For a first order reaction $A \to B$,the reaction rate at reactant concentration of $0.01 \ M$ is found to be $2.0 \times 10^{-5} \ mol \ L^{-1} \ s^{-1}$. The half-life period of the reaction is .......... $sec$.

For a first order gas phase reaction:
$A_{(g)} \rightarrow 2 B_{(g)} + C_{(g)}$
Let $P_0$ be the initial pressure of $A$ and $P_t$ be the total pressure at time $t$. The integrated rate equation is:

Which of the following represents the integrated rate law equation for the gas-phase first-order reaction,$A_{(g)} \rightarrow B_{(g)} + C_{(g)}$? If $P_{i}$ is the initial pressure of $A$ and $P$ is the total pressure of the reaction mixture at time $t$.

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 $1$? ...... $\text{min}$

The half-life for the first-order reaction $N_2O_5 \to 2NO_2 + \frac{1}{2} O_2$ is $2.4 \text{ hours}$. Starting with $10.8 \text{ g}$ of $N_2O_5$ at $STP$,how many liters of oxygen will be obtained after a period of $9.6 \text{ hours}$? (Given: $10^{0.2} = 1.584$)

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 $0.3 \ M$?