DEGREE OF HARDNESS:

The degree of hardness of water is conveniently expressed in terms of equivalent amount of CaCO₃. Although hardness of water is never present in the form of calcium carbonate because it is insoluble in water and hardness is actually caused by bicarbonates, chlorides and sulphates of calcium and magnesium. Choice of CaCO₃ as the standard for reporting hardness of water is due to its molecular weight which is exactly 100 and equivalent weight is 50 (easy for calculations). Moreover it is the most insoluble salt that can be precipitated in water treatment. Thus equivalent of CaCO₃ for hardness producing substance can be calculated by formula.

For calculating the multiplication factor of hardness producing substances to convert into equivalent of CaCO₃, according to following steps given below:

For example: To find the multiplication factor of Mg (HCO₃)₂

Step1. Molar mass of Mg (HCO₃)₂ = 146

Step2. Find molar mass of CaCO₃ (100)

Step3. Multiplication factor =2/2*chemical equivalents 

Step4. Find molar mass of CaCO₃

Multiplication factor = 100/2*73 = 100/146

NOW, we calculate hardness of Mg (HCO₃) in terms of CaCO₃ equivalents.

Suppose, x quantity of Mg (HCO₃)₂ = x.100/146 amount of CaCO₃.

Thus, the factor 100/146 is multiplication factor for Mg (HCO₃)_2. Multiplication factors for different compounds are given in table.

Table: Formulae and multiplication factor of various dissolved salt/Ion

Dissolved             Molar                 Chemical                             Multiplication factor for converting into equivalents of

Salt/ion                 Mass                   Equivalent                          CaCO₃

Ca (HCO₃)₂           162                         81                                 100/162

Mg (HCO₃)₂           146                         73                                 100/146

CaSO₄                  136                         68                                  100/136

CaCl₂                   111                         55.5                                100/111

MgSO₄                  120                         60                                   100/120

MgCl_2­                   95                           47.5                                 100/95

CaCO₃                 100                          50                                    100/100

MgCO₃                 84                            42                                    100/84

Mg (NO₃)₂            148                          74                                     100/148

Ca⁺⁺                   40                            20                                     100/40

Mg⁺⁺                   24                            12                                     100/24

HCO₃-                  61                            61                                     100/2*61

CO₂^-2                  60                            30                                     100/2*17

OH^-                      17                            17                                     100/2*17

H⁺                       1                               1                                      100/2

CO₂                     44                            22                                     100/44

HCl                      36.5                         36.5                                   100/36.5*2

H₂SO₄                 98                             49                                     100/98

FeSO₄.7H₂O        278                            139                                   100/278

Al (SO₄)₃            342                             57                                    100/114

NaAlO₂               82                               82                                    100/164

Thus the various types of hardness in a water sample may be calculated as below:

Temporary hardness = [(hardness due to Ca (HCO₃)₂ + hardness of due to Mg (HCO₃)₂]

Permanent hardness = [(hardness due to CaCl₂ + CaSO₄ + MgSO₄ + MgCl₂ + Mg (NO₃)₂ + Ca (NO₃)₂]

Total hardness = [temporary hardness + permanent hardness]