422 0.5 0.5 CO₂ 0.5 CO₂ Ca2+ HCO3- 3.5 2.700 3.400 SO42- 5.3 5.8 Na сг 3.2 3.2 1 0.3 Ca(HCO3)2 lt 1.8 5.4 5.8 0.10.4 CaSO4 MgSO4 Na2SO4 NaCl (a) 2.900 Ca2+ Ca2+ Mg Na он он- OH CON CO2- SO42- CI 1.422 01 0.800 3.000 are. co₂ 0.188 0 0.200 CO₂ 2- Ca2+ 3.400 (b) 3.889 4.689 5.189 Mg2+ Na+ он HCO3 SO42- сг 0.188 0 1.014 1.389 2.589 4.789 5.189 (c) 2.273 3.073 3.573 HCO3- Ca²+ Mg2+ Na* CO₂ 2- SO42- Cr 0 10.973 3.173 3.573 0.600 (d) 0.973 1.773 3.573 Ca2+ HCO Mg2+ Na CO, 2- S042- Cr 0 | 0.973 0.600 3.173 3.573 (e)/nExample 11.6 Water defined by the following analysis is to be softened by excess-lime treat- ment in a two-stage system (Figure 11.13): CO₂ = 8.8 mg/l as CO2 Alk(HCO3) = 115 mg/l as CaCO3 Ca²+ = 70 mg/1 Mg2+ = 9.7 mg/1 Na+ = 6.9 mg/l SO4² = 96 mg/1 CI¯ = 10.6 mg/l The practical limits of removal can be assumed to be 30 mg/l of CaCO3 and 10 mg/l of Mg(OH)2, expressed as CaCO3. Sketch a meq/l bar graph and list the hypothetical combinations of chemical compounds in the raw water. Calculate the quantity of soft- ening chemicals required in pounds per million gallons of water treated and the theo- retical quantity of carbon dioxide needed to provide a finished water with one-half of the alkalinity converted to bicarbonate ion. Draw a bar graph for the softened water after recarbonation and filtration. Solution: Component CO₂ mg/l 8.8 Equivalent Weight meq/l 22.0 0.40 Ca2+ 70 20.0 3.50 Mg2+ 9.7 12.2 0.80 Na+ 6.9 23.0 0.30 Alk 115 50.0 2.30 SO₁₂- 96 48.0 2.00 CI 10.6 35.5 0.30 412 Chapter 11 Chemical Treatment Processes A hypothetical bar graph for the water after addition of softening chemicals and first- stage sedimentation is shown in Figure 11.14b. The dashed box is the excess-lime addition, 35 mg/l of CaO = 1.25 meq/l. The 0.6 meq/1 of Ca2+ (30 mg/l as CaCO3) and 0.20 meq/l of Mg2+ (10 mg/l as CaCO3) are the practical limits of hardness reduction. The 2.0 meq/l of Na2SO4 results from the addition of soda ash. Alkalinity consists of 0.20 meq/l of OH associated with Mg(OH)2 and 0.60 meq/l of CO32 related to CaCO3. Recarbonation converts the excess hydroxyl ion to carbonate ion; using the rela- tionship in Eq. (11.63) and using 22.0 as the equivalent weight of carbon dioxide pro- vides (1.25 +0.2)22.0 = 31.9 mg/l of CO2. After second-stage processing, final recarbonation converts half the remaining alkalinity to bicarbonate ion by Eq. (11.64), giving 0.5 × 0.8 × 22.0 = 8.8 mg/l of CO2. Therefore the total carbon dioxide reacted is (31.98.8)8.34 = 340 lb/mil gal of CO2. The bar graph of the finished water is shown in Figure 11.14c. 11.16 Process Variations in Lime-Soda Ash Softening 411 The meq/l bar graph of the raw water is shown in Figure 11.14a, and the hypothetical combinations are listed. lime required = stoichiometric quantity + excess lime = 3.5 x 28+ 35 = 133 mg/l of CaO = 1100 lb/mil gal soda ash required = 2.0 x 53 = 106 mg/l of Na2CO3 = 900 lb/mil gal Component meq/l Lime Soda Ash CO₂ 0.4 0.4 0 Ca(HCO3)2 2.3 2.3 0 CaSO4 1.2 0 1.2 MgSO4 0.8 0.8 0.8 3.5 2.0 0 Ca 2+ CO₂ HCO3- 3.5 4.3 4.6 Mg2+ Na SO4² Cr 0.4 2.3 meg 1.2 meq 0.8 meq 0.3 CO₂ (a) 0 0.6 0.8 Ca²+ Ca2+ Mg2+ Na он- OH CO2- SO42- cr 1.25 meg excess lime 0.8 meq hardness 2.0 meq soda ash addition (b) 0 0.6 0.8 Ca2+ Mg2+ Na CO2 HCO SO42- 2.8 Cr 3.1 3.1 0 0.4 0.8 (c) FIGURE 11.14 Milliequivalent bar graphs for Example 11.6. (a) Bar graph and hypothetical chemical combinations in the raw water. (b) Bar graph of the water after lime and soda ash additions and settling but before recarbonation. (c) Bar graph of the water after two-stage recarbonation and final filtration.

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