Chemical Thermodynamics of Tin - Volume 12 - OECD Nuclear ...

B.1 2BThe specific ion interaction equations
439
ο
provide similar calculated results for values of log10
K . As the two-epsilon model has
been used in the current and previous volumes, the relevant parameters have been retained
and augmented in Table B-6.
By using a more elaborate virial expansion, Pitzer and co-workers [1973PIT],
[1973PIT/MAY], [1974PIT/KIM], [1974PIT/MAY], [1975PIT], [1976PIT/SIL],
[1978PIT/PET], [1979PIT] have managed to describe measured activity coefficients of
a large number of electrolytes with high precision over a large concentration range.
Pitzer’s model generally contains three parameters as compared to one in the specific
ion interaction treatment. The use of the treatment requires the knowledge of all these
parameters. The derivation of Pitzer coefficients for many complexes, such as those of
the actinides would require a very large amount of additional experimental work, since
few data of this type are currently available.
The way in which the activity coefficient corrections are performed in this
review according to the specific ion interaction treatment is illustrated below for a general
case of a complex formation reaction. Charges on all species except the hydrogen
ions are omitted for brevity.
mM + qL + nH O(l) M L (OH) + n H
2
m q n
*
m q n
β
q n m
The formation constant of M L (OH) ,
, ,
, determined in an ionic
medium (1:1 salt NX) of the ionic strength I m , is related to the corresponding value at
* ο
zero ionic strength, β
qnm , ,
by Eq. (B.4).
* *
log β = log β + mlog γ + qlog γ + nlog
a
−log γ − nlog
γ
ο
10 qnm , , 10 qnm , , 10 M 10 L 10 H2O
10 qnm , , 10 +
H
+
(B.4)
The subscript (q,n,m) denotes the complex ion, MmL q(OH)
n
. If the concentrations
of N and X are much greater than the concentrations of M, L, MmL q(OH)
and n
H + , only the molalities m N and m X have to be taken into account for the calculation of
the term, ∑ ε ( jkI , ,
m)
mk
in Eq. (B.1). For example, for the activity coefficient of the
k
metal cation M, γ M , Eq. (B.5) is obtained at 298.15 K and 1 bar.
−z
0.509 I
log = + (M ,X, )
2
M
m
10
γM ε Im
mX
1 + 1.5 Im
(B.5)
Under these conditions, I m ≈ m X = m N Substituting the log 10 γ j values in
Eq. (B.4) with the corresponding forms of Eq. (B.5) and rearranging leads to:
log β −ΔzD− nlog a = log β − Δε
I
(B.6)
where, at 298.15 K and 1 bar:
* 2 * ο
10 qnm , , 10 H2O 10 qnm , ,
m
Δz = ( mz − qz − n) + n − mz − qz
(B.7)
2 2 2 2
M L M L
CHEMICAL THERMODYNAMICS OF TIN, ISBN 978-92-64-99206-1, © OECD 2012