Fill in the blanks:
$(1)$ If $t_{1/2} = \frac{0.693}{k}$,then the order of reaction is .......... .
$(2)$ For a zero order reaction,$t_{1/2}$ is proportional to .......... of the initial concentration.
$(3)$ In a first order reaction,the rate of reaction is proportional to the .......... exponent of the concentration of the reactant.

Which of the following statements is correct?

If the half-life periods of a first-order reaction and a zero-order reaction are equal,then the ratio of the initial rates of the reactions will be .............

For the following reaction
$2X + Y \xrightarrow{i} P$
the rate of reaction is $\frac{d[P]}{dt} = k[X]$. Two moles of $X$ are mixed with one mole of $Y$ to make $1.0 \ L$ of solution. At $50 \ s$,$0.5 \ mole$ of $Y$ is left in the reaction mixture. The correct statement$(s)$ about the reaction is(are)
(Use: $\ln 2 = 0.693$)
$(A)$ The rate constant,$k$,of the reaction is $13.86 \times 10^{-4} \ s^{-1}$.
$(B)$ Half-life of $X$ is $50 \ s$.
$(C)$ At $50 \ s$,$-\frac{d[X]}{dt} = 13.86 \times 10^{-3} \ mol \ L^{-1} \ s^{-1}$.
$(D)$ At $100 \ s$,$-\frac{d[Y]}{dt} = 3.46 \times 10^{-3} \ mol \ L^{-1} \ s^{-1}$.

The reaction of ozone with oxygen atoms in the presence of chlorine atoms can occur by a two-step process shown below:
$O_{3(g)} + Cl_{(g)}^{\bullet} \to O_{2(g)} + ClO_{(g)}^{\bullet}$ ..... $(i)$ $K_i = 5.2 \times 10^9 \ L \ mol^{-1} \ s^{-1}$
$ClO_{(g)}^{\bullet} + O_{(g)}^{\bullet} \to O_{2(g)} + Cl_{(g)}^{\bullet}$ ..... $(ii)$ $K_{ii} = 2.6 \times 10^{10} \ L \ mol^{-1} \ s^{-1}$
The closest rate constant for the overall reaction
$O_{3(g)} + O_{(g)}^{\bullet} \to 2O_{2(g)}$ is ........... $L \ mol^{-1} \ s^{-1}$

The rate constant for the reaction $H_2 + I_2 \to 2HI$ is $k_1 = 49$. What is the rate constant for the reverse reaction $2HI \to H_2 + I_2$?