Download Low Temperature Aqueous Ferric Sulfate Solutions on the Surface

Low Temperature Aqueous Ferric Sulfate Solutions on the Surface of Mars
Vincent F. Chevrier and Travis S. Altheide
Supplementary Information:
1. Ferric sulfate characterization
2. Methods
3. Determination of evaporation rate and application to Mars
4. Pitzer model applied to the Fe2(SO4)3 – H2O aqueous system
5. Low temperature density correction using the Pitzer model
6. Eutectic temperature determination
1. Ferric sulfate characterization
The following concentrations of solutions were made using D.I. water and ferric sulfate
((Fe2(SO4)3.nH2O, EMD #FX0235-1 and Mallinckrodt #5036-12): 35, 40, 45, 50, 55, and 60
wt%. The initial sulfate was analyzed using X-ray diffraction and was found to contain a mixture
of amorphous Fe2(SO4)3, rhomboclase, mikasaite and coquimbite. Weight loss measurements
after subsequent heating at 673 K under ambient pressure showed that the originally dried ferric
sulfate contained 3 ± 0.3 wt% H2O. X-ray diffraction analysis of the heated product (containing
only mikasaite Fe2(SO4)3) confirmed the removal of the initial water. Therefore, we corrected
sulfate concentrations for initial water content.
2. Methods
We used the thermo_phrqpitz database in the Geochemist’s Workbench Standard
program (version 6.0) to model the formation and stability of ferric sulphate brines. We updated
the thermo_phrqpitz database to include twenty additional Fe-bearing minerals [Marion et al.,
2008; Tosca et al., 2005] and Pitzer coefficients [Christov, 2004; Marion et al., 2008; Tosca et
al., 2007] for aqueous Fe3+ systems (Table S1). For modeling mineral precipitation, initial
abundances (in mg L-1) for Fe2+/3+, Mg2+, Ca2+, Na+, K+, and Cl- are [Catling, 1999]: 44.7, 24.3,
1
20.0, 18.4, 2.7, and 23.0, respectively. For SO42-, we used a value of 200 mg L-1, to model a
sulphur rich environment.
Conductivity measurements of 58.2 wt% ferric sulfate solutions were acquired using a
Keithley 2700 Voltimeter / Data Acquisition System. Solutions were placed in a 1.5 × 1.9 × 2.0
cm insulated cell. The cell (with solution) temperature was lowered to 170 K using liquid
nitrogen, and then allowed to slowly warm while both temperature and resistance were
monitored.
Evaporation rate of ferric sulfate solutions were measured in our Mars simulation
chamber under 7 ± 0.01 mbar of CO2 for 0.5 to 3 hours at sample surface temperatures ranging
from 257 K to 274 K (Table S2). The average temperature of the atmosphere inside the chamber
was kept at 264 ± 3 K.
Humidity inside the chamber was keep below 1% by carefully
exchanging the atmosphere during each simulation run. The complete procedure for evaporating
liquid water and brine solutions in the simulation chamber has been previously described in
detail [Moore and Sears, 2006; Sears and Chittenden, 2005; Sears and Moore, 2005].
3. Determination of evaporation rate and application to Mars
The evaporation rate E (in mm h-1) was determined from mass loss (in grams) using the
formula:
E
m
t
S
(1.)
 sol
where m/t is the mass loss rate, S is the surface area (cm3) of the sample and ρsol is the density
(g cm-3) of the solution, which was calculated as a function of the temperature, using the Pitzer
model (See section 4, [Marion et al., 2008]).
It has been previously demonstrated that the evaporation rate of liquid water is well
described by a diffusion equation (Fick’s theory) modified by the buoyancy of water molecules
into the heavier CO2 atmosphere [Ingersoll, 1970; Sears and Chittenden, 2005]:
1
E  0.17 DH 2 O / CO2 aH 2 O
 sat
 sol
  g  3
 

 2 


(2.)
2
where E is the evaporation rate, DH2O/CO2 is the interdiffusion coefficient of H2O(g) and CO2(g),
aH2O is the activity of water in the solution, ρsat is the saturation density of water vapour in
equilibrium with pure liquid water, ρsol is the density of the solution, Δρ/ρ is the difference of
density of the gas mixture between the surface of the liquid and the atmosphere, g is the gravity
acceleration, and  is the kinematic viscosity of CO2. Temperature has a strong effect on the
saturation pressure psat (in bars) of water through the following equations:
for liquid water [Murphy and Koop, 2005]:
psat ,liq
6763.22


 4.210 lnT   0.000367T
54.842763  T



 105 exp
1331.22


53.878 

 tanh0.0415T  218.8 
T



  9.44523lnT   0.014025T 



(3.)
for water ice [Murphy and Koop, 2005]:
5723.265


 3.53068lnT   0.00728332T 
psat ,ice  105 exp9.550426 
T


(4.)
From the saturation pressure, the gas density ρsat is defined as follows:
 sat 
p sat
M H 2O T
(5.)
The relative density difference between the surface and the atmosphere ρ/ρ is defined as:



p sat M CO  M H O 
 surf   atm

 surf
PM CO  p sat M CO  M H O 
2
2
2
2
(6.) 2
where P is the total pressure in the atmosphere. In addition, the kinetic parameters are also
temperature dependant. The diffusion coefficient is defined as follow [Boynton and Brattain,
1929]:
3
D H 2O / CO2
 T 2  1 
 1.387  10 
  
 273.15   P 
5
(7.)
In this case P is in bar. The kinetic viscosity  is defined as follows [Crane, 1988]:
3
  1.48  10 5
RT  240  293.15  T  2



M CO2 P  240  T  293.15 
(8.)
3
where R is the ideal gas constant. To determine the total pressure P (mbar) on the surface of
Mars, we use the following equation:
 z 
P  Pz 0 exp  
h
(9.)
where h is the scale height of the atmosphere, Pz=0 = 6 mbar, and Δz is the altitude determined
from Mars Global Surveyor Mars Orbiter Laser Altimeter (MOLA) data [Smith et al., 1999].
If layers of regolith are covering the brine or ice (see Fig. 3C), then the sublimation /
evaporation rate is calculated using a combination between water vapor diffusion in the
atmosphere, as previously defined, and diffusion through a porous medium using the following
semi-empirical equation:
ES 
EBL1
1  BL1
(10.) where ES is the sublimation / evaporation rate in the atmosphere, L is the thickness of the regolith
layer, and
B
DM H 2O p sat
RT sol
(11.)
Here D is the diffusion coefficient of water vapor in the porous medium. We chose an average
value of 5 × 10-4 m2s-1, following previous experimental results [Chevrier et al., 2007; Chevrier
et al., 2008; Hudson et al., 2007].
4. Pitzer model applied to the Fe2(SO4)3 – H2O aqueous system
High concentrations of ferric sulfate combined with the high ionic charge of Fe3+ and SO42‐ create strong interactions and thus a low water activity. The kinetic eq. (2) includes the
liquid water activity (aH2O), which can be calculated using the Pitzer ion interaction model
[Grenthe and Plyasunov, 1997; Pitzer, 1991]. This model accounts for electrostatic, non-specific,
long-range interactions, as described by the Debye-Hückel theory, but also includes terms of
short-range non-electrostatic interactions that become effective at very high concentrations. In
this case the formula of the electrolyte is modeled as Nz++Xz--, where z+ and z- are the charges
of the ions and +, - are the number of ions in the salt formula. In the case of Fe2(SO4)3, z+ = 3,
+ = 2, z- = 2, and - = 3. The activity of water is calculated through the following equation:
4
ln(a H 2O ) 
  H 2O  m k
k
(12.)
55.10
where mk is the molality of the ion k in the solution (in mol kg-1). The osmotic coefficient ФH2O
is calculated as follows [Pitzer, 1991]:
 H 2O
 2  
 1  z  z  f  m NX 
  
3


2  2    2
 B NX  m NX 
   




C NX

(13.)
where mNX is the molality of the salt, BNX and CNX are constants representing specific interactions
between the ions in the solution, and f is the extended form of the Debye-Hückel coefficient
equivalent to:
f 
A Im
(14.)
1 b Im
Here A is the temperature-dependent Debye-Hückel coefficient:
1530.1474


A  0.13422   0.0368329  T  14.62718  ln T  
 80.40631
T


(15.)
where b is a universal parameter with a value of 1.2 kg1/2 mol-1/2 and Im is the ionic strength
calculated as:
Im 
1 n
mi zi2

2 i 1
(16.)
The value of BNX and CNX are calculated using the following equations [Tosca et al., 2007]:
and


 0.00655  0.02515 exp 0.5 I 
B NX  0.63321  11.96824 exp  1.4 I m
(17.)
C NX
(18.)
m
We extracted the water activities from our evaporation data using eq. 2. In Fig. S1 we
compare them to the Pitzer model for the Fe2(SO4)3 – H2O system and observe an excellent
agreement between our data and the model, providing a validation for our thermodynamic and
kinetic approach.
Therefore, we demonstrate that the combination of the Pitzer thermodynamic and diffusion / buoyancy kinetic models can accurately describe the evaporation of highly concentrated brines at any temperature.
It must be stated that we did no include the variations of the Pitzer parameters and density
with temperature. Indeed, most empirical fit of these parameters are only valid over a limited
5
range of temperature, usually ~263 K to 298 K [Marion et al., 2008]. Extrapolation down to 205
K represents a very large step, which validation requires further experimental and theoretical
work. However, we made some preliminary studies showing that the variation of these
parameters should remain quite limited, and in any case not significantly affect the final results.
5. Low temperature density correction using the Pitzer model
The density of the solution sol in eq. (1) and (2) was calculated at different temperatures
using the Pitzer interaction model [Krumgalz et al., 1999; Marion et al., 2005; Marion et al.,
2008]. The brine density is defined as follow:
 sol 
1000   mi M i
1000
  miVi  V ex
(19.)
H O
2
where H2O is the density of pure water, mi is the molality of the ion, Mi its molecular mass, Vi
the partial molal volumes at infinite dilution and Vex the excess volume resulting from water-salt
mixing. The density of pure water (in g cm-3) is defined as [Kell, 1975]:
1000  H 2O
 999.83952  16.94518 T  273.15  7.98704 10 -3 T  273.152 ) 


 - 4.617046 10 5 T  273.153  1.05563 10 -7 T  273.154



 - 2.805425 10 -10 T  273.155



-2
1.0  1.687985 10 T  273.15

(20.)

where H2O is in g cm-3. The Vi parameters are given by Marion et al. (2008) for Fe3+ and by
Marion et al. (2005) for SO42-. The excess volume Vex is defined as [Krumgalz et al., 1999]:
V ex  AV


 V
Im

 V 
ln 1  b I m  2 RT  m N m X  B NX
   m N z  C NX

b
N X
 N



(21.)
In this case AV, BVNX and CVNX are the volumetric Pitzer parameters [Marion et al., 2005; Marion
et al., 2008]. These parameters are calculated as follow [Marion et al., 2005]:
AV  3.73387  0.0289662  T  1.29461  10 3  P  5.62291  10 6  T  P
 7.62143  10 5  T 2  4.099944  10 8  P 2
(22.)
6
V
( 0 )V
(1)V
  NX
  NX
B NX

( 2 )V
NX
 
2
 I
2
1 m
1  1  
1
 
 
I m exp  1 I m
2
1  1   2 I m exp  2 I m
2
2 Im


(23.)
1 and 2 values are presented in Table S3, as well as the Pitzer volumetric parameters. The
model provides a good approximation of data measured at 303 K (Fig S2).
6. Eutectic temperature calculation
For any solution at any eutectic temperature, water ice, liquid and vapor are in
equilibrium. This implies that the activity of water can be defined as:
a H 2O 
p sat ,ice
(24.)
p sat ,liq
With psat,ice and psat,liq being defined by eq. (3) and (4). Thus, the activity of water is entirely
controlled by the temperature. Alternatively, the eutectic temperature for any solution is defined
as:
TE 
1

T0
1
R ln a H 2O
(25.)
H f
where T0 is the eutectic temperature for pure water ice (T0 = 273.25 K) and Hf is the latent heat
of fusion (Hf = 6003.9 J mol-1 at 273.15 K). Satisfying eq. (24) and (25) also implies that the
latent heat of fusion is dependent on the water activity and thus the temperature:
H f 
RTE  T0  ln a H 2O
TE  T0
(26.)
However, since TE is a priori unknown, we used an empirical fit to determine the variation of
Hf with aH2O (calculated using eq. (24), Fig. S3):
1.85714
 1.85921  a H 2O
 a H 2O  0.53822 
1  exp 

0.05031


3
 1.72933  a H 2O
H f  3.34768 
 2.51524  a H2 2O
(27.)
7
The water activity is calculated from the solute concentration using the Pitzer model, as
defined in the previous sections. Then, the eutectic temperature can be directly determined using
eq. (27) and eq. (25). By experimentally determining the freezing temperature of the
concentrated ferric sulfate solutions to be 205.5 K, we could calculate the saturation
concentration, i.e. 48 ± 2 wt%. This indicates that some of our solutions were slightly
supersaturated, which is quite expected since we prepared the brines at ambient temperature. For
the water activity calculation, we used the Pitzer parameters determined at 263 K (Table S3). As
discussed before, extrapolation of these parameters to 205 K requires more work. Making some
preliminary tests with the existing formula indicate a variation of the concentration from 46.5 to
49.5 wt% from 205 to 263 K. This is the reason why the resulting error appears relatively large
(~ 2 wt%).
References
Boynton, W. P., and W. H. Brattain (1929), Interdiffusion of gases and vapors, International
Critical Tables, 5.
Catling, D. C. (1999), A chemical model for evaporites on early Mars: possible sedimentary
tracers of the early climate and implications for exploration, J. Geophys. Res., 104(E7),
16453-16469.
Chevrier, V., D. W. G. Sears, J. Chittenden, L. A. Roe, R. Ulrich, K. Bryson, L. Billingsley, and
J. Hanley (2007), The sublimation rate of ice under simulated Mars conditions and the
effect of layers of mock regolith JSC Mars-1, Geophys. Res. Lett., 34(L02203).
Chevrier, V., D. R. Ostrowski, and D. W. G. Sears (2008), Experimental study of the sublimation
of ice through an unconsolidated clay layer: Implications for the stability of ice on Mars
and the possible diurnal varaitions in atmospheric water, Icarus, in press.
Christov, C. (2004), Pitzer ion-interation parameters for Fe(II) and Fe(III) in the quinary {Na +
K + Mg + Cl + SO4 + H2O} system at T = 298.15 K, J. Chem. thermodynamics, 36, 223235.
Crane (1988), Flow of fluids through valves, fittings, ans pipe, in Technical Paper No. 410,
edited, Crane Company, Joliet, Il.
8
Grenthe, I., and A. Plyasunov (1997), On the use of semiempirical electrolyte theories for the
modeling of solution chemical data, Pure and Applied Chemistry, 69(5), 951-958.
Hudson, T. L., O. Aharonson, N. Schorghofer, C. B. Farmer, M. H. Hecht, and N. T. Bridges
(2007), Water vapor diffusion in Mars subsurface environments, J. Geophys. Res.,
112(E5, E05016).
Ingersoll, A. P. (1970), Mars: Occurrence of liquid water, Science, 168(3934), 972-973.
Kell, G. S. (1975), Density, thermal expansivity, and compressibility of liquid water from 0o to
150oC: Correlations and tables for atmopsheric pressure and saturation reviewed and
expressed on 1968 temperature scale J. Chem. Eng. Data, 20(1), 97-105.
Krumgalz, B. S., A. Starinsky, and K. S. Pitzer (1999), Ion-interaction approach: Pressure effect
on the solubility of some minerals in submarine brines and seawater, J. Sol. Chem., 28(6),
667-692.
Marion, G. M., J. S. Kargel, D. C. Catling, and S. D. Jakubowski (2005), Effects of aqueous
chemical equilibria at subzero temperatures with application to Europa, Geochim.
Cosmochim. Acta, 69(2), 259-274.
Marion, G. M., J. S. Kargel, and D. C. Catling (2008), Modeling ferrous–ferric iron chemistry
with application to martian surface geochemistry, Geochim. Cosmochim. Acta, 72, 242266.
Moore, S. R., and D. W. G. Sears (2006), On laboratory simulation and the effect of small
temperature oscillations about the freezing point and ice formation on the evaporation
rate of water on Mars, Astrobiology, 6(4), 644-650.
Murphy, D. M., and T. Koop (2005), Review of the vapour pressures of ice and supercooled
water for atmospheric applications, Quart. J. R. Meteor. Soc., 131, 1539-1565.
Pitzer, K. S. (1991), Chapter 3. Ion interaction approach: theory and data correlation, in Activity
coefficients in Electrolyte Solutions. 2nd Edition, edited by K. S. Pitzer, pp. 75-154, CRC
Press.
Sears, D. W. G., and J. D. Chittenden (2005), On laboratory simulation and the temperature
dependence of evaporation rate of brine on Mars, Geophysical Research Letters,
32(L23203).
Sears, D. W. G., and S. R. Moore (2005), On laboratory simulation and the evaporation rate of
water on Mars, Geophys. Res. Lett., 32(L16202).
9
Smith, D. E., M. T. Zuber, S. C. Solomon, R. J. Phillips, J. W. Head, J. B. Garvin, W. B.
Banerdt, D. O. Muhleman, G. H. Pettengill, G. A. Neumann, F. G. Lemoine, J. B.
Abshire, O. Aharonson, C. D. Brown, S. A. Hauck, A. B. Ivanov, P. J. McGovern, H. J.
Zwally, and T. C. Duxbury (1999), The global topography of Mars and implications for
surface evolution, Science, 284, 1495-1503.
Tosca, N. J., S. M. McLennan, B. C. Clark, J. P. Grotzinger, J. A. Hurowitz, A. H. Knoll, C.
Schröder, and S. W. Squyres (2005), Geochemical modeling of evaporation processes on
Mars: insight from the sedimentary record at Meridiani Planum, Earth Planet. Sci. Lett.,
240, 122-148.
Tosca, N. J., A. Smirnov, and S. M. McLennan (2007), Application of the Pitzer ion interaction
model to isopiestic data for the Fe2(SO4)3–H2SO4–H2O system at 298.15 and 323.15 K,
Geochim. Cosmochim. Acta, 71, 2680-2698.
10
Table S1.
Binary Pitzer coefficient values of Fe-bearing aqueous species added to the
thermo_phrqpitz database. Values taken from Tosca et al. (2007) and Christov (2004).
Chemical System
FeCl3
Fe2(SO4)3
Fe3+ - HSO4-
α1
2
2
2
α2
1
1
—
β(0)
0.34082
0.56622
0.76349
β(1)
1.6285
12.16131
6.3103
β(2)
1.7199
3.07519
—
Cφ
-0.014
0.000524
-0.00204
Table S3. Binary and volumetric Pitzer coefficient values for ferric sulfate [Marion et al., 2005;
Marion et al., 2008]. Each parameter is calculated as follow: k = a1 + a2 T + a3 T2, where k is the
parameter, and T the temperature.
Parameter
a1
a2
a3
1.04326×101
-1.60×10-3
0.0
1
-1
0.0
Binary Pitzer parameters
(0)

(1)
-4.0043×10

(2)
3.07519
C

1.751×10
0.0
-5.439×10
-3
2.00×10
0.0
-5
0.0
Volumetric parameters
v(0)

v(1)
v
C
V
(0)
V
FeIII
(0)
SO4
0.0
-4.625 10
0.0
-2
1.805063×10
0.0
0.0
-5.70
-3.52433×10
0.0
-1.016×10
2
2.3643
-4
0.0
0.0
-1
0.0
-3.808×10-3
11
Table S2. Data obtained during evaporation experiments of ferric sulfate solutions.
Fe2(SO4)3
(g g-1)b
0.582 0.582 0.582 0.582 0.582 0.582 0.582 0.534 0.534 0.534 0.534 0.534 0.534 0.485 0.485 0.485 0.485 0.485 0.485 0.437 0.437 0.437 0.437 0.388 0.388 0.388 0.388 0.388 0.340 0.340 0.340 0.340 0.340 0.340 0.291 0.291 0.291 Run
time
(hr)
1 1 1 1 3 1 1 1 1 0.5 0.5 0.5 0.5 1 1 1 1 3 1.5 1 1 1 1 0.5 0.5 1 1 1 0.5 0.5 0.5 0.5 1 1 0.5 0.5 0.5 Slope
(g min-1)c
‐3
5.05 × 10 ‐3
3.96 × 10 ‐3
4.98 × 10 ‐3
3.98 × 10 ‐3
3.69 × 10 ‐3
5.30 × 10 ‐3
4.29 × 10 ‐3
7.04 × 10 ‐3
5.11 × 10 ‐2
1.21 × 10 ‐3
8.21 × 10 ‐3
6.78 × 10 ‐3
5.81 × 10 ‐2
1.14 × 10 ‐3
8.82 × 10 ‐2
1.56 × 10 ‐2
1.05 × 10 ‐3
6.90 × 10 ‐2
1.09 × 10 ‐2
1.63 × 10 ‐2
1.18 × 10 ‐2
1.40 × 10 ‐2
1.05 × 10 ‐2
2.30 × 10 ‐2
1.70 × 10 ‐2
1.40 × 10 ‐2
1.70 × 10 ‐2
1.30 × 10 ‐2
2.34 × 10 ‐2
1.75 × 10 ‐2
1.49 × 10 ‐2
1.38 × 10 ‐2
1.78 × 10 ‐2
1.51 × 10 ‐2
3.15 × 10 ‐2
2.47 × 10 ‐2
2.19 × 10 Density
(g cm-3)
2.209 2.283 2.200 2.282 2.363 2.318 2.319 2.132 2.134 1.962 2.026 2.060 2.079 1.911 1.949 1.900 1.943 2.015 1.921 1.750 1.785 1.782 1.799 1.621 1.645 1.662 1.644 1.663 1.503 1.523 1.533 1.538 1.510 1.514 1.406 1.407 1.409 Evaporation
Rate
(mm h-1)
‐2
4.27 × 10 ‐2
3.23 × 10 ‐2
4.22 × 10 ‐2
3.25 × 10 ‐2
2.91 × 10 ‐2
4.27 × 10 ‐2
3.45 × 10 ‐2
6.16 × 10 ‐2
4.46 × 10 ‐1
1.15 × 10 ‐2
7.56 × 10 ‐2
6.14 × 10 ‐2
5.22 × 10 ‐1
1.11 × 10 ‐2
8.44 × 10 ‐1
1.53 × 10 ‐1
1.01 × 10 ‐2
6.39 × 10 ‐1
1.06 × 10 ‐1
1.74 × 10 ‐1
1.23 × 10 ‐1
1.46 × 10 ‐1
1.09 × 10 ‐1
2.64 × 10 ‐1
1.93 × 10 ‐1
1.57 × 10 ‐1
1.93 × 10 ‐1
1.46 × 10 ‐1
2.90 × 10 ‐1
2.14 × 10 ‐1
1.82 × 10 ‐1
1.67 × 10 ‐1
2.19 × 10 ‐1
1.86 × 10 ‐1
4.18 × 10 ‐1
3.27 × 10 ‐1
2.90 × 10 Sample
temp. (K)
270.4 ± 1.4
266.7 ± 0.8
270.8 ± 1.8
266.7 ± 0.8
263.0 ± 0.5
265.0 ± 1.7
264.9 ± 0.9
262.8 ± 0.3
262.7 ± 0.3
274.1 ± 2.0
269.6 ± 0.9
267.4 ± 0.6
266.2 ± 0.3
265.1 ± 1.3
262.0 ± 0.6
266.1 ± 1.8
262.5 ± 0.6
256.8 ± 0.5
264.3 ± 0.9
265.9 ± 1.9
262.0 ± 0.8
262.3 ± 1.1
260.4 ± 1.2
265.6 ± 1.5
262.0 ± 0.9
259.5 ± 0.9
262.1 ± 1.6
259.2 ± 0.8
266.3 ± 1.9
262.4 ± 1.1
260.4 ± 0.6
259.3 ± 0.3
261.8 ± 0.4
260.3 ± 0.6
266.0 ± 1.1
265.6 ± 0.3
265.2 ± 0.5
Initial
temp.
(K)
272.8
267.9
274.3
268.1
261.7
263.3
263.0
263.2
262.6
278.5
271.4
268.3
266.8
267.7
262.9
269.8
263.5
255.7
263.6
269.8
263.7
264.3
260.2
267.8
263.2
261.1
264.0
259.5
270.8
264.4
260.9
259.4
262.4
260.7
268.0
265.7
266.1
End
temp.
(K)
267.8
265.4
268.6
265.9
263.3
266.5
265.1
262.9
262.6
271.6
268.7
266.9
265.5
262.8
261.0
264.1
261.7
257.6
265.7
263.7
260.9
260.4
258.9
263.2
260.8
258.3
259.8
260.9
263.7
260.9
259.3
259.3
260.7
259.4
265.3
265.7
264.5
Atmosphere
temp. (K)
263.8 ± 0.7
263.8 ± 0.7
263.9 ± 1.1
263.4 ± 1.0
264.7 ± 0.3
265.0 ± 0.3
265.0 ± 0.3
265.7 ± 0.3
265.9 ± 0.3
264.9 ± 0.2
264.9 ± 0.2
264.8 ± 0.2
264.9 ± 0.2
263.4 ± 0.3
263.2 ± 0.3
264.0 ± 0.5
264.1 ± 0.4
264.1 ± 0.3
273.2 ± 1.3
265.2 ± 0.2
265.1 ± 0.2
264.3 ± 0.4
263.8 ± 0.3
264.0 ± 0.5
264.2 ± 0.4
264.3 ± 0.4
263.4 ± 0.4
263.6 ± 0.4
264.5 ± 0.3
264.5 ± 0.3
264.7 ± 0.3
264.6 ± 0.2
264.8 ± 0.3
264.0 ± 0.3
265.5 ± 0.5
264.8 ± 0.5
264.6 ± 0.5
Average Rh
(%)d
0.00 ± 0.01
0.00 ± 0.01
0.02 ± 0.03
0.00 ± 0.01
0.25 ± 0.12
0.09 ± 0.01
0.02 ± 0.02
0.04 ± 0.05
0.00 ± 0.01
0.34 ± 0.10
0.15 ± 0.04
0.07 ± 0.02
0.02 ± 0.02
4.26 ± 1.25
2.52 ± 0.24
0.89 ± 0.32
0.41 ± 0.06
1.05 ± 0.01
33.14 ± 3.44
0.46 ± 0.13
0.24 ± 0.03
0.66 ± 0.09
0.50 ± 0.04
1.09 ± 0.21
0.68 ± 0.06
0.50 ± 0.05
1.53 ± 0.28
1.04 ± 0.07
1.53 ± 0.22
0.88 ± 0.09
0.88 ± 0.05
0.77 ± 0.03
1.56 ± 0.13
1.37 ± 0.03
0.94 ± 0.18
0.66 ± 0.04
0.57 ± 0.02
Initial Rh
(%)d
0.02
0.00
0.11
0.01
0.50
0.08 0.05 0.21
0.02
0.55
0.22
0.13
0.03
8.13
2.98
1.62
0.53
1.11
26.00
0.77
0.28
0.92
0.55
1.54
0.81
0.59
2.19
1.18
1.95
1.25
0.94
0.80
1.92
1.40
1.38
0.74
0.60
End Rh
(%)d
0.00
0.00
0.00
0.00
0.08
0.10 0.00 0.01
0.00
0.22
0.11
0.03
0.00
2.99
2.16
0.55
0.33
1.01
37.73
0.30
0.19
0.57
0.46
0.81
0.59
0.42
1.19
0.95
1.23
0.95
0.81
0.75
1.39
1.33
0.75
0.58
0.55
Total
pressure
(mbar)
7.00 ± 0.01 7.00 ± 0.01 7.01 ± 0.01 7.00 ± 0.01 7.00 ± 0.01 7.00 ± 0.01 7.00 ± 0.01 7.00 ± 0.01 7.01 ± 0.01 7.00 ± 0.01 7.01 ± 0.00 7.00 ± 0.01 7.00 ± 0.01 6.99 ± 0.01 7.00 ± 0.01 7.00 ± 0.01 7.00 ± 0.01 7.00 ± 0.03 6.99 ± 0.03 7.00 ± 0.01 7.00 ± 0.01 7.00 ± 0.01 7.00 ± 0.01 7.00 ± 0.01 7.01 ± 0.01 7.01 ± 0.01 7.00 ± 0.01 7.01 ± 0.01 7.00 ± 0.01 7.00 ± 0.01 7.00 ± 0.01 7.00 ± 0.01 6.99 ± 0.01 7.00 ± 0.01 7.00 ± 0.01 7.01 ± 0.01 7.01 ± 0.01 Liquid
water
activity
0.26 0.25 0.25 0.25 0.26 0.31 0.27 0.41 0.32 0.41 0.36 0.34 0.32 0.59 0.55 0.68 0.58 0.54 0.53 0.68 0.62 0.72 0.64 0.91 0.84 0.80 0.86 0.79 0.88 0.83 0.80 0.79 0.85 0.83 1.05 0.92 0.87 12
0.291 0.291 0.291 0.291 0.291 0.291 0.291 0.5 0.5 0.5 0.5 0.5 0.5 0.5 ‐2
2.08 × 10 ‐2
1.71 × 10 ‐2
1.58 × 10 ‐2
1.48 × 10 ‐2
1.94 × 10 ‐2
2.19 × 10 ‐2
1.90 × 10 1.412 1.427 1.430 1.432 1.429 1.428 1.432 ‐1
2.74 × 10 ‐1
2.24 × 10 ‐1
2.06 × 10 ‐1
1.92 × 10 ‐1
2.53 × 10 ‐1
2.87 × 10 ‐1
2.48 × 10 264.3 ± 0.3
260.1 ± 0.4
259.3 ± 0.3
258.6 ± 0.3
259.4 ± 0.6 259.8 ± 0.5 258.7 ± 0.4 264.6
260.9
259.6
259.1
260.5 260.8 259.8 264.1
259.4
259.3
258.2
260.1 259.4 258.1 264.4 ± 0.5
266.3 ± 0.2
266.2 ± 0.3
266.2 ± 0.2
264.8 ± 0.2 264.6 ± 0.3 264.6 ± 0.2 0.53 ± 0.03
1.18 ± 0.03
1.07 ± 0.03
0.99 ± 0.03
0.72 ± 0.07 0.92 ± 0.07 0.77 ± 0.03 0.55
1.23
1.13
1.03
0.83 1.07 0.81 0.50
1.11
1.03
0.95
0.91 0.80 0.70 7.01 ± 0.01 7.01 ± 0.01 7.01 ± 0.01 7.00 ± 0.01 7.00 ± 0.01 7.00 ± 0.01 7.00 ± 0.01 0.87 0.83 0.81 0.80 0.98 1.07 1.02 a
The initial ferric sulfate we used contains about 3 wt% of liquid water.
The relative standard error on the corrected concentrations is about 2.5% of the concentration in g g-1.
c
The standard deviation on the slope is systematically inferior to 1%.
d
Rh designs relative humidity.
b
13
1.0
Water activity
0.8
0.6
0.4
0.2
Pitzer model (Marion et al., 2008,
Tosca et al., 2008)
0.0
0
0.1
0.2
0.3
0.4
Fe2(SO4)3 concentration (g g-1)
0.5
0.6
Figure S1. Comparison between the water activity extracted from our evaporation data using the
diffusion eq. (2), and the Pitzer model for the system Fe2(SO4)3 – H2O using the above equations
and previously determined parameters [Marion et al., 2008; Tosca et al., 2007]. No adaptive
parameters were used in the calculations. The solid curve indicates the saturation curve, while
the dashed part indicates supersaturation. The eutectic point was determined using our
experimental determination of freezing point (TE = 205.5 K). The ferric sulfate concentration was
then determined to be 48 ± 1 wt% using eq. (25) and (27) and the activity of water (aH2O = 0.56)
determined from the Pitzer model (section 3).
14
1.8
Density (g cm-3)
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Fe2(SO4)3 concentration (g g-1)
Figure S2. Density measured as a function of ferric sulfate concentration. The red line represents
theoretical Pitzer modeling at 303.15 K [Marion et al., 2008]. This model provides a quite
accurate description the data, and is therefore used to calculate the density of ferric sulfate
solutions are lower temperatures, down to 255 K.
15
Figure S3. Evolution of the enthalpy of fusion of water ice as a function of the water activity in
solution, determined from the ratio of saturation pressures for vapor above ice and liquid water.
The red line represents the empirical regression using eq. (27).
16