B = B + RT ln aB ,
O
(28)
where B is the standard-state chemical potential of component B and aB is its activity. In
O
many cases, the activity of a mixture component can be approximated by its mole fraction,
defined by
n
xB = nB ,
(29)
T
or its molality, defined by
nB
mB =
(30)
(nA MA )
where MA is the molar mass of solvent A (kg mol1).
These approximations are imperfect, so the deviation of the mole fraction or molality
from the activity defines an activity coefficient (fB or γB), termed rational if the reference
function is the mole fraction:
B = B + RT ln( fBxB ),
O
(31)
or molality-based if the reference function is solution molality:
γ m
B = B + RT ln B OB
O
(32)
mB
O
where mB is the standard state molality, 1 mol kg1.
Electrolyte solutions
Geochemical solutions are electrolyte solutions. Because electrolytes dissolve into
charged ions in solution, the chemicalthermodynamic description of these solutions is
much more difficult than for solutions and mixtures of electrically neutral components.
Consider the simple case of an unhydrated crystalline BνB CνC (cr) composed of νC
moles of anion C zC and BzB (zB and zC are the charge numbers of the subscripted ions)
that dissolves completely in water to form an anionic and a cationic species:
z
zC
Bv Cv (cr) = vB B B (aq) + vC C
(33)
(aq).
B
C
The single-ion activity coefficient γB can be defined by
γ BmB
aB(aq) d=f
e
(34)
O
mB
and related to the chemical potential of the single-ion species by
m γ
B(aq) = B(aq) + RT ln BOB .
O
(35)
mB
For mBC moles of salt, which dissociate into νBmBC moles of cation and νCmBC moles of
anion, the chemical potentials for the salt BC in solution is related to the chemical poten-
tials for the single-ion species by
mBC BC(aq) = mB B(aq) + mC C(aq)
(36)
(From eq 37, the salt BνB CνC will be represented simply as BC). The chemical potentials of
the electrolyte and the single-ion species are related by
BC = vB B + vC C
(37)
13
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