Rate Law Questions

The bromination of acetone that occurs in acid solution is represented by the equation ${\text{CH}}_3{\text{COCH}}_3+{\text{Br}}_2\stackrel{{\text{H}}^{+}}{\to }{\text{CH}}_3{\text{COCH}}_2\text{Br}+{\text{H}}^{+}+{\text{Br}}^{-}$. Based on kinetic data showing the rate is independent of $[{\text{Br}}_2]$, what is the rate equation?

In the reaction ${\text{BrO}}_3^{-}(aq)+5{\text{Br}}^{-}(aq)+6{\text{H}}^{+}\to 3{\text{Br}}_2(l)+3{\text{H}}_2\text{O}(l)$. The rate of appearance of bromine (${\text{Br}}_2$) is related to rate of disappearance of bromide ions as following:

For the reaction $A+B\to \text{products}$, it is observed that:(a) doubling the initial concentration of $A$ only, doubles the rate.(b) doubling the initial concentrations of both $A$ and $B$, there is a change by a factor of $8$ in the rate.The rate of this reaction is:

For the reaction $N_2{O}_5(g)\to 2N{O}_2(g)+\frac{1}{2}{O}_2(g)$ the value of rate of disappearance of $N_2{O}_5$ is given as $6.25\times 10^{-3}{\text{mol L}}^{-1}{\text{s}}^{-1}$. The rate of formation of $N{O}_2$ and $O_2$ is given respectively as:

During the kinetic study of the reaction $2A+B\to C+D$, the following results were obtained:| Run | $[A]$ (M) | $[B]$ (M) | Initial Rate (${\text{mol L}}^{-1}{\text{min}}^{-1}$) ||---|---|---|---|| I | $0.1$ | $0.1$ | $6.0\times 10^{-3}$ || II | $0.3$ | $0.2$ | $7.2\times 10^{-2}$ || III | $0.3$ | $0.4$ | $2.88\times 10^{-1}$ || IV | $0.4$ | $0.1$ | $2.40\times 10^{-2}$ |Based on the above data which one of the following is correct?

The rate of $2{\text{N}}_2{\text{O}}_5\to 4{\text{NO}}_2+{\text{O}}_2$ can be written as:$-\frac{d[{\text{N}}_2{\text{O}}_5]}{dt}=k[{\text{N}}_2{\text{O}}_5]$, $\frac{d[{\text{NO}}_2]}{dt}=k^{\prime }[{\text{N}}_2{\text{O}}_5]$, $\frac{d[{\text{O}}_2]}{dt}=k^{\prime \prime }[{\text{N}}_2{\text{O}}_5]$.The relationship between $k,k^{\prime },k^{\prime \prime }$ is:

In a reaction, $A+B\to \text{Product}$, rate is doubled when the concentration of $B$ is doubled, and rate increases by a factor of $8$ when the concentrations of both the reactants ($A$ and $B$) are doubled. The rate law for the reaction can be written as: