q. write short note on units of hardness and

Question

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