Consider the reaction, $2 \mathrm{A}+\mathrm{B} \rightarrow$ Products When concentration of $\mathrm{B}$…
Consider the reaction,
$2 \mathrm{A}+\mathrm{B} \rightarrow$ Products
When concentration of $\mathrm{B}$ alone was doubled, the half-life did not change. When the concentration of $\mathrm{A}$ alone was doubled, the rate increased by two times. The unit of rate constant for this reaction is
$\mathrm{L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$
no unit
$\mathrm{mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$
$\mathrm{s}^{-1}$
Solution
$2 \mathrm{A}+\mathrm{B} \rightarrow$ Product
When conc. of $\mathrm{B}$ is doubled, the half life did not change, hence reaction is of first order w.r.t. $\mathrm{B}$.
When concentration of $\mathrm{A}$ is doubled, reaction rate is doubled, hence reaction is of first order w.r.t. $\mathrm{A}$.
Hence over all order of reaction is $1+1=2$
So, unit of rate constant $\mathrm{mol}^{-1} \mathrm{~lit~s}^{-1}$.
Hence, (A) is correct.