For a first order reaction,the concentration of reactant was reduced from $0.03 \ mol \ L^{-1}$ to $0.02 \ mol \ L^{-1}$ in $25 \ min$. What is its rate (in $mol \ L^{-1} \ s^{-1}$)?

The following is a first-order reaction:
$N_2O_5 \text{ (solution)} \rightarrow 2 NO_2 \text{ (solution)} + \frac{1}{2} O_2 \text{ (g)}$
In this reaction,$CCl_4$ is the solvent. The rate constant is $k = 5.0 \times 10^{-4} \ s^{-1}$. The initial concentration of $N_2O_5$ is $0.25 \ mol \ L^{-1}$.
$(i)$ What will be the initial rate of reaction?
$(ii)$ Calculate the half-life $(t_{1/2})$.
$(iii)$ How much time is required to complete $75\%$ of the reaction?
$(iv)$ Calculate the concentration of $N_2O_5$ and $NO_2$ after $30 \ min$.

Decomposition of nitrogen pentoxide is known to be a first order reaction. $75\%$ of the oxide had decomposed in the first $24 \ minutes$. At the end of an hour,after the start of the reaction,the amount of oxide left will be

$A$ particular reaction has a rate constant $1.15 \times 10^{-3} \,s^{-1}$. How long does it take for $6 \,g$ of the reactant to reduce to $3 \,g$ (in $\,s$)? $(\log 2 = 0.301)$

For a first order reaction $A \to B$,the reaction rate at reactant concentration of $0.01 \ M$ is found to be $2.0 \times 10^{-5} \ M \ sec^{-1}$. The half-life period of the reaction is .......... $sec$.

Which equation is correct for first order reactions?