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

If $50 \%$ of the reactant is converted into a product in a first order reaction in $25 \ min$,how much of it would react in $100 \ min$ (in $\%$)?

$A$ first-order reaction decomposes such that the time taken for $1/8$ and $1/10$ of the initial concentration to decompose are $t_{1/8}$ and $t_{1/10}$ respectively. Find the value of $\frac{t_{1/8}}{t_{1/10}} \times 10$. (Given: $\log_{10} 2 = 0.3$)

The reaction $A \rightarrow B$ follows first-order kinetics. If it takes $1 \text{ hour}$ to convert $0.8 \text{ mol}$ of $A$ to $0.6 \text{ mol}$ of $B$,how many hours will it take to convert $0.9 \text{ mol}$ of $A$ to $0.675 \text{ mol}$ of $B$?

For a first order reaction,the concentration of reactant decreases from $0.2 \ M$ to $0.1 \ M$ in $100 \ minutes$. What is the rate constant of the reaction?

If $75 \%$ of a first order reaction was completed in $90 \ minutes$,$60 \%$ of the same reaction would be completed in approximately (in minutes)..........
(Take: $\log 2=0.30 ; \log 2.5=0.40)$