Given the following water quality data: CO$2=8\mathrm{.}8$ mg$/$l$,$ Ca$2+=40\mathrm{.}0$ mg$/$l$,$ Mg$2+=14\mathrm{.}7$ mg$/$l$,$ Na$+=13\mathrm{.}7$

mg$/$l$,$ Alkalinity $($HCO$3$

$-)=135$ mg$/$l as CaCO$3,$ SO$42-=29\mathrm{.}0$ mg$/$l$,$ and Cl$-=17\mathrm{.}8$ mg$/$l$.$

$($a$)$ Estimate theoretical stoichiometric doses $($mg$/$l$)$ required if the following combinations of

chemical$($s$)$ are employed to soften the above water:

i$.)$ Lime$/$Soda Ash

ii$.)$ Lime

iii.$)$ Caustic Soda

$($b$)$ In addition, estimate the residual hardness $($mg$/$l as CaCO$3)$ after dosing with each chemical

treatment listed above.

$($c$)$ Estimate the reduction in TDS after dosing with each chemical treatment scheme listed

above