Rate of first order reaction $A \rightarrow \text{product}$ is $0.01 \ mol \ dm^{-3} \ s^{-1}$. Calculate the rate constant if the concentration of the reactant is $0.2 \ M$. (in $s^{-1}$)

In a first order reaction,the concentration of the reactant is reduced to $12.5 \%$ in one hour. When was it half completed?

$A$ 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: $\log_{10} 2 = 0.3$)

The half-life of a first-order reaction is $2000$ years. If the concentration after $8000$ years is $0.02 \, M$,then the initial concentration was $........... \, M$.

For a first-order reaction $A \rightarrow \text{product}$, the rate constant is $k = 2 \times 10^{-2} \text{ s}^{-1}$. If the initial concentration of $A$ is $[A]_0 = 1.0 \text{ mol dm}^{-3}$, find the value of $\log \frac{1}{[A]_t}$ after $t = 100 \text{ s}$.

For a first-order reaction,the concentration of the reactant decreases from $0.8 \, M$ to $0.4 \, M$ in $15 \, \text{minutes}$. The time required for the concentration to change from $0.1 \, M$ to $0.025 \, M$ is ....... $\text{min}$.