Slope of the graph between $\log \frac{[A]_0}{[A]_t}$ ($y$-axis) and time ($x$-axis) for a first-order reaction is equal to:

For a first order reaction,to obtain a positive slope,we need to plot $...$ where $[A]$ is the concentration of reactant $A$.

For a first order reaction,$A \to P$,$t_{1/2}$ (half-life) is $10 \ days$. The time required for $\frac{1}{4}$ conversion of $A$ (in days) is: $(\ln 2 = 0.693, \ln 3 = 1.1)$.

Find the time period of a $1^{st}$ order reaction when the reaction is $\frac{2}{3} ^{rd}$ complete. If the value of the rate constant is $4.3 \times 10^{-4} \, s^{-1}$.

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

The reaction $CH_3COCH_{3(g)} \to C_2H_{4(g)} + H_{2(g)} + CO_{(g)}$ is a first-order reaction. If the initial pressure is $0.40 \ atm$ and the total pressure after $10 \ min$ is $0.50 \ atm$,calculate the rate constant of the reaction. $(\log 3.5 = 0.5441)$