The rate of a first order reaction is $1.5 \times 10^{-2} \ mol \ L^{-1} \ \min^{-1}$ at $0.5 \ M$ concentration of the reactant. The half life of the reaction is ....... $\min$

Calculate the half-life of the first-order reaction $C_2H_4O_{(g)} \to CH_{4(g)} + CO_{(g)}$. If the initial pressure of $C_2H_4O_{(g)}$ is $80 \ mm$ and the total pressure at the end of $20 \ minutes$ is $120 \ mm$,find the half-life in $\text{min}$.

$A$ first order reaction has the rate constant $10^{-2} \ sec^{-1}$. If the initial concentration of reactant is $1 \ M$,then what will be the rate of reaction after $1 \ minute$?

For a first-order reaction,which of the following statements is correct?

For the reaction $2N_2O_5 \rightarrow 4NO_2 + O_2$,the rate constant is $3.0 \times 10^{-5} \ s^{-1}$. If the rate of reaction is $2.40 \times 10^{-5} \ mol \ L^{-1} \ s^{-1}$,calculate the concentration of $N_2O_5$ in $mol \ L^{-1}$.

In a first order decomposition reaction,the time taken for the decomposition of reactant to one fourth and one eighth of its initial concentration are $t_1$ and $t_2 \ s$,respectively. The ratio $t_1 / t_2$ will be: