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

For a first-order reaction,the time taken for the initial concentration to decrease to $1/4$ of its value is $20 \ min$. The time taken for the initial concentration to decrease to $1/16$ of its value will be $......... \ min$.

If the decomposition reaction $A_{(g)} \longrightarrow B_{(g)}$ follows first-order kinetics,then the graph of the rate of formation of $B$,denoted by $R$,against time $t$ will be:

Ethylene is produced by $C_4H_8 (\text{Cyclobutane}) \xrightarrow{\text{Heat}} 2C_2H_4$. The rate constant is $2.3 \times 10^{-4} \text{ s}^{-1}$. In what time will the molar ratio of ethylene to cyclobutane in the reaction mixture attain the value $1$? ...... $\text{min}$

The rate constant of a first order reaction whose half-life is $480 \ s$,is

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? ........ $min.$