Industrial wastewater effluent is discharged into a $1\mathrm{.}0{10}^9{m}^3$ lake and contains $7\mathrm{.}0{10}^{-5}M$ benzene $(C_6{H}_6).$ The industrial wastewater discharge stream has a flowrate of $8\frac{m^3}{s}.$ The stream feeding the lake has a benzene concentration of $1\mathrm{.}0\frac{g}{L}$ and a flowrate of $100\frac{m^3}{s}.$ Benzene has a decay rate of $0\mathrm{.}038da{y}^{-1}.$

a$)$ What order is the reaction rate?

b$)$ What is the concentration of benzene in $\frac{g}{L}$ in the lake after mixing?

c$)$ What is the maximum contaminant limit $($MCL$)$ for benzene $($check Table $6-1)?$ Does the concentration you calculated in $($b$)$ meet the MCL set by the Safe Drinking Water Act? $($Limit is $5\backslash$mu g$/$L$)$

d$)$ Draw a diagram, write governing equations, and state all assumptions.