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

Consider the reaction aX → bY, for which the rate constant at 30°C is $1 \times 10^{-3}\ \text{mol}^{-1}\ \text{L}\ \text{s}^{-1}$. Which of the following statements are true?

A. When concentration of ‘X’ is increased to four times, the rate of reaction becomes 16 times.

B. The reaction is a second order reaction.

C. The half-life period is independent of the concentration of X.

D. Decomposition of N$_2$O$_5$ is an example of the above reaction.

E. vs time is valid for the above reaction.

Choose the correct answer from the options given below: