Calculate the rate constant of the first order reaction if $80 \%$ of the reactant reacted in $15 \ minute$.

If the half-life period of a first order reaction is $138.6 \ minutes$,then the value of the decay constant for the reaction will be:

For a first-order reaction,the rate constant is $3 \times 10^{-6} \, s^{-1}$. If the initial concentration is $0.10 \, M$,the initial rate is.........

$A$ flask contains a mixture of compounds $A$ and $B.$ Both compounds decompose by first-order kinetics. The half-lives for $A$ and $B$ are $300 \ s$ and $180 \ s,$ respectively. If the concentrations of $A$ and $B$ are equal initially,the time required for the concentration of $A$ to be four times that of $B$ (in $s$): (Use $\ln 2 = 0.693$)

$A$ radioactive substance decomposes such that after $100 \ min$,its concentration becomes $1/8$ of the original concentration. Calculate the rate constant $(k)$ and half-life time $(t_{1/2})$.

Isomerisation of gaseous cyclobutene to butadiene is a first order reaction. At $T \ K$,the rate constant of the reaction is $3.3 \times 10^{-4} \ s^{-1}$. What is the time required (in $min$) to complete $90 \%$ of this reaction at the same temperature? $(\log 2 = 0.3)$