For a first-order reaction,the ratio of $t_{3/4}$ to $t_{1/2}$ is ...

Time required for $99.9 \%$ completion of a first order reaction is . . . . . . . times the time required for completion of $90 \%$ reaction. (nearest integer).

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.

Calculate the rate constant of the first order reaction if $20 \%$ of the reactant decomposes in $15 \ minutes$.

The decomposition of substance $A$ in a solution follows first-order kinetics. Vessel-$I$ contains $1 \ L$ of $1 \ M$ solution of $A$. Vessel-$II$ contains $100 \ mL$ of $0.6 \ M$ solution of $A$. If the concentration of $A$ in Vessel-$I$ becomes $0.25 \ M$ in $8 \ hr$,then the time required for the concentration of $A$ in Vessel-$II$ to become $0.3 \ M$ is ......... $hr$.

If the rate constant of a first order reaction is $4.606 \times 10^{-3} \ s^{-1}$,then find the time required for $400 \ g$ of the reactant to reduce to $50 \ g$. (in $min$)