The first order reaction takes $20 \ min$ to complete $15\%$. How much time is required to complete $75\%$ of the reaction (in $min$)?

$A$ first-order reaction takes $16 \text{ minutes}$ for its $50\%$ completion. What fraction of the reactant would react in $32 \text{ minutes}$ from the beginning?

What is the slope of the graph plotted between half-life $(t_{1/2})$ and initial concentration $(a)$ for a $1^{st}$ order reaction?

The integrated rate equation is $Rt = \log C_0 - \log C_t$. The straight line graph is obtained by plotting

The initial concentration of $N_2O_5$ in the first order reaction,$N_2O_5 \rightarrow 2NO_{2(g)} + \frac{1}{2}O_{2(g)}$ was $1.24 \times 10^{-2} \ mol \ L^{-1}$ at $300 \ K$ temperature. The concentration of $N_2O_5$ after $60 \ min$ was $0.20 \times 10^{-2} \ mol \ L^{-1}.$ Calculate the rate constant of the reaction.

For a first order reaction $A \to \text{products}$,the concentration of $[A]$ is reduced from $2 \ M$ to $0.125 \ M$ in one hour. The $t_{1/2}$ of this reaction (in $\text{min}$) is: