$6-15.$ Determine the lime and soda ash dose, in $m\frac{g}{L}$ as CaO and $N{a}_{2}C{O}_3,$ 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 $CaC{O}_3.$ Assume the lime is $90$ percent pure and the soda ash is $97$ percent pure.

$C{a}^{2+}=210\mathrm{.}0$

$M{g}^{2+}=23\mathrm{.}0$

$HC{O}_3^{-}=165\mathrm{.}0$

$C{O}_2=5\mathrm{.}0$

Answers: Total $lime$ addition $=118m\frac{g}{L}as$ CaO

Total soda ash addition $=31m\frac{g}{L}asN{a}_{2}C{O}_3$