What is the half-life of a first-order reaction if the rate constant is $4.2 \times 10^{-2} \text{ day}^{-1}$ (in $\text{ days}$)?

For the reaction shown in the image,the half-life does not depend on the concentration of the reactant. After $10 \, \text{min}$,the volume of $N_2$ gas evolved is $20 \, \text{L}$ and after the completion of the reaction,it is $100 \, \text{L}$. Hence,the rate constant is:

In a first order reaction,the concentration of reactant decreases from $800 \ mol/dm^3$ to $50 \ mol/dm^3$ in $2 \times 10^2 \ s$. The rate constant of the reaction in $s^{-1}$ is:

For the reaction $2N_2O_5 \rightarrow 4NO_2 + O_2$,the rate constant is $3.0 \times 10^{-5} \ s^{-1}$. If the rate of reaction is $2.40 \times 10^{-5} \ mol \ L^{-1} \ s^{-1}$,calculate the concentration of $N_2O_5$ in $mol \ L^{-1}$.

$A$ first order reaction is found to have a rate constant,$k = 5.5 \times 10^{-14} \ s^{-1}$. The half life of reaction is . . . . . . .

The following data were obtained during the first order thermal decomposition of $SO_{2}Cl_{2}$ at a constant volume.
$SO_{2}Cl_{2(g)} \to SO_{2(g)} + Cl_{2(g)}$

Experiment	Time $/$ $s$	Total pressure $/$ $atm$
$1$	$0$	$0.5$
$2$	$100$	$0.6$

Calculate the rate of the reaction when total pressure is $0.65 \ atm$.