Distribution of Solutes Between Steam and Water: Thermodynamic Analysis

Geochimica et Cosmochimica Acta, Vol. 58. No. 13, pp. 2789-2798, 1994
Copyright 0 1994 Elsevier Science Ltd
Printed in the USA. All rights reserved
0016-7037194 $6.00 + .w
Pergamon zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
0016-7037(94~0078-6
Distribution of solutes between coexisting steam and water
JORGE ALVAREZ,HORACK)R. CORTI, ROBERTO~RN~NDEZ-PR~NI,
zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIH
and M. LAURA JAPAS
Departamento Quimica de Reactores, Comisi6n National de Energia Atcimica,Av. Libertador 8250, 1429~CapitalFederal, Argentina
Abstract-For a thorough description of aqueous systems with coexisting liquid-vapor phases, it is necessary
to have a means of describing the concentration of solutes in the two-fluid phases over a wide temperature
range. A genera1 procedure is presented which allows the description of the distribution ratio of solutes
at infinite dilution (k;l) between water and steam over all the range of coexistence of the two-fluid phases.
The procedure has been employed for many different solutes, e.g., nonreactive gases, reactive gases,
nonionic, and ionic solutes. For the gaseous solutes a formulation is given which allows the calculation
of K. over the complete temperature range with good precision.
to describe the tem~mture dependence of the dist~bution
of various solutes in dilute aqueous solutions. The solutes
THE DISTRIBUTION
OFSOLUTES between steam and water over
considered here will cover nonpolar nonreactive gases, gases
the entire temperature range of vapor-liquid coexistence, inwhich undergo protolytic equilib~a zyxwvutsrqponmlkjihgfedcbaZ
in dense water, simple
cluding the region close to zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
T,, (374.i°C), is a property of
electrolytes and, finally, a three-component reactive system.
great practical importance. Areas of interest include the power
Emphasis will be laid upon the establishment of one common
industry which makes use of the steam-water cycle, as well
method for the analysis of all these systems over the complete
as the study of natural geological systems where the migration
range of coexistence of water and steam. In spite of the conof substances is produced in many cases via liquid-gas transfer
venience of having such a general procedure, this goal is selfollowed then by the transport of the solutes dissolved in
dom met; consequently the present work constitutes a singular
steam. There is also a demand for distribution ratios in order
example, albeit an important and useful one, of such a general
to complete the thermodynamic description of natural systhermodynamic method which may be used to describe the
tems which are relevant to geochemists, e.g., hot springs on
behavior of multicom~nent
systems. It is worth emphasizing
the seafloor, geothermal systems, and fluid inclusions involve
that this work does not pretend to be an exhaustive survey
the presence of gases in equilibrium with subcritical water.
of data; whenever critical reviews existed, we have used them
On the other hand, the physical chemistry of these systems
to give quantitative formulations which represent the availis of great interest because it gives information on the effect
able data over the complete range of existence of liquid water.
of density on the macroscopic properties and how these
For those systems where the data is scarce or when a previous
properties change when the critical region is approached. The
critical evaluation would be required, we only attempted a
infinite dilution value of the concentration ratio is related to
more limited formulation applicable to the high temperature
the difference of standard chemical potential of the solute in
region.
steam to that in liquid water. This quantity reflects the change
DISCUSSION
in chemical potential when the solute at infinite dilution is
transferred from the low density vapor to the dense liquid
Thermodynamics
phase; it is a process equivalent to the transfer of solutes at
Let US consider first gaseous solutes which have weak ininfinite diiution between different solvent media, i.e., the
teraction with the solvent, e.g.. hydrogen, nitrogen, oxygen,
medium effect.
noble gases, light hydrocarbons. The best way to describe the
The recent proposal of an asymptotic expression for the
transfer of gaseous solutes from the vapor to the liquid phase
distribution ratio (JAPAS and LEVELTSENGERS, 1989), i.e.,
is through Henry’s constant defined as the limiting value of
an expression which is valid in the vicinity of the solvent’s
the ratio of solute fugacity (fi) to its mole fraction (x) in the
critical point, which unexpectedly was found to apply for
nonionic solutes over a very wide range of solvent densities
liquid in equilibrium with the vapor phase when the solution
becomes infinitely dilute (FERNANDEZ-PRINI
et al., 1992)
(equivalent to a range of temperature of 150 K), is a very
valuable cont~bution to enable a predictive formulation of
the behavior of these systems over the complete liquid-vapor
k,” = limf2.
(1)
x-0 x
coexistence space. A first report (FERNANDEZ-PRINIet al.,
1993a) showing that the asymptotic relation holds also for
In this way Henry’s constant is related to the difference of
electrolytes, has undoubtedly extended the interest in the
standard chemical potential of the solute between the vapor,
general application of this approach to describe the ther&, and the liquid, & phases, and it is only temperature
modynamic behavior of aqueous (as well as nonaqueous)
dependent. Thus,
systems.
In the present work we shall apply a general thermodynamic procedure which has been developed in our laboratory
2789
J. Alvarez et al
7790
The reference state in the vapor phase is the ideal gaseous
solute and that in the liquid phase the solute at infinite dilution.
Considering the conditions which prevail when two-fluid
phases in a binary system coexist at a temperature
7‘ and a
total pressure p, the thermodynamic
analysis yields (FERNANDEZ-PRINI et al., 1992)
where p: is the solvent vapor pressure, y is the mole fraction
of gas in the vapor phase, G2 its fugacity coefficient, and -&’
and F the solute’s activity coefficient and the infinite dilution
partial molar volume in the liquid phase, respectively. Usually
the quantities available through experiment are the pressure,
the temperature,
and X; only seldom the compositions
of
both phases in equilibrium are known with sufficient precision. Therefore, it is better (FERNANDEZ-PRINI and CROVETTO, 1985) to rely only on the composition
of the liquid
phase and use thermodynamic
relationships,
i.e.. equations
of state, to calculate y. The other quantities in Eqn. 3 are not
obtained through measurement;
they require either an equation of state for the binary system (&, y) or a model calculation ($‘, @). We have shown that a self-consistent iterative
procedure may be carried out (ALVAREZ and FERNANDEZPRINI, 1991) to obtain the values of Henry’s constants from
the experimental
(p, T, x) data at high temperature.
In spite
of this success, in the region close to the critical point of
water, say for temperatures
above 580 K, this method of
calculation has an increasing uncertainty. This is due to experimental difficulties as well as to an increasing imprecision
in the equation of state and in the quantities calculated theoretically with the model.
A quantity which is of direct practical interest is the distribution ratio, Qu = y/x, which according to Eqn. 3 is related
to kg by
On the other hand, the distribution ratio at infinite dilution
which is only temperature
dependent may be expressed by
the difference of solute standard chemical potential.
which allows the calculation of KD from the knowledge 01
the properties of the solvent and the change of total pressure
with the composition
of the solution (FERNAUDEZ-PKINI et
al., 1993a). Thus,
k;,
=
which refer to infinite dilution but ut the two d&erent densities
ofthe coexistingfluidphases. This contrasts with Eqn. 2 which
relates In k,” to the standard state of the ideal gaseous solute.
According
constant,
-/
‘dg) ~- I’,(‘) zyxwvutsrqponmlkjihgfedcba
!. 1
where the subscript u indicates vapor-liquid coexistence and
J’, denotes the molar volume of water. A derivation of this
expression is given in the Appendix. As shown by Eqn. 7.
this way of calculating KD does not require the use of an
equation of state or of model calculations, and this is certainly
a very important advantage since, in contrast with the iterative
calculation of kg with Eqn. 3, the validity of Eqn. 7 is not
limited to a given temperature range and it may even be used
close to the critical region. This equation is quite convenient
when the solute is more volatile than the solvent. i.e., when
k;, $ 1. However, for the case of solid solutes. and especially
for electrolytes, Eqn. 7 cannot be used since RI, 4 1. implying
that the second term in the rhs will be very close to -~ izyxwvutsrqpon
and
the resulting Ku will have a rather large uncertainty. In that
case the expression to be used is
which may be obtained from Eqn. 7 by interchanging
the
symbols corresponding
to the vapor and the liquid phases.
JAPAS and LEVELT SENGERS (1989) derived expressions
for kg and for KD which should become asymptotically
valid
as the solvent’s critical point is being approached. These are
and
RT ln KU = &G(J)
- p?(g)).
(lo]
where/‘? is the solvent fugacity, and p: and pL, the solvent
density at T and critical density, respectively. Taking into
account the law of rectilinear diameters zyxwvutsrqponmlkjihgfe
(ROWLINSON and
SWINTON, 1982) which is obeyed in the vicinity ofthe critical
point. the previous expression becomes
In K1, = 2&&I)
p,, \.
!II:
It has been observed that the linear behavior Indicated by
Eqns. 9 and 11 extends far away from the critical point ot
the solvent. The B coefficient in Eqns. 9- 1 I is related to the
critical slope of the pressure as function of composition,
to Eqn. 4 and 5, KD is simply related to Henry’s
k,” = K,@ Fp:.
(6)
that, in principle, it is possible to obtain the same information from any of the two quantities, k; or k;,, both referring to the infinitely dilute solution.
From the thermodynamic
equations characterizing vaporliquid equilibrium it is also possible to obtain an expression
So
+
R7
RT
Thus, In KD is related to the difference of solute’s standard
chemical potentials in the liquid and in the vapour phases
1
It is particularly convenient to use Eqn. II because the limiting value of KD = 1 when 7’ -+ Tc,, is clearly established
and, in principle, a single experimental
datum would suffice
to draw the straight line which characterizes the asymptotic
behavior for a given system. In the case of Eqn. 9, the calculation of the limiting value for T = T,, requires the use of
an equation of state to calculate the coefficient :l, because .,I
= RT,, In (+pz”/@y).
2791
Distribution of solute between steam and water
It should be mentioned that at present there is no means
p?(l) - PC, = i ajti’3,
(13) zyxwvutsrqp
of establishing theoretically the range over which the previous
i=l
relations should hold; this can only be established by experiment. There is however evidence suggesting that the asympwhere t = 1 - T/T,,. The polynomial takes into account the
totic linear relations apply over a wider temperature range
known critical exponent of the temperature dependence of
when there is a big difference of volatility between both comfluid density along the coexistence curve; it reproduces
ponents, e.g., for isotopic mixtures the linear range may be
p:(l) within 0.05 mol dmm3 over the temperature range [500
very small (JAPASet al., 1994). The careful study of the sysK to T,,]. Obviously the coefficients of Eqn. 13, which are
tems HZ-H20 and N2-Hz0 (ALVAREZ and FERNANDEZ- zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIH
reported in Table 1, do not depend on the particular solute.
PRINI, 1991) suggest that in the high-temperature
region a
The following expression was used to describe the vaporconservative estimate of the difference between the value
liquid distribution ratio of the solutes:
predicted with the linear relation and the experimental data
is 10% in KD.
In K. = .A + g i o$i3
In the present work the values required for the thermo1
,=I
dynamic properties of water have been taken from HAAR et
al. (1984).
+ zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQ
(C + DtZJ3 + Et) exp
Volatile Solutes
Nonreactive
where the coefficients ~4, B’, C, D, and E are specific for each
system. The first coefficient is not independent, since Ko( Tc,)
= 1. hence
gases
A survey of Henry’s constants for nonreactive nonpolar
gases dissolved in water over wide temperature ranges has
been recently published (FERNANDEZ-PRINIand CROVETTO,
1989). The information available in the literature was critically analyzed and then processed in such a way that data
from different sources could be evaluated on the same footing.
For the HZ-H20 and Nz-HZ0 systems, Henry’s constants
were taken from ALVAREZ and FERNANDEZ-PRINI(199 1).
In order to calculate K. from Henry’s constant using Eqn. 6
we have used the PENG and ROBINSON(1976, 1980) equation
of state with the values of the cross-interaction parameter
recommended by FERNANDEZ-PRINIand CROVE?TO(1989).
On the basis of the discussion in the previous section, it is
possible to propose a formulation for the infinite dilution
distribution ratio of gases between water and steam of very
wide applicability and which we shall extend below to other
solutes. Since it would be practically more valuable to have
a formulation for In K. as function of temperature rather
than of solvent density, we have proceeded in the following
way. The density of water in equilibrium with steam between
T,, and 500 K was fitted to a polynomial of the form
.A = -Cexp
273.15 - (T,,IK)
100.0
= _oo23719C,
The exponential term in Eqn. 14 was suggested by HARVEY
and LEVELT SENGERS( 1990) as a means of describing the
low-temperature region which is far from T,,. Table 1 reports
the coefficients for inert gases, HZ, 02, N2, and CH4 dissolved
in H20. It also reports in the last column the value of the
coefficient zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPO
2B/R obtained by fitting Eqn. 11 to the data corresponding to T 2 500 K; it is seen that this coefficient is
numerically quite close to B’ obtained when the complete
set of available data were fitted by Eqn. 14, a fact that lends
strong support to the functionality chosen for Eqn. 14. The
capacity of this equation to fit the data over the whole liquidvapor coexistence range, from the triple to the critical temperatures, with a standard deviation which is only slightly
greater than that of much more limited formulations (FERNANDEZ-PRINIand CROVETTO, 1989) is quite remarkable.
In order to test the procedure just described for the calculation of KD from k,“, we have used the information avail-
Table 1, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
Coefficients of equations (11) and (14) for various gas-Hz0 systems. Values
of ai in equation (13) are expressed in mol dm-s.
I
B’
ICI
I
D
E
1 a% 1
2B/R
K drr?/mol
K dm3/mol
123.1941
-75.125
298.827
-234.117
7.2
125.8
135.4272
-75.673
276.266
-209.698
1.6
134.0
127.0588
-57.183
215.804
-168.732
1.8
128.7
124.4726
-87.907
336.754
-262.606
2.7
123.3
113.7488
-7.005
36.593
-37.225
11.5
112.0
131.2241
-17.736
68.965
-58.713
3.8
128.8
124.0282
-45.876
174.752
-136.283
6.4
122.9
125.1614
4.834
-20.824
11.283
7.6
123.2
119.6366
13.836
-42.998
23.839
4.4
119.2
90.7449
31.834
-113.528
79.614
7.2
89.0
(21 = 35.0511
(12 = 23.5673
CIs=-6.1704
(14 =-3.6825
J. Alvarez et al
2792
able from phase diagram studies for the N2-HZ0 and 02H20 systems to calculate the values of zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
KD with Eqn. 7 (FERNANDEZ-PRINI et al., 1993b). For that purpose. the vapor
pressure of the dilute solutions for each isotherm was fitted
The second factor in the rhs member of Eqn. 15 gives the
with a power series in the solute concentration
in the liquid
primary effect of pressure, the third factor corrects for nonphase, X; the linear coefficient gives the value of (dpldx-)F,,.
ideality, and the last one takes account of the effect of pressure
It was found that the linear term was independent
of the
upon the chemical potential of the dissolved solute. Obviously
degree of the polynomial
used if the composition
was reit is necessary to use an equation of state to calculate the
stricted to the range x 5 1 a5 lO_‘.
fugacity coefficients of the solute and to have a value for
Figure 1 shows the plot of T In KD for NZ-H20 and 02CT, normally $? is close to unity and can be neglected below
Hz0 systems against the difference between the water density
580 K (ALVAREZ and FERNANDEZ-PRINI, 1991) if the gas
at T and the critical density of water; according to Eqn. 1I
solubility is not too large.
T In KD should be asymptotically
linear in the water density.
In Fig. 1 the values of KD calculated with (@/LIx-);,, according
to Eqn. 7 are also plotted. For the case of the N2-Hz0 system
Natural systems containing gases which undergo protolyttc
the isothermal solubility of the gas over a sufficiently wide
equilibria in water are ofgreat practical interest. These systems
range of pressures (ALVAREZ and FERNANDEZ-PRINI. 199 1)
contain several solute species in one or in both of the cueiwere used to calculate the quantity (dp/d.x)F,, at the two temisting phases; hence, Ku may be defined in several ways. all
peratures that were studied. For the 02-HZ0 system, the exrelated through the equilibrium reaction constants. We define
perimental data were taken from the phase diagram study of
KIj in terms of those solute species which predominate
in
the system (JAPAS and FRANCK, 1985). It may be seen that
each phase at the extrapolated
conditions. Thus. the distnthe linear behavior extends over a very wide range of tembution of COZ, NHj, and H2S between steam and water will
peratures (about 150 K), and that the data obtained from the
be described in terms of the unionized solute species in both
change of pressure with composition
follow the asymptotic
phases since in pure water these solutes are dissociated to a
linear behavior over that temperature
range as well as those
negligible extent. On the other hand, for the case of HCI the
calculated with Henry’s constants.
definition of KD will take into account the fact that it is apWith Eqns. 4 and 6 it is possible to calculate the solubility
preciably dissociated in water, but associated in steam.
of the gases at a finite gas pressure: thus,
The binary system CO*--Hz0 has been studied by many
authors; however, the values of lig do not provide an unequivocal set of data, especially at high temperatures,
con200 100
300
370
350
sequently the behavior could not be unambiguously
cstab5l
lished (FERNANDEZ-PRINI et al.. 1992). (I‘Rov~ i-1.0 and
WOOD (1992) have reported recently values of kg at three
N,-H,O
4
temperatures
which are very close to 7,,. llsing the PENG
and ROBINSON (1976) equation of state and the values of
&, we have calculated the infinite dilution distribution ratio.
When the whole set of solubility data is plotted as 7’ In k,.,
against solvent density, the three data points of C~ovt:r IO
and WOOD (1992) show a small but appreciable deviation
from the straight line which goes through zero at pc,, this is
I
illustrated in Fig. 2. However the linear dependence of 1.’in
40
30
10
20
0
k;, with solvent density seems to be supported by the calucs
(pi-p,l)/(mol
dm-‘)
of KD determined
with Eqn. 7 employing
the values ot
(a~/&)?;, obtained from the study of T Alit:.UOM HI and
----1
zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
KENNEDY (1964).
4
Oz-W’
The fact that the values of & calculated using the data of
CROVFTTO and WOOD (1992) give negative deviations which
Q 3increase in magnitude when T,, is approached. strongly sugc
gests that these deviations are due to the neglect of the solute’s
L
7
2activity coefficient 77, which is smaller than unity at high
a
temperatures.
Using the perturbation
theory equation proposed by ALVAREZ and FERNANDEZ-PRINI ( 1991), it was
possible to estimate the contribution
of the solute’s action!
coefficient
(Eqns.
4
and
6)
to
7’
In
KIj.
The correction was
30 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
calculated for the three values of k;i reported by C~ovt.r~ o
bi-p,t)/(mol
dm-3)
and WOOD ( 1992) using self-consistent
values for the hardFIG. I. Tin KD(in K) against p: - pCI, the difference between the
sphere equivalent diameters. These corrections resulted in a
pure solvent’s liquid density and its critical value. 0 and 0: data
shift of 93, 107, and 161 K for 7’In k; at 62.1. 631.7, and
from gas solubility measurements
using Eqns. 3 and 6. +: points
642.7 K, respectively, with a conservative estimate of their
obtained with Eqn. 7. Temperatures in Celsius are given in the top
scale.
uncertainty of ?30 K.
ov
51-
o---G
Dist~bution of solute between steam and water
2793
portedby KISHIMA (1989). Two points which were calculated
3
5
c
:
0
2
1
0
0
10
20
30
40
(pi-pcl)/(moldm-3)
from the phase diagram study of CARROLL and MATHER
(1989) using Eqn. 7 have been included in the plot; the agreement with the solubility data is extremely satisfying.
HCl is the most reactive substance of this group of solutes.
In the dense phase it exists essentially in the form of dissociated ions. In order to determine the distribution ratio for
HCl, the data of SIMoNsoN and PALMER( 1993) for the equilibrium concentmtions in steam and water have been used.
In agreement with the SIMONSON and PALMER(1993) tmatment, it was assumed that HCl is associated in the aqueous
gas phase while it is ionized in liquid water. Therefore, it is
convenient to consider the following equilibrium for the distribution of HCl:
FIG. 2. Same graph as in Fig. 1 for the CO*-HZ0 system. 0: calculated from gas solubility data; +: points obtained with Eqn. 7; 0:
data from CROVETTOand zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
WOOD (1992) uncorrected; n : same
zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
as
H+(aq) -+-Cl-(aq) + HCl(g),
previous corrected for solute activity coefficient.
350
After correcting for the solute’s activity coeffi~ent, KD calculated with the gas solubility data and those obtained from
the change of pressure with composition agree very well; this
is very rewarding and an important support for the procedure
we employ to evaluate solute distribution between steam and
water. The convenience of calculating the infinite dilution
distribution ratio with Eqn. 7, whenever this is possible, becomes quite clear since this procedure does not require either
a knowledge of $ or of QY’.However it must be realized
that the uncertainty of the information from the phase diagrams is in general bigger than that of the gas solubility data.
On the other hand, the successful and consistent description
of the distribution in the CO2-H20 system, lends support to
the semi-empirical iterative method proposed by ALVAREZ
and FERNANDEZ-PRINI (199 1) for the systems HZ-H20 and
Nz-HzO.
Table 1 also reports the coefficients of Eqn. 14 for CO*HzO. For this purpose all the high temperature data illustrated
in Fig. 2 were employed and for the low-temperature region
the data compiled by WILHELM et al. (1977) were used.
It should be mentioned that for all these systems we have
verified, whenever possible, that the values of the slopes 3
according to Eqn. 11 agree with those calculated with Eqn.
12 from the information of the critical line, indicated by
subscript crl, using the relation of KRICHEVSKH (1967):
300
200
(16)
100
1.2
'NH,-Hz0
0.9 -
3.0
2.5 _W-W’
40
(pi-p,l)/(mol
t
dm?
HCL-H,O
4
However, the uncertainty in zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
(apfdx)$?j obtained from the
critical line was larger than that of the slopes obtained by
2
plotting Tin ic, against solvent density.
Figure 3 shows the plots of T In iu, against p:(l) - pFl for
NHJ, HIS, and HCI aqueous solutions. The distribution of
0
ammonia between steam and water at high temperatures has
been determined by JONES (1963) and his data are plotted
-2 I
in Fig. 3. In the case of H$-H20, the curve in Fig. 3 cor30
41
0
10
20
responds to the equation given by LEE and MATHER (1977)
(pi-p,i)/(moI
dm?
for In kg as function of temperature. The calculation of KD
FIG. 3. Same graphasin Fig. 1.NH,-H20, 0 (JONES,1993). H$from them was done using the coefficients of the Peng-RobH20, 0 (KISHIMA, 1989). 0~ points obtained with Eqn. 7. Heavy
inson-Stryek-Vera equation of state reported by CARROLL
curve: from LEEand MATHER(I 977). HCI-H20, 0 (SIMONSON
and
PALMER,1993).
and MATHER ( 1989). The open symbol denotes the data re-
1794
J. Alvarer et al.
constant IYn(HCl): zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
though they did not cover regions very close to the criticat
point. SIMONSONand PAUVZER
(1993) extrapolated their data
m&g)
and reported for the same quantity the value 9300 K. On
Kn (HCI) = (17)
m,.,*(l)mc,-(l)+Y .
account of this scatter in the values reported for I5 thr value.
we obtained by linear extrapolation (cf. Fig. 3’)appears ver:
where m,(l) and vn,(g) denote the molality of solute species i
reasonable.
in the coexisting liquid and vapor phases. respectively. In
The slopes of the straight lines of I‘ ln i\!, against watitl
Eqn. 17 it has been assumed that the activity coefficient of
density are reported in Table 7 for NH+ fl?S. and Hc’l in
HCI in steam is unity.
water. For these systems the only information that has hem
Figure 4 illustrates the behavior observed at 573 K for the
fitted is that corresponding to the high tempcraturc range ;t>
HCI-HZ0 system. At room temperature such a plot has been
indicated in column 3.
a textbook exampie to show that HCI is ionized in liquid
water while it is a covalent compound in the vapor phase.
Ionic Solutes
The fact that the modality of HCI in the vapor is linearly
In order to obtain information about the distribution ut
related to the square of the mean activity of HCl(aq). as ilelectrolytes between steam and water, we haye made use ut
lustrated by Fig. 4, implies that HCl dissociates in the dense
the scarce ex~~rnental information available for NaCl and
fluid phase. The data suggest that the assumption about the
KC1 which. consequently. is ofgreat value. KH \fiX:i 1.1%and
different speciation of HCI in each fluid phase remains valid
&~RlWV
(1966) have reported the equilibrium concentl-ation
even close to the critical point of water.
of the two electrolytes in the liquid and vapor solvent phases.
For HCl it is also verified that the linear behavior of 7‘ In
On the other hand BISCHOFFand PIYZEK(1989) have ana-.
KI, with p?(l) applies over a wide range of temperatures, as
lyzed critically the available data for ?iaCL including thasc
shown in Fig. 3. It is clear that the quantity &AHCl). denoting
ofthe first authors. These sources form the basis upon which
the equilibrium constant for reaction (16). will not go to unit)
we have elaborated our analysis of the distribution of iom:
at r,,. rather it will tend to the value of the equilibrium consolutes between water and steam; an additional source
stant for the association of HCI in a fluid having the properties
(KIISKE, 198 I ) could not be used for the reasons discussed
of water at the critical point. i,c..
with the equilib~um
H+(fl) + Cl-(fl) * HCQff).
(IX)
That is. Eqn. 11 becomes
below.
In order to obtain Kn it is necessary to extrapolate the data
to infinite dilution. The success of the extrapolation proctxiur~
will depend on the concentration range of the available data.
the procedure being more successful when the experimental
concentration
range covers a more dilute region. For NaC‘!
and @ = L&,in &,(HC1, 7,,).
and
KCI
the
most
dilute solution where information aboui
The linear extrapolation of the data in Fig. 3 gives for (_
the liquid-vapor compositions is available is 0. I modal salt
the value 79.50 + 50 K, which should be compared to 8800
in the liquid phase; in spite of this limitation the plots ft-ep
i: 50 K obtained by SIMONSON and PALMER(I 993) with a
resentative examples are illustrated in Fig. 5) strongly suggcsl
nonlinear extrapolation of the same data.
that
the correct extrapolation is in terms of equal powers of
There are two sources of ~onductimetri~ data for HCI in
the concentrations in the vapor and in the liquid phases. Thlz
supercritical water which give direct information on the disimplies that the infinite dilution standard states in the vapor
sociation constant. FRANCK (I 956) has studied a wide range
and
liquid phases obtained by extrapolation i)f the cxperioftemperature and density which extended to the near-critical
mental
data (cf. Eqn. 5) refer to the same species in both
region. We have extrapolated his data to the critical point of
fluid phases, i.e., individual ions. If the infinite dilution vaiues
water obtaining @ = (7000 + 200) K. The other source of
obtained by extrapolation corresponded to associated ions 111
conductimetric data is the more recent work of FRANI z and
the vapor and dissociated ions in the liquid, the distribution
MARSHALL(1984)
zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
who reinvestigated the same system, alratio at infinite dilutions should be obtained b> a linear estrapofation
of the square root of the concentration in ~apttr
_._..
_,._..__
._~.
,
i,,,;
0.6 r---against the concentration of salt in the tiquid. as it aas the
$w:
,.I
i
case for HCI (Eqn. 17 and Fig. 3). Moreover the rxtrapolatetl
;
value of the concentration in the vapor as function of the
liquid phase concentration does not go to zero when the
square root of the NaCl concentration in the vapor ic plotted
against the tiquid phase coll~entration (Fig. 5h.c).
tt is important to remark that the choice ofstandard state5
does not imply that the ions are fully dissociated in the actual
RTtn KI, = Z&$(l)
- /-1,:) i P
(113)
solutions, but that even when associated in the vapor phase
there are enough free ions to yield by extrapofation the value
FIG. 4. Vapor concentration of HCI in aqueous solutions against
the mean activity of HCI in the liquid phase for 573 K (SIMONXX
and PALMER,
1993). Concentrations are given in the modality scale.
cl: right ordinates, A: left ordinates.
corresponding to a dissociated infinitely dilute clectroiytc.
Other authors have considered that ion association in the
vapour phase is so large that the standard state obtained b>
extrapolation
of the experimental
points corresponds
to an
associated ion-pair in steam (cf. T~NGER and Pt I DR. IQW!.
2795
Distribution of solute between steam and water
Table 2. Coefficients of equation (11) and temperature
range
of fitting
for various
solutes.
2BJR
‘I’,,,
K dm3/mol
K
473-590
HCI”
30.3f0.5
77.4f0.2
-267zt2
NaCl
-337*3
573-646
KC1
-373*1
573-643
NH3
HzS
473-603
373-623
(a) For HCI equation zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHG
(lla) was used
tribution ratio QD = y/x to zero concentration
using only
In order to obtain the values of zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
KD for NaCl the data for
points for concentrations
in the liquid phase lower than 2
a given isotherm were plotted as function of pressure. At low
molal, the lowest concentration
in the liquid phase being 0.1
temperature
it was possible to extrapolate the observed dismolal. For the isotherms above 623 K a relatively strong
increase of QD with dilution was observed, in these cases the
reciprocal of the distribution
ratio was almost quadratic in
the difference of water vapor pressure between the pure sol573 K
vent and the solution. For the case of KCl, the only available
source (KHAIBULLIN and BORISOV, 1966) reported values of
(a)
QD which did not show any particular trend with solute concentration.
Moreover there were only three points for concentrations lower than 2 molal. Consequently
the KC1 data
were averaged to obtain the infinite dilution value. It is our
contention that the deviation of experimental
points, except
at the highest temperatures, reflects the experimental difficulty
0, ,u,
;, ( a,a,
of such measurements
rather than a trend in concentration.
012345671
For NaCl it has been possible to calculate KD with Eqn. 8
also, using the phase diagram information
available in the
m,,,,(l)
same two sources; this was not the case of KC1 because there
2
.
.
were too few points to allow a reasonable extrapolation
to
-.
infinite dilution. For NaCI-H20, the isothermal vapor pressure of the solutions was fitted using second and third degree
0
0
.
0
polynomials in the vapor phase composition y. Similar results
0
for the linear term were obtained provided y 5 5 10e7 at 573
1
g
K and y 5 10e4 for 643 K. This is in agreement with the
expectations considering the increase in dissociated NaCl in
(b)
573 K
the vapor phase as the temperature,
and consequently
the
density of steam, increases (cf. Fig. 5).
,“/‘,
Figure 6 is a plot of T In KD for NaCLH20 and KCI-HI0
012345671
against the solvent density. It may be seen that for the two
mNac,o)
)
electrolytes the linear behavior is closely followed over the
complete temperature
range that was studied, the lowest
temperature
considered was 573 K because at lower tem0 -D
0
a
0
0” zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
peratures the analytic information
from the vapor phase is
i
0
very unreliable. In the case of NaCl the points obtained from
0
l
’
.
zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
the extrapolated
analytical concentration
ratio defines the
e
0
same straight line as those obtained from the slope of the
-4
l
4
0
.
pressure as function of vapor composition.
The slopes of the
0
(cl
straight lines in Fig. 6 for NaCl and KCI are reported in Table
.
623 K
0
2. The values reflect the fact that KC1 is less volatile than
:
NaCI. The slopes determined
with the value of (@/&x)$$
0
calculated from the equation of state reported by HOVEY et
1.2
1.6
2.0
0.4
0.8
0.0
al. (1990) were -294 and -324 K. dm3 - mol-‘, respectively,
T+.,,(l)
for NaCl and KCI. The differences between the two pairs of
FIG. 5. Vapor concentration
and distribution
quotients of salt in
values is not large; moreover, the equation of state of HOVEY
the NaCl-Hz0
system against liquid phase concentration
(given in
et al. (I 990) was obtained by fitting data of several properties
the molality scale). Open symbols, right ordinates; filled-in symbols.
of the NaCI-HZ0 system and perhaps does not reflect with
left ordinates. (a) and (b) 573 K isotherm. (c) 623 K isotherm.
,?rg,
I
OI?““,“““““‘,‘J
.
.
I
J. Alvarez et al
I.
0
370
360
340
320 300
6
12
16
20
4
(pi-Pcl)/(rnol
;
24
dm-“1
FIG. 6. Same graph as in Fig. I. KCI-HzO. 0; NaCI-H20, 0:
obtained from equilibrium concentration in steam and water: 0,
data for NaCl obtained with Eqn. 8.
too much detail the particular quantity we are interested in
here.
QUIST and MARSHALL
(1968) have determined
the conductivity of supercritical aqueous solutions of NaCl over wide
ranges of temperature
and solvent density. Conductivity
is
one of the most suitable techniques to determine the extent
of ionization of electrolytes. The study was done for supercritical water, but it is possible to extrapolate the results in
density and in temperature to obtain an estimate of the degree
of dissociation
of NaCl in steam when its concentration
is
that in equilibrium
with 0. I and 0.01 molal in the liquid
phase. Table 3 reports the values calculated for the degree of
dissociation
of NaCl at four temperatures.
NaCl is significantly associated in steam, but the fraction of free ions is not
at all negligible suggesting that it is possible that the extrapolation procedures
gives information
about the free ions
rather than about the ion-pair.
If one assumes that Na+ and Cl- ions are strongly associated
in steam, the mole fraction of free ions becomes (cuy), where
LYis the degree of dissociation of the salt in the vapor phase.
Then using Eqn. 11 we have
T lim
x-0
In f
i
= $
(p?(l) - p,,) -~ 7’ In cr” .
ciation. Consequently,
under these conditions of strong association over a narrow concentration
range, Eqn. I9 would
not extrapolate to zero. On the other hand, if the extrapolated
values for the electrolyte corresponded to a partially associated
electrolyte, then aa would change with temperature
and 7‘
In zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLK
KD probably would not show a linear dependence
on the
solvent density. Since, as shown in Fig. 6, neither of the two
situations are observed, we conclude that the values of L,;
obtained by extrapolation
of the experimental
distribution
ratios refer to the same dissociated standard state in both
fluid phases.
There is another study of the distribution ol.NaCl between
steam and water reported in the literature (KUSKE. 198 I i.
The composition of liquid and vapor phases were determined
along several isotherms and isobars at pressures which correspond to the vapor pressure of pure water at each temperature. Extrapolation
of the value of NaCl concentration
m
steam to zero salt in water for isobars and isotherms show
differences which are difficult to understand. These differences
are small at the highest and the lowest temperatures and very
large in the intermediate
range. In all cases the isobars were
studied down to much lower electrolyte concentration.
The
apparent disagreement
between the two types of runs is not
due to their different concentration
range. something that
could occur only if a significantly different speciation existed
over each concentration
range. Even the careful analysis 01
the low concentration
data is ambiguous. Consequently these
data could not be used as another source of information
for
the distribution
ratio.
Systems Involving Chemical Reaction
Ternary and quatemary aqueous systems are of importance
in geochemistry.
Whenever there are no chemical reactions
among the components
of the mixture and the interaction
between solutes can be neglected or easily taken into account
(like in dilute ionic systems), it is possible to deal with these
systems by a trivial extension of the method applied above
for binary mixtures. It is common to have an interest in multicomponent
systems which undergo protolytic reactions to
form new species. In essence this type of process does not
change the number of degrees of freedom of the systems as
a whole, since for each new component
there will be also a
new condition of equilibrium.
Thus, the number of truly
independent
degrees of freedom is constant. Due to the very
strong dependence of the constant of autoprotolysis
of water
on the density, HZ0 in steam (i.e., at T _i- 7; j and ;) rr [I<!I IF zyxwvuts
(19)
1
where (Y~ is the apparent degree of dissociation of the electrolyte when the ratio of concentrations
is extrapolated
to
infinite dilution. This number will be different from unity if
the concentration
range used to extrapolate the behavior is
too limited to perceive an appreciable change in solute spe-
Table
3
N&l
degrerof dissocmtion
steam
for several
and
gas-phase
temperatures
and
concentrations
calculated
from
phase.
They
li,,,;
extrapolated
were
values
reported
by
tions
~~~~~ are
given
II
in temperature
QUIST
arid
,n mol.d~~i-~.
composition
in the
the
dissociation
and
vapor
MARSHALL.
in
liquid
constants,
density
from
1968
Concentra-
the
2797
Distribution of solute between steam and water
nor in the form of associated pairs) exist in the vapor phase.
These results are compared to those calculated with Eqn. 19
from data in the literature, the (T,p)dependence of the three
equilibrium constants were reported by PALMER and SIMONSON (1993). First it should be noted that zyxwvutsrqponmlkjihgfed
T In & obtained
has been studied up to 623 K zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
by PALMER and SIMONSON
from the data for the dist~bution ratios when extrapolated
(1993) with special interest in detecting the presence of NH&l
to the critical density gives 2260 K. Taking into account the
in the vapor phase. The detection of NH.&?1in steam would
experimental uncertainties, this value is relatively close to
be important for the corrosion of materials in the steamthat of the product &(HCl)* KH (1820K at Tc,). Secondly,
water cycle used in the generation of electricity, since it would
the fact that the values of K&NH? + HCl) obtained from the
increase the transport of the aggressive Cl- ion by steam.
Measurements were carried out in excess HCl and also in
study of the (HCl + NH3) aqueous system at T 2 573 K do
not agree with the straight line in Fig. 7 might be attributed
excess NH3 over a wide temperature range. The concentration
to an increasingly implant
~ont~bution of the species
of the solutes however did not change su~cientiy to give a
clear picture of the concentration dependence of the distriNH&l in the vapor phase. This explanation would require
confirmation since the data are somewhat ambiguous; some
bution ratios. Under the experimental conditions the calof the runs in this temperature range show an increase in the
culated amounts of NH4Cl in the vapor for T I 573 K were
at least an order of magnitude smaller than the concentrations
amount of NHdCI in the vapor when the concentration of
WC1 and NH3 in the liquid decreases, while others show a
of HCl and NHa. However, at the highest temperatures the
normal behavior. This difficulty is obviously due to the very
amount of NH&l in steam was estimated to be similar to
complicated nature of the experimental determination; conthose of the nonionic species. From the point of view of the
sequently, at present the question should be considered still
present work these data may be used to illustrate the possibility of describing the steam-water distribution in this system
open for temperatures higher than 580 K.
with the assumption that in the vapor phase only the species
CONCLUSiONS
NH3 and HCI are present. This assumption implies that the
electrolyte dist~bution is governed by the following reaction:
Using analytica data together with information from phase
diagrams, it was possible to obtain a good description of the
NH$(aq) + Cl-(aq) Y=!NH3(g) + HQ(g);
(20)
distribution of solutes between water and steam. The results
and the equilibrium constant is given by
agree with the predicted asymptotic behavior.
Supplementing these results with low-temperature data, it
is possible to propose formulations for the distribution ratio
of solutes at infinite diiution which are valid over all the
This quantity may also be given in terms ofthe distribution
temperature range of coexistence of water and steam. Forratio of NH3 and HCl by
mulations are reported for many gaseous solutes.
essentially not dissociated into ions. Consequently protolytic
equilibria will only predominate in the dense phase.
On the basis of the previous digression we shall analyze
the case of aqueous mixtures of HCI and NHs. This system
Ko(NH3 + HCl) = K,,(NH~)KD(HCl)&.,,
(22)
where rC, is the constant of hydrolysis of ammonium
liquid water:
ion in
NH: + Hz0 = NH3 i- H30+.
(23)
Figure 7 illustrates the behavior found for &(NHS + HCI)
as function ofthe liquid density. The figure contains the values
of this quantity calculated with the data reported by PALMER
and SIMONSON (1993)
for solutions with excess HCI and ex-
thank Dr. D. A. Palmer and Dr. J. M. Simonson for kindly providing us with a preprint of their work. We
are grateful to Dr. M. Simonson for his detailed review of the manuscript and his helpful comments. H. R. Corti and R. Fern~ndez-Prini
are members of Carrera de1 Investigador CONICET.
Acknowkedgmenfs-W e
Ediwrial
handling:
D. J. Wesolowski
REFERENCES zyxwvutsrqponmlkjihgfedc
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200
100
350
300
BISCHOFFJ. L. and PITZER K. S. (1989) Liquid-vapor relations for
41 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
the system NaCI-H20: Summary of the P-T-x surface from 300
1
to 500°C. Amer. J. Sci. 289,2 17-248.
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cess NH3 under the assumption
that no ions (neither
free
Fluid Phase Equil. 74, 21 l-288.
-I31
0
I
10
30
20
(pi-p,l)/(mol
40
dm-?
FIG. 7. Same graph as in Fig, 1 for the NH3-HCI-Hz0 system. n :
runs with excess NH3; 0: runs with excess HCI; ---:
Eqn. 22.
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R. and CROVETTOR. (1985) A critical evaluation
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R. and CROVETTOR. (1989)Evaluation of data
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Press.
2798
J. Alvarez et al.
TAKENOUCHI
S. and KENNEDY G. C. (1964) The binary system H20FERNANDEZ-PRINIR., JAPASM. L., and zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
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Interaction of Iron- based M aterials with W ater and
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APPENDIX
aqueous fluids: I. Hydrochloric acid from 100 to 700°C and at
pressures to 4000 bars. Amer. J. Sci. 284,651- 667.
Derivation of Eqn. 7
HAARL., GALLAGHERJ. S., and KELL G. S. (1984) NBS- NRC Steam
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R. J. (1990) Vapor-liquid phase equilibria of potassium chloride-water mixtures: Equation of state representation for
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JAPAS M. L. and LEVELTSENGERSJ. M. H. (1989) Gas solubility
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Starting with the Gibbs-Duhem relationship for a phase (Yand
using the condition that all phases present are in equilibrium, i.e.;
pT=&=
..-,wehave
- V(a)dp + S(a)dT + xdpz f ii - x)dM ! = 0
Subtracting the previous expression for (Y=zliquid from that for
u = gas, we get
[V(g) - VlWp - IS(g)- SNldT
i- (x - y)(dp* - - i&j = 0.
(Alj
where x is the mole fraction of solute in the liquid and y in the gas
phase, respectively.
Considering that
705- 713.
JONESM. E. (I 963) Ammonia equilibrium between vapor and liquid
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KHAIBULLINLKH. and BORISOVN. M. (1966) Experimental investigation of the thermal properties of aqueous and vapor solutions
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Eqn. Al becomes
8P2 -ccl)
dv\ = 0
+ F
3X
I
f’,Wp - [Sz(U - SW?
[Vz(l)-
We now use the following relationships to transform the previous
equation,
a in [xyz/( I -- x)7,]
a(r2_RT
din yi‘
---I
r7.r
8X
V(g)- V(1) + (A’ - y)[ Vz(I) - L’,(l)]
= (1 - YjI~‘&f -
V,lOl + .vl~‘zW - l’d)l.
So that for binary liquid-vapor equilibria at constant temperature
I(1 - Y)[~,(P) -
V,(l)1+ Y[f’zM- V4M&
Chem. Eng. Data 38,465- 474.
PENG D.-Y. and ROBINSON
D. B. (1976) A new two-constant
of state. Ind. Eng. Chem. Fund. 15, 59- 64.
equation
PENC D. Y. and ROBINSOND. B. (1980) Two- and three-phase equilibrium calculations for coal gasification and related processes. In
But (20 = y/_-t-and dp = ~~p/~x)~.*d~consequently.
& r
1 + ( 1 - Yi[ v&9 -
MARSHALLW. L. (19681 Electrical conductances
of aqueous sodium chloride soI&ons from 0 to 800°C and at
pressures to 4000 bar. J. Phys Chem. 72,684- 703.
ROWLINSONJ. S. and SWINTONF. L. (t982) Liquids and Liquid
M ixtures, 3rd ed. Butterworths.
SIMONSONJ. M. and PALMERD. A. (1993) Liquid-vapor partitioning
of HCl(aq) to 35O’C. Geochim. Cosmochim. Acta 57, 1- 8.
QUIST A. S. and
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Thermodynamicsof Aqueous Sy stems withIndustrialApplications
(ed. S. A: NEWMAN);ACS Symposium Series No. 133,- p. 393.
Now if I +
0,
K
D