If the half-life $(t_{1/2})$ for a first order reaction is $1 \text{ minute}$,then the time required for $99.9\%$ completion of the reaction is closest to

The rate constant for a first order reaction is $60 \text{ s}^{-1}$. How much time will it take to reduce the concentration of the reactant to $1/20^{th}$ of its initial value (in $\text{ s}$)?

The half-life of a first-order reaction is $850 \text{ s}$. The initial concentration of the reactant is $[R]_0 = 0.06 \text{ mol dm}^{-3}$. What concentration $[R]$ would remain after $t = 1200 \text{ s}$?

Time required for $99.9 \%$ completion of a first order reaction is . . . . . . . times the time required for completion of $90 \%$ reaction. (nearest integer).

$A$ reaction that is of the first order with respect to reactant $A$ has a rate constant $6 \ min^{-1}$. If we start with $[A] = 0.5 \ mol \ L^{-1}$,when would $[A]$ reach the value $0.05 \ mol \ L^{-1}$? (in $min$)

The experimental data for decomposition of $N_2O_5$ in the gas phase at $318 \, K$ are given below:

$t/s$	$0$	$400$	$800$	$1200$	$1600$	$2000$	$2400$	$2800$	$3200$
$10^2 \times [N_2O_5] / mol \, L^{-1}$	$1.63$	$1.36$	$1.14$	$0.93$	$0.78$	$0.64$	$0.53$	$0.43$	$0.35$

$(i)$ Plot $[N_2O_5]$ against $t$.
$(ii)$ Find the half-life period for the reaction.
$(iii)$ Draw a graph between $\log[N_2O_5]$ and $t$.
$(iv)$ What is the rate law?
$(v)$ Calculate the rate constant.
$(vi)$ Calculate the half-life period from $k$ and compare it with $(ii)$.