For a first-order reaction, $20 \text{ mmol}$ of reactant is reduced to $10 \text{ mmol}$ in $1.151 \text{ min}$. Find the rate constant $k$. (in $\text{ min}^{-1}$)

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 integrated rate equation for a first-order reaction,$A \rightarrow \text{product}$,is

Which is the correct relation between rate constant and half-life of a first-order reaction?

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: $\ln 2 = 0.69, \ln 10 = 2.3$]

$A$ flask is filled with equal moles of $A$ and $B$. The half-lives of $A$ and $B$ are $100 \, s$ and $50 \, s$ respectively and are independent of the initial concentration. The time required for the concentration of $A$ to be four times that of $B$ is $.... \, s.$
(Given : $\ln 2 = 0.693$ )