For a first order reaction $R \longrightarrow P$,the rate constant is $k$. If the initial concentration of $R$ is $[R_0]$,the concentration of $R$ at any time $t$ is given by the expression:

The rate constant of the reaction $2 NO_2Cl_{(g)} \longrightarrow 2 NO_{2(g)} + Cl_{2(g)}$ is $4.7672 \text{ minute}^{-1}$. Calculate the half-life of the reaction.

The half-life of a first-order reaction is $6.0 \ h$. How long will it take for the concentration of the reactant to decrease from $0.4 \ M$ to $0.12 \ M$ (in $h$)?

For the first order reaction $2 N_2O_{5(g)} \rightarrow 4 NO_{2(g)} + O_{2(g)}$,which of the following statements are correct?
$A.$ The concentration of the reactant decreases exponentially with time.
$B.$ The half-life of the reaction decreases with increasing temperature.
$C.$ The half-life of the reaction depends on the initial concentration of the reactant.
$D.$ The reaction proceeds to $99.6 \%$ completion in eight half-life durations.

For the first order reaction $A \rightarrow 2B$,$1 \ mole$ of reactant $A$ gives $0.2 \ moles$ of $B$ after $100 \ minutes$. The half-life of the reaction is $..... \ min$. [Use: $\ln 2 = 0.69, \ln 10 = 2.3$]

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 $B$?