$[40$ points$]$ Household bleach, sodium hypochlorite $(NaOCl),$ is used as a disinfectant.

Neglecting ionic strength effects, determine the $($i$)pH$ and $($ii$)$ concentrations of the "free

chlorine" species, HOCl and OCl$-,$ in a freshly prepared solution of ${10}^{-3}$MNaOCl in distilled

water. To streamline solving this problem, do not account for carbonate in the system and

assume that $[OC{l}^{-}]>>[HOCl]$ and that $[HOCl]>>[H+].$ Provide reasoning for why these are

valid assumptions.