The Davies equation is an empirical equation appropiate
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, C.W. (1938) J. Chem. Soc., 2093-2098),
but later Davies changed it to 0.3 (Davies, C.W. (1962) Ion Association.
London: Butterworths. p.41).
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 temperature-dependent
solvent parameter A of the
Debye-Hückel model
(A=0.509 at 25°C);
but the value 0.3 in the last term of the equation
is kept temperature-independent.
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 − (2/3) (ln(10)/∑mk)
A I3/2
σ(√I)
+ (ln(10)/∑mk)
A 0.3 I2
|
where
|
σ(x) = |
(3/x3) ((1+x) − 1/(1+x) − 2 ln(1+x))
|
Back to activity coefficient models