What is the unit of the rate constant for a first-order reaction?

Time required for $90 \%$ completion of a first order reaction is '$x$' minute. Calculate the time required to complete $99.9 \%$ of the reaction at the same temperature.

The reaction $A \to B$ follows first order kinetics. The time taken for $0.8 \ mol$ of $A$ to produce $0.6 \ mol$ of $B$ is $1 \ hr$. What is the time taken for the conversion of $0.9 \ mol$ of $A$ to produce $0.675 \ mol$ of $B$?

$A$ first order reaction takes $40 \ min$ for $20 \%$ decomposition. Calculate its rate constant.

$A ( g ) \rightarrow 2 B ( g ) + C ( g )$ is a first order reaction. The initial pressure of the system was found to be $800 \ mm \ Hg$ which increased to $1600 \ mm \ Hg$ after $10 \ min$. The total pressure of the system after $30 \ min$ will be . . . . . . $mm \ Hg$. (Nearest integer)

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: