If the half-life period of a first order reaction is $138.6 \ minutes$,then the value of the decay constant for the reaction will be:

Calculate the rate constant of a first-order reaction if the concentration of the reactant decreases by $90 \%$ in $30 \ minutes$.

For the decomposition of $N_2O_5$ according to the equation $2N_2O_5(g) \to 4NO_2(g) + O_2(g)$,the reaction is of first order. After $30 \, \min$ from the start of the reaction in a closed vessel,the total pressure is $305.5 \, mm \, Hg$,and at the end of complete decomposition,the total pressure is $587.5 \, mm \, Hg$. Calculate the rate constant of the reaction.

The rate constant of a first-order reaction is $1.20 \times 10^{-3} \, s^{-1}$. How much time will it take for $5 \, g$ of the reactant to reduce to $3 \, g$ (in $, s$)?

Half life of a first order reaction is $3 \ minute$. What is the time required to reduce the concentration of reactant by $90 \%$ of its initial concentration?

For a first order reaction with rate constant $k$, the slope of the plot of $\log(\text{reactant concentration})$ against time is