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 CaCO_{3} equivalent present in per million (10^{6}) parts by weight of water.
1 ppm = 1 part of CaCO_{3} equivalent hardness in (10^{6}) parts of water.
(2) Milligrams per litre (mg/l): It is defined as the number of milligrams of CaCO_{3} equivalent hardness present in one litre of water.
1 mg/L = 1 mg of CaCO_{3 }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 = 10^{3}g = 10^{6}mg
= 1000*1000g= 10^{6}mg
1mg/L = 1mg of CaCO_{3} equivalent hardness per 10^{6} parts of water.
1mg/L = 1 part of CaCO_{3} equivalent hardness per 10^{6} parts of water.
1mg/L = 1ppm
(3) Degree Clark (^{0}Cl): It is defined as the parts of CaCO_{3} equivalent hardness per 70,000 parts of water or it is number of grains (1/7000lb) of CaCo_{3} equivalent hardness per gallon (10lb or 70,000 grains) of water. 1^{0} Clark= 1 part of CaCo_{3} per 70,000 part of water.
(4) Degree of French (^{0}Fr): It is defined as the parts of CaCO_{3} equivalent hardness per Lac (100000) parts of water.
1^{0}Fr = 1 part of CaCO_{3} equivalent hardness per (10^{5}) 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 CaCO_{3} per L of water
= 10^{-3} * 50g of CaCO_{3} eq. per litre of water
= 10^{-3} * 1000 * 50 mg of CaCO_{3} eq. per litre of water
= 50mg of CaCO_{3} eq. per litre of water
= 50mg/L of CaCO_{3} eq. per litre of water = 50 ppm
= 50mg of CaCO_{3} eq. per 10^{6} litre of water
= 1 mg of CaCO_{3} eq. per 10^{6} /5 mg litre of water
= 1 part of CaCO_{3} equivalent per 20,000 parts of water.
Relationship between different units of hardness:
1 ppm = 1 part per 1000000 parts of water
1 ^{0}Fr = 1 part per 100000 parts of water
1 ^{0}Cl = 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 = 100000^{0}Fr = 70000^{0}Cl = 1000000 mg/L = 20000meq/L
= 100 ppm = 10^{0}Fr = 7^{0}Cl = 100mg/L = 2 meq/L
1 mg/L = 1 ppm = 0.1^{0}Fr = 0.07^{0}Cl = 0.02 meq/L
1^{0}Cl = 14.3 ppm = 1.433 ^{0}Fr = 14.3 mg/L = 0.286 meq/L
1^{0}Fr = 10 ppm = 10 mg/L = 0.7 ^{0}Cl = 0.2 meq/L
1 meq/L = 50 mg/L = 50 ppm = 5 ^{0}Fr = 0.35 ^{0}Cl