The rate constant and half-life of a first-order reaction are related to each other as -

The first order reaction takes $20 \ min$ to complete $15\%$. How much time is required to complete $75\%$ of the reaction (in $min$)?

Two first order reactions have half-lives in the ratio $3 : 2$. Calculate the ratio of time intervals $t_1 : t_2$ if $t_1$ is the time period for $25\%$ completion of the first reaction and $t_2$ for $75\%$ completion of the second reaction. (in $: 1$)

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.

$N_2O_{(g)} \to N_{2(g)} + \frac{1}{2}O_{2(g)}$
In a closed vessel,the reaction follows first-order kinetics. If starting with pure $N_2O_{(g)}$,the total pressure after time $t$ is $P_t$ and after a very long time is $P_{\infty}$,then which of the following expressions is correct?

For an elementary reaction,$X_{(g)} \rightarrow Y_{(g)} + Z_{(g)}$,the $t_{1/2}$ is $10 \text{ minutes}$. In what period of time would the concentration of $X$ be reduced to $10 \%$ of its original concentration?