The first order integrated rate equation is

Derive the equation showing the relation between the concentration $[R]_1$ and $[R]_2$ at time $t_1$ and $t_2$ for a first-order reaction.

For a first order reaction $(A) \rightarrow$ products,the concentration of $A$ changes from $0.1 \ M$ to $0.025 \ M$ in $40 \ min$.
The rate of reaction when the concentration of $A$ is $0.01 \ M$ is ............$ \times 10^{-4} \ M/min$.

Gaseous cyclobutene isomerizes to butadiene in a first order process which has a $k$ value of $3.3 \times 10^{-4} \ s^{-1}$ at $153^{\circ}C$. The time in minutes it takes for the isomerization to proceed $40\%$ to completion at this temperature is ..........
(Rounded off to the nearest integer)

For the first-order reaction $N_2O_5 \to 2NO_2 + \frac{1}{2}O_2$,the half-life at $30 \ ^\circ C$ is $24 \ \text{hours}$. Starting with $10 \ g$ of $N_2O_5$,how many grams of $N_2O_5$ will remain after $96 \ \text{hours}$ (in $g$)?

Identify True $(T)$ and False $(F)$ statements for the following first order reaction $R \rightarrow P$:
$1. t_{1/2} = \frac{0.693}{2k}$
$2. t_{1/2} \propto k$