Question

For a reaction $2A+B\to P,$ when concentration of B alone is doubled, $t_{\frac{1}{2}}$ does not change and when concentrations of both A and B is doubled, rate increases by a factor of 4. The unit of rate constant is,

• A. $s^{-1}$
• B. $Lmo{l}^{-1}{s}^{-1}$
• C. $mol{L}^{-1}{s}^{-1}$
• D. $L^{2}mol{L}^{-2}{s}^{-1}$

Answer 1

The correct option is B $Lmo{l}^{-1}{s}^{-1}$

Given reaction is,
$2A+B\to P\therefore r=K\left[A{]}^2\right[B]$
For first order reaction, $t_{\frac{1}{2}}=\frac{0.693}{k}$
So $t_{\frac{1}{2}}$ does not depend on the concentration of the reactant for first order reaction.
Hence the order of the reaction with respect to $\left[B\right]$ is one.

Again since when concentrations of both A and B is doubled, rate increases by a factor of 4, so the the order of the reaction with respect to $\left[A\right]$ is also one.
Hence the overall order of the reaction is 2.

$\therefore$ the unit of rate constant is $Lmo{l}^{-1}{s}^{-1}$