$($PLEASE SONT FORGET THE GRAPH$)$

Using the following set of reactions, generate a $log$ Ca vs$.pH$ diagram depicting the solubility of calcite and accounting for hydroxide complexation.

$CaC{O}_3(s),$larr$C{a}^{2+},+C{O}_3^{2-},log{K}_{sp}=-8\mathrm{.}48$

$C{a}^{2+}+O{H}^{-},$larr$CaO{H}^{+},log{K}_1=4\mathrm{.}40$

$H_{2}C{O}_3,$larr$H^{+},+HC{O}_3^{-},log{K}_{al,CO}=-6\mathrm{.}35$

$HC{O}_3^{-},$larr$H^{+},+C{O}_3^{2-},log{K}_{12},CO=-10\mathrm{.}33$

$H_{2}O,$larr$H^{+},+O{H}^{-},log{K}_w=-14\mathrm{.}0$

Assume this conditional system $($closed with solid yet to form; constant $C_{T,CO})$ can be used to predict Ca solubility in a lime$-$soda ash chemical precipitation water softening plant.

i$)$ If the system is operated at $pH9\mathrm{.}30$ and the effluent alkalinity is $35$mgCaCO$\frac{3}{L},$ what is the minimum solubility of $Ca$ in equilibrium with calcite? Report your answer as $(mgC\frac{a}{L}).$ State any assumptions.

ii$)$ If the $pH$ remained constant and the effluent alkalinity increased to $70$mgCaC$\frac{O}{2},$ would $Ca$ solubility increase or decrease? Defend your answer $($but another $logCa-pH$ diagram is not required$).$