Reactant A converts to product D through the given mechanism (with the net evolution of heat):

A → B     slow;     ΔH = +ve

B → C     fast;     ΔH = -ve

C → D     fast;     ΔH = -ve

Which of the following represents the above reaction mechanism?

Drug $X$ becomes ineffective after $50 \%$ decomposition. The original concentration of drug in a bottle was $16 \mathrm{mg} / \mathrm{mL}$ which becomes $4 \mathrm{mg} / \mathrm{mL}$ in 12 months. The expiry time of the drug in months is _________.

Assume that the decomposition of the drug follows first order kinetics.

The reaction $A_2 + B_2 \rightarrow 2AB$ follows the mechanism:

$A_2 \overset{k_1}{\underset{k_{-1}}{\rightleftharpoons}} A + A$ (fast)

$A + B_2 \xrightarrow{k_2} AB + B$ (slow)

$A + B \rightarrow AB$ (fast)

The overall order of the reaction is:

Consider an elementary reaction

$$ \mathrm{A}(\mathrm{~g})+\mathrm{B}(\mathrm{~g}) \rightarrow \mathrm{C}(\mathrm{~g})+\mathrm{D}(\mathrm{~g}) $$

If the volume of reaction mixture is suddenly reduced to $\frac{1}{3}$ of its initial volume, the reaction rate will become ' $x^{\prime}$ times of the original reaction rate. The value of $x$ is :