Medium
The following are the rate constants of two different reactions. What is the overall order of each reaction?
$(a)$ $2.1 \times 10^{-2} \ mol \ L^{-1} \ s^{-1}$
$(b)$ $4.5 \times 10^{-3} \ min^{-1}$
$(a)$ $2.1 \times 10^{-2} \ mol \ L^{-1} \ s^{-1}$
$(b)$ $4.5 \times 10^{-3} \ min^{-1}$
(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 $(a)$: The unit is $mol \ L^{-1} \ s^{-1}$.
Comparing this with $(mol \ L^{-1})^{1-n} \ s^{-1}$,we get $1-n = 1$,which implies $n = 0$. Thus,it is a $0^{th}$ order reaction.
For $(b)$: The unit is $min^{-1}$ (or $s^{-1}$).
Comparing this with $(mol \ L^{-1})^{1-n} \ s^{-1}$,we get $1-n = 0$,which implies $n = 1$. Thus,it is a $1^{st}$ order reaction.
The general unit for the rate constant is $(mol \ L^{-1})^{1-n} \ s^{-1}$,where $n$ is the order of the reaction.
For $(a)$: The unit is $mol \ L^{-1} \ s^{-1}$.
Comparing this with $(mol \ L^{-1})^{1-n} \ s^{-1}$,we get $1-n = 1$,which implies $n = 0$. Thus,it is a $0^{th}$ order reaction.
For $(b)$: The unit is $min^{-1}$ (or $s^{-1}$).
Comparing this with $(mol \ L^{-1})^{1-n} \ s^{-1}$,we get $1-n = 0$,which implies $n = 1$. Thus,it is a $1^{st}$ order reaction.
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