WiSe2021, Water Chemistry
Equations and Tables
Water Chemistry
Appendix 1: Useful relationships and equations from the lecture
A simple help with large logarithms
Free (Gibbs) Energy G
Activity
ln10x = x ln10
Ionic Strength
1
I =   ci  zi2
2 i
Free Energy of Reaction and Q
 r G = RT ln
Standard Free Energy and K
K =e
dG = dH-T*dS (at constant T)
ai =  i
ci
c0
− G
RT
Q
K
0
,
G (in kJ  mol-1 ) = −5.71log K (at 298.15K)
0
Van’t Hoff Equation (temperature
dependency of K)
Henderson-Hasselbalch Equation
log
K T1
=−
K T2
H0  1 1 
 − 
2.3R  T1 T2 
[A - ]
[HA]
pKa = pKaH −   j
pH = pK a + log
Hammett Equation for pKa
Prediction
Mass balances: Equilibrium
Concentration in Phase 1
Ci1 =
Mass balances: Equilibrium
Concentration in Phase 2
Ci 2 =

mtot  fi 2 mtot
Ci1 
1
=
 if Ki12 =

Vi 2
Vi 2 1 + Ki12  r12 
Ci 2 
Alkalinity Equation
Solubility: Hydrolysis Constants
incorporating autoprotolysis of
water
pH-Dependent Solubility of
Carbonates
[Alk]
= [HCO3-] + 2 [CO3-] + [OH-] - [H+]
Complexation: Brutto Constants β,
Hydrolysis Constants *K and *β
i =  Ki
Sorption Isotherms: Linear,
Freundlich, Langmuir
j

mtot  f i1 mtot
1
=
1
Vi1
Vi1 1 +
K i12  r12
K s0
def
K s0 =
( Kw )
pe Values and Redox Potential
pH Adjustment of pe Values
n
Ks0
Ks0
 Me 2+ (aq )  =
=
2−
CO3 (aq )  CT   2
i
i =1
*
,
*
Ki = Ki  K w ,  i =  i  ( K w )
Cs = Kd  Cw , Cs = K F  C
n
w,
k
Cation Exchange Capacity

Ci1 
 if K i12 =

Ci 2 

CEC = 
i =1
Cs =  max 
i
K L  Cw
1 + K L  Cw
ni  zi
m
1
iOx
log
ni
n
iRed
ni
pe = pe 0 +
0
pepH
= pe 0 −
H +
 e−
pH
,
pe 0 =
2.3RT 0
1
0
pe
log( K ) E H =
F
n
,
WiSe2021, Water Chemistry
Appendix 2: Fundamental Thermodynamic Data
Equations and Tables
WiSe2021, Water Chemistry
Equations and Tables
Appendix 3: Dissociation constants of acids (Blue: amphoteric water, yellow: example of multiple species)
Acid
HA
A-
Hydroiodic acid
HI
I-
1011
-11
Perchloric acid
HClO4
ClO4-
1010
-10
9
-9
Ka
-
Hydrobromic acid
HBr
Br
Hydrochloric acid
HCl
Cl-
107
-7
HClO3
ClO3-
103
-3
Sulfuric acid
H2SO4
HSO4
-
2
-2
Nitric acid
HNO3
NO3-
10
-1
Hydronium-Ion (H+(aq))
H3O+
H2O
1
0.0
Trichloroacetic acid
Cl
Chloric acid
OH
Cl
O
O
OH
HO
Cl
O
Cl
O
O
O
O
HO
O
O
Dichloroacetic acid
–
–
O
OH
H
O
H
Cl
Cl
Sulfurous acid
10
2.0•10-1
0.70
5.9•10-2
1.23
3.32•10-2
1.48
1.5•10-2
1.81
-2
1.92
Cl
Cl
Oxalic acid
10
pKa
–
Cl
Cl
HSO3-
H2SO3
-
2-
Hydrogensulfate ion
HSO4
SO4
1.2•10
Phosphoric acid
H3PO4
H2PO4-
7.5•10-3
2.12
4.0•10-3
2.4
3.24•10-3
2.49
1.49•10-3
2.83
1.36•10-3
2.87
+
Glycinium ion
+
NH3
O
NH3
O
OH
O
O
Pyruvic acid
–
O
OH
O
O
O
CH3
CH3
O
O
Malonic acid
O
OH
O
O
–
OH
OH
Chloroacetic acid
–
Cl
Cl
OH
O
O
O
–
WiSe2021, Water Chemistry
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Acid
A-
HA
O
Citric acid
O
O
HO
OH
O
O
–
HO
O
NO2-
4.6•10-4
3.34
HF
F-
3.5•10-4
3.45
-4
3.75
1.4•10-4
3.86
6.46•10-5
4.19
-5
4.2
6.21•10-5
4.21
-5
4.4
2.3•10-5
4.63
1.8•10-5
4.75
1.5•10-5
4.82
1.4•10-5
4.87
O
1.8•10
O
Lactic acid (Milchsäure)
–
OH
O
OH
OH
H3C
H3C
O
O
HO
O
–
O
O
Benzoic acid
–
O
OH
Ascorbic acid (vitamin C)
HO
HO
H
O
HO
O
HO
OH
H
HO
O
–
OH
O
O
OH
O
O
–
OH
O
–
O
HO
O
+
NH3
NH2
OH
H3C
O
O
O
H3C
O
OH H C
3
O
Propionic acid (propanoic acid)
H3C
–
H3C
O
1-Butanoic acid (Buttersäure)
–
OH
O
Anilinium ion
4.0•10
O
OH
Acetic acid
–
OH
O
HO
6.3•10
OH
O
O
O
O
O
O
Succinic acid (Bernsteinsäure)
Dihydrogencitrate ion
3.13
HNO2
Hydrofluoric acid
Formic acid
7.45•10-4
OH
O
Nitrous acid
pKa
OH
OH
HO
Ka
O
–
O
OH
H3C
O
–
WiSe2021, Water Chemistry
Equations and Tables
Acid
A-
HA
Pyridinium ion
NH
+
O
O
O
–
O
O
O
OH
O
O
O
Carbonic acid
–
Hydrazinium ion
2.03•10-6
5.69
-6
5.7
O
4.3•10-7
6.37
-8
7.04
2.0•10
–
O
–
OH
O
O
–
O
HCO3-
H2CO3
-
H2S
HS
9.1•10
H2PO4-
HPO42-
6.2•10-8
7.21
-9
8.23
Hydrogen sulfide
(Schwefelwasserstoff)
Dihydrogenphosphate ion
5.25
–
O
OH
HO
5.6•10-6
–
O
O
–
pKa
N
O
Hydrogenmalonate ion
Hydrogencitrate ion
Ka
H3N
+
NH2
H 2N
NH2
5.9•10
Boric acid
B(OH)3
B(OH)4-
7.2•10-10
9.14
Ammonium ion
NH4,+
NH3
5.6•10-10
9.25
Hydrogen cyanide (Blausäure)
HCN
CN-
4.9•10-10
9.31
1.6•10-10
9.81
1.3•10-10
9.89
CO32-
4.8•10-11
10.32
-
-12
11.62
CH3
Trimethylammonium ion
H3C
N
+
H
CH3
H3C
N
CH3
CH3
Phenol
O
OH
Bicarbonate ion
Hydrogen peroxide
Hydrogenphosphate ion
Water
HCO3-
–
2.4•10
H2O2
HOO
HPO42-
PO43-
2.2•10-13
12.67
H2O
HO-
1.0•10-14
14.0
WiSe2021, Water Chemistry
Equations and Tables
Appendix 3: Hammett constants
Hammett Constants for Some Common Substituents
jmeta
Substituent j
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
H
CH3
CH2CH3
CH2CH2CH2CH3
C(CH3)3
CH = CH2
Ph
CH2OH
CH2Cl
CCl3
CF3
F
Cl
Br
I
OH
0.00
–0.06
–0.06
–0.07
–0.10
0.08
0.06
0.07
0.12
0.40
0.44
0.34
0.37
0.40
0.35
0.10
jpara Substituent j
0.00
–0.16
–0.15
–0.16
–0.20
–0.08
0.01
0.08
0.18
0.46
0.57
0.05
0.22
0.23
0.18
–0.36
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
OCH3
OCOCH3
CHO
COCH3
COOCH3
CN
NH2
NHCH3
N(CH3)2
NO2
SH
SCH3
SOCH3
SO2CH3
jmeta
0.11
0.36
0.36
0.38
0.33
0.62
–0.04
–0.25
–0.15
0.73
0.25
0.13
0.50
0.68
0.05
jpara
 jpara
–0.24
0.31
0.22
0.50
0.45
0.67
–0.66
–0.84
–0.83
0.78
0.15
0.01
0.49
0.72
0.09
1.03
0.82
0.66
0.89
1.25
Ortho-Substituents for substituted anilines and phenols
nols
nols
 phe
 anilines
Substituent j
Substituent j  phe
jortho
jortho
jortho
–
–
–
–
–
–
–
CH3
CH2CH2CH2CH3
CH2OH
F
Cl
Br
I
–0.13
–0.18
0.04
0.54
0.68
0.70
0.63
0.10
0.47
0.67
0.71
0.70
–
–
–
–
–
OH
OCH3
CHO
NH2
NO2
0.00
0.75
1.24
 anilines
jortho
–0.09
0.02
0.00
1.72
Data from Clark and Perrin (1964) and Barlin and Perrin (1966).
Susceptibility factors for various compound classes
Compound
pKaH
ρ
Benzoic acid
4.19
1 (per definition)
Phenol
9.90
2.25
Anilinium ion
4.63
2.90
Pyridinium ion
5.25
5.90
Phenylacetic acid
4.30
0.49
3-Phenylpropanoic acid
4.55
0.21
Phenoxyacetic acid
3.17
0.30
WiSe2021, Water Chemistry
Equations and Tables
Appendix 5: Selected Solubility Products (Ref.: Benjamin, Water Chemistry, McGrawHill, 2002)
Metal
Ag+
Mineral Name
Formula
AgOH(s)
Ag2CO3(s)
Log Ks0
-7,70
Metal
Cu+
-11,07
Fe2+
Ag3PO4(s)
Ag2S(s)
-17,55
AgCl(s)
Al(OH)3(s)
-9,75
-31,62
Al(OH)3(s)
-33,23
Ferrihydrite
Goethite
AlPO4(s)
-22,50
Lepidocrocite
Calcite
CaCO3(s)
-8,48
Aragonite
CaCO3(s)
-8,36
Portlandite
Ca(OH)2(s)
-5,32
Lime
Gypsum
CaO(s)
CaSO4(s)
Hydroxylapatite
Ca5(OH)(PO4)3(s)
Al3+
Gibbsite
Ca2+
Cd2+
Otavite
Greenockite
Co2+
Cr3+
Cu2+
Tenorite
Malachite
Log Ks0
-6,76
Siderite
FeCO3(s)
-10,55
Vivianite
Fe3(PO4)2(s)
FeS(s)
Fe(OH)3(s)
-36,00
α-FeOOH(s)
-41,50
γ-FeOOH(s)
α-Fe203(s)
-46,00
Hg(OH)2(s)
-25,40
HgO(s)
Hg(CN)2(s)
-25,55
4,80
-4,85
HgCO3(s)
-22,52
HgS(s)
Ni(OH)2(s)
-52,01
Fe3+
Hematite
Hg2+
-44,20
Cinnabar
-16,84
-37,11
-40,63
-39,28
-14,27
CdCO3(s)
-13,74
NiCO3(s)
CdS(s)
Cd3(PO4)2(s)
-28,85
-31,30
Co(OH)2(s)
-15,90
Massicot
Hydrocerrusite
Ni3(PO4)2(s)
PbO(s)
Pb3(CO3)2(OH)2(s)
CoCO3(s)
-12,80
Cerrusite
PbCO3(s)
-13,13
Cr(OH)3(s)
-33,13
Galena
-19,36
PbS(s)
Pb3(PO4)2(s)
-28,05
Cu(OH)2(s)
α-Zn(OH)(2(s)
-15,55
ZnCO3 • H2O(s)
-10,26
Zn3(PO4)2(s)
ZnS(s)
-36,70
CuO(s)
Cu2(OH)2CO3(s)
Cu3(PO4)2(H2O)3(s)
CuS(s)
-32,60
-20,38
-33,18
-9,63
-35,12
-35,96
Ni2+
-15,90
Cd(OH)2(s)
CuCO3(s)
Covallite
Nantokite
Formula
CuCl(s)
Fe(OH)2(s)
-48,97
Mineral Name
Pb2+
Zn2+
-17,20
-6,84
-15,09
-45,46
-44,50
-21,97
WiSe2021, Water Chemistry
Equations and Tables
Appendix 6: Typical natural ligand concentration in aqueous systems
Concentration range in log conc. (M)
Ligand
Fresh Water
Seawater
HCO3-
-4 to –2.3
-2.6
CO32-
-6 to –4
-4.5
Cl-
-5 to –3
-0.26
SO42-
-5 to –3
-1.55
F-
-6 to –4
-4.2
HS-/S2- (anoxic conditions)
-6 to –3
-
Amino acids
-7 to –5
-7 to –6
Organic acids
-6 to –4
-6 to –5
Particle surface groups
-8 to -4
-9 to -6
WiSe2021, Water Chemistry
Equations and Tables
Appendix 7: Selected Complex Formation Constants (= Stability Constants) (Ref.:
Benjamin, Water Chemistry, McGraw-Hill, 2002)
Stability constants for some metal – ligand complexes. Values shown correspond to log 
CO32Ag+
Al3+
Ca2+
Cd2+
AIL
1,29
AgL
Cl3,27
AgL2
5,27
AgL3
5,29
AgL4
5,51
4,92
AgL
F0,36
PO43-
NH3
AlHL
22,50
17,02
AlL4
19,72
AlL5
20,80
AlL6
20,50
CdL
16,28
CdL
5,32
CdL
10,17
CdHL
2,90
CdL2
10,37
CdL2
16,53
CdL3
14,83
CdL3
18,71
CdL4
18,29
CdL4
20,90
0,94
CaHL
15,08
CdL
1,10
CdL
3,90
CdL3
6,22
CdL2
3,50
CdL2
2,60
CdL2
1,50
CdHL
12,40
CdL3
2,40
CuL
0,43
6,73
CuL2
9,83
CuL2
CuHL
13,60
CuL3
FeL
Fe3+
Hg2+
2,31
-0,96
CuL
Fe2+
CuL
2,25
0,50
-0,25
CrL
4,92
CuL
1,26
CuL
5,80
0,16
CuL2
10,70
-2,29
CuL3
14,70
CuL4
-4,59
CuL4
17,60
FeL
0,90
FeL2
0,04
3,92
FeL
1,48
FeL
6,20
FeL2
5,42
FeL2
2,13
FeL2
10,80
FeL3
1,13
FeL3
14,00
HgL
6,75
HgL
1,98
HgL2
HgL3
13,12
1,39
CrH2L
22,29
CuHL
16,60
FeH2L
FeL
HgL
18,45
12,75
CaL
CrL2
AgL2
AlL3
1,98
CrL
21,40
AlL2
CdL
1,34
Agl.3
19,80
2,46
CrL
AgL
AlL
2,91
Cr3+
20,38
7,01
CdL
CoL
HS14,05
AgL2
AlL
CaL
2,50
7,36
AgHL
5,40
CoL
CN-
EDTA
AgL
CdL
Co2+
Cu2+
S042AgL
FeHL
22,25
17,78
CoL
18,60
CoHL
21,60
CuL
18,78
CuHL
11,20
FeL
16,70
FeL6
FeHL
20,10
FeHL6
FeL
27,8
FeH2L6
FeL6
FeHL
29,4
CuL3
52,44
50,00 FeL2
45.61 FeL3
8,95
10,99
52,63
HgL
8,76
HgL
18,07
HgL2
HgL3
17,43
18,40
HgL2
HgL3
34,55
14,02
HgL4
14,43
HgL4
19,17
HgL4
41,31
NiL2
14,59
HgL2
37,37
PbL
15,27
PbL2
16,57
38,30
Mg2+
Ni2+
Pb2+
Zn2+
NiL
6,87
NiL
2,29
NiL
0,40
NiL
NiL2
10,11
NiL2
1,02
NiL2
0,96
NiHL
12,47
PbL
7,24
PbL
2,75
PbL
1,60
PbL
PbL2
10,64
PbL2
3,47
PbL2
1,80
PbL2
PbHL
13,20
PbL3
1,70
PbL4
ZnL
5,30
ZnL
2,37
ZnL
ZnL2
9,60
ZnL2
3,28
ZnL2
0,45
ZnHL
12,40
ZnL3
0,50
ZnL4
0,20
1,30
NiL
20,33
NiL3
22,64
NiHL
11,56
43,95
1,25
PbL
17,86
NiH3L3
PbL4
2,56
PbHL
9,68
PbL3
3,42
PbH2L 6,22
1,38
PbL4
3,10
0,43
ZnL
1,15
ZnHL
ZnL4
44,54
15,70
10,60
ZnL
16,44
ZnL2
11,07
ZnL
14,94
ZnHL
9,00
ZnL3
16,05
ZnL2
16,10
ZnL4
16,72
WiSe2021, Water Chemistry
Equations and Tables
Appendix 8: Cation exchange capacities (CEC) of various environmental
materials found in the colloidal size fraction (Ref.: van Loon/Duffy 2005)
Material
CEC range (average)
/cmol(+) kg-1
Kaolinite
3-15 (8)
Halloysite
4-10 (8)
Montmorillonite
80-150 (100)
Chlorite
10-40 (25)
Vermiculite
100-150 (125)
Hydrous iron and
aluminium oxides
Ca. 4
Feldspar
1-2 (2)
Quartz
1-2 (2)
Organic matter
150-500 (200)
WiSe2021, Water Chemistry
Equations and Tables
Appendix 9: List of oxidation states in common compounds in aquatic chemistry
Element
Oxygen
Nitrogen
Sulfur
Iron
Manganese
Carbon
Oxidation State
0
-I
-II
+V
+III
0
-III
+VI
+IV
+II
0
-II
+III
+II
+VII
+VI
+IV
+III
+II
+IV
0
-II
-IV
Species
O2 (molecular oxygen)
H2O2 (hydrogen peroxide)
H2O, SO42-, etc.
NO3- (nitrate)
NO2- (nitrite)
N2 (molecular nitrogen)
NH4+ (ammonium), NH3
SO42- (sulfate)
SO32- (sulfite), HSO3- (bisulfite)
S2O32- (thiosulfate)
S0
H2S, HS- (hydrogen sulfide), S2- (sulfide)
Fe3+, Fe(OH)2+ etc.
Fe2+, Fe(OH)+ etc.
MnO4- (permanganate)
MnO42- (manganate)
MnO2 (s) (manganese dioxide)
MnOOH (s) (manganite)
Mn2+
CO2, HCO3- (bicarbonate), CO32- (carbonate)
C (elemental carbon), CH2O (formaldehyde)
CH3CH2OH (ethanol; average C oxidation
state of -III and -I)
CH4 (methane)
WiSe2021, Water Chemistry
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Appendix 10 Equilibrium constants for environmentally relevant redox processes (Ref.: Pankow 1991)
WiSe2021, Water Chemistry
Equations and Tables
Appendix 11: Equilibrium constants for redox reactions of selected environmentally relevant
organic compounds (Ref.: Schwarzenbach et al. 2002)
+ H2O