Write mass$-$balance expressions for a $0\mathrm{.}0100M$ solution of $HCl$ that is in equilibrium with an excess of solid $BaS{O}_4.$

As shown by Equations $11-1,11-2,$ and $11-3,$ three equilibria are present in this solution. That is$,$

$BaS{O}_4(s)B{a}^{2+}+S{O}_4^{2-}$

$S{O}_4^{2-}+H_3{O}^{+}HS{O}_4^{-}+H_{2}O$

$2H_{2}O{H}_3{O}^{+}+O{H}^{-}$