If the rate constant for a first order reaction is $k$,the time $(t)$ required for the completion of $99\%$ of the reaction is given by:

Identify True $(T)$ and False $(F)$ statements for the following expressions regarding a first-order reaction $R \rightarrow P$:
Statement $I$: $\text{Rate} = -\frac{d[R]}{dt} = k[R]$
Statement $II$: $\text{Rate} = -\frac{d[R]}{dt} = -k[R]$

If the concentration is expressed in moles per litre,the unit of the rate constant for a first order reaction is

The following results were obtained during kinetic studies of the reaction $2A + B \to$ products:

Experiment	$[A]$ $(mol \ L^{-1})$	$[B]$ $(mol \ L^{-1})$	Initial rate $(mol \ L^{-1} \ min^{-1})$
$I$	$0.10$	$0.20$	$6.93 \times 10^{-3}$
$II$	$0.10$	$0.25$	$6.93 \times 10^{-3}$
$III$	$0.20$	$0.30$	$1.386 \times 10^{-2}$

The time (in minutes) required to consume half of $A$ is:

The rate constant of the decomposition of hydrogen peroxide is $0.0204 \text{ min}^{-1}$. Calculate the half-life of the reaction. (in $\text{ min}$)

For a first-order reaction,the concentration decreases from $800 \ mol/dm^3$ to $50 \ mol/dm^3$ in $2 \times 10^4 \ s$. What is the rate constant of the reaction?