In the following first order reactions $A$ $\xrightarrow{K_1} B$ $\xrightarrow{K_2} \text{Product}$,find the ratio $K_1/K_2$ if $90\%$ of $A$ has been reacted in time $t$ while $99\%$ of $B$ has been reacted in time $2t$.

$A$ first order reaction which is $30\%$ complete in $30 \ min$ has a half-life period of .............. $min.$ (in $.2$)

The decomposition of benzene diazonium chloride is a first order reaction. The time taken for the decomposition of $\frac{1}{4}$ and $\frac{1}{10}$ of its initial concentration are $t_{1/4}$ and $t_{1/10}$ respectively. The value of $\frac{t_{1/4}}{t_{1/10}} \times 100$ is (Given: $\log 2 = 0.3, \log 3 = 0.477$)

For the reaction $A \rightarrow B$,the following graph was obtained. The time required (in seconds) for the concentration of $A$ to reduce to $2.5 \ g \ L^{-1}$ (if the initial concentration of $A$ was $50 \ g \ L^{-1}$) is $........$ (Nearest integer). Given: $\log 2 = 0.3010$.

Which of the following is the slope of the graph of rate versus concentration of the reactant for a first-order reaction?

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 $A$?