The rate constant for a first order reaction is $60 \ s^{-1}$. How much time will it take to reduce the initial concentration of the reactant to its $1/16^{th}$ value?

Which is a correct integrated rate equation for a first-order reaction?

In a first order reaction,the concentration of the reactant decreases from $0.6 \ M$ to $0.3 \ M$ in $15 \ min$. The time taken for the concentration to change from $0.1 \ M$ to $0.025 \ M$ in minutes is

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 : $\ln 10 = 2.303, \ln 2 = 0.693$ ]

The following data were obtained during the first order thermal decomposition of $N_{2}O_{5(g)}$ at constant volume:
$2N_{2}O_{5(g)} \rightarrow 2N_{2}O_{4(g)} + O_{2(g)}$

$S.No.$	Time $/$ $s$	Total pressure $/$ $atm$
$1.$	$0$	$0.5$
$2.$	$100$	$0.512$

Calculate the rate constant.

Calculate the rate constant of a first-order reaction if the concentration of the reactant decreases by $90 \%$ in $30 \ minutes$.