In a first order decomposition reaction,the time taken for the decomposition of reactant to one fourth and one eighth of its initial concentration are $t_1$ and $t_2 \ s$,respectively. The ratio $t_1 / t_2$ will be:

The reaction $N_{2}O_{5} \longrightarrow 2NO_{2} + \frac{1}{2}O_{2}$ is first order in $N_{2}O_{5}$ having rate constant $6.2 \times 10^{-4} \ s^{-1}$. What is the value of rate of reaction when concentration of $N_{2}O_{5}$ is $1.25 \ mol \ L^{-1}$?

Rate of first order reaction $A \rightarrow \text{product}$ is $0.01 \ mol \ dm^{-3} \ s^{-1}$. Calculate the rate constant if the concentration of the reactant is $0.2 \ M$. (in $s^{-1}$)

Which equation represents the $1/4^{th}$ life for a first-order reaction?

The following data were obtained during the first order thermal decomposition of a gas $A$ at constant volume:
$A_{(g)} \rightarrow 2 B_{(g)} + C_{(g)}$

$S.No.$	$Time/s$	$Total Pressure/(atm)$
$1.$	$0$	$0.1$
$2.$	$115$	$0.28$

The rate constant of the reaction is . . . . . . $\times 10^{-2} \ s^{-1}$ (nearest integer).

For a homogeneous gaseous reaction $A_{(g)} \to 3B_{(g)}$,if the pressure after time $t$ is $P_t$ and after completion of the reaction the pressure is $P_\infty$,select the correct relation for the rate constant $K$.