Geology Reference
In-Depth Information
For solutes in higher ionic strength solutions, however, Equations
(3.3)-(3.5) tend to underestimate activity coecients in part because of
the assumptions that are inherent in the DH and extended DH Equations,
e.g. only long-range coulombic interactions, ion size parameters are
independent of ionic strength, ions of like charge do not interact, each
ion can construct its own atmosphere of ions of opposite charge. 8,12,15,16
Additional factors are that (i) short-range interactions (including those
between ions of like charge and also between ions and neutral mole-
cules), 12,15-17 rather than the long-range coulombic interactions, between
ions become increasingly important and (ii) the number of water mole-
cules involved in ion hydration spheres means that the activity of water
decreases to a value significantly less than unity. 12 In order to compensate
particularly for the effect of (ii), various empirical correction factors have
subsequently been added to the extended DH expression.
p
p
bI
Truesdell Jones equation ð 3 : 6 Þ
log g i ¼ 0 : 5 z i
I
= 1 þ 0 : 33 a i
I
Davies equation ð 3 : 7 Þ
The Truesdell-Jones 18 equation contains an empirical term, bI,aswellas
the ion size parameter, a i . Values of both a i andbareoftenobtainedby
fitting this equation to the individual activity coecients obtained from
mean salt data using the MacInnes convention (see Example 3.1). 9,10 This
equation is used in some geochemical computer models, e.g.
PHREEQE. 19 The Davies equation, which also incorporates an empirical
term bI but uses an average ion size parameter (a i ¼ 3), is more commonly
used because the ion size parameter is not well defined for all ions. The
Davies equation can be used to calculate activity coecients for mono-
valent and divalent ions in aqueous solutions, where I ¼ 0.1-0.7 mol L 1
and I ¼ 0.1-
p
p bI
log g i ¼ 0 : 5 z i
I
= 1 þ I
0.3 mol L 1 , respectively. Originally, Davies used a value
of 0.2 for b but later suggested that the value be increased to 0.3. 20,21 The
geochemical computer model MINTEQA2 employs the Davies equation
to calculate single-ion activity coecients but uses a value of 0.24 for b. 22
Specific Ion Interaction Theory (SIT) is a more advanced empirical
approach that was developed by Guggenheim 23 and extended by
Scatchard and others. 24-26 The SIT equation has an extended DH term
that accounts for the non-specific long-range interactions but also has an
ion- and electrolyte-specific correction factor, e ij [j], for each pair of ions,
i and j, of opposite charge. Brønsted 27 also recognized the importance of
short-range interactions in higher ionic strength solutions and Equation
(3.8) is often referred to as the Brønsted-Guggenheim equation.
log g i ¼ 'Extended DH' þ S j e ij [j]
B
(3.8)
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