J. Chem. Thermodynamics 39 (2007) 568–575
www.elsevier.com/locate/jct
Thermodynamic properties of soddyite from solubility
and calorimetry measurements
Drew Gorman-Lewis
a
a,*
, Lena Mazeina b, Jeremy B. Fein a, Jennifer E.S. Szymanowski a,
Peter C. Burns a,c, Alexandra Navrotsky b
University of Notre Dame, Department of Civil Engineering and Geological Sciences, 156 Fitzpatrick Hall, Notre Dame, IN 46556, United States
b
NEAT ORU and Thermochemistry Facility, 4411 Chemistry Annex, One Shields Avenue,
University of California at Davis, Davis CA 95616-8779, United States
c
Chemistry Division, Argonne National Laboratory, Argonne, IL 60439, United States
Received 27 July 2006; received in revised form 6 September 2006; accepted 7 September 2006
Available online 14 September 2006
Abstract
The release of uranium from geologic nuclear waste repositories under oxidizing conditions can only be modeled if the thermodynamic properties of the secondary uranyl minerals that form in the repository setting are known. Toward this end, we synthesized soddyite ((UO2)2(SiO4)(H2O)2), and performed solubility measurements from both undersaturation and supersaturation. The solubility
measurements rigorously constrain the value of the solubility product of synthetic soddyite, and consequently its standard-state Gibbs
free energy of formation. The log solubility product (lg Ksp) with its error (1r) is (6.43 + 0.20/0.37), and the standard-state Gibbs free
energy of formation is (3652.2 ± 4.2 (2r)) kJ mol1. High-temperature drop solution calorimetry was conducted, yielding a calculated
standard-state enthalpy of formation of soddyite of (4045.4 ± 4.9 (2r)) kJ Æ mol1. The standard-state Gibbs free energy and enthalpy
of formation yield a calculated standard-state entropy of formation of soddyite of (1318.7 ± 21.7 (2r)) J Æ mol1 Æ K1. The measurements and associated thermodynamic calculations not only describe the T = 298 K stability and solubility of soddyite, but they also can
be used in predictions of repository performance through extrapolation of these properties to repository temperatures.
Ó 2006 Elsevier Ltd. All rights reserved.
Keywords: Soddyite; Uranyl silicate; Gibbs free energy; Enthalpy; Entropy; Solubility; Supersaturation; Solubility product; Calorimetry
1. Introduction
Uranyl silicates are common constituents of the altered
portions of U deposits, and are important for understanding the genesis of such deposits as well as the mobility of
uranium in the environment [1]. Uranyl silicate minerals
consist of three structurally and chemically distinct groups
[2,3]. The uranophane group is the most abundant, and
each of their structures contains sheets of uranyl polyhedra
and silicate tetrahedra, with lower-valence cations and H2O
groups located in the interlayer regions. The weeksite
*
Corresponding author. Present address: Argonne National Laboratory, CHM 200, 9700 S Cass Avenue, Argonne, IL 60439, United States.
Tel.: +1 630 252 3653.
E-mail address: [email protected] (D. Gorman-Lewis).
0021-9614/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jct.2006.09.005
group also corresponds to minerals with sheet structures,
but the sheets contain more silicate that those of the uranophane group. In contrast, soddyite, the chemically simplest
uranyl silicate with formula (UO2)2SiO4(H2O)2, has a
framework structure composed of uranyl polyhedra and
silicate tetrahedra that share vertices.
The performance of geologic nuclear waste repositories
will be influenced by interactions between the spent nuclear
fuel and the environment in which it is placed. Oxidative
weathering of commercial spent nuclear fuel under oxidizing conditions, such as those expected at the proposed
repository at Yucca Mountain, will likely result in the formation of U(VI) mineral phases [1,2,4]; consequently, the
formation and stability of U(VI) minerals will impact the
release of U(VI) from the waste package, and potentially
also from the repository. Uranyl minerals that form in a
D. Gorman-Lewis et al. / J. Chem. Thermodynamics 39 (2007) 568–575
geological repository may also incorporate radionuclides
such as Np into their structures, potentially having a profound impact on the release of such radionuclides [5–7].
Finch et al. [4] examined the alteration products that
formed after groundwater dripped onto the spent nuclear
fuel in a laboratory setting for six years at T = 363 K.
The experiments used two pressurized-water-reactor fuels,
ATM103 and ATM106, with corresponding burn-up
histories of 30 MWd Æ kg1 U and 45 MWd Æ kg1 U,
respectively. The groundwater used was from well J-13 at
the Yucca Mountain site, and was reacted with crushed
Tonopah Springs tuff at T = 363 K for 80 days prior to
use (designated EJ-13 water). Alteration of the spent fuel
in four experiments with different water injection rates
resulted in mostly uranyl compounds. These included several uranyl oxide hydrates as well as the uranyl silicates
soddyite, b-uranophane, Ca(UO2)2(SiO3OH)2(H2O)5 and
Na-boltwoodite, (Na,K)(UO2)(SiO3OH)(H2O)1.5. In similar experiments, Wronkiewicz et al. [8,9] examined nonirradiated UO2 placed under dripping EJ-13 water at
T = 363 K for more than 10 years. Wronkiewicz et al. [9]
found that the alteration phases that formed initially were
uranyl oxide hydrates, followed by uranyl silicates, a paragenetic sequence which is generally consistent with natural
analogues.
Despite the potential importance of U(VI) silicate minerals in the performance of a geologic nuclear waste repository under oxidizing conditions, reliable thermodynamic
data are lacking for most of these minerals. In order to
predict the stability and solubility of U(VI) silicate minerals
as a function of solution composition (pH, ionic strength,
etc.) and temperature, it is necessary to know the
standard-state Gibbs free energy, enthalpy, and entropy
of formation for each phase of interest. These thermodynamic parameters are crucial for predicting repository
performance.
Soddyite is a common uranyl silicate in nature, and has
been found as an alteration product of spent nuclear fuel
under moist oxidizing conditions [4]. Previous studies of
the solubility of soddyite have produced a wide range of
solubility product values. Nguyen et al. [10] and Moll
et al. [11] reported lg Ksp (solubility product) values of
(5.74 ± 0.21) and (6.15 ± 0.53), respectively, for batch dissolution experiments. Perez et al. [12] reported a wide range
of values for the lg Ksp, with values from 2.58 to 6.36, for
experiments conducted in the presence of dissolved Na
and Si. Despite three separate studies measuring the solubility of soddyite, there is a lack of an accepted value for
the solubility product. Part of the problem stems from deficiencies in the previous studies. Reliable thermodynamic
parameters can be derived from solubility studies only
when the following conditions are met: (1) the mineral of
interest is stable under the experimental conditions, (2) a
true equilibrium state is attained during the experiments,
and (3) the pH and metal concentrations present in the
equilibrium state are measured. The first condition should
be established by characterizing the mineral phase both
569
before and after the solubility experiment using X-ray diffractometry (XRD) and/or other spectrometry approaches.
The attainment of equilibrium can only be demonstrated
via reversibility experiments; that is, approaching the equilibrium state from supersaturated as well as from under
saturated conditions with respect to the dissolved species
of interest. All previous studies of the solubility of soddyite
have neglected to demonstrate at least one of the above
three conditions.
The Gibbs free energy of formation of a phase, coupled
with the enthalpy of formation of that phase, can be used
to calculate the standard entropy of formation. With these
thermodynamic parameters, the stability and solubility of
the phase can be calculated as a function of temperature.
High-temperature oxide-melt solution calorimetry has been
applied successfully in order to determine the standard
enthalpies of formation of some uranyl minerals [13–15].
In this study, we synthesized soddyite using mild hydrothermal conditions and thoroughly characterized the mineral using X-ray diffractometry (XRD), Fourier
transform infrared (FT-IR) spectroscopy, thermogravimetry, and chemical analysis. Using batch experiments, we
measured the solubility of soddyite from undersaturation
and supersaturation between pH 3.0 and 3.6, and we characterized the post-experimental mineral residue. High-temperature oxide-melt solution calorimetry was used to
obtain the heat of drop solution of soddyite in molten
sodium molybdate. Although the early studies of uranyl
minerals by high-temperature calorimetry were successful,
the same method cannot be applied to uranyl silicates
because of the lack of solubility of SiO2 in sodium molybdate. Thus, a slightly modified calorimetric method, in
which the solvent is saturated with SiO2 prior to the experiment, was developed. Using the calorimetric and solubility
measurements, we calculate the T = 298 K standard-state
Gibbs free energy, enthalpy, and entropy of formation
from the elements of soddyite.
2. Experimental materials and methods
2.1. Syntheses
Soddyite for the solubility experiments was synthesized
by placing 0.42 g UO2(CH3COO)2(H2O)2 (prepared from
heating 0.5 g UO3 (Strem Chemicals) with 600 cm3 glacial acetic acid (Fisher ACS grade)), 0.25 cm3 of 1 M
Na2SiO2(H2O)5 (Fisher Chemicals ACS grade), and
4.75 cm3 of 18 MX H2O in a 23 cm3 Teflon-lined Parr reaction vessel. This method yielded a run product that
included both soddyite and amorphous silica, so a second
approach was used to produce solids for the drop solution
calorimetry in order to eliminate as much amorphous silica
from the run product as possible. The calorimetry solids
were synthesized by placing 0.21 g UO2(CH3COO)2(H2O)2,
0.25 cm3 of 1 M Na2SiO2(H2O)5, and 4.75 cm3 of 18 MX
H2O in a 23 cm3 Teflon-lined Parr reaction vessel. For both
types of syntheses, the reactants were heated to T = 389 K
570
D. Gorman-Lewis et al. / J. Chem. Thermodynamics 39 (2007) 568–575
for 7 days. The products were recovered by filtration and
rinsed 4 times with boiling 18 MX H2O. The syntheses were
repeated multiple times to produce enough powder for the
experiments. Soddyite containing amorphous silica was
used to determine the final state of soddyite in the calorimetric solvent sodium molybdate. The pure soddyite sample was used for calorimetric measurements without
additional treatment.
Cristobalite used in high-temperature calorimetry was
synthesized by heating quartz (Fluka, 0.999 mass fraction
purity of metal basis) at T = 1773 K for 60 h. XRD showed
complete conversion to cristobalite.
2.2. Characterization
The X-ray powder diffraction patterns were collected
for each batch of soddyite by finely grinding 5 mg of
powder and depositing the paste onto a zero-background
orientated quartz slide. Diffraction patters were collected
using a Bruker D8 Discovery diffractometer equipped
with Cu Ka radiation and a solid-state detector. All
powder diffraction patterns exhibited sharp profiles and
no extraneous peaks, and they confirmed the presence
of soddyite as the only crystalline phase in the syntheses.
FT-IR analyses were performed using an IlluminatIR
FT-IR micro-spectrometer with a diamond total attenuated reflectance (ATR) objective in an open atmosphere,
background spectra taken prior to measurement, over a
frequency range of (400 to 4000) cm1 using (5 to
10) mg of powder placed on a glass slide. The IR spectra
were in good agreement with previously published spectra
for soddyite by Cjeka and Urbanec [16] and amorphous
silica (determined from FT-IR analysis of silica gel).
Thermogravimetry (t.g.a.) and differential scanning calorimetry (d.s.c.) analyses were carried out by heating the
powder to T = 983 K at 10 K Æ min1 under flowing argon
at 50 cm3 Æ min1. Two consecutive runs were performed
with the sample mass between 12 mg and 14 mg. Water
content was calculated from the weight loss. Soddyite
dehydrates at approximately T = 673 K. The water content calculated from the weight loss upon heating was
(5.52 ± 0.15) wt%, which represents (2.05 ± 0.06) H2O
molecules per mole of soddyite, consistent within experimental error with the ideal stoichiometry for soddyite of
(UO2)2SiO4 Æ 2H2O. The molecular weight corresponding
to the ideal stoichiometry is used for further calculations.
Chemical analyses were performed by dissolving (50 to
100) mg of powder in 17 cm3 of 2 M HCl and analyzing
for U and Si concentrations by inductively coupled
plasma-optical emission spectrometry (ICP-OES) with an
analytical uncertainty of 3.5%. The chemical analysis of
the soddyite that was synthesized for the solubility experiments indicated a slight excess (7.1%) of Si that we
attribute to the presence of an amorphous silica phase.
The parallel ICP-OES analysis of the soddyite that was
synthesized for the drop solution calorimetry did not exhibit excess Si.
2.3. Solubility experiments
All solubility measurements were batch experiments
conducted in Teflon reaction vessels. An Orion combination pH electrode that was calibrated daily with 4 NIST
standards was used for pH measurements. Although the
ionic strength of the buffers was not perfectly matched
to the ionic strength of the experiments the additional
error associated with pH measurements as a result of
the difference in ionic strength and liquid-junction error
is likely much smaller than experimental error which
dominates the stated uncertainties for the calculated thermodynamic parameters. All the experiments were conducted at pH values less than 3.9 in order to increase
dissolution reaction kinetics. The low pH conditions also
enabled us to operate under conditions where UO2þ
2 is the
dominant uranium species in solution [17,18], thereby
eliminating the complexities in aqueous uranium speciation that occur under higher pH conditions. In order to
further decrease the time necessary to reach equilibrium,
we started the experiments in solutions containing dissolved U and Si. The initial experimental solutions were
prepared by taking aliquots of silica atomic absorption
spectroscopy standard and uranyl nitrate stock solution,
prepared from adding uranyl nitrate hexahydrate to
18 MX Æ cm3 H2O, and diluting to the desired concentrations. Approximately 350 mg of soddyite were added
to 7 cm3 of the prepared U and Si starting solution.
The pH of the batch experiments was adjusted using minute quantities of 15 M HNO3 (0.999 mass fraction purity
of metal basis), and was continuously monitored throughout each experiment. Reaction vessels were sealed and
agitated slowly end over end. Aliquots of the experimental
solution were taken at various intervals, filtered with
0.1 lm nylon filters, and diluted for ICP-OES analysis
of U and Si concentrations with an analytical uncertainty
of 3.5%. In order to verify the composition of the mineral
residue after 7 days of reaction, and at the end of the
experiment, 10 mg of residue was taken for XRD and
FT-IR analyses. Control experiments, performed without
mineral phases present, indicated that the loss of U and
Si due to adsorption or precipitation reactions under the
experimental conditions was negligible. Initial experimental results indicated that soddyite was stable under the
experimental conditions, but that amorphous silica was
also forming in the reactors. Consequently, we prepared
subsequent experiments as described above and added
(200 to 300) mg of amorphous silica gel in order to
increase the kinetics of the amorphous silica precipitation
reaction. The co-existence of two phases (soddyite and
amorphous silica) in the experimental systems is consistent with the Gibbs phase rule for a two-component system such as these. As long as both phases are stable under
the experimental conditions and we measure all dissolved
element concentrations, the experimental measurements
rigorously constrain the value of the solubility products
for each phase present.
D. Gorman-Lewis et al. / J. Chem. Thermodynamics 39 (2007) 568–575
571
TABLE 1
Calorimetric cycle for calculation of enthalpy of formation of soddyite
Reaction
Heat effect (values are in table 2)
(UO2)2(SiO4) Æ 2H2Oxl,298 K = 2UO3sln,976 K + SiO2xl,976 K + 2H2Og,976 K
UO3xl,298 K = UO3sln,976 K
SiO2cristobalite,298 K = SiO2xl,976 K
H2Ol,298 K = H2Og,976 K
2UO3xl,298 K + SiO2xl,298 K + 2H2Ol,298 K = (UO2)2(SiO4) Æ 2H2Oxl,298 K
DH1 = DHds(soddyite)
DH2 = DHds(UO3)
DH3 = DHds(cristobalite)
DH4 = DHds(H2O)
DH 6 ¼ DH f;oxðsoddyiteÞ ¼ DH 1 þ 2DH 2 þ DH 3 þ 2DH 4
Uxl,298 K + 3/2O2g,298 K = UO3xl,298 K
Sixl,298 K + O2g,298 K = SiO2cristobalite,298 K
H2g,298 K + O2g,298 K = H2Ol,298 K
2Uxl,298 K + Sixl,298 K + 2H2g,298 K + 5O2g,298 K = (UO2)2(SiO4) Æ 2H2Oxl,298 K
DH 7 ¼ DH fðUO3 Þ
DH 8 ¼ DH fðSiO2 Þ
DH 9 ¼ DH fðH2 OÞ
DH 10 ¼ DH fðsoddyiteÞ ¼ DH 6 þ 2DH 7 þ DH 8 þ 2DH 9
xl, solid material; g, gaseous; sln ,solution; and l, liquid.
80
70
-1
The calorimetry of soddyite was performed using a custom-built Tian-Calvet high-temperature micro-calorimeter
[19,20]. Pellets were dropped into a Pt crucible containing
a melt of composition 3Na2O Æ 4MoO3 at T = 976 K. To
provide stirring, prevent local saturation, speed the dissolution, and to maintain an oxidizing atmosphere, oxygen was
flushed over the solvent (30 cm3 Æ min1) and bubbled
through the solvent (3 to 3.5) cm3 Æ min1. To accelerate
precipitation of SiO2 (see discussion below) and to obtain
consistent values of DHds, 50 mg of cristobalite were added
to the solvent prior to dropping the samples. The measured
enthalpies of drop solution, DHds, were used to calculate
enthalpies of formation using the calorimetric cycle
depicted in table 1. References phases were cristobalite
(dropped into sodium molybdate at the same conditions
as described above for soddyite), H2O [21] and UO3 [30].
We have observed previously that silica does not dissolve readily in sodium molybdate, and that the oxidative
dissolution of silicon nitride precipitates as cristobalite.
To further constrain the final state of SiO2 in sodium
molybdate (necessary for writing a well-defined thermodynamic cycle for the heat of formation of soddyite), a series
of experiments was performed. In these experiments, amorphous silica (SiO2 Æ xH2O with x = 1.2 to 1.6, Alfa Aesar,
0.995 mass fraction purity on metals basis), quartz, cristobalite (synthesized as described above) and soddyite
(containing 7 wt% amorphous SiO2) were dissolved into
molten sodium molybdate. The solvent was then quenched
and dissolved in an abundance of water. The collected precipitates were then checked by XRD to determine the
phase(s) present.
and cristobalite as a minor admixture, indicating a slow
transition of quartz to cristobalite during the experiment.
Measured values of DHds for cristobalite (see figure 1)
and quartz gradually decreased, indicating that the apparent value of DHds strongly depends on SiO2 concentration
in the solvent and that the solvent is saturated when
approximately (25 to 30) mg of SiO2 are dropped. The heat
effect after the solvent was saturated showed values close to
the heat content of SiO2, indicating that no silica dissolved.
Calorimetry of cristobalite in sodium molybdate that was
initially saturated with amorphous silica (500 mg in
20.0 g of sodium molybdate) exhibited nearly constant values with an average for six drops of (40.7 ± 0.6) kJ Æ mol1,
which is close to the heat content of cristobalite at
T = 976 K (43.0 kJ Æ mol1, [21]).
The XRD analysis of the precipitate after recovery of
soddyite dissolved in sodium molybdate soddyite showed
that SiO2 from soddyite also precipitates as cristobalite,
indicating that the final state of SiO2 from soddyite dissolution is cristobalite. Thus, cristobalite was used as the reference phase in the calorimetric cycle (table 1) to calculate
the enthalpy of formation of soddyite from elements, DH f ,
ΔH soln / (kJ.mol )
2.4. High-temperature oxide-melt solution calorimetry
60
50
3. Results and discussion
40
3.1. High-temperature oxide-melt solution calorimetry
30
Recovery of a silicate-rich precipitate from the sodium
molybdate indicated the presence of cristobalite under
experimental conditions, demonstrating the instability of
amorphous silica under these conditions. After quartz reaction, the run sediment contained quartz as a major phase
0
10
20
30
40
50
m (SiO2 ) / mg
FIGURE 1. Plot of enthalpy of solution for cristobalite against the mass
of SiO2 in the solvent. At approximately (25 to 30) mg the value of drop
solution reaches the value of heat content of cristobalite (43 kJ Æ mol1
[21]).
572
D. Gorman-Lewis et al. / J. Chem. Thermodynamics 39 (2007) 568–575
TABLE 2
Calorimetric data at T = 976 K in sodium molybdate. Enthalpies of
formation of materials and reference phases
Material
DHds/(kJ Æ mol1)
DH f =ðkJ mol1 Þ
UO3
Water, H2O
Cristobalite,
SiO2 (dropped in solvent
preliminary saturated
with SiO2)
Soddyite, (UO2)2(SiO4) Æ 2H2O
9.49 ± 2.3b
69.0a
40.7 ± 0.6 (6)
Compare: 43.0a
1223.8c
285.8 ± 0.1a
908.4 ± 2.1a
b
c
lg M
-2.00
315.4 ± 3.6 (11)
From oxides:
117.8 ± 4.3
From elements:
4045.4 ± 4.9
and oxides, DH f ox . We used the enthalpy of drop solution
of cristobalite obtained from our work (40.7 ±
0.6 kJ Æ mol1) in these calculations.
The calculated enthalpy of formation from the binary
oxides is (117.8 ± 4.3) kJ Æ mol1 (table 2). Soddyite is
more stable than the mechanical mixture of its constituent
oxides by 117.8 kJ Æ mol1. Previously published values for
the enthalpies of formation from the binary oxides for
rutherfordine and metaschoepite are 99.1 kJ Æ mol1 and
4.4 kJ Æ mol1 [13,14], respectively. Soddyite is more stable
than rutherfordine and metaschoepite with respect to the
enthalpy of formation from the binary oxides. The standard-state enthalpy of formation from the elements of
soddyite is (4045.4 ± 4.9) kJ Æ mol1.
3.2. Solubility experiments
Equilibrium was achieved within 20 days in all experiments as shown in figure 2. Our initial experiment (figure
2a, diamond symbols) contained only soddyite added to
a solution containing aqueous U and Si. The equilibrium
Si concentration was 102.63±0.08, suggesting that Si was
buffered in solution by amorphous silica, which has
-1.00
-1.50
-2.00
lg M
-2.50
-3.00
-3.50
-4.00
-4.50
-5.00
5
10
-2.50
-3.00
Reference [21].
Reference [31].
Reference [32].
0
-1.50
15
20
25
30
35
40
t/days
FIGURE 2a. Plot of logarithm of solubility of soddyite against time for
experiments at pH 3.67 from supersaturation (filled diamonds U and open
diamonds Si) and undersaturation (filled triangles U and open triangles
Si). Silica gel was not added to the experiment.
-3.50
0
10
20
30
40
50
t/days
FIGURE 2b. Plot of logarithm of solubility of soddyite against time for
experiments at pH 3.40 from supersaturation (filled diamonds U and open
diamonds Si) and undersaturation (filled triangles U and open triangles
Si). Silica gel was added to the experiment.
0.00
-0.50
-1.00
-1.50
-2.00
lg M
a
-1.00
-2.50
-3.00
-3.50
-4.00
-4.50
-5.00
0
10
20
30
40
50
t/days
FIGURE 2c. Plot of logarithm of solubility of soddyite against time for
experiments at pH 3.21 (days 19 to 25) and 3.01 (days 26 and beyond)
from supersaturation (filled diamonds U and open diamonds Si) and
undersaturation (filled triangles U and open triangles Si). Silica gel was
added to the experiment.
reported solubility values varying from 102.38 to 102.71
molal [22,23]. Subsequent XRD analysis of the mineral residue from this initial experiment indicated that soddyite
was the only crystalline phase present. However, FT-IR
results demonstrated the presence of amorphous silica. In
light of these results, we chose to add silica gel, in addition
to aqueous Si, to all subsequent experiments to ensure that
the amorphous silica precipitation/dissolution reaction
reached equilibrium within 20 days. Figure 2 illustrates
that the Si concentrations in all subsequent experiments
were in the range reported for the solubility of amorphous
silica. As the pH of the experiments decreased, the U concentrations in solution increased and the Si concentrations
remained constant at a value within the range of reported
amorphous silica solubility values. The XRD and FT-IR
analyses of all subsequent experimental mineral residues
verified that soddyite was the only crystalline phase present
and that amorphous silica remained present and stable as
well.
We based our solubility calculations on the following
stoichiometry for the soddyite dissolution reaction:
D. Gorman-Lewis et al. / J. Chem. Thermodynamics 39 (2007) 568–575
4Hþ þ ðUO2 Þ2 SiO4 ðH2 OÞ2ðsoddyiteÞ ¼
2UO2þ
2 þ SiO2ðaqÞ þ 4H2 O
TABLE 3
Solubility data used for Ksp calculations
ð1Þ
For each solubility measurement on the equilibrium concentration plateau (compiled in table 3), we calculated
the ionic strength of the solution from the concentration
of U and Si, the pH measurement for each sample, and
the known amount of acid added for pH adjustments.
We used the extended Debye–Hückel equation to calculate
the activity coefficients, ci, for each experimental condition:
lg ci ¼
Az2i I 1=2
þ bI;
1 þ aBI 1=2
ð2Þ
where I and zi represent the ionic strength and ionic charge,
respectively, A and B are constants with values of 0.5105
and 0.3285, respectively, and a and b are values for RbNO3
from Helgeson et al. [24] of 5.22 and 0.062, respectively.
Parameters a and b take unique values for a particular electrolyte. Because we did not buffer ionic strength in these
experiments with such an electrolyte, and because values
of a and b have not been determined for uranyl-dominated
systems, RbNO3 was chosen as the most reasonable
approximation to the experimental solutions, based on cation size, of those for which extended Debye–Hückel
parameters are calculated [24]. The standard-states employed in this study for solid phases and for H2O are the
pure mineral or fluid, respectively. The standard-state for
aqueous species is defined as a hypothetical one molal solution whose behavior is that of infinite H2O dilution. Molal
activity coefficients of neutral aqueous species are assumed
to be unity. Using these standard-states, and assuming that
the solid phase is pure and that the activity of water is unity
under the experimental conditions, the solubility product
for each data point was calculated based on the following
mass action equation:
K sp ¼
a2UO2þ aSiO2ðaqÞ
2
a4Hþ
:
573
ð3Þ
When calculating the solubility product, the aqueous complexation reactions listed in table 4 were taken into consideration in order to calculate the activity of the aqueous
uranyl cation under each experimental condition from
our measurement of total aqueous uranium concentration.
The calculated solubility product, averaged for all of the
equilibrium measurements (table 3), with its 1r error is
(6.43 + 0.20/0.37). Our solubility product is within error
of some of the previously published values; however, our
study is the first to rigorously demonstrate attainment of
equilibrium from both supersaturation and undersaturation and to measure equilibrium pH and fully characterize
the final run product identification. With our calculated
solubility product value, in conjunction with the aqueous
complexation reactions and K values listed in table 4, we
extrapolate our results to calculate uranium concentrations
in equilibrium with (soddyite + amorphous silica) at higher
pH values of environmental interest (figure 3). Figure 3 de-
lg U/M
lg Si/M
lg NO
3 =M
pH
Days
1.41
1.41
1.39
1.40
1.40
1.22
1.20
1.21
1.19
1.18
1.18
1.19
1.50
1.50
1.49
1.49
1.45
1.28
1.27
1.28
1.29
1.26
1.20
1.27
2.18
2.20
2.17
2.19
2.20
2.19
2.21
2.20
2.10
2.09
2.10
2.08
2.14
2.07
2.10
2.11
2.11
2.12
2.13
2.44
2.43
2.45
2.48
2.60
2.60
2.60
2.62
2.61
2.62
2.94
2.61
2.58
2.88
2.93
2.61
2.70
2.66
2.59
2.50
2.44
2.50
2.56
2.57
2.56
2.57
2.57
2.45
2.53
2.54
2.54
2.52
2.52
2.54
2.55
2.56
2.55
2.53
2.55
2.42
2.53
2.54
2.55
2.53
2.48
2.52
2.61
2.62
2.62
2.60
2.61
2.61
2.62
2.60
2.48
2.53
2.59
2.61
2.67
2.58
2.62
2.61
2.61
2.61
2.59
2.48
2.46
2.51
2.52
2.52
2.52
2.50
2.54
2.69
2.68
2.67
2.64
2.64
2.68
2.62
2.63
2.64
2.59
2.58
2.57
2.56
2.58
2.46
2.46
2.46
2.46
2.46
2.46
2.46
2.46
2.46
2.46
2.46
2.46
1.97
1.97
1.97
1.97
1.97
1.97
1.97
1.97
1.97
1.97
1.97
1.97
2.05
2.05
2.05
2.05
2.05
2.05
2.05
2.05
1.84
1.84
1.84
1.84
1.84
1.84
1.84
1.84
1.84
1.84
1.84
2.45
2.45
2.45
2.45
2.45
2.45
2.45
2.45
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
3.12
3.15
3.24
3.21
3.23
2.92
2.98
3.03
3.02
3.09
3.14
3.12
3.19
3.19
3.25
3.25
3.25
2.97
3.03
3.04
3.06
3.11
3.14
3.17
3.44
3.41
3.39
3.43
3.43
3.44
3.41
3.43
3.34
3.38
3.40
3.41
3.42
3.40
3.37
3.38
3.40
3.34
3.40
3.62
3.63
3.58
3.57
3.62
3.62
3.63
3.64
3.77
3.75
3.82
3.67
3.68
3.77
3.72
3.68
3.68
3.60
3.63
3.66
3.67
3.67
20
21
22
25
24
26
31
33
38
40
43
44
20
21
22
25
24
26
31
33
38
40
43
45
9
18
22
30
32
35
38
45
1
3
8
15
18
22
30
32
35
38
45
20
21
26
27
31
38
51
73
6
7
10
11
12
14
15
16
17
18
25
32
33
34
picts classical solubility behavior as a function of pH, with
uranium concentrations reaching a minimum of approximately 106 molal between pH 6 and 7. Calculated uranium
574
D. Gorman-Lewis et al. / J. Chem. Thermodynamics 39 (2007) 568–575
TABLE 4
Aqueous phase U(VI) reactions considered in the calculations in this work
with PCO21/4 32 Pa
lg K
I = 0.0, T = 298 K
þ
þ
UO2þ
2 þ H2 O ¼ UO2 OH þ H
0
þ
2H
O
¼
UO
ðOHÞ
þ
2Hþ
UO2þ
2
2
2
2
þ
UO2þ
2 þ 3H2 O ¼ UO2 ðOHÞ3 þ 3H
2þ
2UO2þ
þ
2H
O
¼
ðUO
Þ
ðOHÞ
þ
2Hþ
2
2 2
2
2
þ
2þ
3UO2 þ 5H2 O ¼ ðUO2 Þ3 ðOHÞ5 þ 5Hþ
þ
3UO2þ
2 þ 7H2 O ¼ ðUO2 Þ3 ðOHÞ7 þ 7H
þ
2þ
4UO2 þ 7H2 O ¼ ðUO2 Þ4 ðOHÞ7 þ 7Hþ
2
0
UO2þ
2 þ CO3 ¼ UO2 CO3
2þ
2
UO2 þ 2CO3 ¼ UO2 ðCO3 Þ2
2
4
2
UO2þ
2 þ 3CO3 ¼ UO2 ðCO3 Þ3
2þ
2
2UO2 þ CO3 þ 3OH ¼ ðUO2 Þ2 ðCO3 ÞðOHÞ
3
þ
H4 SiO4ðaqÞ ¼ H3 SiO
4 þH
þ
H4 SiO4ðaqÞ ¼ H2 SiO2
4 þ 2H
þ
þ
UO2þ
þ
H
SiO
¼
UO
H
4
2 3 SiO4 þ H
4ðaqÞ
2
5.20
12.0a
19.2
5.62b
15.55
31.0
21.9
9.70
17.0
23.63
40.82c
9.83d
23.0d
2.5e
kJ mol1 Þ were obtained from Wagman et al. [28] and
Johnson et al. [29], and DGr for each data point was calculated from the corresponding Ksp value with the following
equation:
DGr ¼ 2:303RT lg K sp ;
where R is the universal gas constant and T is absolute temperature. The average standard-state Gibbs free energy of
formation with its 2r error is (3652.2 ± 4.2) kJ Æ mol1.
Chen et al. [30] predicted the standard-state Gibbs free
energy of formation of soddyite from an empirical method
that derives the molar contributions of the structural components to DGf and DH f from thermodynamic data of
phases for which the crystal structures are known. Their
value, 3653.0 kJ Æ mol1, agrees with our value based on
our solubility measurements.
All other stability constants from reference [36].
a
Reference [17].
b
Reference [33].
c
Reference [18].
d
Reference [34].
e
Reference [35].
3.3. Entropy calculations
The standard-state entropy of formation of soddyite,
DS f , can be calculated from the standard-state Gibbs free
energy and enthalpy of formation:
DGf ¼ DH f T DS f ;
concentrations would be correspondingly higher throughout the pH range if we considered the aqueous phase to
equilibrate with (soddyite + quartz) due to the lower activities of silica in equilibrium with quartz. These calculations
demonstrate that soddyite is less soluble than metaschoepite
and rutherfordine in the circumneutral pH range, but
considerably more soluble than uranyl phosphate phases
[25–27].
The standard-state Gibbs free energy of formation of
soddyite was calculated for each equilibrium measurement
from equation the following equation:
DGfðsoddyiteÞ ¼ 2 DGfðUO2þ Þ þ DGfðSiO2ðaqÞ Þ þ 4 DGfðH2 OÞ DGr :
2
ð4Þ
Literature values
DGfðSiO2ðaqÞ Þ ð833:411
for DGfðUO2þ Þ ð953:5 kJ mol1 Þ,
2
kJ mol1 Þ, and DGfðH2 OÞ ð237:129
-2
lg U/M
-3
-4
-5
-6
-7
3
4
5
6
ð5Þ
7
8
9
pH
FIGURE 3. Plot of logarithm of solubility against pH for (soddyite + amorphous silica), determined with the Ksp value from this study and
the aqueous reactions listed in table 3.
DGf
ð6Þ
where
is the standard-state Gibbs free energy of formation of soddyite, as determined from the solubility measurements, and DH f is the standard-state enthalpy of
formation of soddyite, as determined from the calorimetry
measurements. The calculated standard-state entropy of
formation of soddyite, with propagated 2r uncertainty, is
(1318.7 ± 21.7) J Æ mol1 Æ K1.
Alteration of spent nuclear fuel in a geological repository under oxidizing conditions is expected to result in
the formation of a variety of uranyl minerals, and the solubilities of these minerals will impact the release of uranium and other radionuclides that they incorporate.
Therefore, it is crucial to augment the sparse thermodynamic dataset that exists for uranyl minerals in order to
predict repository performance. Standard-state Gibbs free
energies, enthalpies, and entropies of formation for environmentally important uranyl minerals can be used to estimate mineral stabilities and solubilities under the elevated
temperatures of a repository setting. In this study, we calculated the standard-state enthalpy of formation of soddyite from drop solution calorimetric measurements. We
measured the solubility of soddyite as well, using solubility
reversals to rigorously demonstrate that equilibrium was
attained during the experiments. The solubility measurements were used to calculate the standard-state Gibbs free
energy of formation of soddyite, and together with the
enthalpy value, we calculated the standard-state entropy
of formation of soddyite. This study demonstrates the
power of combining solubility and calorimetry measurements to produce reliable and internally consistent thermodynamic data for uranyl minerals. The results of this and
future similar studies of other environmentally relevant
uranyl phases will enable predictions of uranyl mineral
D. Gorman-Lewis et al. / J. Chem. Thermodynamics 39 (2007) 568–575
stabilities and solubilities under realistic repository
conditions.
Acknowledgements
Funding for this research was provided by a US Department of Energy, Office of Science and Technology and
International (OST&I) grant under the Source Term
Thrust program. Journal reviews and the comments made
by the Editor were particularly helpful in improving the
presentation of this work.
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JCT 06-203