A water treatment plant that uses soda ash $($Na $2$ CO $3)$ and unslaked lime in a lime$-$

soda process for softening wishes to produce caustic soda for magnesium removal $($as Mg$($OH$)2)$

according to the reactions

CaO$($s$)+$ H $2$ O $$ Ca$($OH$)2($s$)$

Mg$2++2$HCO $3-+$ Ca$($OH$)2($s$)$ MgCO $3($s$)+$ CaCO $3($s$)+2$H $2$ O

Na$2$ CO $3+$ Ca$($OH$)22$ NaOH $+$ CaCO $3($s$)$

$($a$)$ Identify the process$($es$)$ that are involved in this operation and explain your answers.

$($b$)$ Calculate how much NaOH can be obtained per metric ton of Na $2$ CO $3$