The half-life period of a reaction is $1386 \ s$. What is the value of the specific rate constant for the reaction?

The rate equation for a first-$order$ reaction is given by $R = R_0 e^{-kt}$. $A$ straight line with positive slope is obtained by plotting which of the following? ($R_0 =$ Initial concentration of the reactant,$R =$ concentration of the reactant at time $t$)

The slope of the graph between rate ($Y$-axis) and $[A]$ ($X$-axis) for a first-order reaction is equal to:

The reaction $X \rightarrow$ products is a first order reaction. In $40 \ min$,the concentration of $X$ changes from $1.0 \ M$ to $0.25 \ M$. What is the rate of reaction when $[X] = 0.1 \ M$? $(\log 4 = 0.60)$

The rate of a first-order reaction is $0.04 \ mol \ L^{-1} \ s^{-1}$ at $10 \ s$ and $0.03 \ mol \ L^{-1} \ s^{-1}$ at $20 \ s$ after the initiation of the reaction. The half-life period of the reaction is ......... $s$. (in $.1$)

At $500\,^oC$,cyclopropane isomerizes to propene. This reaction is first order with a rate constant of $6.7 \times 10^{-4}\,s^{-1}$. If the initial concentration of cyclopropane is $0.05\, M$,what will be the molarity of cyclopropane after $30\, min$ (in $, M$)?