If the rate constant for a first order reaction is $k$,then find the time required for completion of $80 \%$ of the reaction.

For a first-order reaction, if the initial concentration $[A]_0 = 1.0 \text{ M}$ and the concentration after time $t = 276 \text{ s}$ is $[A]_t = 0.25 \text{ M}$, find the value of the rate constant $(k)$. (in $\text{ s}^{-1}$)

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:

Which is a correct integrated rate equation for a first-order reaction?

Derive the half-life $t_{1/2}$ of a first-order reaction.

$A$ first-order reaction decomposes such that the time taken for $1/8$ and $1/10$ of the initial concentration to decompose are $t_{1/8}$ and $t_{1/10}$ respectively. Find the value of $\frac{t_{1/8}}{t_{1/10}} \times 10$. (Given: $\log_{10} 2 = 0.3$)