For a first order reaction $A \to$ product,the rate of reaction at $[A] = 0.2 \, mol \, L^{-1}$ is $1.0 \times 10^{-2} \, mol \, L^{-1} \, min^{-1}$. The half-life period for the reaction is .......... $min$.

The following data is obtained during the first order thermal decomposition of $2A_{(g)} \longrightarrow B_{(g)} + C_{(s)}$ at constant volume and temperature. The rate constant in $min^{-1}$ is:

$S$.No.	Time	Total pressure in Pascal
$1$.	At the end of $10 \ min$	$300$
$2$.	After completion	$200$

For a first-order reaction $A \rightarrow \text{Product}$,the rate of reaction is $1 \times 10^{-2} \, \text{mol L}^{-1} \text{min}^{-1}$ when $[A] = 0.2 \, \text{M}$. What is the half-life $(t_{1/2})$ of the reaction?

The decomposition of $N_2O_5$ is a first order reaction represented by $N_2O_5 \to N_2O_4 + \frac{1}{2} O_2$. After $15 \ min$,the volume of $O_2$ produced is $9 \ mL$ and at the end of the reaction,it is $35 \ mL$. The rate constant is equal to:

The reaction $X \rightarrow$ products is a first order reaction. In $40 \ min$,the concentration of $X$ changes from $1.0 \ M$ to $0.25 \ M$. What is the rate of reaction when $[X] = 0.1 \ M$? $(\log 4 = 0.60)$

$75\%$ of a first-order reaction was completed in $32 \text{ minutes}$. When was $50\%$ of the reaction completed? (in $\text{minutes}$)