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

B.1 2BThe specific ion interaction equations
437
• Assumption 1: The activity coefficient γ j of an ion j of charge z j in the solution
of ionic strength I m may be described by Eq. (B.1):
D is the Debye-Hückel term:
2
log
10
γ
j
= zj D ε( j, k, Im)
mk
k
A Im
D =
1 + Ba I
− + ∑ (B.1)
j
m
(B.2)
A and B are constants which are temperature and pressure dependent, a j is an ion size
parameter (“distance of closest approach”) for the hydrated ion j, and I m is the molal
ionic strength:
I
= 1
∑ mz 2
2
m i i
i
The Debye-Hückel limiting slope, A, has a value of (0.509 ± 0.001)
1 1
2 2
kg ·mol − at 298.15 K and 1 bar, (cf. Section B.1.2). The term Ba j in the denominator
of Eq. (B.2) (where a j is an “effective” ion size parameter and B is a constant determined
by the temperature and the physical properties of water) has been assigned an
1 1
2 2
empirical value of 1.5 kg ·mol −
(Eq. (B.2a)). The value 1.5 was proposed by
Scatchard [1976SCA] to minimise the ionic strength dependence of ε ( jk , ) for a number
of electrolytes, and it was found to be particularly appropriate between I m = 0.5 and
3.5 m. A constant value of Ba j for all species simplifies modelling of both binary and
multicomponent aqueous electrolyte systems, and makes it easier to give a consistent
description of mean activity coefficient both in binary and multicomponent solutions
([1959ROB/STO], pp.435-441). Thus,
1
AI 2
m
D = (B.2a)
1
1 + 1.5I
2
m
It should be mentioned that some authors have proposed different values for
Ba j ranging from Ba j = 1.0 [1935GUG] to Ba j = 1.6 [1962VAS]. However, the parameter
Ba j is empirical and as such is correlated to the value of ε ( jkI , , m
). Hence, this variety
of values for Ba j does not represent an uncertainty range, but rather indicates that
several different sets of Ba j and ε ( jkI , , m
) may describe equally well the experimental
mean activity coefficients of a given electrolyte. The ion interaction coefficients at
298.15 K listed in Table B-4, Table B-5, Table B-6 and Table B-7 have thus to be used
1 1
2 2
with Ba j = 1.5 kg ·mol − .
The summation in Eq. (B.1) extends over all ions k present in solution. Their
molality is denoted by m k , and the specific ion interaction parameters, ε ( jkI , , m
), in
general depend only slightly on the ionic strength. The concentrations of the ions of the
ionic medium are often very much larger than those of the reacting species. Hence, the
ionic medium ions will make the main contribution to the value of log 10 γ j for the reacting
ions. This fact often makes it possible to simplify the summation ∑ ε( jkI , , ) m ,
k
m
k
CHEMICAL THERMODYNAMICS OF TIN, ISBN 978-92-64-99206-1, © OECD 2012