Hydrogen sulfide $(H_2(S))$ is an acid that can corrode the steel in expensive equipment installed in wastewater treatment plants. The Henry's law constant for $H_{2}S$ at $25C$ is $3\mathrm{.}49\frac{g}{L}-$atm. $H_{2}S$ gas is also toxic and the lowest$-$observed$-$adverse$-$effect$-$level $($LOAEL$)$ for asthmatic individuals is $2\mathrm{.}8m\frac{g}{m^3}.$ It dissociates in water with an acid dissociation constant $K{a}_1=0\mathrm{.}86{10}^{-7}$ to yield a proton and a bisulfide anion:

$H_{2}S(aq)>H^{+}+H{S}^{-}$

$($a$)$ Find the fraction of $H_{2}S$ in the $H_{2}S($aq$)$ form $($this is the strippable fraction$)$ as a function of $pH,$ and draw a graph of the $H_{2}S$ fraction versus $pH(pH2$ to $pH10).$

$($b$)$ If the total sulfide concentration $-)$ in the raw wastewater in summer $($WW temperature $=25C)$ is $3\mathrm{.}0m\frac{g}{L},$ and the $pH$ of raw wastewater is $7\mathrm{.}5,$ determine the concentration of $H_{2}S$ in the air at sea level. Would the concentration of $H_{2}S$ in the air be a cause of concern? $($ie$.,$ is it above the LOAEL?$)$