The hydrolysis of an organic chloride in the presence of a large excess of water is given by: $R-Cl + H_2O \rightarrow R-OH + HCl$. Which of the following options is correct?

For the reaction $A \to \text{Products}$,the rate of reaction becomes one-fourth when the concentration of $A$ is halved. What is the order of the reaction?

Give the relation between half-life $(t_{1/2})$ and initial concentration of reactant $([R]_0)$ for an $(n-1)^{th}$ order reaction.

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)

For the reaction: $KClO_3 + 6FeSO_4 + 3H_2SO_4 \to KCl + 3Fe_2(SO_4)_3 + 3H_2O$. Determine if the following statement is True $(T)$ or False $(F)$: The reaction is elementary.

For the reaction $A + B \to \text{Product}$,the rate of reaction becomes four times when the concentration of $A$ is doubled. If the rate of reaction does not change when the concentration of $B$ is doubled,the rate law for the reaction will be.....