The rate law for the dimerisation of ${\mathrm{NO}}_2$ into ${\mathrm{N}}_2{\mathrm{O}}_4$ is $-\frac{\mathrm{d}\left[{\mathrm{NO}}_2\right]}{\mathrm{dt}}=\mathrm{k}{\left[{\mathrm{NO}}_2\right]}^2$
Which of the following changes will change the value of the specific rate constant $\mathrm{k}?$

The order of a reaction $\mathrm{A}\to$ product in which half the reagent is reacted is half an hour, three quarters in one hour and seven - eighth in one and half hours is

${\mathrm{S}}_1:$ The frequency factor has the same unit as the rate constant, $\mathrm{K}$.

${\mathrm{S}}_2:$ A plot $\mathrm{\ell n}$ rate vs $\mathrm{\ell n} \mathrm{C}$ for the $\mathrm{nth}$ order reaction gives a straight line with stope $-\mathrm{n}$ intercept ${\mathrm{k}}_{\mathrm{n}}$ in.

${\mathrm{S}}_3:$ The order of a reaction $\mathrm{A}\to$ product in which half the reagent is reacted in half an hour, three quarters in one hour and seven - eighth in one and half hours must be $1$ (unity).

${\mathrm{S}}_4:$ The unit of rate constant for a second order reaction will be ${\mathrm{M}}^{-1}{\mathrm{s}}^{-1}.( \mathrm{M}$ is representing the molarity of solution.)

For the reaction

$2\mathrm{NO}+{\mathrm{Br}}_2⟶2\mathrm{NOBr}$

the following mechanism has been given

$\mathrm{NO}+{\mathrm{Br}}_2\stackrel{fast}{\rightleftharpoons }{\mathrm{NOBr}}_2$

${\mathrm{NOBr}}_2+\mathrm{NO}\stackrel{\mathrm{sl}ow}{⟶}2\mathrm{NOBr}$

Hence, rate law is:

In the reaction $2\mathrm{A}+\mathrm{B}⟶$ Products, the order with respect to $\mathrm{A}$ is found to be one and with respect to $\mathrm{B}$ equal to $2$. Concentration of $\mathrm{A}$ is doubled and that of $\mathrm{B}$ is halved, the rate

of reaction will be