The half-life period $t_{1/2}$ for a first-order reaction is given by:

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:

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 $[X] = 0.1 \ M$? $(\log 4 = 0.60)$

For the decomposition of azomethane,$CH_3N_2CH_{3(g)} \rightarrow CH_3CH_{3(g)} + N_{2(g)}$,a first order reaction,the variation in partial pressure with time at $600 \ K$ is given as shown in the graph. The value of the rate constant $k$ in $s^{-1}$ is $x \times 10^4$. Find the value of $x$.

For which of the following graphs of a first-order reaction will the value of the slope be $\frac{K}{2.303}$?

For a first order reaction $A \rightarrow P$,$t_{1/2}$ (half-life) is $10 \text{ days}$. The time required for $1/4^{th}$ conversion of $A$ (in days) is: