**UNITED STATES DEPARTMENT OF THE INTERIOR**

**U.S. GEOLOGICAL SURVEY**

Thermodynamic Data for Modeling Acid Mine Drainage Problems:

Compilation and Estimation of Data for Selected Soluble Iron-Sulfate
Minerals[^1]

by

Bruce S. Hemingway[^2], Robert R. Seal, II[^3], and I-Ming Chou^3^

Open-File Report 02-161

**Abstract**

Enthalpy of formation, Gibbs energy of formation, and entropy values
have been compiled from the literature for the hydrated ferrous sulfate
minerals melanterite, rozenite, and szomolnokite, and a variety of other
hydrated sulfate compounds. On the basis of this compilation, it appears
that there is no evidence for an excess enthalpy of mixing for
sulfate-H~2~O systems, except for the first H~2~O molecule of
crystallization. The enthalpy and Gibbs energy of formation of each
H~2~O molecule of crystallization, except the first, in the iron(II)
sulfate - H~2~O system is ‑295.15 and -238.0 kJ·mol^-1^, respectively.
The absence of an excess enthalpy of mixing is used as the basis for
estimating thermodynamic values for a variety of ferrous, ferric, and
mixed-valence sulfate salts of relevance to acid-mine drainage systems.

**Introduction**

Remediation of problems that arise from release of the components of
soluble minerals to ground and surface waters associated with active and
abandoned mines will require geochemical modeling of the rock-water
interactions. Such models will depend upon an extensive thermodynamic
data base. However, thermodynamic data necessary for such modeling
calculations are limited. This report is a summary of the procedures
used to develop a database for hydrous iron sulfate compounds during the
mid-1990s at the U.S. Geological Survey.

The soluble iron-sulfate minerals are an important group of phases with
regard to acid-mine drainage. These minerals include melanterite
FeSO~4~·7H~2~O, rozenite FeSO~4~·4H~2~O, szomolnokite FeSO~4~·H~2~O,
copiapite Fe^2+^Fe^3+^~4~(SO~4~)~6~(OH)~2~·20H~2~O, römerite
Fe^2+^Fe^3+^~2~(SO~4~)~4~·14H~2~O, coquimbite
Fe^3+^~2~(SO~4~)~3~·9H~2~O, kornelite Fe^3+^~2~(SO~4~)~3~·7H~2~O,
rhomboclase (H~3~O)Fe^3+^(SO~4~)~2~·3H~2~O, voltaite
K~2~Fe^2+^~5~Fe^3+^~4~(SO~4~)~12~·18H~2~O, and halotrichite-bilinite
Fe^2+^(Al,Fe^3+^)~2~(SO~4~)~4~·22H~2~O, among others. The compounds have
been shown to play important roles in controlling the extreme
mine-drainage compositions from Iron Mountain mine, California, which
reaches pH values less than zero and total iron concentrations over 100
grams per liter (Nordstrom and Alpers, 1999). They are also found in
numerous other acid-mine drainage settings (Alpers and others, 1994;
Jambor and others, 2000).

Despite the importance of the phases, much of the thermodynamic data
necessary for such modeling calculations are not available, or are of
questionable quality. For example, considerable uncertainty exists in
the location of the reaction:

FeSO~4~·4H~2~O + 3H~2~O~(g)~ = FeSO~4~·7H~2~O (1),

(where "g" refers to gas) in terms of temperature and relative humidity
(RH). Published estimates of the relative humidity associated with this
reaction at 25 °C range from a low of \~15 % (Pribylov, 1969) to a high
of \~95 % (DeKock, 1982) with a distinct clustering around 60 to 80 %
(Fig. 1). Results of the ongoing investigations studying dehydration
equilibria between melanterite and rozenite of Chou and others (1999;
2002) are similar to the results of Malinin and others (1979) and yield
an equilibrium relative humidity of approximately 63 %.

This paper reviews the experimental data for soluble iron- and other
sulfate phases and uses these data to construct models for estimating
thermodynamic data at 298.15 K and 1 bar for phases for which no
experimental data exist. Even though our estimations of thermodynamic
properties will greatly enhance the ability to model the geochemistry of
acid-mine drainage, they only serve as interim solutions to our
inadequate understanding of these systems. A more rigorous treatment
must await experimental determination of thermodynamic properties.

![](media/image1.wmf){width="4.284722222222222in"
height="3.283333333333333in"}

> Figure 1. Comparison of estimates for the reaction of rozenite + H~2~O
> to melanterite as a function of temperature and relative humidity.
> Open squares are results of Malinin and others (1979); filled triangle
> is result of Pribylov (1969). Sources of curves are: P, Pribylov
> (1969); PD, Parkinson and Day (1981); MDA, Malinin and others (1979);
> HSC, this study; ES, Ehlers and Stiles (1965); D, DeKock (1982).

**Ferrous sulfates and their hydrates**

Five different ferrous-sulfate hydrate minerals have been identified and
described in the literature. They are, in order of increasing hydration:
szomolnokite FeSO~4~·H~2~O, rozenite FeSO~4~·4H~2~O, siderotil
FeSO~4~·5H~2~O, ferrohexahydrite FeSO~4~·6H~2~O, and melanterite
FeSO~4~·7H~2~O. In nature, melanterite and rozenite are the most
commonly reported phases, followed by szomolnokite and siderotil (Alpers
and others, 1994). Ferrohexahydrite is extremely rare (Fleischer, 1963).
Laboratory studies of evaporating waters and field observations have
defined a general crystallization sequence of these minerals beginning
with melanterite, followed by rozenite, which in turn is followed by
szomolnokite; following szomolnokite are mixed valence salts followed by
ferric salts (Buurman, 1975; Nordstrom and Alpers, 1999; Jambor and
others, 2000). Notably absent from the crystallization sequence are
ferrohexahydrite and siderotil. Jambor and Traill (1963) concluded that
siderotil was not a stable phase in the binary (FeSO~4~ - H~2~O) system,
and required at least 5 mole % of copper substituting for iron to
stablize it relative to melanterite and rozenite. In addition, Ehlers
and Stiles (1965) were able to reverse the transition from melanterite
to rozenite at near ambient temperatures and relative humidities between
70 and 80 % without the appearance of siderotil and ferrohexahydrite.
Therefore, on the basis of these observations, it would appear that
melanterite, rozenite, and szomolnokite are the stable hydrates in the
binary (FeSO~4~ - H~2~O) system at ambient conditions.

The thermodynamic data available for hydrated ferrous sulfates consist
of enthalpy of formation values for melanterite, szomolnokite (Adami and
Kelley, 1963), and rozenite (determined from the data of Larson and
others, 1968), and entropy values for melanterite (Lyon and Giauque,
1949), rozenite (DeKock, 1982), and szomolnokite (Pribylov, 1969). The
Gibbs energy of formation can be calculated for melanterite, rozenite
and szomolnokite, where corrections have been made to insure internal
consistency of ancillary thermodynamic data.

**Enthalpy of formation (∆~f~H°)**

In the iron(II) system, there appears to be little or no excess enthalpy
of mixing for H~2~O and ferrous sulfate (except for the addition of the
first H~2~O molecule). If the enthalpy of formation of szomolnokite
(FeSO~4~·H~2~O) is subtracted from the equivalent value for melanterite
(FeSO~4~·7H~2~O) and divided by 6, the difference in the number of H~2~O
molecules of hydration, the resulting value of -295.15 kJ·mol^-1^ for
each added H~2~O molecule may be used to estimate the value for the
enthalpy of formation of rozenite (FeSO~4~·4H~2~O). The value of -295.15
kJ·mol^-1^ compares favorably with the value of ‑294.8 kJ·mol^-1^
derived from data compiled for numerous hydrated sulfate salts relative
to monohydrates and the value of -304.2 kJ·mol^-1^ derived from data
compiled for numerous hydrated sulfate salts relative to anhydrous
sulfates, as described below. The thermodynamic data used in these
calculations are from Wagman and others (1982) unless otherwise stated.
The value estimated by the summation of the enthalpy of formation of
szomolnokite and 3 times the value derived above for the contribution of
one H~2~O molecule is --2,129.1 kJ·mol^-1^ compared with the measured
value for rozenite of --2,129.2 kJ·mol^-1^. Using this model, we
estimate the enthalpy of formation of ferrohexahydrite (FeSO~4~·6H~2~O)
and siderotil (FeSO~4~·5H~2~O) as -2,719.3 and -2,424.3 kJ·mol^-1^,
respectively.

Hydrated sulfate minerals of other group VIIIA and adjacent group VIIA,
IB and IIB elements of the Periodic Chart show (1) a similar value to
that derived for the iron-sulfate hydrates for the contribution of H~2~O
to the enthalpy of formation, and (2) support for the model of no excess
enthalpy of mixing associated with hydration for the metal sulfate-
H~2~O system as limited above (Figs. 2 and 3). For cobalt (7 hydrate and
6 hydrate), nickel (7 hydrate and 4 hydrate), manganese (7 hydrate and 4
hydrate), copper (5 hydrate and 1 hydrate), zinc (7 hydrate and 1
hydrate), and cadmium (8/3 hydrate and 1 hydrate) hydrated sulfates, the
estimated contributions for one H~2~O are -296.33, -290.74, ‑293.73,
‑298.45, -295.54, and -293.91 kJ·mol^-1^, respectively. Using these
values, we may estimate the enthalpies of formation of other hydrates of
these cations and compare the estimated and experimental values. For
CoSO~4~·H~2~O, CuSO~4~·3H~2~O, FeSO~4~·4H~2~O, MnSO~4·~·H~2~O,
MnSO~4~·5H~2~O, NiSO~4~·6H~2~O, and ZnSO~4~·6H~2~O, the estimated and
measured values for the enthalpy of formation are summarized in Table 1.
The differences between the estimated and experimental values are all
well within experimental error and thus support this model for the
estimation of enthalpy values.

The finding that there is no excess enthalpy of mixing in the metal
sulfate- H~2~O system is important because many of the phases found in
nature will deviate in H~2~O content from that given for the end-member.
This model justifies calculation of the enthalpy of formation of such
materials with non-integer values for the H~2~O content. In further
support of this hypothesis, we may calculate the enthalpy contribution
of one H~2~O

![](media/image2.wmf){width="4.5680555555555555in"
height="2.8520833333333333in"}

> Figure 2. Deviation of estimated enthalpy of formation values
> (∆~f~H°~est.~) from measured values (∆~f~H°~meas.~) for metal-sulfate
> salts relative to the value for XSO~4~·H~2~O. Calculations were made
> assuming an enthalpy contribution for each H~2~O molecule of -294.8
> kJ·mol^‑1^. Note that data for Be and Mg salts (group IIA) were not
> used to generate the values for the enthalpy contribution of
> additional H~2~O molecules because of greater structural differences
> of these compounds relative to the groups VIIA, VIIIA, IB, and IIB
> salts (see text).

![](media/image3.wmf){width="4.3375in" height="2.625in"}

> Figure 3. Deviation of estimated enthalpy of formation values
> (∆~f~H°~est.~) from measured values (∆~f~H°~meas.~) for metal-sulfate
> salts relative to the value for XSO~4~. Calculations were made
> assuming an enthalpy contribution for each H~2~O molecule of ‑304.2
> kJ·mol^‑1^. The distinct slope in the data is due to the difference
> between the enthalpy contribution of the first H~2~O molecule of
> crystallization relative to that of subsequent H~2~O molecules of
> crystallization (see text). Note that data for Be and Mg salts (group
> IIA) were not used to generate the values for the enthalpy
> contribution of additional H~2~O molecules because of greater
> structural differences of these compounds relative to the groups VIIA,
> VIIIA, IB, and IIB salts (see text).
>
> Table 1. Comparison of measured and estimated enthalpy of formation
> values for selected metal sulfates relative to the elements and ideal
> O~2~, S~2~, and H~2~ gases at 298.15 K and 1 bar.

+-----------------------+-----------------------+-----------------------+
| ##### Formula         | ##### Enthalpy of fo  |                       |
|                       | rmation from elements |                       |
+-----------------------+-----------------------+-----------------------+
| #####                 | ##### kJ•mol^-1^      |                       |
+-----------------------+-----------------------+-----------------------+
| #####                 | ##### Measured\*      | ##### Estimated       |
+-----------------------+-----------------------+-----------------------+
| ##### FeSO~4~·4H~2~O  | ##### -2,129.2        | ##### -2,129.1        |
+-----------------------+-----------------------+-----------------------+
| ##### CoSO~4~·H~2~O   | ##### -1,199.6        | ##### -1,201.9        |
+-----------------------+-----------------------+-----------------------+
| ##### NiSO~4~·6H~2~O  | ##### -2,682.8        | ##### -2,685.6        |
+-----------------------+-----------------------+-----------------------+
| ##### MnSO~4~·H~2~O   | ##### -1,376.5        | ##### -1,376.9        |
+-----------------------+-----------------------+-----------------------+
| ##### MnSO~4~·5H~2~O  | ##### -2,553.1        | ##### -2,551.8        |
+-----------------------+-----------------------+-----------------------+
| ##### CuSO~4~·3H~2~O  | ##### -1,684.3        | ##### -1,682.7        |
+-----------------------+-----------------------+-----------------------+
| ##### ZnSO~4~·6H~2~O  | ##### -2,777.5        | ##### -2,782.2        |
+-----------------------+-----------------------+-----------------------+

> \*All data are from Wagman and others (1982), except for the datum for
> CoSO~4~·H~2~O, which is from Goldberg and others (1966), and the datum
> for FeSO~4~·4H~2~O, which is from Larson and others (1968).

molecule from the difference between the enthalpies of formation of
UO~2~SO~4~·3H~2~O and UO~2~SO~4~·1H~2~O, which yields -300.95 kJ·mol^-1^
per H~2~O. We use this value to calculate the enthalpies of formation of
UO~2~SO~4~·3.5H~2~O and UO~2~SO~4~·2.5H~2~O and compare them to the
experimental values given for these phases: -2,906.3 (estimated) and
-2,900.8 (measured), and -2,603.8 (estimated) and -2,607.1 (measured)
kJ·mol^-1^, respectively. Again, the differences between the estimated
and experimental values are within the experimental error.

The enthalpy contribution, except for the first H~2~O molecule, is
different for each chemical system, that is, for Fe versus Mn or Cu. The
differences are small and within the experimental error of such
calculations, which suggests that there will not be large enthalpies of
mixing for the H~2~O component as trace elements substitute for the
end-member cations. The average value for the contribution of one H~2~O
to the enthalpy of formation of the group VIIA, VIIIA, IB, and IIB
hydrated sulfates is -294.8 ± 2.4 kJ·mol^‑1^. For the groups IA, IIA,
IIIA, IVA and VA hydrated sulfates (sulfates of Be, Ca, Mg, La, Zr, and
mixed K-Mg, K-Zn, K-Cu, K-Al, Na-Al, and Na-Zn), the value appears to be
somewhat larger, about -298 to -300 kJ·mol^-1^ probably due to greater
structural differences. There are not sufficient data at this time to
determine the value for the group VIA hydrated sulfates, but data from
(Cr(H~2~O)~6~)~2~(SO~4~)~3~·nH~2~O phases suggest a value close to the
group VIIIA value.

The enthalpy contribution of the first H~2~O molecule also varies with
the cation, but again the calculated values are in agreement within
experimental error. Using data from Fe, Mn, Co, Cu, Cd, and Zn sulfate
and sulfate hydrate, the average enthalpy contribution for the first
H~2~O molecule is -313.8 ± 5.7 kJ·mol^‑1^. This value is more negative
by 19 kJ·mol^-1^ than the average value for additional H~2~O molecules
of hydration. Thus, when considered in terms of hydration from an
anhydrous salt, the average enthalpy contribution per H~2~O molecule is
-304.2 ± 7.9 kJ·mol^‑1^, which has a larger uncertainty than that based
on hydration of a singly hydrated salt (-294.8 ± 2.4 kJ·mol^-1^).
However, for cases where an experimentally determined value for a singly
hydrated salt is lacking, this value may be sufficient as a first-order
approximation.

**Gibbs energy of formation (∆~f~G°)**

The Gibbs energy of formation is the primary thermodynamic quantity
needed for modeling rock-water interactions, when solubility data are
not available. Few values of the Gibbs energy of formation have been
determined for the soluble iron sulfates. The procedure used to estimate
the Gibbs energies listed in Table 2 are discussed below.

The Gibbs energy of formation is related to the enthalpy of formation
through the following thermodynamic equality:

∆~f~G° = ∆~f~H° - T∆~f~S° (2),

where ∆~f~S° is the entropy of formation at temperature T in kelvins. It
has been standard practice to add a constant amount for the entropy
contribution of each H~2~O to the value of the anhydrous metal sulfate
to estimate the entropy of the higher hydrates for which no experimental
data are available (e.g., DeKock, 1982, or Latimer, 1952). This would
suggest that there is little or no excess Gibbs energy of mixing for the
metal sulfate-H~2~O system, except for the first H~2~O molecule.

> Table 2. Thermodynamic properties for selected soluble iron sulfates
> relative to the elements and ideal O~2~, S~2~, and H~2~ gases at
> 298.15 K and 1 bar.

+-----------+-----------------+--------+-------+----------+-----+----+
| ### Phase | ### Formula     | ####   |       |          | ##  |    |
|           |                 |  Forma |       |          | ##  |    |
|           |                 | tion f |       |          | Ref |    |
|           |                 | rom el |       |          | ere |    |
|           |                 | ements |       |          | nce |    |
|           |                 |        |       |          | s\* |    |
+-----------+-----------------+--------+-------+----------+-----+----+
|           |                 | #### E | ###   | #        | ### | ## |
|           |                 | ntropy | # Ent | ### Gibb | # S | ## |
|           |                 |        | halpy | s Energy |     |  H |
|           |                 |        |       |          |     | /G |
+-----------+-----------------+--------+-------+----------+-----+----+
|           |                 | J•m    | kJ•mo | kJ       |     |    |
|           |                 | ol^-1^ | l^-1^ | •mol^-1^ |     |    |
|           |                 | •K^-1^ |       |          |     |    |
+-----------+-----------------+--------+-------+----------+-----+----+
| ####      |                 |        |       |          |     |    |
| ## Aqueou |                 |        |       |          |     |    |
| s species |                 |        |       |          |     |    |
+-----------+-----------------+--------+-------+----------+-----+----+
| Fe^2+^    | Fe^2+^          | 101.6  | -90.0 | -90.5    | 1   | 1  |
+-----------+-----------------+--------+-------+----------+-----+----+
| Fe^3+^    | Fe^3+^          | 278.4  | -49.0 | -16.28   | 1   | 1  |
+-----------+-----------------+--------+-------+----------+-----+----+
| H~2~O     | H~2~O           | 188.8  | -     | -228.6   | 4   | 4  |
|           |                 |        | 241.8 |          |     |    |
+-----------+-----------------+--------+-------+----------+-----+----+
| #####     |                 |        |       |          |     |    |
| # Ferrous |                 |        |       |          |     |    |
|  sulfates |                 |        |       |          |     |    |
+-----------+-----------------+--------+-------+----------+-----+----+
| FeSO~4~   | FeSO~4~         | 120.96 | -     | -828.3   | 9   | 5  |
|           |                 |        | 932.2 |          |     |    |
+-----------+-----------------+--------+-------+----------+-----+----+
| Szo       | FeSO~4~•H~2~O   | 157.7  | -1,2  | -1,081.2 | 8   | 6  |
| molnokite |                 |        | 43.69 |          |     |    |
+-----------+-----------------+--------+-------+----------+-----+----+
| Rozenite  | FeSO~4~•4H~2~O  | 282.4  | -2,   | -1,795.2 | 10  | 10 |
|           |                 |        | 129.2 |          |     |    |
+-----------+-----------------+--------+-------+----------+-----+----+
| Siderotil | FeSO~4~•5H~2~O  | 323.6  | -2,   | -2,033.9 | 10  | 10 |
|           |                 |        | 424.3 |          |     |    |
+-----------+-----------------+--------+-------+----------+-----+----+
| Ferrohe   | FeSO~4~•6H~2~O  | 368.0  | -2,   | -2,271.9 | 10  | 10 |
| xahydrite |                 |        | 719.4 |          |     |    |
+-----------+-----------------+--------+-------+----------+-----+----+
| Me        | FeSO~4~•7H~2~O  | 409.2  | -3,   | -        | 7   | 1  |
| lanterite |                 |        | 012.6 | 2,507.75 |     |    |
+-----------+-----------------+--------+-------+----------+-----+----+
| Hal       | FeAl~2~(        | 1,166  | -1    | -9,306   | 10  | 10 |
| otrichite | SO~4~)4•22H~2~O |        | 1,041 |          |     |    |
+-----------+-----------------+--------+-------+----------+-----+----+
| ## Ferric |                 |        |       |          |     |    |
|  sulfates |                 |        |       |          |     |    |
+-----------+-----------------+--------+-------+----------+-----+----+
| Fe~2~(    | Fe~2~(SO~4~)~3~ | 282.8  | -2,   | -2,254.4 | 2   | 3  |
| SO~4~)~3~ |                 |        | 581.9 |          |     |    |
+-----------+-----------------+--------+-------+----------+-----+----+
| Kornelite | Fe~2~(S         | 590.6  | -4,   | -3,793.7 | 10  | 10 |
|           | O~4~)~3~•7H~2~O |        | 692.2 |          |     |    |
+-----------+-----------------+--------+-------+----------+-----+----+
| C         | Fe~2~(S         | 670.1  | -5,   | -4,250.6 | 10  | 10 |
| oquimbite | O~4~)~3~•9H~2~O |        | 288.2 |          |     |    |
+-----------+-----------------+--------+-------+----------+-----+----+
| Ferri     | Fe~5~(SO~4~)~   | 1,396  | -1    | -9,899   | 10  | 10 |
| copiapite | 6~O(OH)·20H~2~O |        | 1,767 |          |     |    |
+-----------+-----------------+--------+-------+----------+-----+----+
| ###### Mi |                 |        |       |          |     |    |
| xed ferro |                 |        |       |          |     |    |
| us-ferric |                 |        |       |          |     |    |
|  sulfates |                 |        |       |          |     |    |
+-----------+-----------------+--------+-------+----------+-----+----+
| Copiapite | Fe^+2^          | 1,444  | -1    | -9,971   | 10  | 10 |
|           | Fe~4~(SO~4~)~6~ |        | 1,824 |          |     |    |
|           | (OH)~2~·20H~2~O |        |       |          |     |    |
+-----------+-----------------+--------+-------+----------+-----+----+
| Römerite  | Fe^+2^Fe~2~(SO  | 943    | -     | -6,486   | 10  | 10 |
|           | ~4~)~4~·14H~2~O |        | 7,730 |          |     |    |
+-----------+-----------------+--------+-------+----------+-----+----+
| Bilinite  | Fe^+2^Fe~2~(SO  | 1,243  | -1    | -8,410   | 10  | 10 |
|           | ~4~)~4~·22H~2~O |        | 0,121 |          |     |    |
+-----------+-----------------+--------+-------+----------+-----+----+
| Voltaite  | K~2~Fe^         | 1,959  | -1    | -14,499  | 10  | 10 |
|           | +2^~5~Fe~4~(SO~ |        | 6,860 |          |     |    |
|           | 4~)~12~·18H~2~O |        |       |          |     |    |
+-----------+-----------------+--------+-------+----------+-----+----+

> \*References: 1. Parker and Khodakovskii (1995); 2. Barany and Adami
> (1965); 3. Pankratz and Weller (1969); 4. Cox and others (1989); 5.
> Adami and Kelly (1963); 6. Larson and others (1968); 7. Lyon and
> Giauque (1949); 8. DeKock (1982); 9. Pribylov (1969); 10. This study.

The available thermodynamic data for the ferrous sulfate hydrates are
sufficient to develop a model for the contribution of each H~2~O
molecule to the Gibbs energy of formation in nearly the same detail used
in the enthalpy of formation calculations. Four Gibbs energy of
formation values are available for use in estimating the contribution of
each H~2~O molecule. The difference in the Gibbs energies of formation
of the anhydrous sulfate and the heptahydrate (7) divided by the number
of H~2~O molecules yields a value of -241.3 kJ·mol^-1^ for the
contribution of one H~2~O molecule. This value must be modified. It was
shown above that the enthalpy contribution of the first H~2~O molecule
is larger than that for additional H~2~O molecules. In the ferrous
sulfate system, the difference was 20.1 kJ·mol^-1^ in the enthalpy of
formation. This difference divided by 7 is the estimated correction
factor required above and yields a value of -238.4 kJ·mol^‑1^ for the
contribution of H~2~O molecules greater than the first to the Gibbs
energy. The Gibbs energy of formation for melanterite is based upon the
enthalpy of formation reported by Adami and Kelley (1963) and the
entropy reported by Lyon and Giauque (1949). The measurements of the
heat capacity of melanterite between 1 and 300 K (Lyon and Giauque,
1949) fully account for the magnetic heat capacity expected for Fe^2+^
and thus for the magnetic entropy.

We may also calculate the contribution of one H~2~O molecule to the
Gibbs energy of formation by dividing the difference in the Gibbs energy
values of rozenite and szomolnokite by 3. This calculation yields ‑238.0
kJ·mol^-1^ for the contribution of one H~2~O molecule, in good agreement
with the value calculated above. This value was used to calculate the
estimated Gibbs energy values listed in Table 2 beginning with the
experimental Gibbs energy value for melanterite. The values calculated
for the Gibbs energy of formation by this method may be compared with
the experimental values, respectively, for rozenite (‑1,795.2 vs.
‑1,795.9 kJ·mol^-1^) and szomolnokite (-1,081.2 vs. -1,081.9 vs.
kJ·mol^-1^).

In support of the value just selected, we may examine the values for the
contribution of additional H~2~O molecules to the Gibbs energy in other
hydrated metal sulfate systems. Using the same phases as listed above in
the enthalpy calculations unless otherwise stated, for Co, Ni (7 hydrate
and 6 hydrate), Zn, Cu, and Cd sulfate hydrates, we calculate -238.06,
-237.22, -238.45, ‑240.41, and -237.85 kJ·mol^-1^, respectively, for the
contribution of one additional H~2~O molecule. The average of these
values is -238.4 kJ·mol^-1^. This value is in obviously good agreement
with the values calculated above for the ferrous sulfate hydrates.

It should be noted that this estimation scheme empirically describes the
available data, but in the strictest sense, does not satisfy the
thermodynamic properties of ideal mixtures. For ideal mixtures, the
Gibbs energy of mixing is described by the relationship:

∆G ~ideal\ mixing~ = RT$\sum_{i}^{}{X_{i}\text{ln}X_{i}}$ (3),

where R = 8.3144 J·mol^-1^·K^-1^ and X is the mole fraction in the
binary FeSO~4~·(H~2~O·6) - FeSO~4~·7H~2~O. For rozenite (X = 0.5), the
∆G ~ideal\ mixing~ should be -1.7 kJ·mol^-1^ at 298.15 K as opposed to a
value of -0.725 kJ·mol^-1^ based on the data in Table 2 (Fig. 4). The
uncertainty in the measured ∆~f~G° value is at least ± 1.5 kJ·mol^-1^.
Therefore, the measured value is within the limits of its uncertainty
with respect to ideal mixing assuming that the values for the end
members are accurate. Without more data on the Gibbs energy of
intermediate hydrates in various systems, the present study chooses to
retain the additive scheme described above because of its success in
empirically describing the available data. However, the reader is urged
to carefully scrutinize equilibria calculated using these estimates to
insure consistency with natural assemblages and other constraints.

![](media/image4.wmf){width="3.220833333333333in"
height="3.6798611111111112in"}

> Figure 4. Variation of the ideal Gibbs energy of mixing with mole
> fraction of melanterite along the join FeSO~4~·(H~2~O·6)
> (szomolnokite) - FeSO~4~·7H~2~O (melanterite) at 298.15K. Solid curve
> represents ideal mixing calculated on the basis of equation 2. Solid
> circles represent experimentally determined values for szomolnokite (X
> = 0.0), rozenite (X = 0.5), and melanterite (X = 1.0). Note that the
> uncertainty on the ∆~f~G° value for rozenite is at least ± 1.5
> kJ·mol^-1^ and is indicated by the vertical bracket.

**Entropy (S°)**

The entropy of the ferrous sulfate phases listed in Table 2 may be
estimated from the equality given above and the values for the Gibbs
energy and enthalpy of formation. It should be noted that these values
should be used with great care. Because the entropy derived in this
manner is based upon the small difference between two large numbers each
with an associated uncertainty, the uncertainty in the entropy is an
order of magnitude larger than that for the Gibbs energy or enthalpy of
formation. This approach is followed to maintain internal consistency of
the thermodynamic data listed in Table 2.

**Ferrous aluminum sulfate hydrate**

The enthalpy (-11,008.3 kJ·mol^-1^) and Gibbs energy (-9,277.6
kJ·mol^-1^) of formation of halotrichite FeAl~2~(SO~4~)~4~·22H~2~O are
estimated from the summation of the properties of
Al~2~(SO~4~)~3~·6H~2~O, melanterite, and the values calculated above for
the contribution of 9 additional H~2~O molecules. The enthalpy of
formation of halotrichite (-11,008.1 kJ·mol^-1^) was also calculated
from the summation of the enthalpy of Al~2~(SO~4~)~3~·18H~2~O
(alunogen?) plus that for rozenite. The two values estimated for the
enthalpy of formation of halotrichite are derived from two different
sets of data and the results agree to better than 0.1 percent. However,
the correct formula for alunogen appears to have 17 H~2~O molecules of
crystallization and not 18, and the value listed by Wagman and others
(1982) for alunogen is an estimate taken from Kelley and others (1946).
The properties of FeAl~2~O~4~ were compared with the summation of the
properties of Al~2~O~3~ plus fictive FeO (Robie and Hemingway, 1995).
Both the enthalpy and Gibbs energies of formation estimated for
FeAl~2~O~4~ by the summation method were low by about 0.2 percent. The
differences between the measured and estimated values for the enthalpy
and Gibbs energy of formation increases as the difference in mineral
structure increases, for example, 1.6 percent for fayalite vs. the
oxides FeO and SiO~2~. Chen (1975) has proposed a method for estimating
thermodynamic properties based on a knowledge of these
interrelationships (e.g., Hemingway and Sposito, 1996, p. 97). A factor
(0.997) was used to adjust the estimated values for the enthalpy and
Gibbs energy of formation because the reference materials are close in
chemistry and structure in terms of the model used by Chen (1975). The
entropy of halotrichite is calculated from the equality given above and
the values estimated here. The estimated value for the entropy of
halotrichite derived from the adjusted values for the enthalpy of
formation and the Gibbs energy is about 6 percent smaller than the
summation of entropies following the reaction described above. The
entropy follows a similar trend to the properties described in the Chen
(1975) model. The value of 6 percent will be used in calculations
discussed below to estimate the correction necessary when using a
summation approach to estimate the entropy of the hydrated sulfates.

**Ferric sulfates and their hydrates**

Thermodynamic data for ferric sulfate phases are very limited. Wagman
and others (1982) gave a value for the enthalpy of formation of
anhydrous Fe~2~(SO~4~)~3~, ‑2,581.5 kJ·mol^-1^, that is based on the
calorimetric study by Barany and Adami (1965). The heat capacity of
anhydrous ferric sulfate between 50 and 300 K was reported by Pankratz
and Weller (1969). Using these data, DeKock (1982) calculated the Gibbs
energy of ferric sulfate. The Gibbs energy calculated by DeKock (1982)
will be incorrect because the entropy is missing 14.9 J·mol^-1^·K^-1^ in
magnetic entropy per Fe^3+^ in the compound (see for example, Gopal,
1966). Cooke and others (1956) have shown that the magnetic heat
capacity anomaly that can be expected for salts of Fe^3+^ can occur at
very low temperatures. In the case of Fe(NH~3~CH~3~)(SO~4~)~2~·12H~2~O,
a good model for the phases examined here, the maximum in the heat
capacity anomaly arising from the magnetic contribution of Stark
splitting in Fe^3+^ was seen at 0.33 K. They also concluded that the
total magnetic heat capacity, and thus the magnetic entropy, could be
accounted for in the measurements they made between about 0.2 and 20 K.
The estimated entropy reported by Pankratz and Weller (1969) for ferric
sulfate did not include a contribution for the magnetic entropy of
Fe^3+^. The entropy for ferric sulfate is 282.6 J·mol^-1^·K^-1^
(Pankratz and Weller, 1969) plus 2 times 14.9 J·mol^-1^·K^-1^ or 312.4
J·mol^-1^·K^-1^, and the Gibbs energy of formation is -2,263.0
kJ·mol^-1^.

The values derived in the preceding paragraph represent the reference
values upon which the estimated values for the ferric sulfate hydrate
phases reported in Table 2 are based. The difference in the enthalpies
of formation of La~2~(SO~4~)~3~ and La~2~(SO~4~)~3~·9H~2~O is 2,706.7
kJ·mol^-1^ or about 300.7 kJ·mol^-1^ per H~2~O molecule. This value is
used to estimate the enthalpy of formation of coquimbite
(Fe~2~(SO~4~)~3~·9H~2~O). Assuming that the first H~2~O molecule
contributes more than subsequent H~2~O molecules and following the model
discussed above, we estimate the contribution of the additional H~2~O
molecules to be -298 kJ·mol^-1^ of H~2~O and use this value to calculate
the enthalpy of formation of kornelite (7 hydrate) from the value
estimated for coquimbite. The entropies of coquimbite and kornelite are
estimated following the procedure described by DeKock (1982) in which
the contribution of each H~2~O molecule is taken as 39.75
J·mol^-1^·K^-1^. The Gibbs energies of the two phases are calculated
from these data and the equality given above.

The enthalpy of formation and entropy for ferricopiapite were estimated
from the summation of these properties for 2 coquimbite, goethite, and 2
H~2~O (H~2~O value as derived above). The entropy of goethite (60.38
J·mol^-1^·K^-1^) was taken from Khodakovsky and others (1991). These
values were adjusted in accordance with the differences noted above for
summation data.

**Mixed ferrous and ferric sulfates**

There are few thermodynamic data for mixed ferrous and ferric compounds
so the model used to estimate the thermodynamic data for this type of
phase is similar to that used for halotrichite. The mixed iron sulfate
hydrate phases are assumed to have slightly larger (about 0.3 percent)
enthalpies of formation than the summation of values for the ferrous and
ferric sulfate hydrates. The enthalpy of formation for bilinite and
römerite are calculated from the sum of the properties of kornelite and
melanterite (and plus 8 H~2~O molecules for bilinite). The entropies are
calculated from the same summation procedure and corrected by 6 percent
as noted above. The Gibbs energies are calculated from these values
using the equality given above. The values for copiapite are estimated
using the same model as for the other mixed valence iron sulfates, but a
correction is made for the substitution of (OH)~2~ for SO~4~. The
correction is derived from the difference in the properties of FeSO~4~
and Fe(OH)~2~ (359.4 kJ·mol^-1^ and 19.5 J·mol^-1^·K^-1^, respectively,
for the enthalpy and entropy). The values for voltaite are derived from
the summations and suggested adjustments of the enthalpy of formation
and entropy for 5 szomolnokite, 2 kornelite, K~2~SO~4~, and -1 H~2~O.

**Estimated uncertainties**

The uncertainties estimated for the enthalpy and Gibbs energy of
formation values, relative to the elements, derived from the model
calculations used in this study are between 0.3 and 0.7 percent, with
the values for the ferrous and ferric phases at the low end and those of
the mixed phases at the high end.

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[^1]: This report is preliminary and has not been edited or reviewed for
    conformity with U.S. Geological Survey editorial standards.

[^2]: U.S. Geological Survey, 953 National Center, Reston, VA 20192

[^3]: U.S. Geological Survey, 954 National Center, Reston, VA 20192