For a reaction,the rate constant is $2.34 \ s^{-1}$. The half-life period for the reaction is ....... $s.$

Calculate the time in seconds required to reduce the concentration of reactant to half of initial concentration for a first order reaction if the rate constant is $1.386 \times 10^{-3} \ s^{-1}$. (in $s$)

Azo-isopropane decomposes according to the following equation:
$((CH_3)_2CHN = NCH(CH_3)_2)_{(g)} \xrightarrow{250 - 290 ^oC} (N_2)_{(g)} + (C_6H_{14})_{(g)}$
It is a first-order reaction. If the initial pressure is $P_o$ and the total pressure of the mixture at time $t$ is $P_t$,find the rate constant $K$.

For the first-order gaseous reaction $A \rightarrow 2B + C$ at $373 \, K$,starting with pure $A$,the total pressure of the system after $10 \, min$ is $176 \, mm \, Hg$ and after a long time,it is $270 \, mm \, Hg$. Based on this information,calculate: $(1)$ Initial pressure of $A$,$(2)$ Pressure of $A$ after $10 \, min$,and $(3)$ Rate constant.

$10 \ g$ mixture of two gases $A_2$ (mol. wt. $= 20$) and $B_2$ (mol. wt. $= 30$),which decompose by first order kinetics,was taken in a vessel. The half-life of decomposition of $A_2$ and $B_2$ are $2 \ hours$ and $3 \ hours$ respectively. After $6 \ hours$,the weight of the mixture of $A_2$ and $B_2$ is found to be $2 \ g$. Find the weight of $A_2$ in the initial mixture in $g$.

For a first order reaction,a plot of $\log(a-x)$ against time is a straight line with negative slope equal to