The rate constant and half-life of a first-order reaction are related to each other as -

$A$ flask contains a mixture of compounds $A$ and $B.$ Both compounds decompose by first-order kinetics. The half-lives for $A$ and $B$ are $300 \ s$ and $180 \ s,$ respectively. If the concentrations of $A$ and $B$ are equal initially,the time required for the concentration of $A$ to be four times that of $B$ (in $s$): (Use $\ln 2 = 0.693$)

The degree of dissociation of a first-order reaction is

The rate equation for a first-order reaction is given by $[R] = [R]_0 e^{-kt}$. $A$ straight line with a positive slope is obtained by plotting: ($[R]_0 =$ initial concentration of reactant,$[R] =$ concentration of reactant at time $t$)

The first order rate constant for the decomposition of $N_2O_5$ is $6.2 \times 10^{-4} \ s^{-1}$. The half-life period for this decomposition in seconds is:

The reaction $A \to B$ follows first-order kinetics. It takes $1 \ hr$ for $0.60 \ mole$ of $B$ to be formed from $0.80 \ mole$ of $A$. How much time (in $hr$) will it take for $0.675 \ mole$ of $B$ to be formed from $0.90 \ mole$ of $A$?