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:

The rate constant $k$,for the reaction ${N_2}{O_5}_{(g)} \to 2N{O_2}_{(g)} + \frac{1}{2}{O_2}_{(g)}$ is $2.3 \times 10^{-2} \ s^{-1}$. Which equation given below describes the change of $[{N_2}{O_5}]$ with time? $[{N_2}{O_5}]_0$ and $[{N_2}{O_5}]_t$ correspond to concentration of ${N_2}{O_5}$ initially and at time $t$.

Which one of the following formulas represents a first-order reaction?

If $50 \%$ of the reactant is converted into a product in a first order reaction in $25 \ min$,how much of it would react in $100 \ min$ (in $\%$)?

The reaction $A_{(g)} \to 2B_{(g)} + C_{(g)}$ obeys the rate law,$r = K[A]$ where $K = 0.023 \ s^{-1}$. If $2.5 \ moles$ of $A$ were taken in a $5 \ L$ flask,how many moles of $A$ would remain left after $50 \ seconds$?

For the first$-order$ reaction,$T_{av}$ (average life),$T_{50}$ and $T_{75}$ in the increasing order are: