The Davies equation
This is an empirical model appropriate
for ionic strengths up to ≈0.1 M:
| |
log γi = |
−0.5 Zi2
(√I /
(1+√I
) − 0.3 I
)
|
where I is the ionic strength;
γi is the
activity coefficient of an
ion “i” with electric charge Zi.
The last parameter was initially “0.2”
(Davies 1938)
but it was later changed to “0.3” (Davies 1962).
The Davies equation is derived from the
Debye-Hückel model,
simplified by setting åBγ = 1
for all electrolytes, and extended with the empirical term:
+0.15 Zi2 I.
In SPANA (and SED/PREDOM)
the parameter “0.5” is replaced by the
“Aγ” parameter of the
Debye-Hückel model
which is temperature- and pressure-dependent (see Table;
Aγ = 0.509 (mol/kg)−½
at 25°C);
but the value “0.3” in the last term of the Davies equation
is kept constant at all temperatures and pressures.
The activity of water (H2O) is given by:
| |
log aH2O = |
− Φ ∑mk /
(ln(10) 55.508)
|
where “k” are all solute species in the aqeuous solution, and “Φ”
is the osmotic coefficient, which for the Davies equation it is given by:
| |
Φ = |
1 −
(2 AΦ I3/2
(1/∑mk)
σ(√I))
+ (1/∑mk)
ln(10) (Aγ×0.3) I2
|
where AΦ = (1/3) ln(10) Aγ, and
| |
σ(x) = |
(3/x3) ((1+x) − 1/(1+x) − 2 ln(1+x))
|
Note: in the calculations the values of log γi
are cut-off to be in the range ±(20 Zi2), and
log aH2O is cut-off to be in the
range ±4.
References
-
Davies, C.W. (1938) The extent of dissociation of salts in water.
Part VIII. An equation for the mean ionic activity coefficient
of an electrolyte in water, and a revision of the dissociation constants
of some sulphates. J. Chem. Soc., 2093-2098. doi: 10.1039/JR9380002093
-
Davies, C.W. (1962) Ion Association. London: Butterworths. p.41
Models for activity coefficients
Comparison between experimental data and models
