The rate constant of a reaction is $0.69 \times 10^{-1} \ min^{-1}$ and the initial concentration is $0.2 \ mol \ L^{-1}.$ The half-life period is ........ $\sec$

The gaseous reaction $A_{(g)} \to 2B_{(g)} + C_{(g)}$ is a first-order reaction. If the initial pressure $P_A = 90 \ mm \ Hg$ and the total pressure after $10 \ min$ is $180 \ mm \ Hg$,calculate the rate constant of the reaction.

The plot of $\log(a - x)$ versus time $t$ is a straight line,which indicates that the reaction is of ....... order.

The half-life of a first-order reaction is $10 \ min$. If the initial concentration is $0.08 \ mol \ L^{-1}$ and the concentration at some instant is $0.01 \ mol \ L^{-1}$,then $t =$ ........... $\min$.

$A$ first order reaction requires $30 \ min$ for $50\%$ completion. The time required to complete the reaction by $75\%$ will be .......... $\min.$

The half-life period of a first-order reaction is given by: