Rain water droplets equilibrate with gases in the atmosphere. The local$/$regional atmospheric chemistry will control the $pH$ and acidity of rain water. Using the following gas concentrations, dissolution reactions, and acid$-$base reactions,

$($a$)$ Prepare a $logC-pH$ diagram for the system.

$($b$)$ Use the charge balance equation to determine the $pH$ of the solution.

$($c$)$ Determine acidity of the water in equilibrium with these two gases.

$[$acidity$](e\frac{q}{L})=[H^{+}]-[O{H}^{-}]+[H_{2}C{O}_3]-[C{O}_3^{2-}]+[H_{2}S{O}_3]-[S{O}_3^{2-}]$

Report acidity as mgCaCO$\frac{3}{L}.$

$PC{O}_2=400pp{m}_v$;$T=25C$;$P=1$atm

$C{O}_2(g)+H_{2}O(l)H_{2}C{O}_3(aq),K_{H,C{O}_2}={10}^{-1\mathrm{.}47}(\frac{M}{a}tm)$

$H_{2}C{O}_3{H}^{+}+HC{O}_3,K_{31,CO}^3={10}^{-635}$

$HC{O}_3^{-}{H}^{+}+C{O}_3^{2-},K_{22},C{O}_3={10}^{-10\mathrm{.}33}$

$P_{S{O}_2}=35pp{b}_v$;$T=25C$;$P=1$atm

$S{O}_2(g)+H_{2}O(l)H_{2}S{O}_3(aq),K_{H,S{O}_2}=1\mathrm{.}23(\frac{M}{a}tm)$

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

$HS{O}_3^{-}{H}^{+}+S{O}_3^{2-}$

$K_{1,503}={10}^{-1\mathrm{.}86}$

$K_{32,SO3}={10}^{-7,30}$