A water $,$ alk $=185m\frac{g}{L}$ as $CaC{O}_3)$ has a calcium hardness of $195m\frac{g}{L}$ as $CaC{O}_3$

and a magnesium hardness of $65m\frac{g}{L}$ as $CaC{O}_3.$

a$.$ Convert the calcium hardness, magnesium hardness, and alkalinity to units of

$me\frac{q}{L}.$

b$.$ Using the expression for alkalinity, calculate the $C_{t,CO3}(M)$ for this water. Note

that the carbonate system has $p{K}_{a1}=6\mathrm{.}35$ and $p{K}_{a2}=10\mathrm{.}33.$

c$.$ Draw the bar diagram for the water using units of meq$/$L$.($Your bar diagram

should include $4$ species relevant for softening.$)$

d$.$ For this water, determine the amount of carbonic acid, calcium carbonate hardness

only the fraction for which lime needs to be added to increase the $pH),$ calcium

noncarbonate hardness, magnesium carbonate hardness, magnesium noncarbonate

hardness, and the total lime and soda ash required for complete softening $($i$.$e$.,$

excess lime$-$soda softening$).$ Show all calculations, and fill in a table like the one

shown below with your final answers.