$\mathrm{A \rightarrow B}$

The molecule A changes into its isomeric form B by following a first order kinetics at a temperature of 1000 K . If the energy barrier with respect to reactant energy for such isomeric transformation is $191.48 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and the frequency factor is $10^{20}$, the time required for $50 \%$ molecules of A to become B is __________ picoseconds (nearest integer). $\left[\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right]$

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 ________.