What is the value of the slope when a graph is plotted of $\log \frac{[R]_0}{[R]}$ versus $t$ (time) for a first-order reaction?

If the concentration of a first order reaction is increased by $x$ times,then the rate constant $(k)$ becomes

An organic compound undergoes first order decomposition. The time taken for decomposition to $\left(\frac{1}{8}\right)^{\text{th}}$ and $\left(\frac{1}{10}\right)^{\text{th}}$ of its initial concentration are $t_{1/8}$ and $t_{1/10}$ respectively. What is the value of $\frac{t_{1/8}}{t_{1/10}} \times 10$? (Given: $\log 2 = 0.3$)

For a first-order reaction,if the rate constant $K = 5.5 \times 10^{-14} \ s^{-1}$,then its half-life period will be .......

The time of completion of $90\%$ of a first order reaction is approximately

The decomposition of $O_{3(g)}$ follows first order kinetics and is given by $O_{3(g)} \longrightarrow O_{2(g)} + O_{(g)}$. The rate constant for this reaction is $1.0 \times 10^{-3} \ s^{-1}$. The initial pressure of $O_{3(g)}$ is $100 \ atm$. What will be the partial pressure (in $atm$) of $O_3, O_2, O$ respectively after $38.38 \ minutes$?