Stability constants for the formation of rare earth-inorganic complexes as a function of ionic strength

Geochimica d Cosmochimica Copyright 0 1992 Rrgamon

Acta Vol. 56, pp. 3 123-3 I32 Press Ltd. Rintcdin

00167037/92/55.00

U.S.A.

+ .OO

Stability constants for the formation of rare ear&inorganic complexes as a function of ionic strength FRANK J. MILLERO RosenstielSchool of Marineand AtmosphericScience,University of Miami, Miami, FL 33 149, USA

(Received January 21, 1992: accepted in revisedform June 11, 1992)

Abstract-Recent studies have been made on the distribution of the rare earths (La, Ce, IV, Nd, Pm, Sm, Eu, Cd, Tb, Dy, Ho, Er, Tm, Yb, Lu) in natural waters relative to their concentration in shales. These metals have also been used as models for the behavior of the trivalent actinides. The speciation of the rare earths in natural waters is modelled by using ionic interaction models which require reliable stability constants. In this paper the stability constants for the formation of lanthanide complexes (K&:x) with Cl-, NO;, Sd,-, OH-, HCO:, HZPOI, HPO:-, and Ca- determined in NaC104 at various ionic strengths have been extrapolated to infinite dilution using the Pitzer interaction model. The activity coefficients for free ions (ye, yx) needed for this extrapolation have been estimated from the Pitzer equations. The thermodynamic stability constants ( KMX)and activity coefficients of the various ion pairs ( yMX) were determined from ln (K&/YMMYX)= ln

KMX

+ In (SIX).

The activity coefficients of the ion pairs have been used to determine Pitxer parameters (BMx) for the rare earth complexes. The values of B Mx were found to be the same for complexes of the same charge. These results make it possible to estimate the stability constants for the formation of rare earth complexes over a wide range of ionic strengths. The stability constants have been used to determine the speciation of the lanthanides in seawater and in brines. The carbonate complexes dominate for all natural waters where the carbonate alkalinity is greater than 0.001 eq/L at a pH near 8. INTRODUCI’ION RECENT MEASUREMENTS HAVEbeen made on the concentration of the rare earths or lanthanides in a number of different natural waters (DE BAARet al., 1985, 1988; ELDERFIELDand GREAVES,1982; ELDERFIELD and SHOLKOVITZ, 1987; ELDERFIELD, 1988; ELDERFIELD et al., 1990; GERMAN and ELDERFIELD,1989). This work was stimulated by the desire to understand the changes that occur in the rare earths as they are.delivered to the oceans by rivers and eventually become incorporated in the sediments of the world (GOLD BERGet al., 1963). Interest in the rare earths in natural waters also comes from the concern of the release of long-lived radionuclides from repositories for the disposal of nuclear ~~~~~~(CHOPPIN,1986,1989; BRUSH,1990, NIXHE, 1990). The rare earths are frequently used as models for the behavior of the trivalent actinides in natural waters. The fate of radionuclides is frequently studied by using geochemical models (NORDSTROMand BALL, 1984). With the interest in using brines as disposal sites (BRUSH, 1990; NITSCHE,1990; HORITA et al., 1991), there is new interest in modelling the behavior of the lanthanides in brines. Although estimates have been made for the infinite dilution stability constants for the rare earths (SMITH and MARTELL,1976), no studies have been made on the spcciation of the lanthanides in brines. The purpose of the present paper is to use a realistic ion interaction model to estimate the activity coefficients and stability constants of the lanthanide complexes over a wide range of ionic strengths. These results provide data that can be used to determine the speciation and activity of the lanthanides in natural waters.

3123

THERMODYNAMICS OF THE LANTHANIDE METALS IN NATURAL WATERS The interest in the thermodynamics of metals in natural waters results from the need to know the equilibrium speciation or form of the metal (i.e., La3+, LaOH’+, I.&Of, etc.) and the activity or effective concentration of the metal in solution. The speciation of the metal frequently determines its chemical reactivity ( MILLERO,1990), while the activity controls its solubility. To determine the activity or speciation of metals in natural waters ionic interaction models are used ( WHITFIELD, 1979; DICKSON and WHITFIELD, 198 1; TURNER et al., 1981; MILLERO,1982; MILLEROand SCHREIBER, 1982). The two popular models used to account for the ionic interactions are the specific interaction model as formulated by PITZER( 1979) and the ion pairing model as originally formulated by GARRELSand THOMPSON ( 1962). The combination of the two models yields an internally consistent method that can be used to account for the interactions of the metals with the major and minor anions of a given natural water ( MILLERO,198 1,1982; MILLERO and HAWKE,1992). The ionic interactions affecting the nonideal behavior of an ion, i, in an electrolyte solution are related to the stoichiometric or total activity coefficient, yr( i), which is related to the activity, ai, and stoichiometric or total concentration,

[iIT, by ai

=

7r(i)[ilT.

(1)

The value of ~r( i) is controlled by the composition of the natural water at a given temperature and pressure. It can be estimated in an electrolyte solution by using various exten-

F. J. Miller0

3124

sions of the Debye-HCckel equation (DAVIES, 1962; KEILLAND, 1937 ). More reliable estimates can be made by using the specific interaction model that uses parameters derived from experimental m~surements made at the same ionic strength (GU~ENHEI~, 1935; PITZER, 1973). The general equation is In yi = D.H. + Z: mimjBt !i

+ 2 mimjmkC$, ,,k

(3)

where [ i]F is the concentration, and -rF( i) is the activity coeflicient of the free or uncomplexed ion, i. The value of yr( i) is typically assumed to be only a function of the ionic strength and independent of the relative composition. However, if the Pitzer model is used to estimate yr( i), one can account for differences in the composition of the solution ( WHITFIELD, 1975; HARVIEand WEARE, 1980). The activity of i can also be related to the total concentration [ iIT by ai =

[ilT?Tfi)

= [ilflF(ih

(4)

The value of yr depends on solution composition as well as ionic strength. Rearranging Eqn. (4) leads to an expression relating the two activity coefficients: YT(I’)

= ~[ilF/[ilTfYF(i).

(5)

The term [i] F/f i ]T is the fraction of free i in the solution at a fixed composition and constant ionic strength. It is important to note that the chemical forms of the complexes do not affect the thermodynamic activity of i. When the ion does not form an ion pair or [ i]F/ [ i]T = 1.O, the values of TT( i) = Yr( i). If the value of yr( i) is determined for a solution (e.g., Na-Mg-Cl-S04) using the Pitzer equations, the ion pairing model can be used to account for strong internetions between i ( La3+) and minor anions (CO:-). The formation of an ion pair between a rare earth metal (M) and a ligand (X) can be characterized by ll43+ + X” + h4x 3-n.

(6)

The stoichiometric stability constant, K&, for the formation of this ion pair is given by

=

(7)

KMX-fMYX/yMX

where &X is the thermodynamic constant in pure water and the values of yI are the activity coefficients of the ions and the ion pair. The fraction of the free metal ion M3+ is given by [WFI[WT

(2)

where D.H. is some form of the Debye-Hiickel limiting law. The B. and C+ 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. PITZER( 1979) has characterized the interactions of ions in binary solutions (MX) with three parameters, /3!&, @Lx, and C&. The interactions of like charged ions are obtained from tertiary solutions (MX f NX) and are given by @IMN for interactions of cations M and N and by %,,x for the intemctions of A4, N, and anion X. Although reliable Pitzer parameters am available for the major components of natural waters ( HARVIE and WEARE, 1980; HARVIEet al., 1984; PITZER, 1979), values are not available for the strong interactions of metals with the minor anions of natural waters (OH -, CO:-). The strong interactions of cations and anions (e.g., La 3f with CO:-) can be accounted for by considering the fo~ation of ion pairs. When using the ion pairing model the activity of an ion, i, is given by ai = [ilFYF(i)

Kh’

= (1

+

C Gx,[~;Z-]$I-‘. I

(8)

Similarly, the fraction of free anion X”- is given by [~IF/'I~IT=(~

f C Gi~[M:']~)-'

(9)

,

where the summations are made over all the complexes of each cation Mj’ and anion X f- The fraction of a given ion pair can be determined from

= J%JX:-

I;/(

1 +

C

I

Khx,fXP-

13

(

IO1

or i”xl/[xlT

To solve Eqns. (8) to ( 11) and determine the speciation of ions in a natural water one needs to know the values of K:,y over a wide range of ionic strengths in different ionic media. The value of KGx in a given natural water can be estimated by using an experimental value measured in an ionic medium like NaCl or NaClO, at the same ionic strength of the natural water or by estimating the activity coefficients of ions and ion pairs in the natural water (Eqn. 7). The first method is generally preferred if the experimental data is available. It does not require the estimation of activity coefficients, but has other limitations ( MILLEROand SCHREIBER, 1982). The reliability of the literature values of K& at a given ionic strength may be questionable due to the methods used in their determination. The second method requires thermodynamic constants that have been extrapolated to infinite dilution by the same method used to estimate the activity coefficients. Frequently literature infinite dilution constants have been extrapolated by methods (e.g., the Davies equation) that do not give reliable activity coefficients above 0.1 m (MILLERO and SIZHREIBER,1982). Reintegration of older literature thermodynamic constants is often needed in the light of more up to date theory (e.g., PITZER, 1979). Experimental activity coefficients of ions or electrolytes are available over a wide range of ionic strengths ( PITZER, 1979), but values for the ion pairs must be estimated from the measurements of the stability constants at a given ionic strength (MILLERO and SCNREIBER, 1982; MILLERO and HAWKE, 1992). For the major components of natural waters an internally consistent set of activity coefficients and thermodynamic stability constants is available ( HARVIEet al., 1984). These equations ( HARVIE et al., 1984) provide reliable estimates of total or stoichiometric activity coefficients of the major components of natural waters over a wide range of ionic strength and tem~rature ( MOLLER,1988; GREENBERG

3125

Stability constants of REE complex ions and MOLLER, 1989). Unfortunately, the experimental data necessary to extend this treatment to trace metal ions are not always available (MILLEROand HAWKE, 1992). It is possible, however, to use the limited measurements on the stability constants in various ionic media to extend the PITZER ( 1979) ionic interaction model to divalent ( MILLEROand HAWKE, 1992) and trivalent metals. This method has the advantage in that differences in the specific interactions occurring in an ionic media can be considered in a manner consistent with the major components of natural waters. At present, experimental activity coefficients of the lanthanides are available over a wide range of ionic strengths ( PITZER and MAYORGA, 1973), but values for the ion pairs must be estimated from the measurements of the stability constants at a given ionic strength ( MILLEROand SCHREIBER,1982). The Pitzer equations ( HARVIE et al., 1984) provide the framework that can be used to extrapolate measured stability constants to infinite dilution and estimate the desired activity coefficients of ions and ion pairs as a function of ionic strength. In this paper these equations will be used to characterize the formation of rare earth complexes with the major anions of natural waters. ACTIVITY

COEFFICIENTS

OF IONS

The activity coefficients of ions in natural waters can be reliably estimated using the equations of PITZER ( 1973, 1979). Pitzer and coworkers ( PITZER and MAYORGA, 1973, 1974; PJTZER, 1979) have fit the mean activity coefficients of pure electrolytes to equations of the form In Y,,.,~= Z,Z,#

J’

VX)ICMX(12)

is the Debye-Htickel limiting law slope given by

= -0.392[1”2/(

Solute

BOMX

HC104 NaC104 NaF NaCl

0.1747 0.0554 0.0215 0.0765

0.2931 0.2755 0.21 0.2664

0.00819 -0.00118

NaOH NaN03 NaNC03 NaNzPO4 Nazs04 NazC03 NazHP04 Na3P04 La(clo4)3 Ce(C10413 Pr(C10413 Nd(clo413 Pm(clo4) 3

0.0864 0.0068 0.028 -0.0533 0.01958 0.03615 -0.05828 0.17813 0.7720 0.7547 0.7547 0.7540 0.7540

0.0044 -0.00072

Sm(C104); WClO4)3 Cd(ClO4)3 Tb(ClO4)3 Dy(C104)3 Ho(ClO4)3 gr(C104)3 Tm(ClO4)3 yb(C104)3 Lu(C104)3

0.7640 0.7820 0.7820 0.7953 0.8007 0.7987 0.8013 0.7953 0.8040 0.7907

0.253 0.1783 0.044 0.0396 1.1130 1.5098 1.4655 3.8513 6.5333 6.5333 6.5333 6.5333 6.5333 6.5333 6.5333 6.5333 6.5333

BlMx

6.5333 6.5333 6.5333 6.5333 6.5333 6.5333

C%X

0.00127

0.00795 0.00570 0.00520 0.02938 -0.05154 0.00062 0.00627 0.00627 0.00747 0.00747 0.00539 0.00539 0.00539

0.00473 0.00547 0.00508 0.00554 0.00943 0.00527 0.01116

a) Taken from Pitzer (1979). . . The values for Ce. Pm. and Eu ware estimatedby assuming the parametersfor Ce = Pr, Pm - Nd and Eu - Gd.

+ m[ 2vM’X/( v~ + VX)]BM,Y + m2[2(v~v~)‘~5/(uhf +

wheref’

Table 1. Pitzer Parametersfor Some Na+ and C104Salts at 25°C.a

1 + 1.21”2) + (2/1.2)

For l-l, 2-1, 1-2, 3-1,4-l,

y,,,, = y + (MClv,,)‘/[y In (1 + 1.21”‘)].

(13)

and 5-l electrolytes, the values of

BMx and CMx are given by

&WY= 28%~~+ (PLJ2Z)[l

( 19 19) convention. This convention assumes that Tk = ycl = y + ( KCl) at the ionic strength of the solution ( GARRELS and THOMPSON, 1962 ). The value of yw for cations can be estimated from chloride salts

-2Z”2)(

1 + 211’2 - 2Z)]

c‘$Jx = l.SC~~.

(14) (15)

For 2-2 electrolytes, the value of B,+,xis given by a slightly more complicated function involving @Lx, j3hxx, and /3&x terms ( PITZER and MAYORGA, 1974). Values of the parameters p”, /3‘, p2, and Cmhave been tabulated by PITZER( 1979). The Pitzer parameters for Na+ and ClO; salts used in this paper are. given in Table 1 (PITZER and MAYORGA, 1973). One of the simplest ways to estimate the activity coefficients of ions in a given ionic media is to use the values of the mean activity coefficients of MX salts. The separation of these mean activity coefficients into individual ion activity values requires nonthermodynamic assumptions ( MILLEROand SCHREIBER, 1982). This means that the separation of mean activity coefficients into individual ion activity coefficients is model dependent. The most popular way of dividing mean activity coefficients into ionic components is to extend the MACINNES

(16)

and the value of yx for anions can be estimated from potassium salts ‘)‘x= 7 + (XvkX)“/[y

- exp (

+ (KCl)Ivc’

+ (KCl)lvK.

(17)

Since K+ and Cl- salts do not normally form strong ion pairs, this method gives reasonable estimates for the activity coefficients of free ions. Since most natural waters contain Cl- as the major anion, one would expect that chloride salts would yield reasonable values of y.+,. However, the formation of K+ ion pairs plus the dominance of Na+ (not K+) in natural waters complicates the estimations of the values of yx ( MILLEROand SCHREIBER,1982). This problem can be alleviated by estimating the activity coefficients of anions from Na+ salts (MILLERO and SCHREIBER,1982): yx = y + (NaX)‘/[y

+ (NaCl)IvN”.

(18)

For an ionic media like NaCI04 it is also possible to estimate the activity coefficients of cations from ClO; salts: y,,., = y f (MC104)‘/[r

+ (NaC104)]“c’04.

(19)

By using the above techniques to determine the ionic activity coefficients, it is possible to convert Eqn. ( 12) to the following form ( MILLEROand SCHREIBER,1982):

F. J. Miller0

3126

ln-y,=Zffy+B~I+Bff’+CJ*

(20)

where f’=

fl -exp(-2f”*)(l

(21)

+2Z”2-21)].

The coefficients for this equation can be determined from the Pitzer parameters (/I’, ,L3’,and C”) for Na+ and ClO; salts. For mono- and divalent anions the values are given by Bo, = 4@a”Nax - B& = (8f 3)@&

B: = BEi.x - %, = (2/3)&2x c, = 3C&x -

CNa

=

- 2B;,

(22)

- 2Bik

(2”*/3)&2~

-

(23) (24)

2CNa

-3.0

and for trivalent cations by B: = 2~~~~,~~~~- 3&o,,

(25)

BL = (~/2H3k.10,~3 - 3Bho.

(26)

(3”*/4)C%W,o,)3

(27)

CM

=

- 3CCl0,

B;. = 0.2093, BNa ’ - 0.1603, and CNa = 0.00507, and = 0.0123, B&o, = 0.1152, and C,-ro, = -0.00861 ($?LERO and SCHREIBER,1982). These ionic values for Na+ and CIO; are based on the division of salts using the Maclnnes convention ( 7K = ycl = y 3~(KU)). The values of By, B: , and C, for various ions determined for NaC104 solutions in this way are given in Table 2. Implicit in the use of the activity coellicients determined from Table 2 is that Na+ and ClOi salts do not form ion pairs. The activity coef-

$ere

1 0.0

I 1.0

FIG. 1. The activity coe%cient of La’+ in NaCl and NaClO.,solutions calculated from the Pitzer equations.

ficients calculated with Eqn. (20) also assume that the activity coefficients of ions are only affected by ionic strength and independent of any specific interactions between ions. PITZER and KIM ( 1974) have described the general equations that can be used to estimate the activity coefficients of electrolytes (MX) or ions (M, X) in mixed salt solutions. In their simplest form the equations for cations M and anions X are given in ionic form by ( HARVIE and WEARE, 1980) In y,+, = Z%f y + 2 C ma(BM, + ECM,) + Zh c m,m,B&

In yx = Z$f BiO

Bil

El+ Na+

0.6865 0.2093

0.1779 0.1603

f::

1.4724 1.5071 0.0967

2.9211 0.1061

-0.00126 0.02855 0.02610

pr3+

1.4724

2.9211

0.02855

::: $1

1.4711 1.5271 1.4911

2.9211 2.9211

0.02906 0.02906

1.5271 1.5538 1.5644 1.5604 1.5658 1.5538 1.5711 1.5444 -0.1233 0.0967 0.0123 0.1363 -0.1821 -0.0973 -0.4225 -0.3664 -0.3221 -0.5740 -0.2716

2.9211 2.9211

Gd3* Tb3+

Er3+ Tm3+ FCl‘ C104‘ OHNO3HC03li2PO4‘ so42 co32HP0 2PO4$-

a) Determined from the Pitzer Table 1.

2.9211 2.9211 2.9211 2.9211 2.9211 2.9211 0.0504 0.1061 0.1152 0.0927 0.0180 -0.1163 -0.1207 0.4214 0.6861 0.6564 1.4448 parameters

7 + 2 2 m,(&

given in

ZM

2

w%C,,

(28)

-t EC&) (29)

where Zi is the charge and mj is the molality of ion i (c is a cation and a is an anion). The equivalent molality E = C Zcm, = 2 &ma = l/2 C miZi. The parameters B,w and CMXare given by B,,

= P”Mx+ (~~~/2~)

0.02816 0.02816 0.02788 0.02820 0.02803 0.02823 0.02991 0.02811 0.03066 -0.00507 -0.00126 -0.00861 0.00813 -0.00723 -0.00507 0.01878 -0.00545 -0.00524 0.01756 -0.03753

+

+ Z’, C rn~rn*~~ + Zx t: m,m,C,

Ci 0.03318 0.00507

3.0

IQ.5

Table 2. Parameters for the Activity Coefficients of Ions in NaC104 solutionsat 25OC.a Ion

I

I

2.0

B&

x [I - (I + 21”*) exp(-21”*)]

(30)

+ (1 + 21”* -b 21) expf-21”‘)]

(31)

= (@,k,x/212)

X [-I c,,

= cg4,y/21Z~zxl”z.

(32)

To estimate trace activity coefficients in a NaC104 medium the equations become In Y,W= 2%”

+

~~(BMcIo. +

In yx = Z$fy

+

K’MCIO~)

f2@%~MCI0,

+

&#cMClO,)

(33)

f ZxCrw).

(34)

+ 21(B~~x + ZCN~~) i- 12(Zx&w

Although the ionic form of the Pitzer equations are convenient to use, care must be taken when comparisons are made for mixtures of different composition at the same ionic strength (MHLERO and !XHREIBER,1982). To compare ionic

3127

Stability constants of REE complex ions Coefficients for TABLE3. Pitzer Interaction Na+ with Cations(M) and Cl- with Anions (K) i

j

k

Na

Ii K H.% Ca Ba Mn

Cl

Cl

Br Na OH NC3 HC03 H2P04 HP04 SC4 CO3 PC4

St&Xi

. ,

12,

.

,

Conatanh for the Lanthanidaa

.

, .

,

62

64

r I

- I

* I

’ ,

*ijk

eij 0.036 -0.012 0.000 0.000 -0.003 0.0

-0.004 -0.0018 0.000 0.000 0.000 -0.003

0.000 -0.050 0.016 0.036 0.1004 0. -0.035 -0.092 0.0

0.000 -0.006 -0.006 -0.0143 0.0 0.0 0.007 0.006 0.0

56

56

60

66

68

70

72

Lathanide Atomic Number FIG. 3. Stability constants at 25T for the formation of lanthanide complexes LnHCw (0.68 M), LnC03 (0.66 M), Ln(C03); (0.68 M) in NaClO, solutions (CANTRELL and BYRNE, 1987; WNGLER and BRYNE, 1989).

activity coefficients in different solutions, it is necessary to

make an adjustment to a common scale. To make the activity coefficients determined with the Pitzer equations consistent with the values estimated by the mean salt data for MC104 salts one can use the extension of the MacInnes convention ( HARVIE and WEARE, 1980): ri(adj)

(35)

= Yi(Ya/7Kcl)Zi.

A comparison of the values of yM for La3+ calculated using Eqn. (33) from ClO; salts and from Cl- salts is shown in Fig. 1. The values of ye in Cl- solutions are lower due to the stronger interactions of M with Cl than with ClO,. The validity of the activity coefficients determined in NaC104 solutions from Eqns. (33) and (34) can be shown by comparing the measured and calculated dissociation constants for wbonic acid. CANTRELLand BYRNE ( 1987) have determined pK$K: = 7.53 and pK: = 9.56 in 0.7 m NaC104. The activity coefficients for CO, and the activity of water needed in these estimates can be determined from

In ycq

a&o = 1 - 0.01641-

62

64

66

66

70

0.4422 lO-5Z2

aHfl were calculated from the osmotic coefficients in NaC104 from 0.1 to 6 m. The activity coefficients calculated from Eqns. (33) and (34) give pJ$ K: = 7.45 and pK: = 9.66,

using the thermodynamic constants (p& = 1.47, pK, = 6.36, and pK2 = 10.33) calculated from the equations of MILLERO (1979).

The estimates are improved if one accounts for the cationcation (Na-M) and anion-anion ( C104-X) interactions. These interactions can be added by using the Pitzer higher order terms ( PITZERand KIM, 1974):

Stability Conatan~ for Lonthanides

6

60

(36)

The values of y for CO2 are taken from the values in NaCl (THURMOND and MILLERO, 1982), while the values of

5,

58

0.01061’

- 0.48716 10-4Z3. (37)

STAMLIN CONSTANTSFOR THE RARE EARTHS 7,.,.,.,.,,,.! ..I’(

56

= 0.2421-

72

Lathanide Atomic Number FIG. 2. Stability constants at 25°C for the formation of lanthanide complexes LnOH*+ (0.3 M), LnSO: (2 M), LnF*+ ( 1 M), and LnNOF ( I M) in NaClO, solutions (WALKERand CHOPPIN, 1967; G. R. Choppin, pers. commun.).

a,

0

,

I

I

I 1

I 2

3

10.5 FIG. 4. Effect of ionic strength on the stability constants for the formation of GdF*+, L.aF*+and LaSO: in NaClO, at 25°C (WALKER and CHOPPIN, 1967; G. R. Choppin, pers. commun.).

3128

F.J.Millers Table 4.

Pitzer ExtrapolationsFor Various Ion Pairs AVE

Ion Pair

log K

aHX

LsOHLf

5.10

1.17

;;$ YOH*+

5.73 5.79 5.79

1.13 1.11 1.08

0.78 0.51

0.99 1.15

1.08 ?;0.07

TbNO3*+ guHo3*+ L&04+ CeSO4+ EuS04+ GdS04+ Luso4+

3.15 3.36 3.45 3.95 2.97

0.51 0.69 0.64 1.01* 0.60

0.62 + 0.18

1.13 * 0.05

* This point was deleted when determiningthe average. Its inclusiongives a slightlyhigher velue of 0.69 + 0.41.

InY = Ecm(31) + 21%~

mates can be made from experimental measurements ( MILLERO and SCHREIBER, 1982; HARVIE eta]., 1984; MILLERO and THURMOND, 1983 ) . The activity coefficient of an ion pair can be determined from

+ 12~~a~~~~~, (38)

In y = Eqn. (32) + 2BNaM + 12~~=~=,o~.

(39)

Values of hNaMand \IIr.+,MCIo, are given in Table 3 (PITZER, 1979;MILLERO, 1982). The values for QNaMin Cl- media are given for the ClO; values when results are not available in NaC104. The use of these higher order terms for H+ HCO; and CO:- yields pK:K: = 7.48 and pK: = 9.6 f, which are in excellent agreement with the measured values (CANTRELL and BYRNE,~~~~).

-fMX

=

(&fX/f&Xh’M~X.

(40)

The value of yMx and KMx can be determined from experimental measurements of K&, yM, and */x. Unfortunately, not many authors make me~u~ments of K:X over a range of ionic strengths. If an independent estimate of KMx can be determined from dilute solution measurements, it is at least possible to determine YMXat a given ionic strength ( MILLERO and SCHREIBER,1982).A comparison ofthis 7,+,Xwith other ions and nonelectrolyes at the same ionic strength can lead to an educated guess of its ionic strength dependence. Stability constants for the formation of rare earth complexes with the inorganic components of natural waters have been measured by a number of authors in NaC104 solutions

ACTIVITY COEFFICIENTS OF ION PAIRS

The major difficulty with using the ion pairing model as a function of ionic strength is the assignment of activity coefficientstoion pairs (MILLERO and SCHREIBER, 1982).Although it is possible to use estimates from ions and nonelectrolytes of similar structure and charge, more reliable esti-

Table 5. Infinite Dilution StabilityConstants for the Formation of Rare Earth Complexeswith MonovalentAnions at 250Ca. log K LoOH*-

~0~2.

LnCl*-

LnF**

LnHco3*- LnH2PO42.

5.10 5.60 5.60

0.58 0.69 0.69

0.29 0.31 0.32

3.12 3.28 3.48

2.02 1.95 1.89

2.50 2.43 2.37

5.77 5.67 5.81 5.83

0.79 0.88 0.78 0.83

0.32 0.31 0.30 0.28

3.63 3.56 3.58 3.63

1.83 1.79 1.75 1.60

2.31 2.27 2.23 2.21

5.98 5.79

0.51 0.47

0.27 0.28

3.85 3.75

1.71 1.72

2.19 2.20

6.15 6.01 6.04

0.25 0.15

0.28 0.27

3.95 3.98 3.89

1.73 1.76 1.72

2.24 2.21 2.20

6.22 6.19 6.24

0.25 0.20 0.56

0.16 0.27 -0.03

4.02 3.99 4.05

1.79 1.84 1.90

2.27 2.32 2.38

a) Extrapolatedusing log K*'s from Walker and Choppin (1967), Bingler end Byrne (1989),Cant-fell and Byrne (19871, Choppin (1986, 1989, personal communication).

Stability constants ofREE complexions

3129

Table 6. Infinite Dilution StabilityConstants for the Feytion of Rare Earth Complexeswith DivalentAnions at 25O C. log K LnSO4+

LnCO3+

LnHpo4+

La'+ Ce3+ Pr3+

3.21 3.29 3.27

6.82 6.95 7.03

4.87 4.98

$1

3.34 3.26

$1

Lr1(Co3~-)2Ln(HP04)2-

5.08

11.31 11.50 11.65

8.17 8.34 8.50

7.22 7.13

5.27 5.18

11.96 11.80

8.81 8.66

3.37 3.28

7.37 7.30

5.42 5.35

12.24 12.11

9.10 8.96

$:

3.20 3.25

7.50 7.44

5.54 5.49

12.52 12.39

9.37 9.24

5:: Tm3+ $1

3.16 3.15 3.07 3.01 3.06

7.63 7.59 7.55 7.66 7.70 7.67

5.68 5.64 5.60 5.71 5.75 5.73

12.88 12.77 12.65 13.00 13.20 13.08

9.73 9.62 9.49 9.84 10.05 9.95

a) Extrapolatedusing log K*'s from Walker and Choppin (1967), Bingler and Byrne (1989), Cantrell and Byrne (1987), Choppin (1986, 1989, personal communication).

(SILLEN,1964; SMITHand MARTELL, 1976;WALKER and CHOPPIN, ~~~~;BINGLER and BYRNE, ~~~~;CANTRELLand BYRNE, ~~~~;CHOPPIN, 1986,1989).Thevaluesatagiven

ionic strength show a smooth increase with increasing atomic number, as shown in Figs. 2 and 3. Data for stability constants as a function of ionic strength are not as extensive (see Fig. 4). These limited experimental data have been used to estimate the activity coefficients of the lanthanide ion pairs yMx and the infinite dilution thermodynamic stability constant: In yMx = In KMX-lnK~x+lnYM+lnyx.

YMX

=

In YELECT

+

~~CIO,BMX

ln

YELECT

(42)

4f + 4~Na~c~o,&w~o,

=

+

2mNa@I04CNaCI04a

( 43 )

The substitution into Eqn. (4 1) upon rearrangement gives y = In K& - In yM - In yx - In YELE~ = In KMx - 2BMxmclo,.

(41)

If the ion pair is charged its concentration dependence would be of the form ln

where BMx is the Pitzer parameter for the ion pair. The electrical contribution is given by

(44) (45)

The values of y determined from Eqn. (44) have been used to determine the infinite dilution thermodynamic stability constant ( KMx) and the Pitzer parameter ( BMx) for the rare earth ion pairs. The results are given in Table 4. The values

Table 7. The Compositionof The Brines at the WIPP sitea Ion

Brine A

Brine B

Na+

1.77

4.97

$1 K+

0.02 1.44 0.77

0.005 0.02 0.005

clBrso42B(OH)4co32-

5.35 0.01 0.04 0.015 7 10-4

4.93 0.01 0.04 0.0004 6 1O-5

PH aH20 Density

7.56 0.783 1.188

7.22 0.806 1.170

I

7.0

5.1

a) From Brush (1990). The values of the total carbonatewere calculatedfrom the TC02 - 0.01 M at the pH of the brine using values of pK2* - 8.69 and 9.44, respectively,for brines A and 8. These values of pK2* were determinedusing Pitzer's equations.

F. J. Miller0

3130 SPEClATlON OFTHERARE URTHSINSEAWATER 1’

O-

’

’

“I”.

‘.

‘.

“1

*~pg~~~~oo-ooo-

EFFECT OF TCO2 ON THE SPECIATION 1.0

.

,

.

,

.

,

.

I

9

OF d+ ,

*

1

*

,

mmmm ma61-

-l2 0 “0

-2-

I

0 R

. + + +yg@Ll 4 ++y, g -f-I d

_*_ . -3,

96

0 l&05)2

l

MO3

D

blso, L&l

+

l* bl , 56

L@o3)2

mm + + l +++:ag. +

;-

LaCl=loso4 i

I,

60

62

9.

64

5.

I.

66

8.

70

66

72

-0.2: 0.m

.

, 0.002

*

( 0.004

ATOMIC NUMBER

of Bnrx for MOH ‘+ of 1.I 3 rt 0.05 are the same within experimental error, with the value of 1.08 f 0.05 for the J4NOp ion pairs. The average value of 1.I 1 is selected as the best value for rare earth ion pairs of charge MX2”. The average value of &.,x for the MsO$ is 0.62 + 0.18 (if the GdSO4+pair is deleted). All of these results indicate that the activity coefficients of the rare earth ion pairs are the same for a given charge type and are independent of the rare earth metal ion. This allows one to estimate the infinite dilution constants for a number of rare earth ion pairs using measurements made at a given ionic strength. The resutting stability constants are tabulated in Tables 5 and 6. At the ionic strength of seawater the activity coefficient of the L&Y’+ (0.35) and LnSO4+ ( 1.27) rare earth ion pairs are similar, respectively, to ion pairs of the same charge: Cu(C0~)3(0.32) and CuHCOf ( 1.26) (MILLERO and HAWKE, 1992). More results for a number of different type ion pairs are needed before one can interpret the magnitude of the activity coefficients of these ion pairs.

OF ME

, 0.006

.

( 0.006

.

, 0.010

*

, 0.012

I 0.014

TCO2, M

FIG. 5. The speciation of the rare earths in seawater fpH = 8. I, I = 0.72, Cl = 0.565, SO, = 0.0273, AC = carbonate alkalinity = [HC03] + 2[COj]).

SPE’XTION

.

FIG. 7. The effect of the level of the total carbonate on the speciation of the rare earths in brines (I = 6 M, Cl = 6 M, SO, = 0.04, AC = carbonate alkalinity = [ HCOl] + 2 [CO,]).

CALCULATIONS

FOR NATURAL WATERS

The stability constants for the rare earths in NaClO, calculated from the Pitzer model can be used to determine the speciation and activity in two ways. First, one can assume that the stability constants and activity coefficients of the rare earths in a natural water are the same as the values in NaC104 at the same ionic strength. This will give reasonable estimates for the speciation and activity of these ions in a given water. To demonstmte the use of the rare earth stability constants, cakuiations were made in seawater (MILLERO and SOHN, 199 i ) and the WIPP brines (see Table 7). The resultant speciation of the rare earths in seawater and the WIPP (waste isolation project program) brines calculated in this manner are shown in Figs. 5 and 6. The results in seawater are similar to the earlier work of CANTRELL and BYRNE ( I987), as expected. The calculations in the WIPP brines are strongly dependent upon the value selected for the free carbonate concentration. The ~~cu~tions shown in Fig. 6 are for WIPP brines A and B (BRUSH, 1990)) with a total carbonate Tco2

RARE EARTHS IN WIPP BRINE A

1’ ‘I ’ ”

@’ * ”

I

“I.

0.20

I

I

I

I 0.0

8 0.1

I 0.2

0.16 0.16

__3HLf., 56

, 56

60

), 62

). 64

, 66

.

, 68

,

, 70

, 72

ATOMIC NUMBER

w 0.3

B” NaCl FIG. 6. The speciation of the rare earths in the WlPP brineA (pH= 7.5, I = 7.01, Cl = 5.35 M, SO, = 0.04 M, and AC = carbonate alkalinity= [ HCO,] + 2 [CO,] = 0.01).

FIG. 8. Comlation of the Pitzer param&em for monovalent cations in NaCl and NaCIO, at 25°C (PITZERand MAYORGA,1973).

3131

Stability constants of REE complex ions = [HC03] + [CO,] = 0.01 mol/L. The calculations were made at the total carbonate levels for the pH of the brines (see Table 7). The actual levels of free CO:- may be lower due to complexation with Mg2+ and Ca2+ in the brines (the HARWE et al., 1984, model gives fractions of free carbonate of 0.5 to 0.7 for the brines). In short, the level of the carbonate in a given brine controls the major speciation. Calculations as a function of Tco2 shown in Fig. 7 for a 6 M NaCl brine (SO, = 0.04, pH = 8.0) indicate that at a Tco,lower than 0.00 1 free Ln3+ becomes competitive with Ln carbonate complexes. Both calculations indicate that the carbonate complexes dominate if carbonate is a major component of the solution. The competition of organic ligands for the rare earths requires further study. The speciation calculations of Choppin in seawater ( CHOPPIN, 1989) and in WIPP brines (Choppin, pers. commun.) indicate that all the known organic ligands are not competitive with carbonate at their present concentrations. A more reliable method ( HARVIEet al., 1984) to estimate the stability constants for natural waters is to use the known interaction coefficients for the rare earth chlorides and the infinite dilution stability constants determined in this study. Although this is more work, it is the most desirable approach to adding divalent and trivalent metals to a complete natural water model. If this approach is used, it is not necessary to consider the formation of chloride complexes. Since the sulfate Pitzer parameters are available for only one rare earth ( RARD, 1990), it is necessary at present to keep the rare earth sulfates complexes in the model. To use the Pitzer mode1 in natural waters largely of NaCl, it is necessary to estimate the activity coefficients of the ion pairs in a NaCl medium. Since experimental measurements are not available, this must be done at present by using a semi-empirical approach. As shown in Fig. 1, the activity coefficients of cations in NaCl are smaller than the values in NaClO,. Since the Pitzer @LXparameters in NaCl and NaC104 for monovalent, divalent, and trivalent cations show a linear correlation (see Figs. 8, 9, and lo), it is possible to estimate the appropriate ion pair parameters using this correlation. These linear correlations give /3LX(NaC104) = 0.0562 + 0.561j3LX( NaCl)

(46)

0.80-

0.79-

g

/ 0LO /// / 0SlVl

0.76-

% 0.770.760.7% 0.74 ‘, 0.57

I 0.56

I 0.59

I 0.61

I 0.60

I 0.62

I 0.63

I 0.64

B” NaCl FIG.

IO. Correlation of the Pitzer parameters for trivalent cations in NaCl and NaC104 at 25°C (PITZER and MAYORGA, 1973). The values for Er and Tb are inside the same circle.

for monovalent

cations (u = 0.02),

/3$.,X(NaC10,) = -0.0097

+ 1.430&(NaCl)

(47)

for divalent cations ((r = 0.04), and /3’&X(NaC104)= 0.0523 + 1.201&(NaCl)

(48)

for trivalent cations ( u = 0.08 ) . The deviations for Zn 2+ are probably due to the formation of the ZnCl+ complex and the resultant lowering of the Pitzer parameter in chloride solutions. If one adjusts the activity coefficients of the ion pairs using these correlations, one does not significantly change the speciation of the rare earths in seawater or in the WIPP brines. This is partly due to the fact that the lower values of /3$X(NaCl) for the ion pairs are compensated by the lower values of @LX(NaClO,) for the rare earth cations. Further measurements of the stability constants for the formation of rare earth complexes are necessary before one can make a better estimate of the activity coefficients of ion pairs in natural waters made up largely of NaCl. Future stability constant studies should be made over a wide ionic strength range and in NaCl media so that more reliable estimates can be made on the activity coefficient of ion pairs in natural waters.

0.6-

Acknowledgments-The author acknowledges the support of the National Science Foundation (OCE-89-22580 1and the Office of Naval Research (NO00 14-90-J 12i5) for this study: This work was initiated due to the interest and help of Dr. Greg Choppin, who was kind enough to supply reliable stability constants for the formation of rare earth complexes in NaC104 solutions. It also benefited from the review of Dr. R. Byrne. It is dedicated to my departed friend Bob Garrels. He was someone I always respected as a scientist and human being. I will always remember the encouragement he gave me in my early struggles in the field of geochemistry.

0.4-

Editorial handling: H. C. Helgeson REFERENCES I 0.3

I 0.4

0.5

B” NaCl FIG, 9. Correlation of the Pitzer parameters for divalent cations in NaCI and NaClO, at 25°C ( PITZER and MAYORGA, 1973).

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