If the half-life $(t_{1/2})$ of a reaction is $69.3 \ s$ and the rate constant $(k)$ is $10^{-2} \ s^{-1}$,then the order of the reaction is:

Half-life of a first order reaction is $20 \ s$ and initial concentration of reactant is $0.2 \ M$. The concentration of reactant left after $80 \ s$ is (in $M$)

Find the time period of a $1^{st}$ order reaction when the reaction is $\frac{2}{3} ^{rd}$ complete. If the value of the rate constant is $4.3 \times 10^{-4} \, s^{-1}$.

For a first-order reaction,the ratio of the time required for $99.9\%$ completion to the time required for $50\%$ completion is:

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

$A$ reaction has a rate constant $k = 2.4 \times 10^{-4} \ s^{-1}$. Find the ratio of $t_{99.9}$ to $t_{50}$.