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C 2002)
Journal of Solution Chemistry, Vol. 31, No. 2, February 2002 (°
Solubility of Siderite (FeCO3 ) in NaCl Solutions
∗
Carlos A. R. Silva,1 Xuewu Liu,2 and F. J. Millero2
Received June 21, 2001; revised December 3, 2001
The solubility of siderite (FeCO3 ) at 25◦ C under constant CO2 partial pressure [ p(CO2 )]
was determined in NaCl solutions as a function of ionic strength. The dissolution of
FeCO3 (s) for the reaction
FeCO3 (s) + 2H+ = Fe2+ + CO2 (g) + H2 O
∗
K so
= [Fe2+ ] pCO2 /[H+ ]2
has been determined as a function of pH = − log[H+ ]. From these values we have determined the equilibrium constant for the stoichiometric solubility to FeCO3 (s) in NaCl
£
∗
= [Fe2+ ] CO2−
K sp
3
¤
These values have been fitted to the equation
∗
] = −10.9 + 2.518 I 0.5 − 0.657 I
log[K sp
o ) − 10.9 in water is
with a standard error of s = 0.15. The extrapolated value of log(K sp
in good agreement with data in the literature (−10.8 to −11.2) determined in solutions
of different composition and ionic strength.
The measured values of the activity coefficient, γ T (Fe2+ ) γ T (CO2−
3 ), have been
used to estimate the stability constant for the formation of the FeCO3 ion pair,
K ∗ (FeCO3 ). The values of K ∗ (FeCO3 ) have been fitted to the equation (s = 0.09)
log[K ∗ (FeCO3 )] = 6.3 − 2.3135 I 0.5 + 0.7091 I
The value of log[K o (FeCO3 )] in water found in this study (6.3 ± 0.2) is slightly higher
than the value found from extrapolations in 1.0 m NaClO4 solutions (5.9 ± 0.2). These
differences are related to the model used to determine the activity coefficients of the
Fe(II) and carbonate species in the two solutions.
KEY WORDS: Siderite; solubility; activity coefficients; sodium chloride; Pitzer
equations.
1 Departamento
de Oceanografia e Limnologia, Centro de Biociências, Universidade Federal do Rio
Grande do Norte, CP 1202, 59075-970, Brasil.
2 Rosenstiel School of Marine and Atmospheric Science, University of Miami, 4600 Rickenbacker
Causeway, Miami, Florida 33149-1098; e-mail: [email protected]
97
C 2002 Plenum Publishing Corporation
0095-9782/02/0200-0097/0 °
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1. INTRODUCTION
Among the most chemically reactive and common minerals in the aquatic
systems, carbonate minerals play an important role in the cycling of the chemical elements. Under anoxic conditions, the solubility of ferrous iron (Fe2+ )
is frequently controlled by the siderite or ferrous carbonate (FeCO3 )(1) by the
equilibrium
FeCO3 (s) = Fe2+ + CO2−
3
(1)
A number of workers(2–8) have determined the stoichiometric solubility product of
FeCO3 (s) at low ionic strengths (≤1 m). If the activity of FeCO3 (s) is assumed to
be 1.0, the stoichiometric solubility product is defined by
£
¤
¡
¢
∗
o
K sp
= [Fe2+ ] CO2−
γ T (Fe2+ ) γ T CO2−
= K sp
(2)
3
3
o
where K sp
is the infinite-dilution solubility in water and γ T (i) and [i] are the total
activity coefficient and concentration of species i. The subscript T is used to denote
the total activity coefficient (which accounts for all of the ionic interaction in the
solution).(9) Ideally one would like to be able to calculate the solubility product
o
and estimates of the activity coefficient of Fe2+ and CO2−
from values of K sp
3 .
2−
2+
and
CO
can
form
comSince Fe can form complexes with OH− and CO2−
3
3
plexes with Mg2+ , Ca2+ , and Fe2+ , one has to account for the formation of these
complexes(9) in natural waters. At the present time, Pitzer(10) computer codes are
available(9) that can be used to determine the activity coefficients of Fe2+ and CO2−
3
in dilute solutions of most natural waters made up of the major seasalts [Na+ ,
−
2−
−
−
−
Mg2+ , Ca2+ , K+ , Sr2+ , Cl− , SO2−
4 , HCO3 , Br , CO3 , B(OH)4 , F , CO2 , and
2−
2+
B(OH)3 ]. The data for examining the interactions of Fe and CO3 in concentrated solutions are presently not available. In this study, the solubility of FeCO3 (s)
was measured at 25◦ C in NaCl solutions as a function of ionic strength. These results have been used to examine the interactions of Fe2+ and CO2−
3 at high ionic
strengths.
2. EXPERIMENTAL
2.1. Preparation of Solid FeCO3
Ferrous carbonate was prepared using deoxygenated Milli-Q water (Millipore) and a mixture of ferrous sulfate heptahydrate (reagent grade) and sodium
bicarbonate (reagent grade) according to the methods of Greenberg and Tomson.(8)
The prepared seed crystal was heated in a water bath at 50◦ C for 10 days. As shown
by Bruno et al.,(7) preparations of FeCO3 (s) by these methods provides high-purity
crystalline siderite.
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2.2. Working Vessel
The measurements were made in a Plexiglas vessel designed for temperaturecontrolled reactions.(11) Four holes were made in the top of the vessel for connecting
a combination electrode (8102 ORION), a bubbler, titration tube, and a tube used
to take out the sample. The measurements were made at 25◦ C using a Neslab water
bath set with a Guiline Platinum resistance thermometer. The measurements were
made in reagent-grade NaCl as a function of the molal ionic strength.
The NaCl solutions (0.1, 0.7, 1.4, 2.0, 2.5, 4.0, and 5.5 m) were prepared
with deoxygenated Milli-Q water and sodium chloride (reagent grade) in a glove
box devoid of oxygen. Approximately 9 cm3 of a siderite solution was introduced
with a syringe under a stream of CO2 (research grade) into the working vessel.
The solutions were bubbled with 5% CO2 gas (CO2 /N2 —Anaerobic Biological
Atmosphere) at a total pressure of 1 atm. The CO2 /N2 gas was passed over four
oxygen scavenger traps (purple vanadium chloride) and a 0.1 µm Vacu-Guard
Whatman filter before it was passed through the test solution. The solution was
stirred to suspend the solid particles in the solution. Measurements at high pH
were unsuccessful due to the oxidation of Fe(II) to Fe(III) over time.
2.3. Titration and Total Iron Ferrous Analysis
The solubility measurements were carried out by titrating the initial solutions
[NaCl + FeCO3 (s)] with bicarbonate (2.0 m NaHCO3 ) over the pH range of 5.76 to
7.77. After each addition, the solutions were equilibrated at a constant temperature
while bubbling with CO2 (g). The equilibrium was assumed when the potential of
the glass electrode remained within 0.1 mV for 24 h.(7) The inner electrolyte
solution of the combination pH electrode was filled with 3.0 M NaCl to reduce
the liquid junction potential. The emf of the electrode system was related to the
molal concentration of the proton [H+ ] by
E = E ∗ − (RT /F) ln[H+ ]
(3)
where E ∗ is the apparent standard potential in the NaCl media. The values of E ∗
were determined by titrating each NaCl solution with 0.2489 M HCl.
A syringe of 10 cm3 and an Acro-disc PF syringe filter (0.8 µm/0.2µm) were
used to collect filtered solutions under vacuum conditions. The filtered solutions
were immediately transferred to a glass vial containing 0.1 M HCl for weighing
and analysis of total dissolved iron using the Ferrozine method.(12)
3. RESULTS AND DISCUSSION
The solubility of FeCO3 (s) in NaCl solutions was measured by monitoring
the ferrous iron concentrations [Fe2+ ] as a function of hydrogen concentrations
at constant CO2 (g) partial pressure. The effects of pH on the concentration of
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Silva, Liu, and Millero
Table I. Values of log [Fe(II)] in NaCl Solutions as a Function of pH for Equilibrated
Solutions of FeCO3 (s) at Constant pH
m (mol-kg−1 )
pH
log[Fe(II)]
m (mol-kg−1 )
pH
log[Fe(II)]
0.1
5.76
5.83
6.00
6.23
6.33
−2.897
−3.122
−3.360
−3.833
−4.297
2.5
6.39
6.50
6.73
6.95
−2.884
−3.302
−3.639
−4.020
4.0
0.7
5.86
5.95
6.33
6.39
6.50
−2.859
−3.048
−3.833
−4.009
−4.189
6.50
6.58
6.74
6.91
7.18
−2.981
−3.063
−3.323
−3.645
−4.228
5.5
1.4
5.97
6.15
6.39
−2.254
−2.652
−3.034
6.73
6.99
7.25
7.39
7.77
2.0
6.22
6.35
6.49
6.97
7.13
−2.830
−2.958
−3.240
−4.171
−4.570
−3.027
−3.379
−3.850
−4.228
−5.024
Fe2+ in NaCl at different ionic strengths are given in Table I and shown in Fig. 1.
The slope of each curve was nearly −2 (−2.0 ± 0.1) and is independent of ionic
strength, in accord with the work of Bruno et al.(7) In the range 5.76 ≤ pH ≤
7.77, the [Fe2+ ] released during the dissolution of FeCO3 (s) is a result of the
reaction
FeCO3 (s) + 2H+ = Fe2+ + CO2 (g) + H2 O
(4)
∗
The constant K so
is defined as
∗
K so
= [Fe2+ ] p(CO2 )/[H+ ]2
(5)
∗
K so
where p(CO2 ) is the partial pressure of CO2 (in bars). The values of
have
been determined from plots of log { p(CO2 )/[H+ ]2 } vs. log[Fe2+ ] and the results
are summarized in Table II and shown as a function of I 0.5 in Fig. 2. These results
have been fitted to the linear equation (σ = 0.15)
∗
log(K so
) = 6.95 + 0.988 I 0.5
(6)
∗
The interpolated value of logK so
(7.9 ± 0.15) in 1.0 m NaCl is in reasonable
agreement with the value found by Bruno et al.(7) in 1.0 M NaClO4 (7.65 ± 0.1).
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Solubility of Siderite
101
Fig. 1. Solubility of FeCO3 (s) as a function of log(Fe2+ ) and pH in NaCl solutions at 25◦ C and
p(CO2 ) = 0.05 bar.
∗
The measured values of K so
can be used to determine the dissolution of
FeCO3 (s) given by
FeCO3 (s) = Fe2+ + CO2−
3
∗
The stoichiometric solubility product K sp
for this equilibrium is given by
£
¤
∗
K sp
= [Fe2+ ] CO2−
3
∗ ] and Product
Table II. The Solubility Constant log[K so
∗ ] for FeCO (s) in NaCl Solutions
log[K sp
3
Molality
(mol-kg−1 )
∗ ) bar
log(K so
∗)
log(K sp
0.1
0.7
1.4
2.0
2.5
4.0
5.5
−7.26 ± 0.12
−7.52 ± 0.04
−8.39 ± 0.05
−8.41 ± 0.06
−8.52 ± 0.09
−8.81 ± 0.06
−9.25 ± 0.08
−10.22 ± 0.12
−9.53 ± 0.04
−8.58 ± 0.05
−8.61 ± 0.06
−8.55 ± 0.09
−8.56 ± 0.06
−8.61 ± 0.08
(7)
(8)
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∗ ) as a function of the square root of
Fig. 2. Values of log(K so
ionic strength I .
where [Fe2+ ] was obtained from experimental analysis and [CO2−
3 ] was calculated
from the values of p(CO2 ) and pH. The CO2 equilibrium is controlled by the
following equilibria(13,14)
CO2 (g) = CO2 (aq);
+
CO2 (aq) + H2 O = H +
HCO−
3;
2−
+
HCO−
3 = H + CO3 ;
K 0∗ = [CO2 ]/ p(CO2 )
K 1∗
+
[HCO−
3 ]/[CO2 ]
= [H ]
£
¤
−
K 2∗ = [H+ ] CO2−
3 /[HCO3 ]
(9)
(10)
(11)
From these stoichiometric dissociation constants the concentrations of [CO2−
3 ]
may be determined from
£ 2− ¤
CO3 = K 0∗ K 1∗ K 2∗ p(CO2 )/[H+ ]2
(12)
∗
can be defined as
and K sp
∗
∗
K sp
= K 0∗ K 1∗ K 2∗ K so
(13)
The stoichiometric values of K 0∗ , K 1∗ , and K 2∗ in NaCl solutions have been
determined from the Pitzer(10) equations of Millero and Roy,(14) which are based
∗
determined
on the measurements of Thurmond and Millero.(15) The values of pK sp
∗
from Eq. (13) are given in Table II. The values of log K sp have been extrapolated to
infinite dilution using the equation
©
¡
¢ª
∗
− log γ F (Fe2+ )γ F CO2−
(14)
Y = log K sp
3
(9)
where γ F (Fe2+ ) γ F (CO2−
3 ) is the trace activity coefficient product of the free ions
(see Table IV). The value of Y should be constant if the trace or free activity
coefficients accounted for all of the ionic interactions in the solution. As discussed
later, this is not the case due to the formation of the ionic complex FeCO3 .
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103
∗ ) − log{γ (Fe2+ ) γ (CO2− )]
Fig. 3. Values of Y = log(K sp
F
F
3
as a function of molality m.
A plot of Y versus the molal ionic strength (I ) in Fig. 3 gives a value of log
o
∗
= −10.9 ± 0.2. The experimental values of log K sp
are plotted versus I 0.5 in
K sp
Fig. 4 and have been fitted to the equation (s = 0.15)
∗
) = −10.9 + 2.518 I 0.5 − 0.657 I
log(K sp
(15)
∗
at 1 m (−9.0 ± 0.2) determined from Eq. (15) is higher than
The value of log K sp
∗
the value (log K sp = −9.55 ± 0.2) determined from the measurements of Bruno
et al.(7) in 1 m NaClO4 . If the carbonate constants in 1 m NaCl (K 0∗ = 10−1.57 , K 1∗ =
∗
= −9.3 ± 0.2 is
10−5.94 , and K 2∗ = 10−9.50 )(14) are used, a value of log K sp
found for 1 m NaClO4 , which is in better agreement with our value. Since the
∗ ) as a function of the square root
Fig. 4. Values of log(K sp
of ionic strength I .
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Silva, Liu, and Millero
Table III. Comparisons of the Solubility Product of FeCO3 (s) in
Water at 25◦ C
◦C
Solution
Ionic strength
(mol-kg−1 )
∗)
log (K sp
25
25
25
25
25
30
43
50
NaCl
Water
Water
NaClO4
NaClO4
Water
Water
NaClO4
0.1 to 5.5
∼0.01
∼0.01
0.1
1.0
∼0.01
∼0.01
1.0
−10.9 ± 0.2
−10.8
−11.0
−10.2
−10.8
−10.7
−10.9
−11.2
Ref.
This study
a
b
c
d
e
a
f
a Greenberg
and Tomson, 1992 (Ref. 8).
1991 (Ref. 6).
c Singer and Stumm, 1970 (Ref. 4).
d Bruno et al., 1992 (Ref. 7).
e Latimer, 1952 (Ref. 3).
f Reiterer et al., 1981 (Ref. 5).
b Braun,
carbonate constants in NaCl and NaClO4 solutions are similar,(16) this is a reasonable calculation.
As shown in Table III, our value for the solubility product extrapolated to ino
) = −10.9) is in good agreement with literature data.(3,5–8)
finite dilution (log(K sp
o
Part of the differences in logK sp
is related to the different methods used to extrapolate the results to infinite dilution. To make a reliable extrapolation to pure water,
it is necessary to have a reliable model to estimate the activity coefficients.
The activity coefficients for free ions in NaCl and NaClO4 solutions can be
estimated from Pitzer’s equations.(9,14,16) These models consider the changes in the
interactions of Fe2+ and CO2−
3 with NaCl as well as the formations of complexes
(i.e.,
FeCO3 o ).(17) The measured solubility constants for
between Fe2+ and CO2+
3
the dissolution of FeCO3 (s) is related to the activity coefficients by
¡
¢
∗
o
= K sp
γ T (Fe2+ ) γ T CO2−
(16)
K sp
3
The measured activity coefficient products determined from
¡
¢
∗
o
/K sp
= K sp
γ T (Fe2+ ) γ T CO2−
3
(17)
are given in Table IV and shown as a function of the concentration of NaCl in Fig. 5.
The values of the total activity product can be compared to the trace activity coef2+
and CO2−
ficients, γF (Fe2+ ) γF (CO2−
3 ), determined in NaCl devoid of Fe
3 . The
(9)
values determined from the Pitzer equation are given in Table IV and shown as a
function of the concentration of NaCl in Fig. 5. The trace activity coefficients are
higher than the measured values. This is due to the formation of FeCO3 complexes
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105
Table IV. Values of the Total Activity Product, γ T γ T = γ T (Fe2+ ) γ T (CO2−
3 ), the Stability Constant
0,
for the Formation of the FeCO3 Complex, logK ∗ (FeCO3 ), and the Solubility Product in Water, logK sp
at 25◦ C
Measured
I
γT γT
γ F (Fe2+ )
γ F (CO2−
3 )
Calc.
γT γT
Calc.
Log K ∗ (FeCO3 )
Calc.
∗)
log (K sp
0.0
0.1
0.7
1.4
2.0
2.5
4.0
5.5
1.0000
0.2089
0.0427
0.0048
0.0051
0.0045
0.0046
0.0051
1.0000
0.3896
0.2550
0.2656
0.3019
0.3474
0.5871
1.0833
1.0000
0.3333
0.1227
0.0727
0.0532
0.0433
0.0288
0.0240
1.0000
0.0323
0.0115
0.0049
0.0047
0.0044
0.0046
0.0055
6.30
5.41
4.80
4.59
4.51
4.48
4.53
4.71
—
—
—
−10.89
−10.94
−10.91
−10.90
−10.87
Mean: −10.9 ± 0.03
that lower the activity coefficients. The values of the total activity coefficients are
related to the free activity coefficients by
¡
¢
¡
¢
= αFe αCO3 γ F (Fe2+ ) γ F CO2−
(18)
γ T (Fe2+ ) γ T CO2−
3
3
The fraction of the free Fe2+ and CO2−
3 can be determined from
¡
£
¤ ¢−1
αFe = [Fe2+ ]F /[Fe2+ ]T = 1 + K ∗ (FeCO3 ) CO2−
3 F
£
¤ £ 2− ¤
∗
2+
−1
αCO3 = CO2−
3 F / CO3 T = (1 + K (FeCO3 ) [Fe ]F )
Fig. 5. Measured and calculated values of the activity coefficient product, γ T (Fe2+ ) γ T (CO2−
3 ), as a function of molality
at 25◦ C. The line is calculated using log K o (FeCO3 = 5.9).
(19)
(20)
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The values of K ∗ (FeCO3 ) are the stoichiometric constants for the formation of the
FeCO3 ion pair
Fe2+ + CO2−
3 = FeCO3
(21)
2+
2+
The terms [Fe2+ ]F and [CO2−
3 ]F are the concentration of free Fe (=[Fe ]T αFe )
2−
2−
and free CO3 (= [CO3 ]T αCO3 ), respectively. The stoichiometric association constant K ∗ (FeCO3 ) is related to the thermodynamic value, K o (FeCO3 ) by
©
¡
¢ª
(22)
K ∗ (FeCO3 ) = K o (FeCO3 ) γ F (FeCO3 )/γ F (Fe2+ ) γ F CO2−
3
Since the total concentrations of [Fe2+ ]T = [CO2−
3 ]T when FeCO3 (s) dissolves,
the fraction of free ions are also equal [Fe2+ ]F = [CO2−
3 ]F and can be estimated
from combining Eqs. (19, 20, and 22). This gives the quadratic equation
£
¤
∗
0.5
(23)
[Fe2+ ]F = CO2−
3 F = {−1 + [1 + 4K (FeCO3 )] }/2K ∗ (FeCO3 )
The values of K ∗ (FeCO3 ) needed to determined [Fe2+ ]F = [CO2−
3 ]F depends
on the value selected for the thermodynamic value (K o (FeCO3 ). The literature values for log [K o (FeCO3 ) vary from 5.5(7,18) to 5.7.(19) The latter value was redetermined from the solubility measurements of FeCO3 (s) of Bruno et al.(7) in NaClO4
solutions by King.(19) Bruno et al.(7) determined the constant for the reaction
Fe2+ + CO2 (g) + H2 O = FeCO3 + 2H+ ,
log β11 = −12.98 ± 0.16
(24)
The value of K ∗ (FeCO3 ) at 1 m can be determined from
K ∗ (FeCO3 ) = β11 /K 0∗ K 1∗ K 2∗ = 10−12.9 /(10−7.62 10−9.52 ) = 104.24
(25)
CO2−
3
(0.0952) in 1.0 m NaClO4
The free activity coefficients of Fe2+ (0.254) and
gives a value of log [K o (FeCO3 ) m o )] = 4.24 + 1.62 = 5.9 ± 0.2, which is
slightly higher than the value determined by King.(19)
By adjusting the values of K o (FeCO3 ), one can determine γ T (Fe2+ ) γ T (CO2−
3 )
[Eq. (18)] and compare them with the values determined from the measured val∗
. A value of log K o (FeCO3 ) = 6.3 ± 0.2 gives the best fit of γ T (Fe2+ )
ues of K sp
2−
γ T (CO3 ) (see Table IV and Fig. 5). This value of K o (FeCO3 ) is higher than the
values determined by King(19) from the measurements made in 1.0 m NaClO4 by
Bruno et al.(7) The value of log K o (FeCO3 ) = 6.6 determined by Mattigod and
Sposito(20) are the only literature values as large as found in this study. It should
be pointed out that the value of log K o (FeCO3 ) = 5.7 does not give a reliable fit
of our measured values of γ T (Fe2+ ) γ T (CO2−
3 ) (see Fig. 5).
The values of log K ∗ (FeCO3 ) calculated from Eq. (22) are given in Table IV.
These results are shown in Fig. 6 and have been fitted to the equation (s = 0.1)
log (K ∗ (FeCO3 ) = 6.3 − 2.3135 I 0.5 + 0.7091 I
(26)
It should be pointed out that we have assumed that the activity coefficient of the
ion pair is γ F (FeCO3 ) = 1.0 in all of these calculations.
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107
Fig. 6. Values of log K ∗ (FeCO3 ) for the formation of the
FeCO3 complex in NaCl as a function of the square root
of ionic strength I .
o
One can also determine the value of K sp
from the calculated values of
2−
2+
γ T (Fe ) γ T (CO3 ) by rearranging Eq. (16). The values above 0.7 m, calculated in
o
= −10.9 ± 0.03
this manner, are given in Table IV. The average value of log K sp
is in excellent agreement with the extrapolated value.
In summary, our solubility measurements of FeCO3 (s) in NaCl solutions over
a wide range of ionic strength and pH < 7.2 can be adequately represented using
o
and K o (FeCO3 ) and a Pitzer model. The resultant
infinite dilution constants for K sp
values of both thermodynamic constants depend on the model used to determine
the activity coefficients of Fe(II) and carbonate species. The small differences in
our values in NaCl and literature results in NaClO4 are related to differences in the
activity coefficients in the solutions. Since most natural waters contain NaCl as the
major component, our results may prove more useful in examining the behavior
of Fe2+ in anoxic waters containing carbonate.
ACKNOWLEDGMENTS
The Oceanographic Section of the National Science Foundation supported
this research. Carlos A. R. Silva wishes to acknowledge the support of the Conselho
Nacional de Desenvolvimento Cientı́fico e Tecnológico (CNPq – Processo
200992/97), sponsor of his post-doctoral stay at the Rosenstiel School.
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P2: GCR
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