pH Control Using CO2
Transcript of pH Control Using CO2
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Terms and Conditions for Possession and Use:
References:
Trussell, R. R. (1998). "Spreadsheet water conditioning." Journal / American Water Works Association 90(6):
Spreadsheets are a powerful tool for solving water chemistry problems.
Thomas, J. F. and R. R. Trussell "COMPUTER APPLICATION TO WATER CONDITIONING CALCULATION
It is shown how a simple program was developed and how it can be applied to water conditioning
Trussell, R. and Thomas, J.F. (1971). A Discussion of the Chemical Character of Water Mixtures. Jour AW
This spreadsheet calculation tool is the property of Trussell Technologies, Inc, herein TT, and is made availa
public use at no fee. Though this spreadsheet model was developed by TT for conducting various calculation
theoretical and empirical principles, TT provides no guarantee of the accuracy of these calculations. By using
spreadsheet, the user acknowledges and agrees that he or she is using it at his or her own risk. In using thespreadsheet, the user takes all responsibility for its accuracy and the appropriateness of the uses of informati
generated. In addition, in downloading, utilizing, or modifying the spreadsheet, the user hereby agrees to ind
defend, and hold harmless TT, its owners, directors, employees, agents, and volunteers against any and allresulting from the access or use of this spreadsheet by the user, or any other entity or person directly or indir
employed by the user, for any purpose whatsoever. This spreadsheet program is copyrighted by Pasadena P
Co. 3780 Canfield Rd, Pasadena, CA 91107.
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70-81.
S." Journal / American Water Works Association 62(4): 245-248.
roblems. A specific example is described in detail and work in progress which involves more complex proble
A, 63(1), 49-51.
le for
using
this
n
mnify,
laimsctly
ublishing
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s is discussed. Simple bicarbonate-alkalinity system is used to demonstrate the computer's application. The
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redicted titration values shown along with the actual laboratory titration curve were calculated.
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Instructions for Blending Spreadsheet:
This spreadsheet is designed to calculate the pH that will result from the blending of two water sources using
assumption that carbonic acid is the dominant buffer of the system. The uncertainty of estimation is higher fo
where either of the water sources are saturated with respect to Calcium Carbonate because precipitation of cmay occur before mixing of the two waters occurs. The possibility of precipitation before blending is indicated
CCPP calculations above zero, as indicated on the inputs page. Water Quality Inputs can be entered in the n
worksheets, with the third worksheet designating the volumetric contribution of each water source, but other
quality characteristics calculated based on worksheets, "Input-A", and "Input-B". The results of blending can b
the worksheets, "Input-Mix", and "Mix Results." Reference calculations can be found on all the subsequent w
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the
r the case
rbonatesby the
xt three
ater
e seen on
rksheets.
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Input Water Quality Total Inorganic
Cation Anion Ct = 0.3
mg/L meq/L mg/L meq/L DIC = 4.0Ca
++4 as Ca 0.2 Alk 20 as CaCO3 0.4 Ionic Str = 0.0006
Mg++
1.0 as Mg 0.1 Cl-
1 as Cl 0.0
Na+
4 as Na 0.2 SO4=
0 as SO4 0.0 Calcium Carbo
K+
0.1 as K 0.0 NO3-
0.0 as NO3 0.0 pHs = 9.43
NH4+
0.0 as NH4 0.0 F-
0.7 as F 0.0 S.I. = 0.07
S cations = 0.46 S anions = 0.47 CCPP = 0
Instructions:
20 C Light yellow boxes are
293.2 K Light Green boxes are
pH = 9.50 units
R. Trussell, Tru
Other Measures
Temperature at which pH was measured =
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arbon
mM/L
mg/L as C
ate Saturation
pH units
pH units
mg/L as CaCO3
fordata input
foroutput only
ssell Tech. 2009
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Input Water Quality Total Inorganic
Cation Anion Ct = 3.0
mg/L meq/L mg/L meq/L DIC = 35.7Ca
++152 as Ca 7.6 Alk 135 as CaCO3 2.7 Ionic Str = 0.0231
Mg++
39.0 as Mg 3.3 Cl-
53 as Cl 1.5
Na+
50 as Na 2.2 SO4=
430 as SO4 9.0 Calcium Carbo
K+
5.0 as K 0.1 NO3-
1.0 as NO3 0.0 pHs = 7.23
NH4+
1.0 as NH4 0.1 F-
1.0 as F 0.1 S.I. = 0.07
S cations = 13.21 S anions = 13.22 CCPP = 3
Instructions:
20 C Light yellow boxes are
293.2 K Light Green boxes are
pH = 7.30 units
R. Trussell, Tru
Other Measures
Temperature at which pH was measured =
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arbon
mM/L
mg/L as C
ate Saturation
pH units
pH units
mg/L as CaCO3
fordata input
foroutput only
ssell Tech. 2009
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Input Water Quality Total Inorganic
Anion Ct = 1.0
mg/L meq/L mg/L meq/L DIC = 12.6Ca
++44.0 as Ca 2.2 Alk 51.1 as CaCO3 1.0 Ionic Str = 0.0067
Mg++
11.3 as Mg 0.9 Cl-
15.0 as Cl 0.4
Na+
16.4 as Na 0.7 SO4=
116.1 as SO4 2.4 Calcium Carbo
K+
1.4 as K 0.0 NO3-
0.3 as NO3 0.0 pHs = 8.06
NH4+
0.3 as NH4 0.0 F-
0.8 as F 0.0 S.I. = -0.20
S cations = 3.90 S anions = 3.91 CCPP = -1
Instructions:
20 C Light yellow boxes are
293.2 K Light Green boxes are
pH of mixture, calculated = 7.86 units
R. Trussell, Tru
Calculation from Mixture
Temp of Blended Water, Calculated =
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arbon
mM/L
mg/L as C
ate Saturation
pH units
pH units
mg/L as CaCO3
fordata input
foroutput only
ssell Tech. 2009
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73%, 7.9
6.00
6.50
7.00
7.50
8.00
8.50
9.00
9.50
10.00
0% 25% 50% 75% 100%
pH
% Water A
pH vs % Water A
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Blending Two WatersWater Input Info:
Water 1 Water 2
Temp,C= 20.0 20.0
pH= 9.5 7.3
Alky, mg/L= 20.0 135.0
8.50
9.00
9.50
10.00
pH
p
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Reaction pK TC A1 A2 A3 A4
293.15
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A5 Reference
1,684,915.0
563,713.9
0.0 Harned & Owen, 1958
h pH is measured)
ich pH is measured
Plummer & Busenberg, 1982
Plummer & Busenberg, 1982
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pK2 = 10.376
pKs = 8.454
E = 80.040A = 0.506
I = 0.0006
I = 0.0246pfm = 0.0121
pCa = 4.000
HCO3-= 0.00035
pHCO3 = 3.451
pHs = 9.433
* 19th Edition, 1995.
Calculation of the Saturation
pH by Standard Methods*
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Calculation of the Calcium Carbonate Precipitation Potenti
EquationsKso = Ca*Ct*a 2 Defining Initial Calcium CCAlk = Ct*s + D Ca = 4 mg/L as Ca mole/L
after ppt of X moles of CaCO3 Ca = 0.1 mmole/L -1.33E-06
Kso = [Ca - X][Ct - X]a 2 Ca = 0.0001 mole/L
Alk - 2X = [Ct- X]s + D
[s -2]X = Ct*s + D - Alk
X = [Ct*s + D - Alk]/[s - 2]
finding CCPP by trial and error
pH H F s a 2 D X F[pH] DpH
7 1.00E-07 5.27E-14 8.11E-01 3.71E-04 -2.96E-08 1.08E-04 1.00E+00 3.5
10.5 3.16E-11 3.30E-17 1.59E+00 5.91E-01 2.23E-04 -8.72E-04 -1.57E+02 1.75
8.75 1.78E-09 7.82E-16 1.02E+00 2.50E-02 3.95E-06 5.46E-05 9.27E-01 0.875
9.625 2.37E-10 1.21E-16 1.16E+00 1.62E-01 2.97E-05 -2.31E-05 -6.25E-01 0.4375
9.1875 6.49E-10 2.97E-16 1.06E+00 6.58E-02 1.08E-05 3.42E-05 7.03E-01 0.21875
9.40625 3.92E-10 1.87E-16 1.10E+00 1.04E-01 1.79E-05 1.31E-05 3.34E-01 0.109375
9.515625 3.05E-10 1.50E-16 1.13E+00 1.30E-01 2.31E-05 -2.50E-06 -2.89E-02 0.0546875
9.460938 3.46E-10 1.67E-16 1.12E+00 1.17E-01 2.03E-05 5.84E-06 1.75E-01 0.0273438
9.488281 3.25E-10 1.58E-16 1.12E+00 1.23E-01 2.17E-05 1.81E-06 7.90E-02 0.01367199.501953 3.15E-10 1.54E-16 1.13E+00 1.27E-01 2.24E-05 -3.07E-07 2.67E-02 0.0068359
9.508789 3.10E-10 1.52E-16 1.13E+00 1.29E-01 2.27E-05 -1.39E-06 -6.72E-04 0.003418
9.505371 3.12E-10 1.53E-16 1.13E+00 1.28E-01 2.25E-05 -8.48E-07 1.31E-02 0.001709
9.50708 3.11E-10 1.52E-16 1.13E+00 1.28E-01 2.26E-05 -1.12E-06 6.25E-03 0.0008545
9.507935 3.11E-10 1.52E-16 1.13E+00 1.28E-01 2.27E-05 -1.26E-06 2.80E-03 0.0004272
9.508362 3.10E-10 1.52E-16 1.13E+00 1.29E-01 2.27E-05 -1.33E-06 1.06E-03 0.0002136
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137768933.xls.ms_office
Temperature Coefficients for a Variety of Acid-Base and Solubility Constan
Formula used for pK's: pK =a1 +a2/T +a3Log[T] +a4T +a5/T 2 T = 293.15
Reaction pK[TK] A1 A2 A3 A4 A5 Reference
HSO4-= H
++ SO4
= 1.94 -56.889 2,307.9 19.886 0.006473 0.0 Nordstrom etal, 1990
HPO4=
= PO4 + H+ 2.13 -3.212 602.7 0.000 0.011198 0.0 Data in Sillen & Martell,
H3PO4 = H2PO4-+ H
+ 2.13 -7.345 1,195.0 0.000 0.018400 0.0 Harned & Owen, 1958
Citric Acid, K3 3.15 -43.320 2,253.0 15.720 0.000000 0.0 Data in Sillen & Martell,
HAc = Ac-+ H
+ 4.77 -49.400 2,391.4 18.650 0.000000 0.0 Data in Sillen & Martell,
Citric Acid, K2 4.78 -58.020 2,903.7 21.440 0.000000 0.0 Data in Sillen & Martell,
Al3+
+ H2O = Al(OH)2+
+ H+ 5.15 38.253 656.3 -14.327 0.000000 0.0 Nordstrom etal, 1990
Ca(OH)2s = Ca2+
+ 2OH- 5.03 -118.300 4,968.7 43.120 0.000000 0.0 Data in Sillen & Martell,
H2CO3 = HCO3-+ H
+ 6.38 356.309 -21,834.4 -126.834 0.060920 1,684,915.0 Plummer & Busenberg,
Citric Acid, K1 6.38 -81.730 3,771.8 30.500 0.000000 0.0 Data in Sillen & Martell,
H2S = HS-+ H
+ 7.07 -29.337 6,067.6 0.000 0.053588 0.0 Data in Sillen & Martell,
H2PO4- = HPO4=
+ H+ 7.22 -4.408 1,836.0 0.000 0.018300 0.0 Harned & Owen, 1958
HOCl = OCl-+ H
+ 7.58 -18.731 4,245.5 0.000 0.040344 0.0 Data in Sillen & Martell,
CaCO3s = Ca2+
+ CO3= 8.45 171.907 -2,839.3 -71.595 0.077993 0.0 Plummer & Busenberg,
HCN = CN-+ H
+ 9.36 1.875 2,193.5 0.000 0.000000 0.0 Data in Sillen & Martell,
B(OH)3 + H2O = B(OH)4-
+ H+
9.28 -3.687 2,291.9 0.000 0.017560 0.0 Owen & King, 1943NH4
+= NH3 + H
+ 9.41 -2.111 3,083.3 0.000 0.003415 0.0 Data in Sillen & Martell,
Si(OH)4 + H2O = SIO(OH)3-+ H
+ 9.91 302.372 -15,669.7 -108.185 0.050698 1,119,669.0 Busey & Mesmer, 1977
Al3+
+ 2H2O = Al(OH)2+
+ 2H+ 10.45 -88.500 9,391.6 27.121 0.000000 0.0 Nordstrom etal, 1990
HCO3-= CO3
=+ H
+ 10.38 107.887 -5,151.8 -38.926 0.032528 563,713.9 Plummer & Busenberg,
Al3+
+ 3H2O = Al(OH)3s + 3H+ 11.13 -8.623 5,791.0 0.000 0.000000 0.0 Nordstrom etal, 1990
Mg(OH)2s = Mg2+
+ 2OH- 10.83 16.570 -1,682.4 0.000 0.000000 0.0 Data in Sillen & Martell,
H2O2 = HO2-+ H
+ 11.75 5.573 1,811.6 0.000 0.000000 0.0 Data in Sillen & Martell,
H2O = H+
+ OH- 14.16 -6.088 4,471.0 0.000 0.017060 0.0 Harned & Owen, 1958
Al3+
+ 3H2O = Al(OH)3+ 3H
+ 17.44 -226.374 18,247.8 73.597 0.000000 0.0 Nordstrom etal, 1990
Al3+
+ 4H2O = Al(OH)4-
+ 4H+ 23.19 -51.578 11,168.9 14.865 0.000000 0.0 Nordstrom etal, 1990
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137768933.xls.ms_office
K
,1971
,1971,1971
,1971
,1971
,1971
,1971
,1971
,1971
,1971
,1971
,1971
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Ionic Strength Corrections Using the Davies EquationForm: Log[g z] = -A*Z2[I/(1+I) - 0.3I]
I = 0.000604 Ionic Strength I = 0.024578
Z A*Z2
Log[g z] g zg 1 = 1 0.506 -0.012 0.973g 2 = 2 2.026 -0.048 0.895g 3 = 3 4.557 -0.108 0.779g 4 = 4 8.102 -0.193 0.641
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Correction of pK values for Ionic Strength
Reaction Symbol pK K K' pK'HSO4- = H+ SO4= KSO4_2 1.94 1.14E-02 1.24E-02 1.91
HPO4= = PO4- + H+ KPO4_3 2.13 7.47E-03 8.58E-03 2.07
H3PO4 = H2PO4- + H+ KPO4_1 2.13 7.49E-03 7.70E-03 2.11
Citric Acid, K1 KCa_3 3.15 7.11E-04 7.31E-04 3.14
HAc = Ac- + H+ KAc_1 4.77 1.70E-05 1.75E-05 4.76Citric Acid, K2 KCa_2 4.78 1.66E-05 1.81E-05 4.74
Al3+ + H2O = Al(OH)2+ + H+ KAl_1 5.15 7.15E-06 6.22E-06 5.21
Ca(OH)2s = Ca2+ + 2OH- KCa[OH]2_s 5.03 9.33E-06 1.20E-05 4.92
H2CO3 = HCO3- + H+ KCO2_o 6.38 4.15E-07 4.27E-07 6.37
Citric Acid, K3 KCa_1 6.38 4.14E-07 4.76E-07 6.32
H2S = HS- + H+ KH2S_1 7.07 8.51E-08 8.75E-08 7.06
H2PO4-= HPO4
=+ H
+KPO4_2 7.22 6.03E-08 6.55E-08 7.18
HOCl = OCl- + H+ KHOCl_1 7.58 2.64E-08 2.72E-08 7.57
CaCO3s = Ca2+ + CO3= KCaCO3_so 8.45 3.52E-09 4.39E-09 8.36
HCN = CN- + H+ KHCN_1 9.36 4.39E-10 4.51E-10 9.35
B(OH)3 + H2O = B(OH)4- + H+ KB[OH]3_1 9.28 5.26E-10 5.41E-10 9.27
NH4+ = NH3 + H+ KNH3_1 9.41 3.91E-10 3.80E-10 9.42Si(OH)4 + H2O = SIO(OH)3- + H+ KSi[OH]4_1 9.91 1.24E-10 1.27E-10 9.90
Al3+ + 2H2O = Al(OH)2+ + 2H+ KAl_2 10.45 3.57E-11 3.88E-11 10.41
HCO3- = CO3= + H+ KCO2_2 10.38 4.21E-11 4.58E-11 10.34
Al3+ + 3H2O = Al(OH)3s + 3H+ KAl[OH]3_s 11.13 7.39E-12 7.19E-12 11.14
Mg(OH)2s = Mg2+ + 2OH- KMg[OH]2_ 10.83 1.48E-11 1.74E-11 10.76
H2O2 = HO2- + H+ KH2O2_1 11.75 1.77E-12 1.82E-12 11.74
H2O = H+ + OH- Kw 14.16 6.84E-15 7.04E-15 14.15
Al3+ + 3H2O = Al(OH)3 + 3H+ KAl_3 17.44 3.60E-18 2.80E-18 17.55
Al3+ + 4H2O = Al(OH)4- + 4H+ KAl_4 23.19 6.38E-24 5.11E-24 23.29
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Reaction pK TC A1 A2 A3 A4 A5
293.15
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Reference
Harned & Owen, 1958
asured)
easured
Plummer & Busenberg, 1982
Plummer & Busenberg, 1982
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pK2 = 10.376
pKs = 8.454
E = 80.040A = 0.506
I = 0.0231
I = 0.1521pfm = 0.0633
pCa = 2.420
HCO3-= 0.00270
pHCO3 = 2.569
pHs = 7.227
* 19th Edition, 1995.
Calculation of the Saturation
pH by Standard Methods*
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Calculation of the Calcium Carbonate Precipitation Potenti
EquationsKso = Ca*Ct*a 2 Defining Initial Calcium CCAlk = Ct*s + D Ca = 152 mg/L as Ca mole/L
after ppt of X moles of CaCO3 Ca = 3.8 mmole/L 3.28E-05
Kso = [Ca - X][Ct - X]a 2 Ca = 0.0038 mole/L
Alk - 2X = [Ct- X]s + D
[s -2]X = Ct*s + D - Alk
X = [Ct*s + D - Alk]/[s - 2]
finding CCPP by trial and error
pH H F s a 2 D X F[pH] DpH
7 1.00E-07 5.81E-14 8.28E-01 5.40E-04 -2.08E-08 2.00E-04 5.22E-01 3.5
10.5 3.16E-11 4.65E-17 1.67E+00 6.73E-01 2.50E-04 -7.76E-03 -7.40E+03 1.75
8.75 1.78E-09 8.88E-16 1.03E+00 3.53E-02 4.45E-06 -3.89E-04 -4.30E+01 0.875
7.875 1.33E-08 6.61E-15 9.78E-01 4.74E-03 5.80E-07 -2.07E-04 -4.35E+00 0.4375
7.4375 3.65E-08 1.89E-14 9.31E-01 1.66E-03 1.80E-07 -6.78E-05 -7.29E-01 0.21875
7.21875 6.04E-08 3.27E-14 8.89E-01 9.58E-04 7.06E-08 4.69E-05 6.70E-02 0.109375
7.328125 4.70E-08 2.48E-14 9.12E-01 1.26E-03 1.22E-07 -1.50E-05 -2.77E-01 0.0546875
7.273438 5.33E-08 2.85E-14 9.01E-01 1.10E-03 9.53E-08 1.48E-05 -9.33E-02 0.0273438
7.246094 5.67E-08 3.05E-14 8.95E-01 1.03E-03 8.28E-08 3.05E-05 -1.04E-02 0.01367197.232422 5.86E-08 3.16E-14 8.92E-01 9.92E-04 7.67E-08 3.87E-05 2.90E-02 0.0068359
7.239258 5.76E-08 3.10E-14 8.94E-01 1.01E-03 7.97E-08 3.46E-05 9.49E-03 0.003418
7.242676 5.72E-08 3.08E-14 8.95E-01 1.02E-03 8.13E-08 3.26E-05 -3.90E-04 0.001709
7.240967 5.74E-08 3.09E-14 8.94E-01 1.01E-03 8.05E-08 3.36E-05 4.56E-03 0.0008545
7.241821 5.73E-08 3.08E-14 8.95E-01 1.02E-03 8.09E-08 3.31E-05 2.09E-03 0.0004272
7.242249 5.72E-08 3.08E-14 8.95E-01 1.02E-03 8.11E-08 3.28E-05 8.50E-04 0.0002136
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137768933.xls.ms_office
Temperature Coefficients for a Variety of Acid-Base and Solubility Constan
Formula used for pK's: pK =a1 +a2/T +a3Log[T] +a4T +a5/T 2 T = 293.15
Reaction pK[TK] A1 A2 A3 A4 A5 Reference
HSO4-= H
++ SO4
= 1.94 -56.889 2,307.9 19.886 0.006473 0.0 Nordstrom etal, 1990
HPO4=
= PO4 + H+ 2.13 -3.212 602.7 0.000 0.011198 0.0 Data in Sillen & Martell,
H3PO4 = H2PO4-+ H
+ 2.13 -7.345 1,195.0 0.000 0.018400 0.0 Harned & Owen, 1958
Citric Acid, K3 3.15 -43.320 2,253.0 15.720 0.000000 0.0 Data in Sillen & Martell,
HAc = Ac-+ H
+ 4.77 -49.400 2,391.4 18.650 0.000000 0.0 Data in Sillen & Martell,
Citric Acid, K2 4.78 -58.020 2,903.7 21.440 0.000000 0.0 Data in Sillen & Martell,
Al3+
+ H2O = Al(OH)2+
+ H+ 5.15 38.253 656.3 -14.327 0.000000 0.0 Nordstrom etal, 1990
Ca(OH)2s = Ca2+
+ 2OH- 5.03 -118.300 4,968.7 43.120 0.000000 0.0 Data in Sillen & Martell,
H2CO3 = HCO3-+ H
+ 6.38 356.309 -21,834.4 -126.834 0.060920 1,684,915.0 Plummer & Busenberg,
Citric Acid, K1 6.38 -81.730 3,771.8 30.500 0.000000 0.0 Data in Sillen & Martell,
H2S = HS-+ H
+ 7.07 -29.337 6,067.6 0.000 0.053588 0.0 Data in Sillen & Martell,
H2PO4- = HPO4=
+ H+ 7.22 -4.408 1,836.0 0.000 0.018300 0.0 Harned & Owen, 1958
HOCl = OCl-+ H
+ 7.58 -18.731 4,245.5 0.000 0.040344 0.0 Data in Sillen & Martell,
CaCO3s = Ca2+
+ CO3= 8.45 171.907 -2,839.3 -71.595 0.077993 0.0 Plummer & Busenberg,
HCN = CN-+ H
+ 9.36 1.875 2,193.5 0.000 0.000000 0.0 Data in Sillen & Martell,
B(OH)3 + H2O = B(OH)4-
+ H+
9.28 -3.687 2,291.9 0.000 0.017560 0.0 Owen & King, 1943NH4
+= NH3 + H
+ 9.41 -2.111 3,083.3 0.000 0.003415 0.0 Data in Sillen & Martell,
Si(OH)4 + H2O = SIO(OH)3-+ H
+ 9.91 302.372 -15,669.7 -108.185 0.050698 1,119,669.0 Busey & Mesmer, 1977
Al3+
+ 2H2O = Al(OH)2+
+ 2H+ 10.45 -88.500 9,391.6 27.121 0.000000 0.0 Nordstrom etal, 1990
HCO3-= CO3
=+ H
+ 10.38 107.887 -5,151.8 -38.926 0.032528 563,713.9 Plummer & Busenberg,
Al3+
+ 3H2O = Al(OH)3s + 3H+ 11.13 -8.623 5,791.0 0.000 0.000000 0.0 Nordstrom etal, 1990
Mg(OH)2s = Mg2+
+ 2OH- 10.83 16.570 -1,682.4 0.000 0.000000 0.0 Data in Sillen & Martell,
H2O2 = HO2-+ H
+ 11.75 5.573 1,811.6 0.000 0.000000 0.0 Data in Sillen & Martell,
H2O = H+
+ OH- 14.16 -6.088 4,471.0 0.000 0.017060 0.0 Harned & Owen, 1958
Al3+
+ 3H2O = Al(OH)3+ 3H
+ 17.44 -226.374 18,247.8 73.597 0.000000 0.0 Nordstrom etal, 1990
Al3+
+ 4H2O = Al(OH)4-
+ 4H+ 23.19 -51.578 11,168.9 14.865 0.000000 0.0 Nordstrom etal, 1990
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K
,1971
,1971,1971
,1971
,1971
,1971
,1971
,1971
,1971
,1971
,1971
,1971
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Ionic Strength Corrections Using the Davies EquationForm: Log[g z] = -A*Z2[I/(1+I) - 0.3I]
I = 0.02312 Ionic Strength I = 0.152052
Z A*Z2
Log[g z] g zg 1 = 1 0.506 -0.063 0.864g 2 = 2 2.026 -0.253 0.558g 3 = 3 4.557 -0.570 0.269g 4 = 4 8.102 -1.013 0.097
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Correction of pK values for Ionic Strength
Reaction Symbol pK K K' pK'HSO4- = H+ SO4= KSO4_2 1.94 1.14E-02 1.77E-02 1.75
HPO4= = PO4- + H+ KPO4_3 2.13 7.47E-03 1.55E-02 1.81
H3PO4 = H2PO4- + H+ KPO4_1 2.13 7.49E-03 8.67E-03 2.06
Citric Acid, K1 KCa_3 3.15 7.11E-04 8.23E-04 3.08
HAc = Ac- + H+ KAc_1 4.77 1.70E-05 1.97E-05 4.71Citric Acid, K2 KCa_2 4.78 1.66E-05 2.57E-05 4.59
Al3+ + H2O = Al(OH)2+ + H+ KAl_1 5.15 7.15E-06 3.45E-06 5.46
Ca(OH)2s = Ca2+ + 2OH- KCa[OH]2_s 5.03 9.33E-06 3.46E-05 4.46
H2CO3 = HCO3- + H+ KCO2_o 6.38 4.15E-07 4.80E-07 6.32
Citric Acid, K3 KCa_1 6.38 4.14E-07 8.59E-07 6.07
H2S = HS- + H+ KH2S_1 7.07 8.51E-08 9.84E-08 7.01
H2PO4-= HPO4
=+ H
+KPO4_2 7.22 6.03E-08 9.34E-08 7.03
HOCl = OCl- + H+ KHOCl_1 7.58 2.64E-08 3.06E-08 7.51
CaCO3s = Ca2+ + CO3= KCaCO3_so 8.45 3.52E-09 1.13E-08 7.95
HCN = CN- + H+ KHCN_1 9.36 4.39E-10 5.08E-10 9.29
B(OH)3 + H2O = B(OH)4- + H+ KB[OH]3_1 9.28 5.26E-10 6.09E-10 9.22
NH4+ = NH3 + H+ KNH3_1 9.41 3.91E-10 3.38E-10 9.47Si(OH)4 + H2O = SIO(OH)3- + H+ KSi[OH]4_1 9.91 1.24E-10 1.43E-10 9.84
Al3+ + 2H2O = Al(OH)2+ + 2H+ KAl_2 10.45 3.57E-11 5.54E-11 10.26
HCO3- = CO3= + H+ KCO2_2 10.38 4.21E-11 6.52E-11 10.19
Al3+ + 3H2O = Al(OH)3s + 3H+ KAl[OH]3_s 11.13 7.39E-12 6.39E-12 11.19
Mg(OH)2s = Mg2+ + 2OH- KMg[OH]2_ 10.83 1.48E-11 3.54E-11 10.45
H2O2 = HO2- + H+ KH2O2_1 11.75 1.77E-12 2.04E-12 11.69
H2O = H+ + OH- Kw 14.16 6.84E-15 7.92E-15 14.10
Al3+ + 3H2O = Al(OH)3 + 3H+ KAl_3 17.44 3.60E-18 9.69E-19 18.01
Al3+ + 4H2O = Al(OH)4- + 4H+ KAl_4 23.19 6.38E-24 1.99E-24 23.70
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Reaction pK TC A1 A2 A3 A4
293.15
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A5 Reference
1,684,915.0
563,713.9
0.0 Harned & Owen, 1958
ch pH is measured)
ich pH is measured
Plummer & Busenberg, 1982
Plummer & Busenberg, 1982
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pK2 = 10.376
pKs = 8.454
E = 80.040A = 0.506
I = 0.0067
I = 0.0818pfm = 0.0373
pCa = 2.959
HCO3-= 0.00102
pHCO3 = 2.992
pHs = 8.059
* 19th Edition, 1995.
Calculation of the Saturation
pH by Standard Methods*
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Calculation of the Calcium Carbonate Precipitation Potenti
EquationsKso = Ca*Ct*a 2 Defining Initial Calcium CCAlk = Ct*s + D Ca = 43.96 mg/L as Ca mole/L
after ppt of X moles of CaCO3 Ca = 1.099 mmole/L -1.33E-05
Kso = [Ca - X][Ct - X]a 2 Ca = 0.001099 mole/L
Alk - 2X = [Ct- X]s + D
[s -2]X = Ct*s + D - Alk
X = [Ct*s + D - Alk]/[s - 2]
finding CCPP by trial and error
pH H F s a 2 D X F[pH] DpH
7 1.00E-07 5.53E-14 8.19E-01 4.46E-04 -2.54E-08 1.38E-04 9.44E-01 3.5
10.5 3.16E-11 3.89E-17 1.63E+00 6.33E-01 2.36E-04 -2.52E-03 -1.17E+03 1.75
8.75 1.78E-09 8.32E-16 1.03E+00 2.96E-02 4.19E-06 -5.94E-05 -4.44E+00 0.875
7.875 1.33E-08 6.23E-15 9.75E-01 3.95E-03 5.46E-07 -1.44E-06 3.47E-01 0.4375
8.3125 4.87E-09 2.25E-15 1.00E+00 1.09E-02 1.53E-06 -2.86E-05 -9.02E-01 0.21875
8.09375 8.06E-09 3.73E-15 9.89E-01 6.60E-03 9.17E-07 -1.61E-05 -1.20E-01 0.109375
7.984375 1.04E-08 4.82E-15 9.83E-01 5.11E-03 7.09E-07 -9.22E-06 1.43E-01 0.0546875
8.039063 9.14E-09 4.24E-15 9.86E-01 5.81E-03 8.07E-07 -1.28E-05 1.97E-02 0.0273438
8.066406 8.58E-09 3.98E-15 9.88E-01 6.19E-03 8.60E-07 -1.45E-05 -4.81E-02 0.01367198.052734 8.86E-09 4.11E-15 9.87E-01 6.00E-03 8.33E-07 -1.36E-05 -1.37E-02 0.0068359
8.045898 9.00E-09 4.17E-15 9.87E-01 5.90E-03 8.20E-07 -1.32E-05 3.14E-03 0.003418
8.049316 8.93E-09 4.14E-15 9.87E-01 5.95E-03 8.26E-07 -1.34E-05 -5.24E-03 0.001709
8.047607 8.96E-09 4.16E-15 9.87E-01 5.93E-03 8.23E-07 -1.33E-05 -1.04E-03 0.0008545
8.046753 8.98E-09 4.17E-15 9.87E-01 5.91E-03 8.21E-07 -1.32E-05 1.05E-03 0.0004272
8.04718 8.97E-09 4.16E-15 9.87E-01 5.92E-03 8.22E-07 -1.33E-05 6.31E-06 0.0002136
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Temperature Coefficients for a Variety of Acid-Base and Solubility Constan
Formula used for pK's: pK =a1 +a2/T +a3Log[T] +a4T +a5/T 2 T = 293.15
Reaction pK[TK] A1 A2 A3 A4 A5 Reference
HSO4-= H
++ SO4
= 1.94 -56.889 2,307.9 19.886 0.006473 0.0 Nordstrom etal, 1990
HPO4=
= PO4 + H+ 2.13 -3.212 602.7 0.000 0.011198 0.0 Data in Sillen & Martell,
H3PO4 = H2PO4-+ H
+ 2.13 -7.345 1,195.0 0.000 0.018400 0.0 Harned & Owen, 1958
Citric Acid, K3 3.15 -43.320 2,253.0 15.720 0.000000 0.0 Data in Sillen & Martell,
HAc = Ac-+ H
+ 4.77 -49.400 2,391.4 18.650 0.000000 0.0 Data in Sillen & Martell,
Citric Acid, K2 4.78 -58.020 2,903.7 21.440 0.000000 0.0 Data in Sillen & Martell,
Al3+
+ H2O = Al(OH)2+
+ H+ 5.15 38.253 656.3 -14.327 0.000000 0.0 Nordstrom etal, 1990
Ca(OH)2s = Ca2+
+ 2OH- 5.03 -118.300 4,968.7 43.120 0.000000 0.0 Data in Sillen & Martell,
H2CO3 = HCO3-+ H
+ 6.38 356.309 -21,834.4 -126.834 0.060920 1,684,915.0 Plummer & Busenberg,
Citric Acid, K1 6.38 -81.730 3,771.8 30.500 0.000000 0.0 Data in Sillen & Martell,
H2S = HS-+ H
+ 7.07 -29.337 6,067.6 0.000 0.053588 0.0 Data in Sillen & Martell,
H2PO4- = HPO4=
+ H+ 7.22 -4.408 1,836.0 0.000 0.018300 0.0 Harned & Owen, 1958
HOCl = OCl-+ H
+ 7.58 -18.731 4,245.5 0.000 0.040344 0.0 Data in Sillen & Martell,
CaCO3s = Ca2+
+ CO3= 8.45 171.907 -2,839.3 -71.595 0.077993 0.0 Plummer & Busenberg,
HCN = CN-+ H
+ 9.36 1.875 2,193.5 0.000 0.000000 0.0 Data in Sillen & Martell,
B(OH)3 + H2O = B(OH)4-
+ H+
9.28 -3.687 2,291.9 0.000 0.017560 0.0 Owen & King, 1943NH4
+= NH3 + H
+ 9.41 -2.111 3,083.3 0.000 0.003415 0.0 Data in Sillen & Martell,
Si(OH)4 + H2O = SIO(OH)3-+ H
+ 9.91 302.372 -15,669.7 -108.185 0.050698 1,119,669.0 Busey & Mesmer, 1977
Al3+
+ 2H2O = Al(OH)2+
+ 2H+ 10.45 -88.500 9,391.6 27.121 0.000000 0.0 Nordstrom etal, 1990
HCO3-= CO3
=+ H
+ 10.38 107.887 -5,151.8 -38.926 0.032528 563,713.9 Plummer & Busenberg,
Al3+
+ 3H2O = Al(OH)3s + 3H+ 11.13 -8.623 5,791.0 0.000 0.000000 0.0 Nordstrom etal, 1990
Mg(OH)2s = Mg2+
+ 2OH- 10.83 16.570 -1,682.4 0.000 0.000000 0.0 Data in Sillen & Martell,
H2O2 = HO2-+ H
+ 11.75 5.573 1,811.6 0.000 0.000000 0.0 Data in Sillen & Martell,
H2O = H+
+ OH- 14.16 -6.088 4,471.0 0.000 0.017060 0.0 Harned & Owen, 1958
Al3+
+ 3H2O = Al(OH)3+ 3H
+ 17.44 -226.374 18,247.8 73.597 0.000000 0.0 Nordstrom etal, 1990
Al3+
+ 4H2O = Al(OH)4-
+ 4H+ 23.19 -51.578 11,168.9 14.865 0.000000 0.0 Nordstrom etal, 1990
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,1971
,1971,1971
,1971
,1971
,1971
,1971
,1971
,1971
,1971
,1971
,1971
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Ionic Strength Corrections Using the Davies EquationForm: Log[g z] = -A*Z2[I/(1+I) - 0.3I]
I = 0.006683 Ionic Strength I = 0.081751
Z A*Z2
Log[g z] g zg 1 = 1 0.506 -0.037 0.918g 2 = 2 2.026 -0.149 0.710g 3 = 3 4.557 -0.335 0.462g 4 = 4 8.102 -0.596 0.253
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Correction of pK values for Ionic Strength
Reaction Symbol pK K K' pK'HSO4- = H+ SO4= KSO4_2 1.94 1.14E-02 1.48E-02 1.83
HPO4= = PO4- + H+ KPO4_3 2.13 7.47E-03 1.15E-02 1.94
H3PO4 = H2PO4- + H+ KPO4_1 2.13 7.49E-03 8.16E-03 2.09
Citric Acid, K1 KCa_3 3.15 7.11E-04 7.75E-04 3.11
HAc = Ac- + H+ KAc_1 4.77 1.70E-05 1.86E-05 4.73Citric Acid, K2 KCa_2 4.78 1.66E-05 2.15E-05 4.67
Al3+ + H2O = Al(OH)2+ + H+ KAl_1 5.15 7.15E-06 4.66E-06 5.33
Ca(OH)2s = Ca2+ + 2OH- KCa[OH]2_s 5.03 9.33E-06 2.02E-05 4.69
H2CO3 = HCO3- + H+ KCO2_o 6.38 4.15E-07 4.52E-07 6.34
Citric Acid, K3 KCa_1 6.38 4.14E-07 6.36E-07 6.20
H2S = HS- + H+ KH2S_1 7.07 8.51E-08 9.27E-08 7.03
H2PO4-= HPO4
=+ H
+KPO4_2 7.22 6.03E-08 7.80E-08 7.11
HOCl = OCl- + H+ KHOCl_1 7.58 2.64E-08 2.88E-08 7.54
CaCO3s = Ca2+ + CO3= KCaCO3_so 8.45 3.52E-09 6.98E-09 8.16
HCN = CN- + H+ KHCN_1 9.36 4.39E-10 4.78E-10 9.32
B(OH)3 + H2O = B(OH)4- + H+ KB[OH]3_1 9.28 5.26E-10 5.73E-10 9.24
NH4+ = NH3 + H+ KNH3_1 9.41 3.91E-10 3.59E-10 9.45Si(OH)4 + H2O = SIO(OH)3- + H+ KSi[OH]4_1 9.91 1.24E-10 1.35E-10 9.87
Al3+ + 2H2O = Al(OH)2+ + 2H+ KAl_2 10.45 3.57E-11 4.62E-11 10.34
HCO3- = CO3= + H+ KCO2_2 10.38 4.21E-11 5.45E-11 10.26
Al3+ + 3H2O = Al(OH)3s + 3H+ KAl[OH]3_s 11.13 7.39E-12 6.78E-12 11.17
Mg(OH)2s = Mg2+ + 2OH- KMg[OH]2_ 10.83 1.48E-11 2.47E-11 10.61
H2O2 = HO2- + H+ KH2O2_1 11.75 1.77E-12 1.93E-12 11.72
H2O = H+ + OH- Kw 14.16 6.84E-15 7.46E-15 14.13
Al3+ + 3H2O = Al(OH)3 + 3H+ KAl_3 17.44 3.60E-18 1.66E-18 17.78
Al3+ + 4H2O = Al(OH)4- + 4H+ KAl_4 23.19 6.38E-24 3.21E-24 23.49