CHLORINE IN CAST IRON PIPES. $(20$ pts$)$

Water pipe corrosion occurs when the iron in the pipes is oxidized from $F{e}^{2+}$ to $F{e}^{3+}$ by the

oxidizing agent used as disinfectant in the tap water. Hypochlorous acid $(HOCl)$ is a strong oxidant

that inactivates pathogens, but it also oxidizes iron when we use cast iron pipes.

$($a$)$ HOCl is a weak acid that dissociates to $H^{+}$and $OC{l}^{+}$with a $K_4$ of $2\mathrm{.}9{10}^{-5}M.$ The molecular

weight of HOCl is $52\mathrm{.}46\frac{g}{m}ol.$ The target concentration of HOCl at equilibrium is $3m\frac{g}{L}$ with a

$pH$ value of $7\mathrm{.}2,$ how much HOCl $($in $mg)$ would you initially add to $1L$ of water to disinfect it$?(8$

pts$)$

$($b$)$ Write the two half reactions and the overall chemical equation for the oxidation of $F{e}^{2+}$ to $F{e}^{3+}$

with HOCl being converted to $Cl.($Hint: Write two half reactions, then add them together$)(5pts$

$($c$)$ A water treatment plant adds HOCl to its water as it leaves the water treatment plant. The HOCl

concentration decreases as the water moves through the distribution system. If the flow rate from

the water treatment plant is $2,000m^{3}h{r}^{-1}$ and the distribution pipe is a cast iron pipe with a cross

sectional area of $0\mathrm{.}70m^2,$ what will be the approximate HOCl concentration at a home $20km$ from

the water treatment plant? The first order rate constant $($k$)$ for HOCl is $0\mathrm{.}30h{r}^{-1}.$ Assume the initial

HOCl concentration is equal to the concentration in part $($a$)$ at equilibrium $(3mgL)$ and ignore

impacts of changing $pH.$ No corrosion inhibitor is added to the distribution system. Assume this

system is a Plug Flow Reactor $($PFR$).(7$ pts$)$