BAR DIAGRAM METHOD FOR WATER SOFTENING PROBLEMS
Given a water having the following composition:
Ca++ - 40 mg/L = 2 meq/L
HCO3¯- 61 mg/L = 1 meq/L
Mg++ - 24 mg/L = 2 meq/L
SO42¯ - 192 mg/L = 4 meq/L
Na+ - 46 mg/l = 2 meq/L
Cl¯ - 35.5 mg/L = 1 meq/L
These totals must balance
+ 6 meq/L
-6 meq/L
a) Put these in the form of a bar diagram expressing all concentrations in terms of CaCO3 (50
mg/L CaCO3 = 1 meq/L)
0
100
200
Ca++
Mg++
HCO3¯
SO42¯
50
300
Na+
Cl¯
250
From diagram you can see that
Total hardness = 200 mg/L as CaCO3
Ca hardness = 100 mg/L as CaCO3
Mg hardness = 100 mg/L as CaCO3
Total alkalinity = bicarbonate alkalinity = 50 mg/L as CaCO3
So
carbonate hardness = 50 mg/L as CaCO3
non-carb. hardness = 150 mg/L as CaCO3
For excess lime softening
1. Add 1 meq/L of Ca(OH)2 to convert HCO3¯ to CO32¯
Ca(OH)2 + Ca (HCO3) 2 → 2CaCO3 ↓ + 2H2O
2. Add 2 meq/L of Ca(OH)2 to provide OH¯ for Mg precipitation
Ca(OH)2 + MgSO4 → Mg(OH)2 ↓ + CaSO4
3. Add 1 meq/L excess Ca(OH)2 to raise pH and allow Mg(OH)2 to precipitate.
Bar Diagram - 1
Excess
200 150
50
0
Ca
Ca
Ca
OH
OH
OH
100
Ca
200
Ca
Mg
HCO30
300
Na
SO4
Cl
50
250
→ CO32¯
This leaves
200
300
Ca
Na
OH
SO4
Cl
50
250
However in practice not all the CaCO3 and Mg(OH)2 will precipitate. Usually will have 40 mg/L
of CaCO3 and 25 mg/L of Mg(OH)2 left so we really have
25
265
Mg
Ca
OH
CO3
75
365
Na
SO4
Cl
115
315
For single stage softening we now have a water with a high pH, excess lime and Mg(OH)2.
Recarbonation will allow precipitation of CaCO3 and reduce pH.
CO2 + Ca(OH)2 → CaCO3 ↓ + H2O
CO2 + Mg(OH)2 → MgCO3 ↓ + H2O
So add 1 meq/L for excess lime added and 0.5 meq/L for the Mg(OH)2 left. Leaving
25
215
Mg
315
Ca
CO3
Na
SO4
65
Cl
265
Care must be taken here to avoid reducing pH to the point where CO32¯→ HCO3 as Ca(HCO3)2
will not precipitate.
Bar Diagram - 2
This water is still not completely satisfactory as we have
(1) CaCO3 still present -- which will precipitate in pipe lines, valves, etc.
(2) Non-carbonate hardness (CaSO4) which will prevent soap lathering.
For single stage softening we could convert the CO32¯ to HCO3¯ by adding more CO2 at this stage
CO2 + CO32¯ + H2O → 2HCO3¯
but this would leave l.3me/l carbonate hardness and 3 me/l non-carbonate hardness.
So, go to soda ash for removal of non-carbonate hardness
1. Add 3 meq/L Na2CO3
150
0
190
Na
Ca
CO3
CO3
290
Na
315
Mg
SO4
Cl
65
265
This will leave
40
290
Ca
Na
CO3
315
Mg
SO4
Cl
65
265
To avoid CaCO3 precipitation, now add 1.3 meq/L of CO2 to convert CO3 to HCO3 leaving a water
with a composition like this:
40
290
Ca
Na
HCO3
315
Mg
SO4
65
Bar Diagram - 3
Total chemical additions
Ca(OH)2 - 4 meq/L = 200 mg/L as CaCO3
Na2CO3 - 3 meq/L = 150 mg/L as CaCO3
CO2
- First stage 1.5 meq/L
2nd stage 1.3 meq/L
Total 2.8 meq/L = 140 mg/l as CaCO3
If lime is 95% pure and we treat 10 mgd (Imp)
mg 37
1
 
 10  10 = 15,570 #/day Ca(OH)2
l
50 0.95
53
- 150   10  10 = 15,900 #/day pure Na2CO3
50
22
- 140   10  10 = 6,160 #/day CO2
50
Require - 200
This could have been calculated in a manner similar to that in “chemical requirements”.
E.g., lime for CO2
-
0
HCO3-
-
1
Mg
-
2
Excess
-
1
4
meq/q
Soda ash for non-carbonate hardness - 3 meq/L
CO2 - for excess lime
- 1 meq/L
- for expected residual Mg(OH)2 - 0.5 meq/L
- for expected CO32¯ at the end of softening process
- l.3 meq/L
2.8 meq/L
Note that CO2 additions will depend largely on the final pH desired. They cannot therefore be
taken as absolute numbers hut will be adjusted in the treatment plant depending upon the water
quality desired.
Bar Diagram - 4
In large treatment plants, economies are often affected by removing the sludges and
1. Remixing CaCO3 and Mg(OH)2 sludges in first stage softening and/or the CaCO3
sludges in second stage softening in the flash mixers to aid in flocculation and
sedimentation.
2. Heating CaCO3 to produce lime and CO2 (recycling)
CaCO3 → CaO + CO2
CaO + H2O → Ca(OH) 2
Water softening sludges may also be used as soil additives in agriculture.
Several points must be noted carefully in the use of the above procedures.
1. Equivalent weight of CO2 = 22 (not 44 as you might expect). The equivalent weight of
44 occurs only in reactions such as
Na2CO3 + CO2 + H2O → 2NaHCO3
i. e., only a single valence change as CO32-→HCO-. In this case the equivalent weight
of Na2CO3 is 106 not 53.
2. Capacity of CO2 equipment will be 7 - 10 times greater than the calculated value as gas
transfer efficiency ranges from 10 - 15%.
3. The procedure outlined is for two stages softening. Waters having different quantities
of alkalinity and hardness may be treated by:
(a) single stage lime softening;
(b) excess lime softening;
(c) split treatment (only part of the water given excess lime)
(d) ion exchange softening.
Bar Diagram - 5