Calculate the quantities of reagents required to soften `10^(3)` L of water containing `Ca(HCO_3)_2` `Mg(HCO_3)_2` and `CaSO_4` as 20.0 g, 15.0 g and 5.0 g per litre respectively by lime soda process.

Explanation

`20.0 g of Ca(HCO_(3))_(2)-=(20xx100)/(162)=12.34 g of CaCO_(3)`
`15.0 g of Mg(HCO_(3))_(2)-=(15xx100)/(146)=10.27g of CaCO_(3)`
`5.0 of CaCO_(4)-=(5xx100)/(136)=3.67g of CaCO_(3)`
Lime requirement:
`=(74)/(100)` [ Temporary Ca- Hardness`+2xx` Temporary Mg-Hardness `+` Permanent Mg-hardness]
`=(74)/(100)[12.34+2xx10.27]`
`=(24.33g)/(L)` of `CaCO_(3)eq`
`=24.33xx(10^(3)g)/(10^(3)L)`
`=(24.33gk)/(10^(3)L) of CaCO^(3) eq`
Soda requirement:
`=(106)/(100)` [permanent Ca-hardnes`s^(+)` Permanent Mg-hardness]
`=(106)/(100)[3.67]`
`k=(3.89g)/(L) of CaCO_(3)` equivalent
`=3.89xx(10^(3)g)/(10^(3)L)` of `CaCO_(3)eq`
`=(3.89kg)/(10^(3)L) of CaCO_(3) eq`