Debye-Huckel parameters

SED & PREDOM / Activity Coefficient Models

Table of Debye-Hückel parameters

The following table lists values for the parameters in the Debye-Hückel model, A_γ, A_Φ and B_γ, at selected temperatures and pressures. These values have been calculated from the density and dielectric constant of water, which are also listed in the table.

The density of fluid water, “ρ”, has been calculated using the model by Wagner and Pruss (2002). The dielectric constant of water (relative permittivity, denoted here as “ε_r”) has been calculated using the equations from Fernández et al. (1997) (at temperatures ≤ 600°C) and from Johnson and Norton (1990) and Johnson et al. (1992) (at temperatures above 600°C).

For convenience, the table lists also the values of åB_γ obtained with å = 4.5685 Å, corresponding to åB_γ = 1.5 (mol/kg)^−½ at 25°C. Note that these values presupose that å does not change with either temperature or pressure.

The table also lists the parameter b_γ,NaCl for the simplified HKF model (see equations and Table A-2 in Oelkers and Helgeson 1990).

(°C)

(bar)

(g/cm³)

ε_r

(−)

A_γ

(mol/kg)^−0.5

A_Φ

(mol/kg)^−0.5

B_γ

(mol/kg)^−0.5Å⁻¹

åB_γ

(mol/kg)^−0.5

b_γ,NaCl

(kg/mol)

−20

2000

1.0879

105.0

0.4392

0.3371

0.3217

1.47

0.089

0.9998

87.93

0.4902

0.3763

0.3245

1.48

0.041

0.9970

78.38

0.5101

0.3915

0.3285

1.50

0.064

0.9880

69.93

0.5340

0.4099

0.3325

1.52

0.074

0.9748

62.42

0.5624

0.4316

0.3368

1.54

0.077

100

1.014

0.9583

55.53

0.5990

0.4597

0.3420

1.56

0.076

150

4.76

0.9170

44.03

0.6871

0.5274

0.3528

1.61

0.067

200

15.6

0.8647

34.74

0.8052

0.6180

0.3647

1.67

0.048

250

39.8

0.7990

27.00

0.9716

0.7458

0.3782

1.73

0.021

300

85.9

0.7123

20.14

1.242

0.9535

0.3951

1.80

−0.024

350

165.3

0.5745

13.04

1.888

1.449

0.4229

1.93

−0.107

400

2000

0.7925

19.41

1.088

0.8348

0.3917

1.79

0.017

450

2000

0.7427

16.17

1.244

0.9546

0.4008

1.83

−0.004

500

2000

0.6914

13.44

1.432

1.099

0.4102

1.87

−0.028

550

2000

0.6398

11.16

1.657

1.272

0.4197

1.92

−0.055

600

2000

0.5894

9.28

1.922

1.475

0.4290

1.96

−0.085

700

2000

0.4986

7.02

2.283

1.753

0.4297

1.96

−0.149

800

2000

0.4267

5.39

2.712

2.082

0.4321

1.97

−0.210

900

2000

0.3725

4.40

3.001

2.303

0.4271

1.95

−0.261

1000

2000

0.3315

3.79

3.136

2.407

0.4169

1.90

−0.301

The pressures between 100 and 350°C correspond to the liquid-vapour equilibrium for H₂O. For temperatures < 100°C the reference pressure of 1 bar is used. Below 0°C and above the critical point of water the table lists values at 2 kbar.

Other tables of Debye-Hückel parameters may be found for example in Bradley and Pitzer (1979) (Table II), Helgeson et al. (1981) (Table 1, p.1294-1295), Beyer and Staples (1986) (Table II), Archer and Wang (1990) (Table 5), and Fernández et al. (1997) (Table 17).

References

D.G. Archer and P. Wang, J. Phys. Chem. Ref. Data, 19 (1990) 371-411; doi: 10.1063/1.555853
R.P. Beyer and B.R. Staples, J. Sol. Chem., 15 (1986) 749-764; doi:10.1007/BF00646716
D.J. Bradley and K.S. Pitzer, J. Phys. Chem., 83 (1979) 1599-1603; doi: 10.1021/j100475a009
D.P. Fernández, A.R.H. Goodwin, E.W. Lemmon, J.M.H. Levelt Sengers and R.C. Williams, J. Phys. Chem. Ref. Data, 26 (1997) 1125-1166; doi: 10.1063/1.555997
H.C. Helgeson, D.H. Kirkham, G.C. Flowers, Amer. J. Sci., 281 (1981) 1249–1516; doi:10.2475/ajs.281.10.1249
J.W. Johnson and D. Norton, Amer. J. Sci., 291 (1991) 541–648; doi:10.2475/ajs.291.6.541
J.W. Johnson, E.H. Oelkers, H.C. Helgeson, Comp. & Geosci., 18 (1992) 899–947; doi:10.1016/0098-3004(92)90029-Q
E.H. Oelkers and H.C. Helgeson, Geochim. Cosmochim. Acta, 54 (1990) 727-738; doi: 10.1016/0016-7037(90)90368-U
W. Wagner and A. Pruβ, J. Phys. Chem. Ref. Data, 31 (2002) 387-535; doi: 10.1063/1.1461829

Debye-Hückel model
Models for activity coefficients