$($b$)$ If the water contains $2m\frac{g}{L}$ of $F{e}^{2+}$ and $1m\frac{g}{L}$ of $N{H}_3$ as $N,$ what concentration of free chlorine $($in $m\frac{g}{L}$ as $C{l}_2)$ would we have to add to the water in the bottle to ensure a sufficient level of free chlorine remains after the reactions with $F{e}^{2+}$ and $N{H}_3$ to achieve the desired level of Giardia cyst inactivation? You can assume a stoichiometry of $[HOCl]$:$[F{e}^{2+}]=0\mathrm{.}5$ for reaction of free chlorine with $F{e}^{2+},$ and a stoichiometry of $[HOCl]$:$[N{H}_3]=1\mathrm{.}5$ for reaction of free chlorine with $N{H}_3,$ that each reaction proceeds instantaneously, and that the bottle behaves as a batch reactor.

Note: Assume that free chlorine is not consumed in this water by any other reactions than the reactions with $F{e}^{2+}$ and $N{H}_3,$ and that the free chlorine concentration remains constant once the $F{e}^{2+}$ and $N{H}_3$ are fully consumed. Recall that M${}_{}$WFe=56gmol,MWN=14gmol, and $MWC{l}_{Cl}=70\mathrm{.}9\frac{g}{m}ol.$