Consider the reaction, $2A+B\to \text{Products}$. When concentration of $B$ alone was doubled, the half-life did not change. When the concentration of $A$ alone was doubled, the rate increased by two times. The unit of rate constant for this reaction is:

1. Effect of $B$: The half-life ($t_{1/2}$) of a first-order reaction is independent of initial concentration. Since doubling $[B]$ doesn't change $t_{1/2}$, the reaction is $1^{st}$ order with respect to $B$.Rate $\propto [B{]}^1$.2. Effect of $A$: Doubling $[A]$ doubles the rate, which means the rate is directly proportional to $[A]$. Thus, the reaction is $1^{st}$ order with respect to $A$.Rate $\propto [A{]}^1$.Overall rate law: $\text{Rate}=k[A{]}^1[B{]}^1$.Overall order = $1+1=2$.The unit for a $n^{th}$ order rate constant is $({\text{mol L}}^{-1}{)}^{1-n}{\text{s}}^{-1}$.For $n=2$: $({\text{mol L}}^{-1}{)}^{-1}{\text{s}}^{-1}={\text{L mol}}^{-1}{\text{s}}^{-1}$.