, mol^{-1} \, L \, s^{-1}$

(A) The order of a reaction can be determined from the units of the rate constant $(k)$.
The general unit for the rate constant is $(mol \, L^{-1})^{1-n} \, s^{-1}$,where $n$ is the order of the reaction.
For case $(a)$: The unit is $s^{-1}$. This corresponds to $(mol \, L^{-1})^{1-n} = 1$,which implies $1-n = 0$,so $n = 1$. Thus,it is a $1^{st}$ order reaction.
For case $(b)$: The unit is $mol^{-1} \, L \, s^{-1}$. This corresponds to $(mol \, L^{-1})^{1-n} = mol^{-1} \, L^1$. Comparing the exponents,$1-n = -1$,which implies $n = 2$. Thus,it is a $2^{nd}$ order reaction.