For the given first order reaction $A \rightarrow B$,the half-life of the reaction is $0.3010 \ min$. The ratio of the initial concentration of reactant to the concentration of reactant at time $2.0 \ min$ will be equal to $........$ (Nearest integer).

Decomposition of $A$ is a first order reaction at $T \ K$ and is given by $A_{(g)} \rightarrow B_{(g)} + C_{(g)}$. In a closed $1 \ L$ vessel, $1 \ bar$ of $A_{(g)}$ is allowed to decompose at $T \ K$. After $100 \ minutes$, the total pressure was $1.5 \ bar$. What is the rate constant (in $min^{-1}$) of the reaction? (Given: $\log 2 = 0.3$)

$10 \ g$ mixture of two gases $A_2$ (mol. wt. $= 20$) and $B_2$ (mol. wt. $= 30$),which decompose by first order kinetics,was taken in a vessel. The half-life of decomposition of $A_2$ and $B_2$ are $2 \ hours$ and $3 \ hours$ respectively. After $6 \ hours$,the weight of the mixture of $A_2$ and $B_2$ is found to be $2 \ g$. Find the weight of $A_2$ in the initial mixture in $g$.

The half-life period of a first-order reaction is $138.6 \ min$. The rate constant of the reaction is: (in $min^{-1}$)

$A$ reaction has a half-life of $1 \, \text{min}$. The time required for $99.9 \, \%$ completion of the reaction is ......... $\text{min}$. (Round off to the nearest integer)
[Use: $\ln 2 = 0.69, \ln 10 = 2.3$]

$A$ first order reaction is $10 \%$ completed in $20 \, \text{minutes}$. What will be the time for $19 \%$ completion of the reaction? (in $\text{min}$)