The half-life period of a $1^{st}$ order reaction is $60 \ minutes$. What percentage will be left over after $240 \ minutes$ (in $\%$)?

$A$ first order reaction takes $40 \ min$ for $20 \%$ decomposition. Calculate its rate constant.

Sucrose hydrolyses in acid solution into glucose and fructose following first order rate law with a half-life of $3.33 \ h$ at $25^{\circ} C$. After $9 \ h$,the fraction of sucrose remaining is $f$. The value of $\log _{10} (\frac{1}{f})$ is ..... $\times 10^{-2}$. (Rounded off to the nearest integer) [Assume : $\ln 10 = 2.303, \ln 2 = 0.693$ ]

Identify $True$ $(T)$ and $False$ $(F)$ statements of the following for a first order reaction $R \rightarrow P$.
$I. \log \frac{[R]}{[R]_0} = -\frac{kt}{2.303}$
$II. \log \frac{[R]}{[R]_0} = \frac{kt}{2.303}$

The decomposition of substance $A$ in a solution follows first-order kinetics. Vessel-$I$ contains $1 \ L$ of $1 \ M$ solution of $A$. Vessel-$II$ contains $100 \ mL$ of $0.6 \ M$ solution of $A$. If the concentration of $A$ in Vessel-$I$ becomes $0.25 \ M$ in $8 \ hr$,then the time required for the concentration of $A$ in Vessel-$II$ to become $0.3 \ M$ is ......... $hr$.

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