Calculate the time needed for a reactant to decompose $99.9 \%$ if the rate constant of a first-order reaction is $0.576 \ min^{-1}$.

For a first order reaction $A_5 \rightarrow 5 B_2$,the concentration vs time plot is as shown. The half-life of the reaction is

Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law,with $t_{1/2} = 3.00 \ h$. What fraction of sample of sucrose remains after $8 \ h$ $?$

For the first order reaction $A \rightarrow 2B$,$1 \ mole$ of reactant $A$ gives $0.2 \ moles$ of $B$ after $100 \ minutes$. The half-life of the reaction is $..... \ min$. [Use: $\ln 2 = 0.69, \ln 10 = 2.3$]

$t_{1/4}$ for a first-order reaction is given as:

Thermal decomposition of a compound is of first order. If $50\%$ of a sample of this compound is decomposed in $120 \ min$,then how long will it take $90\%$ of the compound to decompose? ........ $min.$