Question

Calculate the amount of lime and soda required for softening 50,000 litres of hard water
containing: MgCO 3 = 144 ppm, CaCO 3 = 25 ppm, MgCl 2 = 95ppm, CaCl 2 = 111ppm, Fe 2 O 3 =
25ppm and Na 2 SO 4 = 15ppm
[Given: At. Wt of Mg= 24, C=12, O=16, Ca=40, Cl=35.5, Fe= 55.85, Na= 23, S= 32]

Answer 1

MgCO 3 = 144 ppm, CaCO 3 = 25 ppm, MgCl 2 = 95ppm, CaCl 2 = 111ppm, Fe 2 O 3 = 25ppm and Na 2 SO 4 = 15ppm

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Answer 2

The amount of lime and soda required for softening 50,000 liters of hard water is lime 7.2 kg and soda is 10.6 kg respectively.

Explanation:

• The given water sample contains the following salts MgCO 3 = 144 ppm, CaCO 3 = 25 ppm, MgCl 2 = 95ppm, CaCl 2 = 111ppm, Fe 2 O 3 =25ppm and Na 2 SO 4 = 15ppm

• Hardness caused by each salt is calculated as follows and its contribution for the use of lime and soda is calculated as follows

• $MgCO 3 = 144 ppm$,Multiplication factor is  $100/84$ ,Hardness by the salt is $144$×  $100/84$$=171.43 mg/l$  
• $CaCO 3 = 25 ppm$, Multiplication factor is  100/100 Hardness by the salt is ,$25$×  $100/100$$=25mg/l$    
• $MgCl 2 = 95ppm, 100/95 ,95$×  $100/95=100mg/l$     Hardness by the salt is $100 mg/l$
• $CaCl 2 = 111ppm, 100/111 ,111$×  $100/111=100mg/l$   Hardness by the salt is $100 mg/l$                                                                                        Fe2O 3 =25ppm and   No contribution in Hardness                                                                      Na2SO4 = 15ppm  No contribution in Hardness        

• Lime requirement=74/100(Temp Calcium as calcium carbonate +2(Temp Magnesium as Magnesium carbonate)+Perm Magnesium as Magnesium chloride)× Volume of water.

       =74/100 (25+171.43+100)×50000

       =7.2kg

Lime requirement=7.2kg

• Soda requirement=106/100(Perm Calcium  as Calcium chloride +Perm Magnesium as Magnesium chloride)×volume of water

      =106/100(100+100)×50000

      =10.6 kg

Soda requirement =10.6 kg