Calc.  SED & PREDOM / Ionic Strength

The simplified Helgeson-Kirkham-Flowers (HKF) model:
    log γi = A Zi2 (I  /  (1+BI )) − log(1+0.018 ∑mk) + b I

where I is the ionic strength, γi is the activity coefficient of an ion “i” with electric charge Zi A is the Debye-Hückel slope (see the table below);  B (= åBγ in the Debye-Hückel eqn.) includes the distance of closest approach (effective ionic radii);  and b is a solute specific parameter. The sum is made over all solute species “k” in the aqeuous solution. See the list of references.

In SPANA (and SED/PREDOM) the HKF model is simplified by using the NaCl parameters:

The HKF parameters A, B, and b for this simplified model are (Helgeson et al. 1981, Oelkers and Helgeson 1990):

t (°C) A B b
0 0.4911.210.041
25 0.5091.220.064
50 0.5341.240.074
100 0.6001.270.076

The activity of water (H2O) is given by
    log aH2O = Φ ∑mk / (ln(10) 55.508)

where “Φ” is the osmotic coefficient, calculated using the simplified HKF model as follows:
    Φ = ln(1+0.018 ∑mk)/(0.018 ∑mk) − (2/3) (ln(10)/∑mk) A I3/2 σ(BI) (ln(10)/∑mk) (b/2) I

where
    σ(x) = (3/x3) ((1+x) − 1/(1+x) − 2 ln(1+x))

References


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