Determination of the solubility products of sodium carbonate minerals and an application to trona deposition in Lake Magadi (Kenya)

Gwchimtcn et Cosmcchtmica Acta Vol. 48. pp. 571-581 B Pergamon Res Ltd. 1984.Printed #IIU.S.A.

0016-7037/84/S

Ml + .oo

determination of the solubility products of sodium carbonate minerals and an application to trona deposition in Lake Magadi (Kenya) CHRSTOPHE MONNIN and JACQUE SCHOTT Laboratoire de Min&alogie et Cristallographie, Universite Paul-Sabatier, 38. rue des Trente-Six Ponts, 3 1062 Toulouse Cedex, France (Received March 8, 1983; accepted in

revisedform December 13, 1983)

ion-interaction model of PITZER (1973), is very effective in deriving stability relationships at high concentrations for the system Na-Cl-HCO#ZOX-OH-H20. The solubility products of the main sodium carbonates have been calculated from solubility data between 5 and 5O’C. The stability diagram in log Pcm - temperaturn coordinates and the invariant points deduced from the newly determined data are in good agreement with the most recent measurements. These results are used to calculate the activities of the major dissolved species in Lake Magadi brines Abstract-The

(Kenya). The thermodynamic treatment confirms the main conclusions reached earlier by EUGSTER(1970, 1980) mainly from field observations. Trona precipitation occurs at equilibrium while natron is likely 10 form when the temperature decreases below 25’C. After the salt deposition the CO2 supply from the atmosphere is too slow to allow equilibrium between the atmosphere and the brines. In the next stages of evaporative concentration thermonatrite and halite precipitate. The deposition of the latter salts along with the observed HCO; depletion suggest that fractional crystallization is likely to control trona deposition.

THE THERMODYNAMICdescription of concentrated solutions such as seawater, saline lakes and hydrothermal brines is one of the major challenges in geochemistry. For many years chemists have been unable to predict with accuracy the distribution of species in solutions of ionic strength greater than 1, and in seawater until recently many problems remained, even with major species as important as sulfates. With the ion-interaction model recently developed by Pitzer and coworkers (for reviews see PITZER, 1979, 1980, 198 1) these problems are being solved. Indeed Pitzer’s equations have already proven very useful for the study of the seawater system Na-K-Ca-Mg-Cl-Sod-Hz0 (WHITFIELD, 1975; HARVIE and WEARE, 1980). Calculations of mineral associations in this system (EUGSTER et ai., 1980) gave a very good account of observed natural parageneses and salt deposits (HARVIE ef al., 1980). This model also allowed the thermodynamic description of carbonate-free natural brines (KRUMGALZand MILLERO, 1982) at concentmtions for which classical models based on the ion-pairing phenomenology give inaccurate results (GUEDDARIef al., 1983). The recent derivation of Pitzer parameters for NaHC03 and Na2C03 in single electrolyte solutions and in mixtures with NaCl (PEIPER and PITZER, 1982) allows an extension of the ion-interaction model. As a step toward the prediction of solubilities of carbonate minerals in concentrated natural waters, the goal of this paper is the study of the Na-OH-Cl-HC03CO&Z02-H20 system at concentrations up to 12 moles/Kg Hz0 and in a limited temperature range. In particular we have derived the solubility products of sodium carbonate minerals at different temperatures from selected solubility data, and, as an application,

we have made an attempt to solve some intricacies of sodium carbonates deposition in Lake Magadi (Kenya). THE ION INTERACTION MODEL Description In the ion-interaction model the thermodynamic properties of concentrated solutions are described as a virial expansion of the molality (note that such series expressions in virial coefficients are used for describing the properties of non-ideal gases and crystalline solutions). For electrolytes one must add a Debye-Hiickel term for the electrostatic effects, and the effects of short range forces may be expressed by a series in increasing power of molality (PITZER. 1973). For example, the excess Gibbs energy per kg of water can be expressed in the following form

GeXlnJP

=.M

+ C Z: h,,(I)m,m,

(j(I) = Debye-Htickel term where I is the ionic strength; m,, m,, etc. = molalities of the various ions or neutral solutes; A,, and w,,~are the virial coefficients for binary and ternary interactions respectively). One of the main features of Pitzer’s model is the prediction of the thermodynamic properties of complex mixtures from those of binary and ternary solutions with a common ion. We shall not recall here the main equations for a multicomponent electrolyte solution, which can be found iYinumerous papers(see PITZER and KIM, 1974: P~TZER1979, 1980,198 1: HARVIEand WEARE,1980). These equations involve a number of adjustable parameters which are to be calculated from experimental data. For typical strong electrolytes one need not explicitly retognize equilibria within the solution between alleged aqueous species. lt is worth noting that the term “typical strong electrolyte” covers a much wider variety of salts (e.g. sulfates of divalent cations) than the ion pairing models. For weaker electrolytes, the interpretation of experimental data requires the assumption of an equilib~um within the solution between charged species such as H+, HSO;, SO;for sulfuric acid (PITZERef u/., 1977) or between charged and

C. Monnin and J. Schott

572

neutral species as H+, H*PO; and H$O, for phosphoric acid (PTTZER and SILVESTER, 1975). In this case, one has to calculate the distribution of the various aqueous species through an iterative solution of tbe laws of mass action for the equilibria within the solution. The Na-Cl-HCO&O~OH-HJO

The dependance of K,, on temperature and wntc strength can be represented by:

s):vtem

In a recent study, F%IPER and PITZER (1982) examined the properties of solutions containing mixtures of sodium carbonate, bicarbonate and chloride within the framework of the specific ion-interaction theory. In such a system it is necessary to recognize the two dissociations of carbonic acid: H&X& % H’ f HCO,

Ifi,)

(2)

HCO; % H’ + CO,

(K-Z).

13)

Another equation is given by the dissociation of water H&&t) II? H+(aq) f OH-(aqf

(k;.).

(4)

As sodium carbonate solutions are alkaline, H” can be neglected and the system to be consideted is reduced to the following species: Na-Cl-HCO&O,-H&OrOH-H20. By combining relations (2). (3) and (4) and by writing

one obtains the following reactions: (I) CO;-(aq) + 11~00) it HCO;(aq) + OH “(aq) +_

mffcoj’

mOH-

mfl,;

(II)

Y Lm

*G

The equiiibrium constants for the above reactions can be from the following expmion ~PEIPERand PITTER. 1982).

cakulati

tn j&)r = -32.234 + 50130.2

I n1

Y, = ~1,!- 0, 1 4’.exp(d,li ‘i

;i :

The values of the coefftcients 2,. h!, c,. 4 3r.c p~vrn I!? Table 1. In our work the species distribution was calculated by an iterative solution of the law of mass action for the simultaneous equilibria (1) and (II). The unknowns are rrzoH . rnH(.“,. equations are prow;- and mHa,. Two supplement vided by the electroneutrality equation and mass bakmce fo. carbon in a closed system. As pointed out by F’EIPER(pers. commun.), this type of calculation does not take into account the increase in the molaiities due to the decrease of the quantity of water by the hydrolysis reaction. However, this effect has been found to be numericaily insignificant. Given an initial estimate for the activity coefficients and the activity of water. an equilibrium distribution is calculated. which IS used ttt improve the y’s and G. This is repeated until convergenrc within the desired accuracy.

The intem~ion parameters for this system have tin estimated by PEIPERand PITZERf 1982) and by HARVE ( 19821. These two determinations made fram different sets of data and type of measurements have lead to somewhat differenr values for the adjustable parameters. Thus, it is important to retail here the way the dete~inatio~s have been carried out in order to evaluate the parameters needed to build a consisten model for solubility predictions. al Singleelectrolylepurameters. For a hnuted temperature range around 25°C the single salt pammete~ pro‘, dl”. i’” can be represented by:

f .8457096(7’ I &J X801538* lif.4(7+ - 7-i;)

with r, = 298.15 K. In (K&r

wtth

Choice of interaction parameter wluc.v rn thr, Na-cl-nCO~COrOH-k&O sptem

YLcmYkm

2HCOF(aq) t=i CO;-(aq) f CO,(g) + I&0(1)

- 330.089 In +-

solutions, Peiper and Pitzer expressedl it as the ratlo of Henr?‘s law constant at infinitedilution to that at finite ronc?ntration

= -18.006 - 1274

-19.99$[

ltln

f ( 0)I

In (&), = -23.802 C 1768

-31.25

c

$-- i +ln

(

)I To

L

The Debye-Hiickel limiting law slope for the osmotic coefficient is given by PITZER et al. (1977). A, = .3770 + 4.684. IO-??- - 273.15)

t 3.74. Wh(T - 273.15)’ One must also calculate the activity coefficient of the neutral species H2COX(aq). For the solubility of C02(g) in NaCl

with

X = @‘O’. /Y” or f’“,

For NaOH and Nail, these coeffitints are taken from fiTZtK and MAYORGA(1973) and SILVESTERand PITZER (1977). The same coefficients for carbonate species were estimated by Peiper and Pitzer from the emf data of Hamed and coworkers (HARNEDand DAVIS, 1943; WARNEDand BONNER. 1945; HARNEDand WHOLES, 194 1)and of Roy d al. ( I98 I 1. and from the isopiestic data of ROBINSON and MAVASKILL. ( 1979) and of WHITE and BATES( 1980). On the other hand, HARVIE (1982) calcutated these parameter values at 25°C mainly from solubiiity measurements. The two sets of coefficients are very close and we used Feiper and Pitzer’s values (Table 2). b] Mixing parameters. For solutions of a moderate concentmtion range (1 up to 2), the 8 and $ parameters can be omitted (WHITFELD,1975; P~TZERand KIM, 1974). but they are clearly required for the more concentrated solutions. Irr turn, their determination can be made only from data obtained at these high concentrations. In the case of unsymmetrical electrolytes, the asymmetric mixing theory (PITzEn, 1975) improves the description of concentrated solutions. For example, HARVE. and WEARI’ (1980) found it necessary in modeling the solubilitv ofgvpsum

573

Solubility of Na carbonate minerals Table 1.- Parameters for the lea.51 J

after

b. 3

7

I

5652.1_+ 0.4

2

-33.4732 0.003

3

equation giving Henry’s and Pitrer (1982).

Peioer

-653.32

0.2

and

‘r?,(I) depends only on the charges of ions i and j and the ionic strength. These terms are defined by complex integrals, but PKZER (1975) gave a simple and elegant approximation to calculate them. Such a simplification results in a fair agreement between these values and those tabulated from direct numerical integration (PITZER, 1975). In the expressions:

%;,(I) =

z [J(x,,) -

“f);,(j)

_

=

T + 3‘-

‘hJ(x,,) - ‘h.I(x,)]

[x,,J’(x,,) - ‘hxJyx,3 - l/ujjs(x,)l

with X, = 6lz,t,l&\r we used the following equations for J(x) and J’(x) J(X) = ~$4 + C,x6* expf-C@)]+ and Jyx)

=

9

dj

-155.3: 0.2

-2.504, 0.010

1.1695, 0.0012

-0.006491_+ O.OOCQO2

in NaCl solutions. We used the full theory in our work. The complete expression for @,,is:

conSfant

‘j

3.9398: o.cO14

0.037177_+ 0.000006

law

-0.001981+

-2.276~ 0.010

0.000002

-2.163~ 0.010

BOG~YAVLENSKJI and MANNAN~KOVA (1955) and the poorer data of FREETH (1922)for the NaCI-NaHCOJ-Ha0 system. The value used by HARV~E(1982) for &,was derived from an earlier report of P~TZERand PEIPER (1980) which was later rejected by these authors (PEIPERand RTZER, 1982). We choose the first set of coefficients which are derived from more reliable and accurate experimental data. BonHCOjand $NkOn.HeO,are never required as long as the con~ntmtions of OH and HCOX can never be high at the same time. Peiper and Pitzer found no need to use ‘tin,,, and to fit the data they considered. But, if these pa* N,HCOFCO, rameters are not taken into account. the model fails to reproduce the reliable solubihty data of HILL and BACON(1927) for Na2COpNaHCOr-HI0 mixtures (Fig. 1). As HARVIE (1982) determmed OnColCo,and &.nCOm, from these data we retained his values. For the Cl-CO9 interaction parameters we used another way of checking the model: we calculate the solubiity products of the minerals at equilibrium with the solution and plot them versus a parameter of the solution such as the ionic strength, I. If the model is accurate, and the solubility data reliable, the computed Ksp must be constant as 1 increases. This is illustrated in Fig. 2, on which are plotted computed Ksp values for natron (Na2C0,- IOHzO) versus I. The Calculations were made with three different sets of %cofl and

C, = 4.581

I

Ioatron

C, = .7237

I

I

k@%

c, = .0120 ‘)

C, = .X8.

”

lrona

4

‘O,,is an adjustable parameter which must be evaluated from data on ternary mixtures with a common ion. If Ef?,j(I)is omitted, then Setimay be relabelled without the subscript 8,. Peiper and Pitzer estimated &,_u~, and +Nna_HCOS from the emf data of HARNEDand BONNERf 1945), HARNEDand DAVIES(1943) and from the recent additional data of ROY et al. (198 1) relative to higher concentration. Harvie’s value for $ is determined from the solubility m~su~ments of

Table 2.- Single eleccralyte parameters NaCl

NaHCo3

NESOli

i+a2c03

6”

0.076ja o.otma0.028

0.0362

;d

0.2bb4a 0.00127a

0. 0.004ba 253a

0.044 -

0.0052 1.51

1036B0/6T

4.7159

O.@

1 .o

1.79

!03681/6T

0.700?

0.13Ab

,.I0

2.05

1036C~IET

-0.1054b

-o.1894b

,0562ao/hT2

-I .49e

-2.0

-2.6

“4.22

-2.1

-4.3

-16.8

IO562B~fET2

0.2143’

105&2C*f6T2

cl.I 4MC

-

0.29

a - Pltzer and !ayarga (1973) b - Silvesrer and Pitrer (1977) c - Silvester and F%taer (1978)

-

-

I-

O

1

NoHC03

mololity

-

FIG. I. Solubilities in the Na-HCO&03-Hz0 system at 25°C. 0, measured (HILL and BACON, 1927); A, measured (FREETH, 1922); +, calculated with KS,,(Nahcolite) = .407 and ko,-HCO, = AWCO,..CO, = 0.

574

C. Monnin and J. Schott

qNvalues for the same solubility data of FREETH (1922) in the systems Na2COs-NaCIand NazCOI-NaHCO1-NaC1. AS Harvie’s values for ‘t?and $.N.-CICO,were fitted to these data it is not surprising that they give a constant value for Ksp.Moreover, this value is the mean value of Ksp derived from a broader set of solubiiities including systems without chloride (see below) and the solubiiity of sodium carbonate decahydrate in pure water. The curve drawn for ‘&o, = %&.cxo, = 0 obviously shows that these parameters are required. It is worth noting that Peiper and Pitzer’s parametes fail to give a constant value of Ecsp.They have been calculated from the isopiesticmeasurements of WHITEand BATEs( 1980).

If one includes Harvie’s parameters to analyse these data, the model fails to reproduce the measured osmotic coefhcients, exhibiting in the worst case(i.e. equimolal solutions of Na$X& and NaCI, an ionic strength fraction of NaCl = S371) a deviation of .03 (about 5%). Figure 2 illustrates the inconsistency of the isopiestic measurements of White and Bates and of the sotubitity data of Freeth. We chose Harvie’s values which are better suited for solubility prediction. 8,,, and /tNpCI.oHare taken from PKZER and KIM (1974). Unlike WARVIE (1982) we found no need of &,9, and $Na-OHCO,. Finally, mixing parameters used in this study are summarized in Table 3. DETERMINATION OF THE SOLUBILITY PRODUCTS OF SODIUM CARBONATES FROM SOLUBILITY DATA

Using Pitzer’s equations and the parameters given in Tables 2 and 3, we calculated the solubility products of the main sodium carbonates from solubilities measured in the following systems: Na2C0,-NaCI; Na2C03NaOH; Na2C03-NaHC@; NaHCO,-NaCI; NaKOjNaHC03-NaCl; Na&O,NaOH-NaCI. The salts under investigation were

a

9

ir!

1’ -s’

FIG. 2. Calculation of the solubility product of natron at 25°C from the data of FREETH( 1922) (&led dots: Na-CO,HCQ-Cl system; open dots: Na-CO&l system). 0: sBcI_col = 0 (&IPER = 0, tiN~CISO~ = 0; A: %-co, = -.053, $p*s<,-(~,, and PITZER, 1982); 0: sBct.co,= -.02, I/+-,~~.,_~~~, -z .0085 (HARVIE,1982); 0: saturated solution of pure sodium carbonate (ROBINSON and MACASKILL, 19791.

thermonatrite, it is equal to 6% if the data for tonic strengths above I I are discarded. Thermonatrite forms from solutions of Iow water activity at 25°C. this is obtained with a high concentration of NaOH for which the model loses its accuracy. This explains the high values given by the error-handling routine in least Nahcolite: NaHCOj ; Ksp = ~~=~~~~~~~~~~~~ squares calculations (see below). For example, in a Natron: Na2C03- iOH,O; Ksp = mf&,m~~,~&as~~ko solution containing 11.2 moles NaOH/KgHzO Sodium carbonate heptahydrate: Na2C03 +7Hz0 (I = I I .7 I: U, = .387) we calculated K.sl; (thenno Thermonatrite: Na2C03 +Hz0 natrite) = 7.72 which is twice the mean value. This Trona: Na,CO,-NaHC03 - 2HZO: limitation prevented us from calculating K,sp fop Na2C03 which forms at an even lower u,. :.t” from even more concentrated solutions. We also considered halite for which solubilities are Because of the complex formula of trona, the unoften given in these systems. certainty in its Ksp is greater. Moreover, Freeth’s solAs emphasized above, Pitzer’s equations are valiubihties in the Na,CO,-NaHC03-NaC1 system lead to dated by calculating constant values of Ksp over a anomalously high values of Ksp. In general, the data large range of ionic strengths. Also, as we made a careful choice of the values of the various virial coefncients, we now rely on the model to discard some experimental data. This allows us to have an idea of _^_-._..__~-.._. “_ “..__. _. the reliability of the measurements carried out by var\IWi,J @i j ious authors. I___.L_..__^__.__ -.03” Cl-OH OO@ The main source of data is the work of FREETH _.&J4 m5b Cl-CO3 (1922)who studied the six systems considered above. .0359’ Cl-HCO> !!IrrI We also used measurements by HOSTALEK (1956) OH-HCXI~ for the Na2C0,-NaOH system, B~GOYAVLENSKI and ()C” ?’ OH-CO3 MANNANIKOVA(1955) for NaHCO,-NaCI, WECXH_.04b.d .;,;: HC03-CO, EIDERand MEHL ( 1928) and HILL and BACON (1927) _ ..II_..I _.__ -. I -_ for Na2COI-NaHCOA . Most of these data, along with a- Pltzer and Mayarga OU71J other less important ones, are quoted in LINKE’Shandb- Harvie (19821 book of solubilities ( 1965). c- Peiper and Pitzer (1982) d- Higher order @lwrrostatic The results of our catculations for irsp at 25°C are terms are included: this vnlxi~ shown in Fig. 3. The standard deviation is 50/o for is se. 1.J nahcolite. 2% for natron. 4% for Na,CO? - 7Hz0. For I-. Th,s study.

Solubility of Na carbonate minerals I

/

/

I

,

I

r

I

d

i

c

a

’

’

’

1

’

’

Na2C03 ,7 Hz0

natron 45-

Xl-

@F

_---------

_--

0

350

_____gcrsl_@Q--__.3010

n

f

’

’

’

I

/

’

’

’

y”

I 10

5

c

4. @@

.45-

0 0

~__________~@_____~

a, --fJ____n+O__A____ 0

a

AAo

.f.O-

0

3-

thermonatrite

A

0

0

0

.35-

nahcol~ te

.30-

I

II

I4

0 0 y” .5 -

’

’

’

’

1

’

1

5

’

’e

1

I

’

I

‘1

I

trona 4 0 00 .30 .2-

,, ___w:--_-____-

f 5

I

I

I

I 10

1 I

FIG. 3. Calculated solubility products of the main sodium carbonates from solubility data at 25°C versus the ionic strength I. (0 NaEO,-NaHCOrNaC1; A Na2COI-NaHC03 ; 0 NaHCO,-NaCl; 0 Na2COx-NaOHNaCI; 0 Na2COI-NaCI).

C. Monnin and J. Schott

576

for trona sotubiiity in various systems show great dispersion, and many data were judged to be unreliable. At 25“C this leads us to rely ortty on Hill and Bacon’s data, which give a standard deviation of 2%. Using the vaiues of the mixing parameters determined at 25*C, we calculated, through the same procedure, the Ksp for sodium carbonates at different temperatures. When pIotted versus ionic strength, the calculated Ksp remains constant only between 5 and 50°C. Thus, it is evident that B and # parameters can be considered independent of temperature only within this limited range. As with trona, some experimental data did not lit the observed general trends and were discarded (i.e. Freeth’s measurements of trona saturation in Na&O,-NaHCOS-NaCl solutions at 20°C and Bogoyavlenski and Mannanikova’s data at 38°C). It is also worth noting that the scatter in the data and hence the standard deviations are generally greater than those observed at 25’C. On Fig. 4 are plotted the Ksp for sodium carbonates on an Arrhenius type diagram. A Ieast squares procedure was used to calculate the slope and the intercept of the function InQ?=A

+$_

Weighting for the Leastsquares calculation was based upon the standard deviation ui of each value of Ksp: more precisely wi the weight of each point was given by: (BEV~NGTQN,i 969).

c

~._-oo-t>oo----titermonatrtte

1

_/

I

3

3.5

103/FK

FIG. 4. Arrhenius type plot for sodium carbonates between 15 and 45°C.

Table

4 gives the dimensionie~

cntrop~es A$

(PITZER and BREWER, 1979) and the enthafples with the dimension

temperature

T

for the reactions of

dissolution of the various salts. It should be noted that onlythermonatrite has a decreasing solubility product with temperature. Table 5 gives our Ksp values ar 25°C along with some taken from the literature. Although we used most of Harvie’s interaction parameters, there is a slight difference between the two sets of values. These differences are not significant 1: we take into account the unce~nti~ (Table 4) coming from the least squares fit of tn Ksp V~JESUS i il: Note also that our values are based on a much broader array of data than those of Harvie In a recent paper, VANDERZEE( 1982f revtewed the enthalpies and entropies of the reactions of dissolution of sodium carbonates and gave recommended vaiues based mainly on calorimetric measurements. Calculations of Ksp from these values (using R ‘- 8.3144 J - K-’ -mol.-‘) show that they tend to be lower than our solubility products (Table 5). Our calculated en,. tropies and enthalpies differ substantially from Vandenee’s results. however it is important to maintain internal consistency in our calculations between the solubility products. the activity coefficients, the activity of water and the sofubility of salts in pure water (RODGERS,f981;PITZER,1979). Forexampie,natron solubility in pure water at 2S”C is 2.767 mole/Kg H20, the measured a, is .8976 for thrs solution (ROBINSONand MACASKILL,1979). From this expermental data. if we use Vanderzee’s value for natron soiub~lity product and we calculate with our modei the saturation degree of the solution, we would find a supersaturated solution in contact with the solid.

577

Solubiiity of Na carbonate minerals

I

I

-

I

te

nahcoll

B\ \

-.!

a slight discordance for the boundary between trona and thermonatrite but we tend to believe our data because it is likely that the very low reported PCO, (- 10es) is difficult to measure with accuracy. In Table 6 our calculated temperatures and compositions of solution for the invariant points of the system are compared to the data of Hill and Bacon. Our calculated tem~ratures agree with those of the latter authors. More precisely we believe the invariant point for trona + nahcolite + natron + solution to be closer to 21 ‘C (WEGSCHEIDERand MEHL, 1928: HILL and BACON, 1927) than to 20°C (EUGSTER 1966; HATCH 1972). The composition of the solution at equilibrium with the assemblage trona f natron + heptahydrate (32’C) given by Hill and Bacon seems to be erroneous; the equilib~um Pro2 calculated from this composition conflicts with the general trend. Finally our calculated activities of water agree well with Hatch’s measurements.

tro na

\

natron r

-_E j-

4

APPLICATION: ACXWZTY PRODUCTS OF ‘I-HE MAJOR DISSOLVED COMPONENTS OF LAKE MAGADI (KENYA)

i

i-

FIG. 5. Stability fields of sodium carbonates in the Pm - Tcoordinates {O:calculated values (this work); q: HATCH f 1972); A: EUGSTER(1966)).

As both an illustration and a further test of our newly determined the~~ynamic constants, we have calculated the stability field of sodium carbonate minerals in equilibrium with Na-HC03-CO3 aqueous SOlutions in log P,,i temperature coordinates (Fig. 5). EUGSTER( 1966) has drawn such a diagram from measured Pco2 above the solution in equilibrium with two solid phases. Our calculations allow us to refine Eugster’s diagram which was inferred from rather sparse data. On the other hand, HILL and BACON (1927) and, more recently, HATCH (1972) gave the temperatures and compositions of the solutions (or a, and PC& for the invariant points in the NaHC03-Na2C03-Hz0 system. Our calculations are in good agreement with Eugster’s data for the nahcolite-trona boundary. There is

Located in the South of Kenya, Lake Magadi has been extensively studied by Eugster, Jones and coworkers (EUGSTER, 1970, 1980; JONES et al., 1977). It has been described as “an ephemeral saline lake at the peak of its trona productivity” (EUGSTER, 1980). Extensive sampling of the inflow and lake waters have allowed the development of an hydrologic model for water circulation. Evaporative concentration has been shown to be the overall process leading to the formation of the lake brines. These brines, which exhibit a very alkaline pH, up to 11, are of the Na-Cl-CO, type; these ions constitute about 98% of the total solutes (Table 7). Trona is the main evaporite formed from these waters and it accumulates on to a thick bed at a rate of .3 cm/year (EUGSTER, 1970). The thermodynamic model proposed in the first part of this paper can be applied to calculate the degree of saturation of the waters with respect to the salts which are likely to precipitate. For this purpose we used the analyses of EUGSTER( 1970) and JONES et al. (1977) for the main lake surface waters and the interstitial brines of the salt deposit. These analyses give the carbonate and bicarbonate contents for a number of samples, which allows avoiding the use of pH mea-

Table 6.- Calculatedcompositionsfor the invariantpoints in the Na-HCO3-CO-I%20systcar comparedto the data of (a) Hill and Bacon ii927fand (b) Hatch (1972).

%a

mHco3

Yo,

T=Zl.IS'C Trona + Natron + Nabcclite

4.9e 5.00

.57= .578

T = 32'C Natron + mona + Na2C03,7H*0

&Ma 8.56

.031a 4.31= ,058 4.25

T - 35.2'c Trona+Themonatrite 9.39' + Na2C03,7H20 9.16

2*19(a) 2.216

.037a 4.67a .038

4.56

moH

P co2

aY

0

.908~.003b .9068 1.33 10-3

-

.807~.002b

.0016 -

8076

I.01 10-5

.780-'.003b

.0025 .7827

-6 4.55 IO

C. Monnin and J. Schott

578

surements in the various calculations. For example, the CO* equilibrium pressure of the solution can be expressed by: Pco* =

ditcoj * Yhico, mC0,

3 * YNaK-06s

.kll.

However, JONES et al. ( 1977) noted that, in the very concentrated brines, which exhibit a high carbonate content, the bicarbonate concentration is very low and its titration is not accurate. For those samples, the bicarbonate content is not given. We thus could not calculate the trona and nahcolite saturation indices and the equilibrium Pco, for the brines displaying an ionic strength higher than 9.5. Nevertheless, the fact that we neglected HCO; in those samples (along with SO;- throughout this study) does not introduce any significant error (i.e. in the worst case. a few percent loss in the charge balance of the solution). The calculations were carried out for the temperature given for each sample. When it is not given, the temperature can be estimated from the general trends (for example, we chose T = 30°C for the interstitial brines F, G. H, I and J). Figures 6 to 11 give our results. The ionic strength is used as a concentration scale. Note that chloride has been shown to be conservative (EUGSTER, 1970) and its molality could also be used as a concentration factor. On Fig. 6 is plotted the trona saturation index versus the ionic strength. Despite a great dispersion of the points, one can see that trona reaches saturation at an ionic strength around 7. In fact. the calculated saturation indices do not reach exactly 1, but the uncer-

omotn

lake

. borehole

tainty on trona Ksp (Table 4) allows us to constder that saturation is reached. Figure 7 shows the variation of the equilibrium Pco2 of the brines UVSU.~the ionic strength. Al I - 7, which is associated with the beginning of trona formation. Pco2 start5 decreasing sharply and reaches values several hundred times lower than the atmospheric value. As noted hk EtJGSTER ( I970), trona formation removes large amounts of bicarbonate from solution, which results in a decrease in the equilibrium Pco,. Moreover the results of our calculations show that, after the beginning of trona formation. the waters do not equilibrate with the atmosphere. This means that the CO1 supply. either from the atmosphere or from biogenic sources, is too slow to make up for bicarbonate consumptron due to trona crystallization. Figure 8, on which is plotted the nahcolite saturatton index, shows that trona formation prevents nahcolite from precipitating. It should be noted that the quantities plotted on Figs. 6, 7 and 8 (1.~ Q/h’ trorta Pco2 and Q/K nahcolite) heavily depend on the htcarbonate content. This explains the disperston of the points if we keep in mind the remark from JONES ~?i al. (1977) about the bicarbonate titration, The dispersion is not reduced when considering a temperature effect as for natron (see below). On Fig. 9a is shown the variation of natron saturation index with the ionic strength. The calculations were made for the temperature of each sample. Once more, one can observe a wide scatter of tbe points. But if we carry the same calculations for a unique

waters brines

FIG. 7. Equilibrium CO2 pressure for Lake Magad surhcr FIG. 6. Trona saturation index for L.ake Magadi brines.

waters.

579

Solubility of Na carbonate minerals

o matn l

lake

borehoie

t

I

I

5 natron

waters

0 trona

brines

U thermonatn

te

~

FIG. 8. Nahcolite saturation index in Lake Magadi.

temperature (Fig. 9b is calculated for 25”C), the scatter disappears and the points line up on a smooth curve, which proves the great dependency of natron saturation index upon temperature. This is clearIy illustrated by Fig. 10 on which are plotted the saturation indices of sample M520 versus temperature. One can see that natron formation is favored by low temperatures. In this exampie natron reaches saturation for T below 20°C. This is consistent with the report of EUGSTER (1980) who observed the formation of natron crystals during cool nights, these crystals being redissolved the next morning when temperature increases again. Figures 9 and 10 also illustrate the fact that two Magadi brines of the same ionic strength can exhibit very different natron saturation indexes if their temperatures are not the same. Thermonatrite and halite (Fig. I I), reach saturation during extreme desiccation of the brines, at ionic strengths above 10. Indeed, EUGSTER (1980) noted that thermonat~te has been found to form in shallow surface pools during the late stages of evaporation of the brines. During this process NaCI concentration increases sufficiently for halite to precipitate and this phenomenon is effective enough to allow commercial production of NaCI.

To sum up, the evaporative concentration of Lake Magadi waters leads to the formation of trona (for 1 - 7) and then of halite and the~onat~te (or hahte and natron depending on temperature), these two salts precipitating in similar concentration ranges (I- 10.5). The variance of the Na-CLCOz-H20 system implies that, for given T and P, only two solids can coexist at equilib~um, i.e., in the presence of halite, thermonatrite formation must lead to trona redissolution. This redissolution should result in a notable increase of the eq~ilib~um Pcot of the solution via the reaction: 2Na,CO, - NaHCO, - ZH@(s) r=! 3Na2COX x H,O(s) + CO,(g) + 2HzOO). As thermonat~te appears only in very concentrated brines in which there are no significant amounts of bicarbonate, it seems likely that trona does not redissolve. This can happen via a fractional crystallization process in which the solid does not stay in contact

I

~

1%

4

11

1

-

&.g-

lake waters . borehole brtnes

j*o_ O

11

o matn

0

--_---__,_“_

_

-

-

-

-

o”

-

-

l lO .50%

OO

l

*P

I

I

l I

rOb 1

I

5

t

PP 00

‘. I

,

I

10

FIG. 9, Natron saturation index calculated a) for the temperature given for each sample, b) for an assumed temperature of 25’C for ail Magadi waters.

t*c

FIG. 10. Calculated evolution of the saturation state of sample M520 with temperature.

I1

1.0

4u

3u

I

580

c’. Monnln and J. Schott

FIG. 1I. Saturation indices of a) thermonatrite and b) halite in Lake Magadl brines.

with the solution from which it precipitated and is hence protected from any further reaction with the brine.

1. The ion-interaction theory developed by Pitzer and coworkers has been shown to be very efficient in treating the carbonate system in a wide concentration range. At high ionic strengths (above 5) the mixing parameters are necessary and they must be carefulliy evaluated from the most reliable experimental data. Furthermore, we have shown that the variation with temperature of only the single electrolyte parameters has to be taken into account when solubility data are analyzed in a limited temperature range around 25°C (between 5 and 50°C). 2. From solubility measu~ments, we have derived solubility products ofthe main sodium carbonates and their stability fields in the systems Na-HC03-C03-H20 between 5 and 50°C. 3. This model has been used to compute the saturation indexes of the main minerals likely to form from Lake Magadi brines. The model confirms the field observations made earlier by Eugster. As evaporative concentration proceeds, first trona and then thermonatrite and halite precipitate. ARer trona deposition, there is a disequilibrium between the brines and the atmosphere, and trona deposition is likely to occur viu a fractional crystallization process. 4. Pitzer’s model in&ding weak electrolytes is a powerful tool for the study of any type of natural concentrated solutions around 25°C. In the near future we hope to enlarge the temperature range and hence approach the hydrot~e~al field. research was supported by CNRS via ATP “C%othermie” of PIRSEM. We thank K. S. Pitter, J. C. Peiper for helpful discussions and preprints of their papers, and B. Jones and two anonymous reviewers for heipfui comments on the manuscript. Corrections by J. I. Drever and W. Murphy improved the writing.

Acknowledgements-This

REFERENC’KS BERGR. L. and VANDERZEEC. E. (1978)Thermtrdynamtcs of carbon dioxide and carbonic acid: (a) the standard enthalpies of solution of Na#ZO&). NaHCO,(s) and CO, in water at 298.15 K; (b) the standard enthalpies of formation. standard Gibbs energiesof formation and standard entropies of C02(aq), HCOj(aq). CO:-laq), NaHCO&). NazCO&), Na2C0, - H&)(s) and NazCO,. IOH@( I Uitarn 7%rrm 10, 1113-1136. BEVINGTONP. R. ( 1969) Data Reducfron and Errf~.r Anuiy,vu ./i,r the Physical Sciences. McGraw Hill. 336 p B~G~YAVLENSKII P. S. and MANNANIK~VAA. S. f 19S5)The system NaCI-NaHCOrH20 at 25°C. %h. %X-i Khrm 28, 325-328.

CODATA (197X) Recommended key values for themwdy namics. 1977. Report of the CODATA Task Group 011 Key Values for Thermodynamics. 1977. .I C%m? Yfhcprm 10,903-906.

EUGSTERH. P. (1966) Sodium marinate-bi~ar~oate minerals as indicators of Pm. J. GW&N Rrs. 71, 3369-77 EUGSTERH. P. (1970) Chemistry and origin of the brines of Lake Magadi (Kenya). h4inerul .‘&c~.4mcr S/X*? Pap 3.

213-235. EUGSTER H. P. (1980) Lake Magadi. Kenya. and its precursors, In Hypersaiine Brines and Evaporitic Environments. (ed.

A. NISSENBAUM)Chapter 15. 195-230. Elsevier. 270 p, EUGSTERH. P., HARVIF.C. E. and WEARE J. 11. (19801 Mineral equilibria in the six component seawater system, Na-K-Mg~a-SOL-~I-H~O at 25°C. ~e~)chim C!~,~rn~~~jrn Acta 44, 1335-1347. FREETHF. A. (1922) The system Na@-C02-NaC1-ZizO, con,, sidered as two four-component systems. &II,. S/j< 3,cmdorr. Phil. Trans. A223, 35-87.

CUEDARRIM., MOM\~INC., PERRETD.. FRITZB. and TAKUS Y. (1983) Geochemistry of the brines ofChott El Jerid in Southern Tunisia: application of Pitzer’s equations. Chem Cd

39,

165-178.

WARNEDH. S. and SCHOLESS. K. JK. ( 194 1f Ihe toni7&on of HCO; from 0” to SO”. J .lmcr. c’hem SW 63, 1X%1709.

HARNED H. S. and DAVIES R. JK. (1943) The ionization constant of carbonic acid in water and the volubility of carbon dioxide in water and aqueous salt solutions from 0” to 50’. J. Amer. Chem. SK 65, 2030-2037 HARNEDH. S. and E%ONNER F. T. (1945) The first ionization of carbonic acid in aqueous solutions of sodium chloride. J. Amer. Chem. Sac. 67, 1026- 103 I.

HARVIEC. E. and WEARE J. H. (1980) The prediction at mineral sofubilities in natural waters: the Na-K-Mg-Ca-CISO,-Hz0 system from zero to high concentrations at 25°C. Geochim. Cosmochim. Acta 44,98 I-997.

HARVIEC. E., WEARE J. H.. HARDIP L. A and ~.~UGSTEP

Solubility of Na carbonate minerals H. P. (1980) Evaporation of seawater: calculated mineral sequences. Science 208, 498-500. HARV~EC. E. (1982) Theoretical investigation in geochemistry and atom surface scattering. Ph.D. Thesis. Univ. California at San Diego, La Jolla, California. HARV~EC. E., EUGSTER H. P. and WEARE J. H. (1982) Mineral equilibria in the six component seawater system, Na-K-Mg-Ca-SO&l-H,0 at 25’C: II. Compositions of the saturated solutions, Geochim. Cosm~him. Acta 46,16031618. HATCH J. R. ( 1972) Phase relationship in part of the system sodium carbonate-calcium carbonate-carbon dioxydewater at one atmosphere pressure. Ph.D. Thesis. University of Illinois, Urbana, Illinois, 92 p. HILL A. E. and BACON L. R. (1927) Ternary systems, VI sodium carbonate, sodium bicarbonate and water. J. Amer. Chem. Sot. 49, 2487-2495. HOSTAI_EKZ. ( 1956) The ternary system water-sodium carbonate-sodium hydroxyde. Chem. Listy SO, 7 16-720. JONES B. F., EUGSTERH. P. and Rrmc S. I... (1977) Hydrochemistry of the Lake Magadi basin, Kenya. Geochim. Cosmochim. Acta 41, 53-72. KRUMGAU B. S. and MILLEROF. J. (1982) Physicochemical study of the Dead Sea waters, I: Activity coefficient of maior ions in Dead Sea water. Mar. Chem. il. 209-223. L~NKEW.-F. (1965) Solubilities ofInorganic and’Metat Organic Compounds. Vol. II. Amer. Chem. Sot., 19 14 p. PEEPERJ. C. and PITZER K. S. (1982) Thermodynamics of aqueous carbonate solutions including mixtures of sodium carbonate, bicarbonate and chloride. J. Chem. Thermodynamics 14,6 13-638. PITZER K. S. (1973) Thermodynamics of electrolytes. I. Theoretical basis and general equations. J. Phys. Chem. 77,268-277. PITZERK. S. ( 1975) ~e~~~arni~ of electrolytes. V. Elf& of higher order electrostatic terms. j. Sol. Chem. 4, 249265. PITZER K. S. (1979) Theory: ion interaction approach. In Activity Coeficients in Eiectrolytes Solutions (ed. R. PYTKOWICZ) vol. I, 157-209, CRC Press, Cleveland, 288 p. PITZERK. S. (1980) Thermodynamic of aqueous electrolytes at various temperatures, pressures and compositions. ACS Symp. Ser. 133,45 l-466. PITZER K. S. f 1981) Characteristics of very concentrated aqueous solutions. In Chemistry and geochemistry ofsolutions at high temperatures and pressures (eds. D. T. RICHARD and F. E. WICKNAN), 249-273. Pergamon, 564 p. PITZER K. S. and MAYORGAG. (1973) The~~ynami~ of electrolytes: II. Activity and osmotic coefficients for strong

581

electrolytes with one or both ions univalent. J. Phys. Chem. 71,23OO-2308. P~TZERK. S. and KIM J. J. (1974) Thermodynamics of electrolytes. IV. Activity and osmotic coefficients for mixed electrolytes. J. Amer. Chem. Sot. 96, 5701-5707. PITZERK. S. and SYLVESTER L. F. (1975) Thermodynamics of electrolytes. VI. Weak electrolytes including H,PO,. J. Sol. Chem. 5,269-278. PITZER K. S. and BREWERL. ( 1979) Simplification of thermodynamic calculations through dimensionless entropies. High Temps. Sci. 11, 49-53. PITZERK. S. and PEIPERJ. C. (1980) Activity coefficient of aqueous NaHC03. J. Phys. Chem. 84,2396-2398. PITZERK. S., ROY R. N. and SILVESTERL. F. (1977) Thermodynamics of electrolytes. VII. Sulfuric Acid. J. .4mer. Chem. Sot. 99, 4930-4936. ROBINSONR. A. and MACASKILLJ. B. (1979) Osmotic coefficients of aqueous sodium carbonate solutions at 25°C. J. Sol. Chem. 8, 35-40. RODGERSP. S. K. (198 1) The~~y~rni~ of geothermal fluids. Ph.D. Thesis. UC Berkeley, Berkeley, California. ROY R. N.. GIBBONSJ. J., TROWERJ. K., LEEG. A., HARTLEY J. and MACKG. (198 I) The ionization constant of carbonic acid in solutions of sodium chloride from e.m.f. measurements at 278.15. 298.15 and 318.15 K. J. Chem. Therm. 14,473-483. SILVESTERL. F. and PITZER K. S. (1977) Thermodynamics of electrolytes. 8. High temperature properties, including enthalpy and heat capacity, with application to sodium chloride. .I. Phys. Chem. 81(19X 1822-1828. SILVESTERL. F. and PITZERK. S. (1978) Thermodynamics of electrolytes. X. Enthalpy and the effect of temperature on the activity coefficients. J. Sol. Chem. 7, 327-337. VANDERZEEC. E. (1982) Thermodynamic relations and equilibria in (Na2COj -t NaHCOx + H,O): standard Gibbs energies of formation and other properties of sodium hydrogen carbonate, sodium carbonate heptahydrate, sodium carbonate decahydrate trona: (Na2COx.NaHC03* 2H,O) and Wegscheider’s salt: (Na,CO>+ NaHCO,). J. Chem. Therm. 14,219-238. WEGSCHEIDER R. and MEHLJ. (1928) iiber Systeme Na2COr NaHCOI-Hz0 und das Existenzgebiet der Trona. Monatsch. Chem. 49,283-3 15. WHITE D. R. and BATESR. G. (1980) Osmotic coefficients and activity coefficients of aqueous mixtures of sodium chloride and sodium carbonate at 25°C. Aus. J. Chem .,.. 2% 1903-1908. WHITHELDM. (1975) The extension of chemical models for sea water to include trace components at 25°C and I atm. Geochim. Cosmochim. Acta 39, 154% 1557. ‘_,