You conducted a batch experiment in the lab for $10$ minutes to degrade a toxic compound, which follows first order kinetics. The compound degrades from $2 \times 10^{-3} \mathrm{M}$ to $2 \times 10^{-4} \mathrm{M}$. The information from the lab experiment will be used to design a plug flow reactor in field conditions.
Given field conditions:
- Flow rate of contaminated water to be treated: $1 \mathrm{~m}^{3} /$ hour
- Concentration of toxic compound in contaminated water: $5 \times 10^{-1} \mathrm{M}$
- Target concentration of toxic compound in treated water: $1 \times 10^{-4} \mathrm{M}$
- Temperature is same in lab and field conditions.
The required volume of the plug flow reactor is $\_\_\_\_\_\_\_ \: \mathrm{m}^{3}$. (rounded off to two decimal places)
