For a certain reaction $R \rightarrow$ Product, the plot of concentration $[R]$ vs time has a negative slope as shown. The order of reaction is :

Given below is an expression for the rate constant of a first-order reaction occurring at a certain temperature, $\mathrm{T}(\mathrm{K})$.

$$ \operatorname{lnk}=14.34-\frac{1.25 \times 10^4}{T} $$

The energy of activation in $\mathrm{kcal} \mathrm{mol}^{-1}$ for the reaction is :

(Given: $\mathrm{k}^{-1} \mathrm{~s} \mathrm{~s}^{-1}, \mathrm{R}=1.987 \mathrm{cal} \mathrm{mol}^{-1} \mathrm{~K}^{-1}$ )

If the rate constant of a reaction is $0.03 \mathrm{~s}^{-1}$, how much time does it take for $7.2 \mathrm{~mol} \mathrm{~L}^{-1}$ concentration of the reactant to get reduced to $0.9 \mathrm{~mol} \mathrm{~L}^{-1}$ ? (Given: $\log 2=0.301$ )

If the half-life ( $t_{1 / 2}$ ) for a first order reaction is 1 minute, then the time required for $99.9 \%$ completion of the reaction is closest to :