Identify True $(T)$ and False $(F)$ statements for the first order reaction $R \rightarrow P$ given below:
$I. \ k = \frac{1}{t} \ln \frac{[R]_0}{[R]}$
$II. \ k = \frac{1}{t} \ln \frac{[R]}{[R]_0}$

$A$ particular reaction has a rate constant $1.15 \times 10^{-3} \,s^{-1}$. How long does it take for $6 \,g$ of the reactant to reduce to $3 \,g$ (in $\,s$)? $(\log 2 = 0.301)$

Half life of a first order reaction is $3 \ minute$. What is the time required to reduce the concentration of reactant by $90 \%$ of its initial concentration?

The first order decomposition of $H_2O_2$ in an appropriate medium is characterised by a rate constant of $0.2303 \ min^{-1}$. What is the time (in $min$) required to complete $9/10$ fraction of the reaction?

The decomposition of substance $A$ follows first-order kinetics. Flask $I$ contains $1 \ L$ of $1 \ M$ solution of $A$,and flask $II$ contains $100 \ mL$ of $0.6 \ M$ solution of $A$. After $8 \ hours$,the concentration of $A$ in flask $I$ becomes $0.25 \ M$. How many hours will it take for the concentration of $A$ in flask $II$ to become $0.3 \ M$?

Consider a general first order reaction $A_{(g)} \rightarrow B_{(g)} + C_{(g)}$. If the initial pressure is $200 \ mm$ and after $20 \ minutes$ it is $250 \ mm$,then the half-life period of the reaction (in minutes) is. $(\log 2 = 0.30, \log 3 = 0.48, \log 4 = 0.60)$