What is the relationship between the half-life period $(t_{1/2})$ and the initial concentration $([R]_0)$ for a reaction of order $n$?

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 $Cl_{2(aq)} + H_2S_{(aq)} \to S_{(s)} + 2H^{+}_{(aq)} + 2Cl^{-}_{(aq)}$,the rate law is $r = K[Cl_2][H_2S]$. Which of the following mechanisms is/are consistent with this rate law?
$A. \ H_2S \rightleftharpoons H^{+} + HS^{-}$ (fast)
$Cl_2 + HS^{-} \to 2Cl^{-} + H^{+} + S$ (slow)
$B. \ Cl_2 + H_2S \to H^{+} + Cl^{-} + Cl^{+} + HS^{-}$ (slow)
$Cl^{+} + HS^{-} \to H^{+} + Cl^{-} + S$ (fast)

If a reaction occurs in the following two steps:
$i) \ 2 ClO^{-} \rightarrow ClO_2^{-} + Cl^{-}$
$ii) \ ClO_2^{-} + ClO^{-} \rightarrow ClO_3^{-} + Cl^{-}$
Find the reaction intermediate.

$A$ chemical reaction takes place in two steps as follows:
$(i) \ NO_2Cl_{(g)} \xrightarrow{K_1} NO_{2(g)} + Cl_{(g)}$
$(ii) \ NO_2Cl_{(g)} + Cl_{(g)} \xrightarrow{K_2} NO_{2(g)} + Cl_{2(g)}$
Identify the reaction intermediate.

Why can’t molecularity of any reaction be equal to zero?