Calculate the half-life period of a first-order reaction if the rate constant of the reaction is $0.02 \ min^{-1}$. (in $min$)

The half-life of a first order reaction $X \to Y$ is $100 \ min$. The concentration of $X$ would be reduced to $10 \%$ of the initial concentration in .......... $min$.

For a first-order reaction,the time taken for the concentration of the reactant to reach $3/4$ of its initial value is $t_{1/4}$. If the rate constant for the reaction is $K$,then $t_{1/4}$ can be expressed as: (in $/K$)

For the decomposition of azoisopropane to hexane and nitrogen at $543 \ K,$ the following data are obtained.

$t \ (sec)$	$P \ (mm \ of \ Hg)$
$0$	$35.0$
$360$	$54.0$
$720$	$63.0$

Calculate the rate constant.

Calculate the half-life of a first order reaction from the rate constants given below:
$(i) \ 200 \ s^{-1}$
$(ii) \ 2 \ min^{-1}$
$(iii) \ 4 \ years^{-1}$

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. $(\log 2 = 0.30, \log 3 = 0.48, \log 4 = 0.60)$