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Question

Permanent hardness is due to Cl and SO24 of Mg2+ and Ca2+ and is removed by adding Na2CO3.


CaSO4+Na2CO3CaCO3+Na2SO4
CaCl2+Na2CO3CaCO3+2NaCl

Which of the following statements is/are correct?

A
If hardness is 100 ppm CaCO3, the amount of Na2CO3 required to soften 10 L of hard water is 1.06 g.
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B
If hardness is 100 ppm CaCO3, the amount of Na2CO3 required to soften 10 L of hard water is 10.6 g.
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C
If hardness is 420 ppm MgCO3, the amount of Na2CO3 required to soften 10 L of hard water is 53.0 g.
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D
If hardness is 420 ppm MgCO3, the amount of Na2CO3 required to soften 10 L of hard water is 5.3 g.
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Solution

The correct options are
A If hardness is 100 ppm CaCO3, the amount of Na2CO3 required to soften 10 L of hard water is 1.06 g.
D If hardness is 420 ppm MgCO3, the amount of Na2CO3 required to soften 10 L of hard water is 5.3 g.
Molecular weight of CaCO3 =40+12+3×16=100 g/mol
Molecular weight of Na2CO3=46+60=106 g/mol

i. CaSO4xmol+Na2CO3xmolCaCO3xmol+Na2SO4

ii. CaCl2ymol+Na2CO3ymolCaCO3ymol+2NaCl

iii. 100 ppm CaCO3100 g CaCO3 in 106 mL =100100 mol in 106 mL

Moles of Na2CO3 required = Moles of CaCO3
100100 mol in 106 mL
1 mol in 106 mL
1106×10×103 mL per 10 L =1×102 mol in 10 L

Therefore, moles of Na2CO3 required
=1×102 mol in 10 L
=1×102×106 g per 10 L
=1.06 g

Similarly, for 100 ppm MgCO3 (Molecular weight of MgCO3=24+60=84 g/mol),

iv. MgSO4xmol+Na2CO3xmolMgCO3x mol+Na2SO4

v. MgCl2ymol+Na2CO3ymolMgCO3ymol+2NaCl

vi. 420 ppm MgCO3420 g MgCO3 in 106 mL
42084=5 mol in 106 mL

Moles of Na2CO3 required moles of MgCO3
5 mol in 106 mL
5106×10×103 mL per 10 L
5×102 mol in 10 L

Moles of Na2CO3 required 5×102 mol per 10 L
5×102× per 10 L
=5.3 g per 10 L

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