For a first order reaction,the velocity constant is $K = 10^{-3} \ s^{-1}$. The two-third life for it would be ........... $s$.

The half-life period of a first-order chemical reaction is $6.93 \, \text{min}$. The time required for the completion of $99 \%$ of the chemical reaction will be ........ $\text{min}$. $(\log 2 = 0.301)$

$t_{87.5}$ is the time required for the reaction to undergo $87.5 \%$ completion and $t_{50}$ is the time required for the reaction to undergo $50 \%$ completion. The relation between $t_{87.5}$ and $t_{50}$ for a first order reaction is $t_{87.5} = x \times t_{50}$. The value of $x$ is $......$. (Nearest integer)

The reaction $X \rightarrow$ products is a first-order reaction. If the concentration of reactant $X$ decreases from $0.1 \, M$ to $0.025 \, M$ in $40 \, \text{minutes}$,what will be the rate of the reaction when the concentration of the reactant is $0.01 \, M$?

The rate constant for a first-order reaction is $0.02232 \ min^{-1}$. Calculate the time required for $75 \%$ completion of the reaction. (in $min$)

$A$ first-order reaction is $50\%$ complete in $45 \text{ minutes}$. How many hours will it take for the reaction to be $99.9\%$ complete?