Q. Write short note on units of hardness and their relationship.

Sol. Units of hardness and their relationship.

(1)         Parts Per million (ppm): It is defined as the number of parts by weight of CaCO₃ equivalent present in per million (10⁶) parts by weight of water.

1 ppm = 1 part of CaCO₃ equivalent hardness in (10⁶) parts of water.

(2)         Milligrams per litre (mg/l): It is defined as the number of milligrams of CaCO₃ equivalent hardness present in one litre of water.

1 mg/L = 1 mg of CaCO₃ equivalent hardness present per litre of water.

It can be easily proved that 1mg/L = 1 ppm, for water

Weight of 1 litre of water = 1kg = 10³g = 10⁶mg

= 1000*1000g= 10⁶mg

1mg/L = 1mg of CaCO₃ equivalent hardness per 10⁶ parts of water.

         1mg/L = 1 part of CaCO₃ equivalent hardness per 10⁶ parts of water.

1mg/L = 1ppm

(3)         Degree Clark (⁰Cl): It is defined as the parts of CaCO₃ equivalent hardness per 70,000 parts of water or it is number of grains (1/7000lb) of CaCo₃ equivalent hardness per gallon (10lb or 70,000 grains) of water. 1⁰ Clark= 1 part of CaCo₃ per 70,000 part of water.

(4)         Degree of French (⁰Fr): It is defined as the parts of CaCO₃ equivalent hardness per Lac (100000) parts of water.

1⁰Fr = 1 part of CaCO₃ equivalent hardness per (10⁵) parts of water.

(5)         Milli equivalent per litre (meq/L): It is defined as the number of milli equivalents of hardness present per litre.

1 meq/L = 1 meq of CaCO₃ per L of water

                 = 10^-3 * 50g of CaCO₃ eq. per litre of water

                   =   10^-3 * 1000 * 50 mg of CaCO₃ eq. per litre of water

                 = 50mg of CaCO₃ eq. per litre of water

                 = 50mg/L of CaCO₃ eq. per litre of water = 50 ppm

                 = 50mg of CaCO₃ eq. per 10⁶ litre of water

                 = 1 mg of CaCO₃ eq. per 10⁶ /5 mg litre of water

                  = 1 part of CaCO₃ equivalent per 20,000 parts of water.

Relationship between different units of hardness:

1 ppm = 1 part per 1000000 parts of water

1 ⁰Fr = 1 part per 100000 parts of water

1 ⁰Cl = 1 part per 70000 parts of water

1 mg/L = 1 part per 1000000 parts of water

1 meq/L = 1 part per 20000 parts of water

Hence: 1000000 ppm = 100000⁰Fr = 70000⁰Cl = 1000000 mg/L = 20000meq/L

= 100 ppm = 10⁰Fr = 7⁰Cl = 100mg/L = 2 meq/L

    1 mg/L     = 1 ppm = 0.1⁰Fr = 0.07⁰Cl = 0.02 meq/L

1⁰Cl = 14.3 ppm = 1.433 ⁰Fr = 14.3 mg/L = 0.286 meq/L

1⁰Fr = 10 ppm = 10 mg/L = 0.7 ⁰Cl = 0.2 meq/L

1 meq/L = 50 mg/L = 50 ppm = 5 ⁰Fr = 0.35 ⁰Cl