The reaction $2A \rightarrow 2B + C$ has a rate constant of $1.2 \times 10^{-2} \ s^{-1}$. Which of the following is correct?

$A$ and $B$ decompose via first order kinetics with half-lives $54.0 \, min$ and $18.0 \, min$ respectively. Starting from an equimolar non-reactive mixture of $A$ and $B$,the time taken for the concentration of $A$ to become $16$ times that of $B$ is ...... $min.$ (Round off to the Nearest Integer).

Regarding the half-life period of a first-order reaction,which one of the following statements is generally false?

For the first-order gaseous reaction $A \rightarrow 2B + C$ at $373 \, K$,starting with pure $A$,the total pressure of the system after $10 \, min$ is $176 \, mm \, Hg$ and after a long time,it is $270 \, mm \, Hg$. Based on this information,calculate: $(1)$ Initial pressure of $A$,$(2)$ Pressure of $A$ after $10 \, min$,and $(3)$ Rate constant.

For a first-order reaction,the ratio of the time required for $99.9\%$ completion to the time required for $50\%$ completion is:

Calculate the rate constant of a first order reaction if the half-life of the reaction is $40 \ minute$.