The city of Houghton recently discovered that one of its wells was contaminated with $100\frac{g}{L}$ methyl tert butyl ether $($MtBE$)($molecular weight is $88\frac{g}{\text{m}\text{o}\text{l}})$ because of the gasoline spill from a gas station. Calculate the effluent concentrations of MtBE for $H_2{O}_2$ dosage at $1\mathrm{.}0mM(34m\frac{g}{L})$ if one completely mixed flow reactor is used with $1,000L$ of volume and two treatment trains $($note that each photoreactor has $12$ low pressure UV lamps that emit photon at only $254nm$ wavelength with $15kWh$ power per each lamp and $30\%$ of power efficiency$)(10$ points$).$ In addition, calculate the EE$/$O values for each $H_2{O}_2$ dose and discuss how EE$/$O and effluent concentrations of MtBE are changed as a function of the $H_2{O}_2$ doses. $(10$ points$).$

During normal pumping of the well field, the flow rate is $1\mathrm{.}0\frac{m^3}{s}.$ The $pH,$ alkalinity and DOC concentrations are $7\mathrm{.}0,500m$g$/$L as $CaC{O}_3,$ and $0\mathrm{.}5mg\frac{C}{L},$ respectively. You can assume that $HC{O}_3^{-}($molecular weight is $61\frac{g}{m}ol)$ is the only species at $pH=7\mathrm{.}0.$ You can assume that $H_2{O}_2($molecular weight is $34\frac{g}{m}ol)$ is the major species even though $H_2{O}_2$ dissociates into $H{O}_2^{-}$in water.

The molar absorptivity of MtBE,$HC{O}_3^{-},$ and $C{O}_3^{2-}$ are negligible but those of $H_2{O}_2$ and NOM are $19\mathrm{.}6$ and $0\mathrm{.}0196\frac{L}{m}$olcm. Only quantum yield of $H_2{O}_2$ is used as $0\mathrm{.}5$ and the quantum yields of other species are zero. The second order rate constants of hydroxyl radicals with MtBE,$HC{O}_3,H_2{O}_2$ and NOM are $1\mathrm{.}6{10}^9{M}^{-1}{s}^{-1},8\mathrm{.}5{10}^6{M}^{-1}{s}^{-1},2\mathrm{.}7{10}^7{M}^{-1}{s}^{-1},$ and $3\mathrm{.}9{10}^{8}M{c}^{-1}{s}^{-1}.$ The $E\frac{E}{O},kW\frac{h}{m^3},$ is calculated as $\frac{P}{Qlog(\frac{C_i}{C_r})}$ where $P$ is the power, $kW,Q$ is the flow rate, $\frac{m^3}{h},$ and $C_i$ and $C_f$ are the influent and effluent concentrations. You can modify the following initial steady$-$state concentration of hydroxyl radicals.

where

$,P$ is the lamp power, $W,{}_{is\text{t}\text{h}\text{e}\text{l}\text{a}\text{m}\text{p}\text{e}\text{f}\text{f}\text{i}\text{c}\text{i}\text{e}\text{n}\text{c}\text{y}\text{,}}{N}_{av}$ is the Avogadro's number, $6\mathrm{.}023{10}^{23}$ molecules $\frac{?}{\text{m}\text{o}\text{l}},h=$ Planck's constant, $6\mathrm{.}62{10}^{-34}J*s,v=$ frequency of light, $s^{-1}.$ You can assume all lights are absorbed inside the photoreactor.