Consider the following first order gas phase reaction at constant temperature $$ \mathrm{A}(\mathrm{g}) \rightarrow 2 \mathrm{B}(\mathrm{~g})+\mathrm{C}(\mathrm{g})$$

If the total pressure of the gases is found to be 200 torr after 23 $$\mathrm{sec}$$. and 300 torr upon the complete decomposition of A after a very long time, then the rate constant of the given reaction is ________ $$\times 10^{-2} \mathrm{~s}^{-1}$$ (nearest integer)

[Given : $$\log _{10}(2)=0.301$$]

Given below are two statements :

Statement I : The rate law for the reaction $$A+B \rightarrow C$$ is rate $$(r)=k[A]^2[B]$$. When the concentration of both $$\mathrm{A}$$ and $$\mathrm{B}$$ is doubled, the reaction rate is increased "$$x$$" times.

Statement II :

The figure is showing "the variation in concentration against time plot" for a "$$y$$" order reaction.

Consider the following reaction

$$\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}$$

The time taken for A to become $$1 / 4^{\text {th }}$$ of its initial concentration is twice the time taken to become $$1 / 2$$ of the same. Also, when the change of concentration of B is plotted against time, the resulting graph gives a straight line with a negative slope and a positive intercept on the concentration axis.

The overall order of the reaction is ________.

Consider the two different first order reactions given below

$$\begin{aligned} & \mathrm{A}+\mathrm{B} \rightarrow \mathrm{C} \text { (Reaction 1) } \\ & \mathrm{P} \rightarrow \mathrm{Q} \text { (Reaction 2) } \end{aligned}$$

The ratio of the half life of Reaction 1 : Reaction 2 is $$5: 2$$ If $$t_1$$ and $$t_2$$ represent the time taken to complete $$2 / 3^{\text {rd }}$$ and $$4 / 5^{\text {th }}$$ of Reaction 1 and Reaction 2 , respectively, then the value of the ratio $$t_1: t_2$$ is _________ $$\times 10^{-1}$$ (nearest integer). [Given : $$\log _{10}(3)=0.477$$ and $$\log _{10}(5)=0.699$$]