The rate constant of esterification is given by $k = k^{\prime} [H_2O]$. If the rate constant $k = 2.0 \times 10^{-3} \ min^{-1}$,calculate $k^{\prime}$. (Assume $[H_2O] = 55.5 \ mol \ L^{-1}$)

For the reaction:
$2NO_{2(g)} + O_{3(g)} \to N_2O_{5(g)} + O_{2(g)}$
The rate law is $R = K[NO_2]^1 [O_3]^1$.
Which of these possible reaction mechanisms is consistent with the rate law?
Mechanism $I$:
$NO_{2(g)} + O_{3(g)} \to NO_{3(g)} + O_{2(g)}$ (slow)
$NO_{3(g)} + NO_{2(g)} \to N_2O_{5(g)}$ (fast)
Mechanism $II$:
$O_{3(g)} \rightleftharpoons O_{2(g)} + [O]$ (fast)
$NO_{2(g)} + [O] \to NO_3$ (slow)
$NO_{3(g)} + NO_{2(g)} \to N_2O_5$ (fast)

Higher order $(> 3)$ reactions are rare due to:

For a second-order reaction,the rate constant is $8 \times 10^{-5} \, M^{-1} \, \text{min}^{-1}$. In how much time will a $1 \, M$ solution decrease to $0.5 \, M$?

For the reaction $2NO_{(g)} + O_{2_{(g)}} \rightarrow 2NO_{2_{(g)}}$,the volume of the reaction vessel is suddenly reduced to half of its original volume. If the reaction is first order with respect to $O_2$ and second order with respect to $NO$,the rate of the reaction will:

In the reaction $X \to Y$,if the concentration of reactant $X$ is increased by $1.5$ times,the rate of reaction increases by $1.837$ times. Determine the order of the reaction with respect to $X$.