$6-13.$ Determine the lime and soda ash dose, in $m\frac{g}{L}$ as $CaC{O}_3,$ to soften the following water to a final hardness of $80\mathrm{.}0m\frac{g}{L}$ as $CaC{O}_3.$ The ion concentrations reported below are all $m\frac{g}{L}$ as $CaC{O}_3.$

$C{a}^{2+}=120\mathrm{.}0$

$M{g}^{2+}=30\mathrm{.}0$

$HC{O}_3^{-}=70\mathrm{.}0$

$C{O}_2=10\mathrm{.}0$

Answers: Total lime addition $=100m\frac{g}{L}$ as $CaC{O}_3$

Total soda ash addition $=40m\frac{g}{L}$ as $CaC{O}_3$