The rate constant of a first-order reaction is $10^{-3} \ min^{-1}$ and the initial concentration of the reactant is $0.2 \ mol \ dm^{-3}$. What percentage of the reactant will be converted into product in $200 \ min$?

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 $10 \ minute$?

At $30^{\circ}C$,the half-life for the decomposition of $AB_{2}$ is $200\,s$ and is independent of the initial concentration of $AB_{2}$. The time required for $80\%$ of the $AB_{2}$ to decompose is $....s$ (Given: $\log 2 = 0.30; \log 5 = 0.70$)

$A$ substance $A$ decomposes by a first order reaction starting initially with $[A]_0 = 2.00 \, M$ and after $200 \, \min$,$[A]_t = 0.15 \, M$. For this reaction,what is the value of the rate constant $k$?

The half-life for the reaction $N_2O_5 \rightleftharpoons 2NO_2 + \frac{1}{2}O_2$ is $24 \ hr$ at $30 \ ^\circ C$. Starting with $10 \ g$ of $N_2O_5$,how many grams of $N_2O_5$ will remain after a period of $96 \ hr$?

For the reaction shown in the image,the half-life does not depend on the concentration of the reactant. After $10 \, \text{min}$,the volume of $N_2$ gas evolved is $20 \, \text{L}$ and after the completion of the reaction,it is $100 \, \text{L}$. Hence,the rate constant is: