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

For the reaction $2A + B \to \text{product}$,the rate law is given by $\frac{-d[A]}{dt} = k[A]$. At a time $t = \frac{t_{1/2}}{\ln 2}$,what is the concentration of the reactant $A$?

The integrated rate equation for a first-order reaction is:

$N_2O_{(g)} \to N_{2(g)} + \frac{1}{2}O_{2(g)}$
In a closed vessel,the reaction follows first-order kinetics. If starting with pure $N_2O_{(g)}$,the total pressure after time $t$ is $P_t$ and after a very long time is $P_{\infty}$,then which of the following expressions is correct?

For a first order reaction,the rate constant is $0.6932 \ hr^{-1}$,then the half-life for the reaction is ......... $hr$.

$A$ first order reaction has the rate constant,$k = 4.6 \times 10^{-3} \ s^{-1}$. The number of correct statement/s from the following is/are
Given : $\log 3 = 0.48$
$A.$ Reaction completes in $1000 \ s$.
$B.$ The reaction has a half-life of $500 \ s$.
$C.$ The time required for $10 \ \%$ completion is $25$ times the time required for $90 \ \%$ completion.
$D.$ The degree of dissociation is equal to $(1 - e^{-kt})$.
$E.$ The rate and the rate constant have the same unit.