Table II Temperature dependence of Pitzer interaction parameters. 25°C-centric equation used to derive parameters: χ(T) = a1 + a2[{1/T}-{l/298.15}] + a3 In{T/298.15} + a4{T - 298.15}.
Pitzer interaction parameters | |||||||
|---|---|---|---|---|---|---|---|
Ion interactions | Coefficients | a 1 | a 2 | a 3 | a 4 | Reference | |
Ca++ | Cl- |
| 4.46 × 10-1 | 2.21 × 102 | 1.61 × 10-11 | 2.28 × 10-4 | Sterner et al. [34] |
| -1.66 × 10 | -8.83 × 103 | 7.10 × 10-11 | -2.49 × 10-2 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| -1.73 × 10-2 | -1.30 × 101 | -3.87 × 10-13 | -3.15 × 10-5 | |||
Ca++ | HCO3- |
| 4.00 × 10-1 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
| 2.98 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
Ca++ | HSO4- |
| 2.15 × 10-1 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
| 2.53 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
Ca++ | NO3- |
| 1.48 × 10-1 | -4.88 × 101 | -7.47 × 10-2 | -1.70 × 10-4 | Oakes and Felmy [28] |
| 2.44 | -2.24 × 104 | -9.93 × 101 | 1.19 × 10-1 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| -4.12 × 10-3 | -1.79 × 101 | -1.19 × 10-1 | 1.87 × 10-4 | |||
Ca++ | SO4-- |
| 1.50 × 10-1 | 0.00 | 0.00 | 0.00 | Greenberg and Moller [21] |
| 3.00 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
H+ | Cl- |
| 1.77 × 10-1 | -3.35 × 101 | -2.62 × 10-1 | 1.26 × 10-4 | Holmes et al. [27] |
| 2.93 × 10-1 | 3.40 × 103 | 1.98 × 101 | -2.79 × 10-2 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 3.62 × 10-4 | -2.91 × 10-11 | 0.00 | -3.04 × 10-5 | |||
H+ | HSO4- |
| 2.09 × 10-1 | 1.05 × 103 | 5.96 | -8.78 × 10-3 | Holmes and Mesmer [24] |
| 4.41 × 10-1 | 2.96 × 102 | 2.37 | -4.63 × 10-3 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
H+ | NO3- |
| 1.26 × 10-1 | 5.60 × 102 | 4.92 | -9.95 × 10-3 | Felmy et al. [32] |
| 2.88 × 10-1 | 2.71 × 10-7 | 1.59 × 10-9 | 1.34 × 10-3 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| -5.60 × 10-3 | -6.58 | -5.77 × 10-2 | 1.10 × 10-4 | |||
H+ | SO4-- |
| 9.86 × 10-2 | -6.70 × 103 | -4.17 × 101 | 6.37 × 10-2 | Pabalan and Pitzer [47] |
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 5.93 × 10-2 | -3.03 × 103 | -1.61 × 101 | 2.02 × 10-2 | |||
K+ | Cl- |
| 4.78 × 10-2 | -3.43 × 102 | -1.38 | 1.34 × 10-3 | Greenberg and Moller [21] |
| 2.16 × 10-1 | -5.76 × 102 | -2.88 | 4.64 × 10-3 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| -7.49 × 10-4 | 3.65 × 101 | 1.48 × 10-1 | -1.47 × 10-4 | |||
K+ | CO3-- |
| 1.29 × 10-1 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
| 1.43 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 4.99 × 10-4 | 0.00 | 0.00 | 0.00 | |||
K+ | F- |
| 8.09 × 10-2 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
| 2.02 × 10-1 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 9.30 × 10-4 | 0.00 | 0.00 | 0.00 | |||
K+ | HCO3- |
| -1.07 × 10-2 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
| 4.78 × 10-2 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
K+ | HSO4- |
| -3.00 × 10-4 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
| 1.74 × 10-1 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
K+ | NO3- |
| -8.16 × 10-2 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
| 4.94 × 10-2 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 6.60 × 10-3 | 0.00 | 0.00 | 0.00 | |||
K+ | OH- |
| 1.30 × 10-1 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
| 3.20 × 10-1 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 4.10 × 10-3 | 0.00 | 0.00 | 0.00 | |||
K+ | SO4-- |
| 5.55 × 10-2 | -1.42 × 103 | -6.75 | 8.27 × 10-3 | Greenberg and Moller [21] |
| 7.96 × 10-1 | 2.07 × 103 | 2.33 × 10-10 | 2.36 × 10-2 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| -1.88 × 10-2 | 0.00 | 9.09 × 10-13 | -2.66 × 10-15 | |||
Mg++ | Cl- |
| 3.51 × 10-1 | -6.56 × 101 | -5.25 × 10-1 | 4.47 × 10-4 | Pabalan and Pitzer [47] |
| 1.65 | -2.87 × 103 | -2.30 × 101 | 4.95 × 10-2 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 6.53 × 10-3 | -2.67 × 101 | -2.14 × 10-1 | 3.11 × 10-4 | |||
Mg++ | HCO3- |
| 3.30 × 10-2 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
| 8.50 × 10-1 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
Mg++ | HSO4- |
| 4.75 × 10-1 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
| 1.73 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
Mg++ | NO3- |
| 3.67 × 10-1 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
| 1.58 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| -2.06 × 10-2 | 0.00 | 0.00 | 0.00 | |||
Mg++ | SO4-- |
| 2.23 × 10-1 | -5.69 × 103 | -3.28 × 101 | 4.73 × 10-2 | Pabalan and Pitzer [47] |
| 3.38 | -2.32 × 104 | -1.39 × 102 | 2.18 × 10-1 | |||
| -3.53 × 101 | 2.17 × 106 | 1.40 × 104 | -2.28 × 101 | |||
| 2.44 × 10-2 | 1.89 × 103 | 1.08 × 101 | -1.56 × 10-2 | |||
MgOH+ | Cl- |
| -1.00 × 10-1 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
| 1.66 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
Na+ | Cl- |
| 7.46 × 10-2 | -4.71 × 102 | -1.85 | 1.66 × 10-3 | Greenberg and Moller [21] |
| 2.75 × 10-1 | -5.21 × 102 | -2.88 | 4.71 × 10-3 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 1.54 × 10-3 | 4.81 × 101 | 1.75 × 10-1 | -1.56 × 10-4 | |||
Na+ | CO3-- |
| 3.62 × 10-2 | 1.11 × 103 | 1.12 × 101 | -2.33 × 10-2 | He and Morse [26] |
| 1.5 | 4.41 × 103 | 4.46 × 101 | -9.99 × 10-2 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 5.20 × 10-3 | 0.00 | 0.00 | 8.88 × 10-16 | |||
Na+ | F- |
| 2.15 × 10-2 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
| 2.11 × 10-1 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
Na+ | HCO3- |
| 2.80 × 10-2 | 6.83 × 102 | 6.90 | -1 .45 × 1 0-2 | He and Morse [26] |
| 4.40 × 10-2 | 1.13 × 103 | 1.14 × 101 | -2.45 × 10-2 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
Na+ | HSO4- |
| 7.34 × 10-2 | 5.26 × 101 | 4.21 × 10-1 | -8.21 × 10-4 | Holmes and Mesmer [24] |
| 3.00 × 10-1 | 4.70 × 103 | 2.68 × 101 | -3.74 × 10-2 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| -4.62 × 10-3 | -5.82 × 10-11 | -2.27 × 10-13 | 6.82 × 10-6 | |||
Na+ | NO3- |
| 3.57 × 10-3 | -7.03 × 102 | -3.35 | 3.98 × 10-3 | Archer [33] |
| 2.32 × 10-1 | -2.73 × 103 | -1.30 × 101 | 2.07 × 10-2 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| -4.15 × 10-5 | 6.48 × 101 | 3.18 × 10-1 | -3.84 × 10-4 | |||
Na+ | OH- |
| 8.83 × 10-2 | -1.20 × 103 | -6.11 | 7.43 × 10-3 | He and Morse [26] |
| 2.44 × 10-1 | 1.63 × 103 | 9.48 | -1.16 × 10-2 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 4.00 × 10-3 | 8.82 × 101 | 4.07 × 10-1 | -4.76 × 10-4 | |||
Na+ | SO4-- |
| 1.21 × 10-2 | -2.19 × 103 | -1.01 × 101 | 1.20 × 10-2 | Greenberg and Moller [21] |
| 1.12 | -1.27 × 104 | -6.72 × 101 | 8.91 × 10-2 | |||
| 0.00 | 0.00 | 0.00 | 0.00 | |||
| 6.57 × 10-3 | 3.39 × 102 | 1.48 | -1.64 × 10-3 | |||
Ca++ | H+ | s θ MM' | 9.20 × 10-2 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
Ca++ | K+ | s θ MM' | 1.16 × 10-1 | 9.31 × 10-10 | 0.00 | 1.42 × 10-14 | Greenberg and Moller [21] |
Ca++ | Na+ | s θ MM' | 5.00 × 10-2 | 1.86 × 10-9 | 7.28 × 10-12 | 0.00 | Greenberg and Moller [21] |
Ca++ | Mg++ | s θ MM' | 7.00 × 10-3 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
H+ | K+ | s θ MM' | 5.00 × 10-3 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
H+ | Mg++ | s θ MM' | 1.00 × 10-1 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
H+ | Na+ | s θ MM' | 3.60 × 10-2 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
K+ | Mg++ | s θ MM' | 0.00 | 0.00 | 0.00 | 0.00 | Pabalan and Pitzer [47] |
K+ | Na+ | s θ MM' | -3.20 × 10-3 | 1.40 × 101 | 9.09 × 10-13 | -2.66 × 10-15 | Greenberg and Moller [21] |
Mg++ | Na+ | s θ MM' | 7.00 × 10-2 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
Cl- | CO3-- | s θ XX' | -2.00 × 10-2 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
Cl- | HCO3- | s θ XX' | 3.00 × 10-2 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
Cl- | HSO4- | s θ XX' | -6.00 × 10-3 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
Cl- | NO3- | s θ XX' | 1.60 × 10-2 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
Cl- | OH- | s θ XX' | -5.00 × 10-2 | 0.00 | 0.00 | 0.00 | Pabalan and Pitzer [47] |
Cl- | SO4-- | s θ XX' | 7.03 × 10-2 | 1.83 × 102 | 1.33 | -2.33 × 10-3 | Greenberg and Moller [21] |
CO3-- | HCO3- | s θ XX' | -4.00 × 10-2 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
CO3-- | OH- | s θ XX' | 1.00 × 10-1 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
CO3-- | SO4-- | s θ XX' | 2.00 × 10-2 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
HCO3- | SO4-- | s θ XX' | 1.00 × 10-2 | 0.00 | 0.00 | 0.00 | Pitzer [13] |
HSO4- | SO4-- | s θ XX' | -1.17 × 10-1 | -3.09 × 103 | -1.40 × 101 | 1.54 × 10-2 | Holmes and Mesmer [24] |
OH- | SO4-- | s θ XX' | -1.30 × 10-2 | 0.00 | 0.00 | 0.00 | Pabalan and Pitzer [47] |
CO2(aq) | Ca++ | s λ NM | 1.98 × 10-1 | -6.51 × 104 | -4.03 × 102 | -6.18 × 10-1 | He and Morse [26] |
CO2(aq) | H+ | s λ NM | 0.00 | 0.00 | 0.00 | 0.00 | He and Morse [26] |
CO2(aq) | K+ | s λ NM | 4.58 × 10-2 | 1.37 × 104 | 8.36 × 101 | -1.28 × 10-1 | He and Morse [26] |
CO2(aq) | Mg++ | s λ NM | 1.95 × 10-1 | -3.96 × 103 | -3.17 × 101 | 5.70 × 10-2 | He and Morse [26] |
CO2(aq) | Na+ | s λ NM | 7.75 × 10-2 | -1.92 × 104 | -1.17 × 102 | 1.75 × 10-1 | He and Morse [26] |
SiO2(aq) | H+ | s λ NM | 0.00 | 0.00 | 0.00 | 0.00 | Felmy et al. [32] |
SiO2(aq) | Mg++ | s λ NM | 8.21 × 10-2 | -3. 83 × 10-9 | -2.33 × 10-11 | -1.81 × 10-3 | Felmy et al. [32] |
SiO2(aq) | Na+ | s λ NM | -7.89 × 10-2 | -1.44 × 10-7 | -8.64 × 10-10 | 1.19 × 10-4 | Felmy et al. [32] |
CO2(aq) | Cl- | s λ NX | 2.02 × 10-2 | 5.08 × 103 | 3.01 × 101 | -4.47 × 10-2 | He and Morse [26] |
CO2(aq) | HSO4- | s λ NX | -3.00 × 10-3 | 0.00 | 0.00 | 0.00 | He and Morse [26] |
CO2(aq) | SO4-- | s λ NX | 1.39 × 10-1 | 4.99 × 104 | .09 × 102 | -4.55 × 10-1 | He and Morse [26] |
SiO2(aq) | Cl- | s λ NX | 1.42 × 10-1 | 1.67 × 102 | 1.51 | -3.22 × 10-3 | Felmy et al. [32] |
SiO2(aq) | NO3- | s λ NX | 1.34 × 10-1 | 6.30 × 103 | 3.55 × 101 | -5.02 × 10-2 | Felmy et al. [32] |
SiO2(aq) | SO4-- | s λ NX | 7.76 × 10-2 | 1.56 × 10-7 | 9.33 × 10-10 | 5.53 × 10-4 | Felmy et al. [32] |
Ca++K+ | Cl- | ψ MM'X | -4.32 × 10-2 | -2.71 × 101 | -3.64 × 10-12 | 3.55 × 10-15 | Greenberg and Moller [21] |
Ca++Na+ | Cl- | ψ MM'X | -3.00 × 10-3 | 0.00 | 1.14 × 10-13 | -6.66 × 10-16 | Greenberg and Moller [21] |
Ca++Na+ | SO4-- | ψ MM'X | -1.20 × 10-2 | 0.00 | 4.55 × 10-13 | -2.66 × 10-15 | Greenberg and Moller [21] |
K+Mg++ | Cl- | ψ MM'X | -2.20 × 10-2 | -1.43 × 101 | 0.00 | 0.00 | Pabalan and Pitzer [47] |
K+Na+ | Cl- | ψ MM'X | -3.69 × 10-3 | -5.10 | -3.41 × 10-13 | 6.66 × 10-16 | Greenberg and Moller [21] |
K+Na+ | SO4-- | ψ MM'X | 7.32 × 10-3 | -7.16 × 101 | -3.94 × 10-1 | 6.07 × 10-4 | Greenberg and Moller [21] |
Mg++Na+ | Cl- | ψ MM'X | -1.20 × 10-2 | -9.51 | 0.00 | 0.00 | Pabalan and Pitzen [47] |
Ca++Cl- | SO4-- | ψ MXX' | -1.80 × 10-2 | -6.98 × 10-10 | -2.73 × 10-12 | 1.78 × 10-15 | Greenberg and Moller [21] |
K+Cl- | SO4-- | ψ MXX' | -1.62 × 10-3 | 3.76 × 101 | 2.90 × 10-12 | 2.85 × 10-4 | Greenberg and Moller [21] |
H+HSO4- | SO4-- | ψ MXX' | 0.00 | 0.00 | 0.00 | 0.00 | Holmes and Mesmer [24] |
Mg++Cl- | SO4-- | ψ MXX' | -7.96 × 10-3 | 3.26 × 101 | 0.00 | 0.00 | Pabalan and Pitzer [47] |
Na+Cl- | OH- | ψ MXX' | -6.01 × 10-3 | -9.93 | 0.00 | 0.00 | Pabalan and Pitzer [47] |
Na+Cl- | SO4-- | ψ MXX' | -9.09 × 10-3 | -7.86 × 101 | -5.52 × 10-1 | 9.46 × 10-4 | Greenberg and Moller [21] |
Na+HSO4- | SO4-- | ψ MXX' | 1.44 × 10-2 | 2.58 × 102 | 1.16 | -1.26 × 10-3 | Holmes and Mesmer [24] |
Na+OH- | SO4-- | ψ MXX' | -9.10 × 10-3 | -1.17 × 101 | 0.00 | 0.00 | Pabalan and Pitzer [47] |
CO2(aq) | Ca++Cl- | ξ NMX | -1.61 × 10-2 | 6.25 × 103 | 3.90 × 101 | -6.04 × 10-2 | He and Morse [26] |
CO2(aq) | H+Cl- | ξ NMX | -4.65 × 10-3 | -1.31 × 103 | -7.26 | 9.96 × 10-3 | He and Morse [26] |
CO2(aq) | H+SO4-- | ξ NMX | 0.00 | 0.00 | 0.00 | 0.00 | He and Morse [26] |
CO2(aq) | K+ Cl- | ξ NMX | -1.27 × 10-2 | -9.33 × 103 | -5.65 × 101 | 8.56 × 10-2 | He and Morse [26] |
CO2(aq) | K+SO4-- | ξ NMX | -4.10 × 10-4 | -1.12 × 105 | -6.84 × 102 | 1.04 | He and Morse [26] |
CO2(aq) | Mg++Cl- | ξ NMX | -1.53 × 10-2 | -3.32 × 103 | -1.97 × 101 | 2.94 × 10-2 | He and Morse [26] |
CO2(aq) | Mg++SO4-- | ξ NMX | -9.28 × 10-2 | -6.09 × 104 | -3.64 × 102 | 5.44 × 10-1 | He and Morse [26] |
CO2(aq) | Na+Cl- | ξ NMX | -5.50 × 10-4 | -3.97 × 103 | -2.44 × 101 | 3.73 × 10-2 | He and Morse [26] |
CO2(aq) | Na+SO4-- | ξ NMX | -3.73 × 10-2 | -8.84 × 103 | -5.48 × 101 | 8.49 × 10-2 | He and Morse [26] |
SiO2(aq) | H+NO3- | ξ NMX | -3.30 × 10-3 | 0.00 | 0.00 | 0.00 | Felmy et al. [32] |
SiO2(aq) | Mg++ Cl- | ξ NMX | -5.15 × 10-2 | 1.50 × 10-8 | 8.99 × 10-11 | 5.94 × 10-4 | Felmy et al. [32] |
SiO2(aq) | Na+Cl- | ξ NMX | -8.48 × 10-15 | -1.84 × 10-8 | -1.11 × 10-10 | -2.00 × 10-4 | Felmy et al. [32] |
