What is the half-life of a first-order reaction if the time required to decrease the concentration of the reactant from $0.8 \text{ M}$ to $0.2 \text{ M}$ is $12 \text{ hours}$ (in $\text{ hours}$)?

Identify $True$ $(T)$ and $False$ $(F)$ statements of the following for a first order reaction $R \rightarrow P$.
$I. \log \frac{[R]}{[R]_0} = -\frac{kt}{2.303}$
$II. \log \frac{[R]}{[R]_0} = \frac{kt}{2.303}$

Consider a certain reaction $A \rightarrow \text{Products}$ with $k = 2.0 \times 10^{-2} \ s^{-1}$. Calculate the concentration of $A$ remaining after $100 \ s$ if the initial concentration of $A$ is $1.0 \ mol \ L^{-1}$.

Which of the following is the correct equation for a first-order reaction?

For the first-order gaseous reaction $A \rightarrow 2B + C$ at $373 \, K$,starting with pure $A$,the total pressure of the system after $10 \, min$ is $176 \, mm \, Hg$ and after a long time,it is $270 \, mm \, Hg$. Based on this information,calculate: $(1)$ Initial pressure of $A$,$(2)$ Pressure of $A$ after $10 \, min$,and $(3)$ Rate constant.

Time required to decompose $SO_2Cl_2$ to half of its initial amount is $60 \ min$. If the decomposition is a first order reaction,calculate the rate constant of the reaction. (in $min^{-1}$)