$(25$ Points$)$ The water defined by the analysis given below is to be softened by excess$-$lime $($and soda ash$)$ treatment.

a$)(10$ points$)$ Sketch an meq$/$L bar graph.

b$)(15$ points$)$ Calculate the softening chemicals required $($including quick lime$,$ soda ash in $m\frac{g}{l}).$

$C{O}_2=15m\frac{g}{L}$

$C{a}^{2+}=60m\frac{g}{L}$

$M{g}^{2+}=24m\frac{g}{L}$

$N{a}^{+}=46m\frac{g}{L}$

$HC{O}_3^{-}=200m\frac{g}{L}asCaC{O}_3$

$S{O}_4^{2-}=96m\frac{g}{L}$

$C{l}^{-}=35m\frac{g}{L}$