Calculate the amount of limen, `Ca(OH)_(2)`, required to remove hardness of 50,000 litres of well water which has been found to contain 1.62 g of calcium bicarbonate per 10 litre.

Explanation

(i) Calculation of total `Ca(HCO_(3))_(2)` present
10 L of water contains `Ca(HCO_(3))_(2)=1.62 g`
`therefore 50, 000 L` of water will contain `Ca(HCO_(3))_(2)=(1.62)/(10)xx50000 g=8100 g`
(ii) Calculation of lime required. The balanced equation for the reaction involved is :
`{:(" "Ca(HCO_(3))_(2),+," "Ca(OH)_(2),rarr,2CaCO_(3)+2H_(2)O),(" 1 mole",," 1 mole",,),(40+(1+12+48)xx2=162 g,,40+(16+1)xx2=74 g,,):}`
`162 g Ca(HCO_(3))_(2)` required lime = 74 g
`therefore 8100g Ca(HCO_(3))_(2)` will required lime `=(74)/(162)xx8100 g=3700 g = 3.7 kg`