Consider a reaction, `2A + B rarr` 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 :

Options

A. `L mol^(-1)s^(-1)`
B. `s^(-1)`
C. `mol L^(-1)s^(-1)`
D. no unit

Answer

A

Explanation

Rate law is of the type
Rate `=k[A]^(x)[B]^(y)`
Order with respect to `B(y)` is `1` because the half life did not change, when the concentration of `B` alone was doubled and half-life is independent of the concentration of reactant only for first order reaction.
Order with resepect to `A(x)` is also `1` because the rate increases by two times, when the concentration of `A` alone was doubled. This is possible only when the concentration of `A` and rate are directly proportional to each other. Hence the overall order of reaction is `1+1=2` . The unit of rate constant are given as:
`(mol L^(-1))^(1-n)sec^(-1)`
Here `n=2` , thus, unit of `k` are `Lmol^(-1)s^(-1)`