A sample of water contains following impurities :

Mg(HCO3)2 =73 mg/lit , MgSO4 = 120 mg/lit , CaCl2 = 222 mg/lit and Ca(NO3)2 = 164 mg/lit . The purity of lime is 74% and soda is 90% . Calculate the quantity of lime and soda needed for softening of 50,000 litres of water .

#### Solution

Impurities(mg/lit) |
MultiplicationFactor |
CaCO_{3} equivalents (mg/lit) |
Requirement |

Mg(HCO_{3})2 |
100/146 | 73 x 100/146 =50 | 2L |

MgSO_{4} |
100/120 | 120 x 100/120 =100 | L + S |

CaCl_{2} |
100/111 | 222 x 100/111 =200 | S |

Ca(NO_{3})_{2} |
100/164 | 164 x 100/164 =100 | S |

Lime Requirement = 74/100 x [CaCO_{3} equivalent of 2x Mg(HCO_{3})_{2} + MgSO_{4} ]

= 74/100 x [100 + 100 ]

=148 ppm .

Lime Required for 50,000 litres of water with 74% purity

= 148 x 50,000 x 100/74

= 10,000 gm .

Soda Requirement = 106/100 x [CaCO_{3} equivalent of MgSO_{4} + CaCl_{2} + Ca(NO_{3})_{2} ]

= 106/100 x [100 + 200 + 100 ]

= 424 ppm .

Soda Requirement for 50,000 litres of water with 90% purity

=424 x 50,000 x 100/90

= 23,556 gm .

The Lime Requirement is 10,000 gm and Soda Requirement is 23,556 gm .