Given below are two statements :

$$ \mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1} \text { and } 1 \mathrm{cal}=4.2 \mathrm{~J} $$

Statement I : When $\mathrm{Ea}=12.6 \mathrm{kcal} / \mathrm{mol}$, the room temperature rate constant is doubled by a $10^{\circ} \mathrm{C}$ increase in temperature ( 298 K to 308 K )

Statement II : For a first order reactions $\mathrm{A} \rightarrow \mathrm{B}$,

Here $[A]_0$ is the initial concentration of $A$ and $t_{1 / 2}$ is half life of reaction.

In the light of the above statements, choose the correct answer from the options given below :

First order gas phase reaction

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

$p_t=$ initial pressure of gas $\mathrm{A}, p_t=$ total pressure of the reaction mixture at time $t$

Expression of rate constant ( $k$ ) is

Consider the given graph showing variation of reactant concentration with time.

Three different reactions were started with identical initial concentration of reactants. Which of the following statement is correct?

Consider the first order reaction $\mathrm{R} \rightarrow \mathrm{P}$.

The fraction of molecules decomposed in the given first order reaction can be expressed as