The half-life period of a first-order reaction is $1386 \text{ s}$. The rate constant of the reaction is:

What is the time needed to reduce the initial concentration of reactant to $10 \%$ in a first order reaction if its half life time is $10 \ minute$?

$A$ first order reaction has a rate constant of $2.303 \times 10^{-3} \; s^{-1}$. The time required for $40 \; g$ of this reactant to reduce to $10 \; g$ will be.....$s$
[Given that $\log_{10} 2 = 0.3010$]

For the reaction $A \rightarrow B$,the following graph was obtained. The time required (in seconds) for the concentration of $A$ to reduce to $2.5 \ g \ L^{-1}$ (if the initial concentration of $A$ was $50 \ g \ L^{-1}$) is $........$ (Nearest integer). Given: $\log 2 = 0.3010$.

The gaseous reaction $A_{(g)} \to 2B_{(g)} + C_{(g)}$ is a first-order reaction. If the initial pressure $P_A = 90 \ mm \ Hg$ and the total pressure after $10 \ min$ is $180 \ mm \ Hg$,calculate the rate constant of the reaction.

In a first order reaction,$60 \%$ of the reactant converts into product in $45 \ minutes$. Calculate the rate constant of the reaction.