If the rate constant for a first order reaction is $k$,then find the time required for completion of $80 \%$ of the reaction.

What is the half-life of a first-order reaction if the time required to decrease the concentration of the reactant from $0.4 \ M$ to $0.1 \ M$ is $x \ \text{hours}$?

$A \rightarrow$ products is a first-order reaction. The following data is obtained for this reaction at $T \ K$. The value of $x : y$ is:

Rate $(\text{mol } L^{-1} \ \text{min}^{-1})$	$[A]$
$0.2$	$0.02 \ M$
$0.4$	$x \ M$
$1.0$	$y \ M$

What is the half-life of a first order reaction if the time required to decrease the concentration of the reactant from $1.0 \ M$ to $0.25 \ M$ is $10 \ hours$ (in $hours$)?

The initial concentration of $N_2O_5$ in the following first order reaction $N_2O_{5(g)} \rightarrow 2NO_{2(g)} + 1/2O_{2(g)}$ was $1.24 \times 10^{-2} \, mol \, L^{-1}$ at $318 \, K$. The concentration of $N_2O_5$ after $60 \, minutes$ was $0.20 \times 10^{-2} \, mol \, L^{-1}$. Calculate the rate constant of the reaction at $318 \, K$.

Ethylene is produced by $C_4H_8 (\text{Cyclobutane}) \xrightarrow{\text{Heat}} 2C_2H_4$. The rate constant is $2.3 \times 10^{-4} \text{ s}^{-1}$. In what time will the molar ratio of ethylene to cyclobutane in the reaction mixture attain the value $1$? ...... $\text{min}$