A surface water is coagulated with a dosage of $30m\frac{g}{l}$ of aluminum sulfate as alum and an equivalent dosage of lime to neutralize the hydrogen ions produced in the hydrolysis of aluminum.

$($a$)$ How many pounds of alum are needed per mil gal of water treated?

$($b$)$ How many pounds of quicklime are required?

$($c$)$ How many pounds of sludge are produced per mil gal of water treated?

$A{l}_2(S{O}_4{)}_3*14H_{2}O+3Ca(OH{)}_{2}2Al(OH{)}_{3,\text{a}\text{m}\text{d}\text{a}\text{r}\text{r}}+3CaS{O}_4+14H_{2}O$