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 .......... $min$.

An organic compound undergoes first order decomposition. The time taken for decomposition to $\left(\frac{1}{8}\right)^{\text{th}}$ and $\left(\frac{1}{10}\right)^{\text{th}}$ of its initial concentration are $t_{1/8}$ and $t_{1/10}$ respectively. What is the value of $\frac{t_{1/8}}{t_{1/10}} \times 10$? (Given: $\log 2 = 0.3$)

For a first order reaction,the half-life period is $5 \ min$. What time will it take for $99.9 \%$ completion of the reaction (in $min$)?

If the rate constant of a first order reaction is $4.606 \times 10^{-3} \ s^{-1}$,then find the time required for $400 \ g$ of the reactant to reduce to $50 \ g$. (in $min$)

For a first order reaction,the slope of the graph of $\log_{10}[A]_t$ versus time is equal to:

$A ( g ) \rightarrow 2 B ( g ) + C ( g )$ is a first order reaction. The initial pressure of the system was found to be $800 \ mm \ Hg$ which increased to $1600 \ mm \ Hg$ after $10 \ min$. The total pressure of the system after $30 \ min$ will be . . . . . . $mm \ Hg$. (Nearest integer)