CHAPTER 8 . Speciation of Metals in Natural Waters
199
The fraction of the metal and ligand complexed respectively to various ligands (Xi)
and metals (Mi ) are given by:
aMX= aMK*MX[Xd
I
I
(8.15)
aMp<: = axKMjx[Md
(8.16)
These equations can be solved by a series of iterations. Although trace metals do
not affect the concentration of the major ligands in the solution (Cl, OH, S04' C0 3 ),
the major cations (Mg, Ca) must be considered. This is normally done first so that the
concentration of the free major ligands can be estimated before the iteration of the
trace metal speciation. In the next section, we will outline the model that we have developed to calculate the trace activity coefficients in natural waters over a wide range
of composition (Na, Mg, Ca, K, Sr, Cl, S04' HC03, Br, C03, B(OH)4' F) with major (Cl,
S04' C03) and trace (OH, P04) ligands.
8.3
Estimation of the Activity Coefficients of Ions in Natural Waters
To estimate the activity coefficients of ions in mixed electrolyte solutions, a self-consistent model valid over a wide range of ionic strengths and composition is needed
(Millero 1982,2001). One would also like to know the form or speciation of metals in
waters of interest. The estimation of the activity coefficients of ions in natural waters
can be determined by using the ion pairing model (Garrels and Thompson 1962;
Truesdale and Jones 1969; van Breeman 1973; Dickson and Whitfield 1981; Turner et al.
1981; Millero and Schreiber 1982) and the specific interaction model (Pitzer 1979, 1991
Harvie and Weare 1980; Harvie et al. 1984; Millero 1982; Millero and Roy 1997; Millero
and Pierrot 1998). The recent progress in using these models to estimate the activity
of ionic solutes and speciation of metals is described elsewhere (Millero 2001). The
specific interaction model as formulated by Pitzer (1979,1991) is used to estimate the
activity coefficients in our model. The general equation is given by:
In}'; = D.H. + L.ijmimjB& + L.ijkmimjmkC &k
(8.17)
where D.H. is a form of the Debye-Huckellimiting law. The Blj and Cljk parameters are
related to the binary (ions i and j) and ternary (ions i,j and k) interactions and can be
a function of ionic strength. The activity coefficient of a cation (M) in a mixed electrolyte is given by:
In I'M = z~F + 2 Lama(BMa + BCMa ) + Z~R + ZMS + Lcmc(2~c + Lama PMca )
+ LaLa,mama' Paa'M + Lcmc2E~c + Z~Rl + Z~R2
It can be attributed to six contributions:
(8.18)
1. The Debye-Huckel term (Z~F) is the limiting law, which is only a function of ionic strength.
199
The fraction of the metal and ligand complexed respectively to various ligands (Xi)
and metals (Mi ) are given by:
aMX= aMK*MX[Xd
I
I
(8.15)
aMp<: = axKMjx[Md
(8.16)
These equations can be solved by a series of iterations. Although trace metals do
not affect the concentration of the major ligands in the solution (Cl, OH, S04' C0 3 ),
the major cations (Mg, Ca) must be considered. This is normally done first so that the
concentration of the free major ligands can be estimated before the iteration of the
trace metal speciation. In the next section, we will outline the model that we have developed to calculate the trace activity coefficients in natural waters over a wide range
of composition (Na, Mg, Ca, K, Sr, Cl, S04' HC03, Br, C03, B(OH)4' F) with major (Cl,
S04' C03) and trace (OH, P04) ligands.
8.3
Estimation of the Activity Coefficients of Ions in Natural Waters
To estimate the activity coefficients of ions in mixed electrolyte solutions, a self-consistent model valid over a wide range of ionic strengths and composition is needed
(Millero 1982,2001). One would also like to know the form or speciation of metals in
waters of interest. The estimation of the activity coefficients of ions in natural waters
can be determined by using the ion pairing model (Garrels and Thompson 1962;
Truesdale and Jones 1969; van Breeman 1973; Dickson and Whitfield 1981; Turner et al.
1981; Millero and Schreiber 1982) and the specific interaction model (Pitzer 1979, 1991
Harvie and Weare 1980; Harvie et al. 1984; Millero 1982; Millero and Roy 1997; Millero
and Pierrot 1998). The recent progress in using these models to estimate the activity
of ionic solutes and speciation of metals is described elsewhere (Millero 2001). The
specific interaction model as formulated by Pitzer (1979,1991) is used to estimate the
activity coefficients in our model. The general equation is given by:
In}'; = D.H. + L.ijmimjB& + L.ijkmimjmkC &k
(8.17)
where D.H. is a form of the Debye-Huckellimiting law. The Blj and Cljk parameters are
related to the binary (ions i and j) and ternary (ions i,j and k) interactions and can be
a function of ionic strength. The activity coefficient of a cation (M) in a mixed electrolyte is given by:
In I'M = z~F + 2 Lama(BMa + BCMa ) + Z~R + ZMS + Lcmc(2~c + Lama PMca )
+ LaLa,mama' Paa'M + Lcmc2E~c + Z~Rl + Z~R2
It can be attributed to six contributions:
(8.18)
1. The Debye-Huckel term (Z~F) is the limiting law, which is only a function of ionic strength.