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 initial rates of decrease of $I_2$ in acetone-iodine reaction catalysed by $H^{+}$ are given in the table.

Experiment	Initial $[I_2]$ $(mol \ L^{-1})$	Initial $[H^{+}]$ $(mol \ L^{-1})$	Initial $[CH_3COCH_3]$ $(mol \ L^{-1})$	Initial rate $(mol \ L^{-1} \ s^{-1})$
$1$	$0.01$	$0.1$	$0.1$	$0.096$
$2$	$0.01$	$0.2$	$0.1$	$0.192$
$3$	$0.02$	$0.2$	$0.1$	$0.192$
$4$	$0.01$	$0.2$	$0.2$	$0.384$

The order with respect to $I_2, H^{+}$,acetone and total order of the reaction respectively are:

If $r = k[A]^2[B]$ is the rate law equation for the reaction $A + B \rightarrow C$,at $[A] = 1 \ M$ and $[B] = 0.2 \ M$,calculate the rate of reaction if the rate constant is $6.25 \ M^{-2} \ s^{-1}$. (in $M \ s^{-1}$)

Why is the hydrolysis of an ester slow at the beginning and fast after some time?

$Zn + 2H^{+} \to Zn^{2+} + H_2$
The half-life period is independent of the concentration of zinc at constant $pH$. For the constant concentration of $Zn$,the rate becomes $100$ times when $pH$ is decreased from $3$ to $2$. Identify the correct statements $(pH = -\log [H^{+}])$:
$(A)$ $\frac{dx}{dt} = k[Zn]^0[H^{+}]^2$
$(B)$ $\frac{dx}{dt} = k[Zn][H^{+}]^2$
$(C)$ Rate is not affected if the concentration of zinc is made four times and that of $H^{+}$ ion is halved.
$(D)$ Rate becomes four times if the concentration of $H^{+}$ ion is doubled at constant $Zn$ concentration.

The given data are for the reaction:
$2NO_{(g)} + Cl_{2(g)} \to 2NOCl_{(g)}$ at $298 \ K$

Experiment	$[Cl_2] \ (M)$	$[NO] \ (M)$	Rate $(mol \ L^{-1} \sec^{-1})$
$I$	$0.05$	$0.05$	$1 \times 10^{-3}$
$II$	$0.15$	$0.05$	$3 \times 10^{-3}$
$III$	$0.05$	$0.15$	$9 \times 10^{-3}$

The rate law for the reaction is: