$A$ and $B$ decompose via first order kinetics with half-lives $54.0 \, min$ and $18.0 \, min$ respectively. Starting from an equimolar non-reactive mixture of $A$ and $B$,the time taken for the concentration of $A$ to become $16$ times that of $B$ is ...... $min.$ (Round off to the Nearest Integer).

Calculate the rate constant for the first order reaction,$A \rightarrow B$ if the rate of reaction is $5.4 \times 10^{-6} \ mol \ dm^{-3} \ s^{-1}$ and $[A]=0.3 \ M$.

Assertion : For a first order reaction,$t_{1/2}$ is independent of initial concentration.
Reason : For a first order reaction,rate constant $k \propto [R]$.

For the reaction $2N_2O_{5(g)} \rightarrow 4NO_{2(g)} + O_{2(g)}$,which is a first-order reaction with respect to $N_2O_5$,which of the following plots gives a straight line?

In a first order reaction,the concentration of the reactant is reduced to $(1/8)^{th}$ of its initial concentration in $23.03 \ min$. What is the half-life period of the reaction (in $min$)?

$A$ flask contains a mixture of compounds $AB$ and $XY$. Both decompose by first-order kinetics upon heating. If the half-life periods of $AB$ and $XY$ are $30 \ min$ and $10 \ min$ respectively,how many minutes will it take for the concentration of $AB$ to be four times the concentration of $XY$? (Assume initial concentrations of $AB$ and $XY$ are equal.)