Find the rate constant of a first-order reaction in $sec^{-1}$ having a half-life of $2.5 \ hours$.

For a first-order reaction, $20 \text{ mmol}$ of reactant is reduced to $10 \text{ mmol}$ in $1.151 \text{ min}$. Find the rate constant $k$. (in $\text{ min}^{-1}$)

$N_2O_5 \rightarrow 2NO_{2(g)} + \frac{1}{2}O_{2(g)}$ is a first order reaction. $k = 5 \times 10^{-4} \ s^{-1}$. The initial concentration of $N_2O_5 = 0.2 \ mol \ L^{-1}$. After how much time will its concentration be $25 \%$ of the initial concentration (in $s$)?

The rate constant of a first-order reaction is $10^{-3} \ min^{-1}$ and the initial concentration of the reactant is $0.2 \ mol \ dm^{-3}$. What percentage of the reactant will be converted into product in $200 \ min$?

The following results are obtained in one pseudo first order reaction:

Time $(s)$	$0$	$30$	$60$	$90$
Concentration $(mol \ L^{-1})$	$0.551$	$0.312$	$0.173$	$0.085$

$(a)$ Calculate the average rate of reaction between $30$ and $60$ seconds.
$(b)$ Calculate the rate constant $(k)$ of this first order reaction.

For a first order reaction $A \rightarrow B$,the rate constant,$k = 5.5 \times 10^{-14} \, s^{-1}$. The time required for $67 \, \%$ completion of reaction is $x \times 10^{-1}$ times the half life of reaction. The value of $x$ is $....$ (Nearest integer)