Calculate the half-life of a first-order reaction if the rate constant of the reaction is $2.772 \times 10^{-3} \ s^{-1}$. (in $s$)

$t_{1/4}$ for a first-order reaction is given as:

$A$ first order reaction takes $40 \ min$ for $30 \%$ decomposition. Calculate $t_{1/2}$.

The degree of dissociation of a first-order reaction is

Identify $True$ $(T)$ and $False$ $(F)$ statements for the following equations related to a first-order reaction $R \rightarrow P$:
$(i) \ln [R] = -kt + \ln [R]_{0}$
$(ii) \ln [R] = +kt + \ln [R]_{0}$

The slope of a graph $\log [A]_t$ versus '$t$' for a first-order reaction is $-2.5 \times 10^{-3} \,s^{-1}$. Find the rate constant of the reaction.