A $3L$ glass container is partially filled with $V_w=1L$ of pure water. The remaining $2L$ contains

clean air $(\{$:$P=1(atm),(T)=25C).$ Solid iron sulfide $($ FeS$(s))$ is added to the water in sufficient

quantity so that some solid will remain in the system at equilibrium. The container is quickly sealed

before any reactions occur. Iron sulfide dissolves to $F{e}^{2+}$ and $S^{2-}.$ The sulfide participates in acid$-$

base chemistry, combining with protons to form both $H{S}^{-}$and $H_{2}S($aq$).$ The aqueous hydrogen

sulfide can escape into the gas phase as $H_2{S}_{(g)}.$

FeS$(s)harrF{e}^{2+}+S^{2-},K_{sp}=4\mathrm{.}9{10}^{-18}$

$H_{2}S(aq)harr{H}^{+}+H{S}^{-},K_{a1}=1{10}^{-7}$

$H{S}^{-}harr{H}^{+}+S^{2-},K_{a2}=6\mathrm{.}2{10}^{-8}$

The Henry's constant for $H_{2}S$ is $0\mathrm{.}115mo\frac{l}{L}\frac{?}{\text{a}\text{t}\text{m}}$

Ideal gas law: $PV=nRT,R=0\mathrm{.}08205atmLmol{e}^{-1}{K}^{-1}$

$($a$)$ Identify all the unknowns in the system $($both water and air phase$).(3$ pts$).$

$($b$)$ Write a complete set of algebraic equations to solve for the equilibrium $pH$ of the water. $(8$ pts$)$

$($c$)$ Solve the above set of equations using EES, Excel, Maple, or equation solver of your choice. $(5$

pts$)$

$($d$)$ In water phase, what proportion of the total sulfides $($S$2-,$ HS$-,$ H$2$S$)$ is in the completely

unprotonated form of sulfide, at equilibrium? If you cannot figure out how to solve part $($c$),$ then

guess a $pH$ in order to calculate this proportion. Your guess should be reasonable! $(5$ pts$)$