Aqueous nonelectrolyte solutions. Part XV. The deuterium sulfide- deuterium oxide system and the deuterium sulfide D-hydrate

Article abstract of DOI:10.1139/v98-133

The univariant (1₁1₂g) saturation vapor pressure of liquid deuterium oxide (phase I₁) with liquid deuterium sulfide (phase I₂) in equilibrium with a gas phase (g) has been measured in a stirred titanium reaction vessel at 19 temperatures from 33.003 to 18.905°C and at total pressures from 2.4500 to 1.7428 MPa. The univariant (hl₁g) saturation vapor pressure of deuterium sulfide D-hydrate (phase h) in equilibrium with liquid deuterium oxide and a gas phase has been measured at 58 temperatures from 30.666 to 2.798°C and at pressures from 2.2959 to 0.11629 MPa. The maximum temperature for deuterium sulfide D-hydrate with a gas phase, the invariant quadruple point Q(h1₁1₂g), has been determined from the cut of the (h1₁g) and the (l₁1₂g) curves at temperature 30.770°C with standard error 0.0043°C and at pressure 2.3263 MPa with standard error 0.00018 MPa. The univariant (s₁1₁g) equilibrium of D-ice (phase s₁) with liquid deuterium oxide and a gas phase containing deuterium sulfide has been measured at 11 temperatures from 3.8061 to 3.4540°C and at pressures between 0.00242 and 0.10542 MPa. The lowest temperature for stability of deuterium sulfide D-hydrate with liquid deuterium oxide, the invariant quadruple point Q(hs₁1₁g), has been determined directly at 3.3917°C with standard error 0.0009°C and at pressure 0.12364 MPa with standard error 0.000011 MPa. This quadruple point Q(hs₁1₁g) has also been defined by the cut of the (hl₁g) and the (s₁1₁g) curves at temperature 3.3912°C with standard error 0.0006°C and at pressure 0.12363 MPa with standard error 0.000002 MPa. The deuterium sulfide - deuterium oxide gas mixture, represented by a Redlich-Kwong equation of state, has been used to evaluate the fugacities and compositions of the gaseous and liquid deuterium oxide phases for all equilibria. Raoult's law using fugacities has been used to evaluate the saturation mole fraction of deuterium oxide in liquid deuterium sulfide and the Henry's law constant for deuterium oxide solubility in liquid deuterium sulfide between 33.003 and 18.905°C. Data for the (I₁1₂g) and (s₁1₁g) equilibria have been accurately represented by simple two-parameter equations. Data for the (hl₁g) equilibrium have required a model with seven significant parameters for proper representation between 30.666 and 2.798°C.

Full text of DOI:10.1139/v98-133

1
119
Aqueous nonelectrolyte solutions. Part XV. The
deuterium sulfide – deuterium oxide system and
the deuterium sulfide -hydrate
D
Colin W. Clarke and David N. Glew
Abstract: The univariant (l l g) saturation vapor pressure of liquid deuterium oxide (phase l ) with liquid deuterium
1
2
1
sulfide (phase l ) in equilibrium with a gas phase (g) has been measured in a stirred titanium reaction vessel at 19
2
temperatures from 33.003 to 18.905°C and at total pressures from 2.4500 to 1.7428 MPa. The univariant (hl g)
1
saturation vapor pressure of deuterium sulfide D-hydrate (phase h) in equilibrium with liquid deuterium oxide and a gas
phase has been measured at 58 temperatures from 30.666 to 2.798°C and at pressures from 2.2959 to 0.11629 MPa.
The maximum temperature for deuterium sulfide D-hydrate with a gas phase, the invariant quadruple point Q(hl l g),
1
2
has been determined from the cut of the (hl g) and the (l l g) curves at temperature 30.770°C with standard error
1
1 2
0
.0043°C and at pressure 2.3263 MPa with standard error 0.00018 MPa. The univariant (s l g) equilibrium of D-ice
1 1
(
phase s ) with liquid deuterium oxide and a gas phase containing deuterium sulfide has been measured at 11
1
temperatures from 3.8061 to 3.4540°C and at pressures between 0.00242 and 0.10542 MPa. The lowest temperature for
stability of deuterium sulfide D-hydrate with liquid deuterium oxide, the invariant quadruple point Q(hs l g), has been
1
1
determined directly at 3.3917°C with standard error 0.0009°C and at pressure 0.12364 MPa with standard error
.000011 MPa. This quadruple point Q(hs l g) has also been defined by the cut of the (hl g) and the (s l g) curves at
0
1
1
1
1 1
temperature 3.3912°C with standard error 0.0006°C and at pressure 0.12363 MPa with standard error 0.000002 MPa.
The deuterium sulfide – deuterium oxide gas mixture, represented by a Redlich–Kwong equation of state, has been
used to evaluate the fugacities and compositions of the gaseous and liquid deuterium oxide phases for all equilibria.
Raoult’s law using fugacities has been used to evaluate the saturation mole fraction of deuterium oxide in liquid
deuterium sulfide and the Henry’s law constant for deuterium oxide solubility in liquid deuterium sulfide between
3
3.003 and 18.905°C. Data for the (l l g) and (s l g) equilibria have been accurately represented by simple two-
1 2 1 1
parameter equations. Data for the (hl g) equilibrium have required a model with seven significant parameters for proper
1
representation betweem 30.666 and 2.798°C.
Key words: deuterium sulfide – deuterium oxide system, clathrate D-hydrate of deuterium sulfide, deuterium sulfide D-
Clarke and Gh lye dwr ate1s 1t a2 b9i lity, freezing of deuterium oxide – deuterium sulfide, phase equilibria of deuterium sulfide – deuterium oxide.
Résumé : Opérant dans une cuve réactionnelle de titane sous agitation, à 19 températures allant de 33,003 à 18,905°C
et à des pressions totales allant de 2,4500 à 1,7428 MPa, on a mesuré la tension de vapeur de saturation à une variable
(
1 1 g) de l’oxyde de deutérium liquide (phase 1 ) avec du sulfure de deutérium liquide (phase 1 ) en équilibre avec
1
2
1
2
une phase gazeuse (g). Opérant à 58 températures allant de 30,666 à 2,798°C et à des pressions allant de 2,2959 à
,11629 MPa, on a aussi mesuré la tension de vapeur de saturation à une variable (h1 g) du D-hydrate de sulfure de
0
1
deutérium (phase h) en équilibre avec de l’oxyde de deutérium liquide et une phase gazeuse. En se basant sur le point
de jonction des courbes (h1 g) et (1 1 g) à une température de 30,770°C avec une erreur-type de 0,0043°C et à une
1
1 2
pression de 2,3263 MPa avec une erreur-type de 0,00018 MPa, on a déterminé la température maximale du D-hydrate
du sulfure de deutérium, le point quadruple invariant Q(h1 1 g). Opérant à 11 températures allant de 3,8061 à
1
2
3
,4540°C et à des pressions allant de 0,00242 à 0,10542 MPa, on a mesure l’équilibre à une variable (s 1 g) de la
1 1
glace-D (phase s ) avec de l’oxyde de deutérium liquide et une phase gazeuse contenant du sulfure de deutérium.
1
Opérant à 3,3917°C avec une erreur-type de 0,0009°C et à une pression de 0,12364 MPa avec une erreur-type de
0
,000011 MPa, on a déterminé directement la température minimale pour la stabilité du D-hydrate de sulfure de
deutérium avec de l’oxyde deutérium liquide, le point quadruple invariant Q(hs 1 g). Ce point quadruple, Q(hs 1 g), a
1
1
1 1
aussi été défini par le point de rencontre des courbes (h1 g) et (s 1 g) à la température de 3,3912°C avec une erreur-
1
1 1
type de 0,0006°C et à une pression de 0,12363 MPa avec une erreur type de 0,000002 MPa. On a utilisé le mélange
gazeux sulfure de deutérium – oxyde de deutérium représenté par l’équation d’état de Redlich–Kwong pour évaluer les
fugacités et les compositions des phases gazeuses et liquides de l’oxyde de deutérium de tous les équilibres. On a fait
appel à la loi de Raoult utilisant des fugacités pour évaluer la fraction molaire de saturation de l’oxyde deutérium dans
Received January 26, 1998.
1
C.W. Clarke and D.N. Glew. Exploratory Research Laboratory, Dow Chemical Canada Inc., Sarnia, ON N7T 7M1, Canada.
1Retired. Author to whom correspondence may be addressed. Telephone: (519) 337-3136. Present address: 536 Highbury Park,
Sarnia, ON N7V 2J9, Canada.
Can. J. Chem. 76: 1119–1129 (1998)
© 1998 NRC Canada

1
120
Can. J. Chem. Vol. 76, 1998
le sulfure de deutérium liquide et on a utilisé la constante de la loi de Henry pour évaluer la solubilité de l’oxyde de
deutérium dans le sulfure de deutérium liquide entre 33,003 et 18,905°C. On peut donner une représentation graphique
correcte des données des équilibres (1 1 g) et (s 1 g) en faisant appel à des équations simples à deux paramètres. Pour
1
2
1 1
donner une représentation adéquate des données pour l’équilibre (h1 g) entre 30,666 et 2,798°C, on doit faire appel à
1
un modèle à sept paramètres significatifs.
Mots clés : système sulfure de deutérium – oxyde de deutérium, clathrate du D-hydrate de sulfure de deutérium, stabi-
lité du D-hydrate du sulfure de deutérium, congélation de l’oxyde de deutérium – sulfure de deutérium, équilibre de
phase du sulfure de deutérium – oxyde de deutérium.
[
Traduit par la Rédaction] Clarke and Glew
The upper motor body was 90 mm high with a lower flange
F1, the middle shaft body was 170 mm high with an upper
flange F1 and a lower flange F2, and the lower impellor
body was 100 mm high with an upper flange F2. Each pair
of flanges was drawn together by six hexagonal nuts on
As part of a continuing study (1, 2) of the structural and
thermodynamic properties of aqueous nonelectrolyte solu-
tions and of their solid clathrate hydrate solutions, it became
of interest to compare the thermodynamic properties of
nonelectrolyte solutions in deuterium oxide with their solid
clathrate D-hydrate solutions. The properties of aqueous hy-
drogen sulfide solutions (3, 4) and of the hydrogen sulfide
gas hydrate (5–7) were well known, but the properties of
deuterium sulfide solutions in deuterium oxide and of the
deuterium sulfide D-hydrate had not been reported in the lit-
erature. Due to the importance in Canada of the hydrogen
sulfide – water dual temperature exchange process (8, 9) for
the initial extraction of deuterium oxide from water, it was
desirable to know the equilibrium properties of deuterium
sulfide with deuterium oxide and of deuterium sulfide D-hy-
drate.
9
.5 mm lug-bolts and was sealed by compression of an en-
closed 1.6 mm thick gasket of polytetrafluoroethylene.
The central stirrer shaft, 336 mm long, 6.35 mm o.d., was
of type-316 stainless steel and carried the rotor of the induc-
tion motor at its upper end and a two-blade titanium impel-
lor at its lower end. The bearing at the bottom of the stirrer
shaft was polytetrafluoroethylene and at the top a nylon
sleeve. The induction rotor, 51 mm high × 32 mm o.d., was
protected from corrosion by an epoxy resin coating that had
been baked to enhance its chemical resistance. The upper
motor body was 41.5 mm o.d. and carried the external stator
of the induction motor (not shown) and enclosed the internal
rotor with a clearance of 1.6 mm. The underside of the upper
flange pair F1 was supported 14 mm above the insulated top
cover of the thermostat tank (not shown) and was about
The present experimental study, performed between 1963
and 1966, defines part of the deuterium sulfide – deuterium
oxide system up to 33°C and the conditions for formation of
deuterium sulfide D-hydrate with liquid deuterium oxide.
3
2
6 mm above the level of the thermostat water. The lower
20 mm of the titanium vessel, comprised of the shaft body,
the lower flange pair F2, and the impellor body, was im-
mersed in the thermostat water. The shaft body was 15.9 mm
o.d. and enclosed the drive shaft with a radial clearance of
Materials
1
.6 mm.
Deuterium oxide was 99.75% pure with 0.25 wt.%
protium oxide as supplied by Atomic Energy of Canada
Limited: a complete isotopic analysis of this deuterium ox-
ide has been reported earlier (10). Deuterium sulfide was
prepared by the reaction of deuterium oxide with CP grade
aluminum sulfide as described previously (11, 12).
The lower impellor body was 63.5 mm o.d. and enclosed
a stirred internal cell space, 80 mm high × 50.8 mm i.d., this
3
provided a maximum cell volume of ~158 cm of which
3
9
0 cm was occupied by deuterium oxide. A titanium
thermowell, 6.35 mm o.d., containing a 10-junction copper-
constantan thermocouple, was located 5 mm from the cell
wall and extended 64 mm from the top of the cell to 16 mm
above the bottom. The lower end of the drive shaft was re-
duced to 4.76 mm o.d. and was threaded enabling two nuts
to fix the position of the upper collar, 14 mm high × 9.5 mm
o.d., 4.77 mm i.d., of the impellor. The titanium impellor
was composed of two vertically aligned, symmetrically op-
posed blades, 42 mm × 6 mm × 1.6 mm, welded along the
upper collar. The impellor was located centrally within the
cell and its blades swept out a cylinder, >30 mm high ×
Apparatus
The deuterium oxide – deuterium sulfide system was stud-
ied in a continuously stirred titanium pressure vessel, which
was suspended in an enclosed and insulated water thermo-
stat bath. The vessel was constructed of titanium to resist
corrosion and was stirred continuously by an impellor oper-
ated by magnetic induction. All metal fittings, valves, and
tubing used to connect the titanium vessel to the pressure
gauge and to the vacuum filling system were of type-316
stainless steel, which was completely resistant to corrosion
by wet deuterium sulfide.
1
6 mm o.d., within the stirred liquid sample.
Temperature measurement
Titanium pressure vessel
The original experimental temperatures were measured on
the International Practical Temperature Scale of 1948 (IPTS-
48), and these have been converted to the International Tem-
perature Scale of 1990 (ITS-90), using the approximate dif-
ferences given in Table 4 of Goldberg and Weir (13). This
The titanium pressure vessel, shown in Fig. 1, was axially
symmetric and 360 mm high, and was constructed from
three machined titanium bodies, which were aligned verti-
cally on top of each other by two pairs of flanges F1 and F2.
©
1998 NRC Canada

Clarke and Glew
1121
Fig. 1. Titanium pressure vessel.
Pressure measurement
The top of the motor body of the titanium vessel was con-
nected via Swagelok fittings to small-bore high-pressure
tubing, 1.6 mm i.d., 6.35 mm o.d., and high-pressure bonnet
bar stock valves to (i) the quartz pressure gauge, (ii) the deu-
terium sulfide storage cylinder, and (iii) the high-vacuum
system. For pressure measurements with the titanium vessel
above 25°C the high-pressure tubing was heated electrically
to about 40°C using a thermally and electrically insulated
external winding of a flat, 3.2 mm in width nichrome heat-
ing ribbon: the motor body and the high-pressure valves
were heated by infra-red lamps.
Pressure was measured using fused quartz spiral precision
Bourdon gauges manufactured by Texas Instruments Incor-
porated, which were completely resistant to corrosion. The
temperature of the compartment containing the capsule of
the quartz spiral was controlled at 35°C, and the gauge was
capable of measuring absolute pressure with an accuracy of
0
.020% at low pressure and 0.030% at high pressures (11):
the precision of pressure measurement was better by a factor
of two. An electrical output from the quartz gauge was re-
corded continuously to follow the attainment of equilibrium.
All pressures have been corrected to the standard accelera-
–
2
tion due to gravity, 9.80665 m s .
Over the wide range of pressure exhibited by the deute-
rium sulfide D-hydrate, pressure was measured using three
different capsules containing quartz spirals of different sen-
sitivity: (i) the 16 psi capsule was used for pressures be-
tween 0.1163 and 0.1980 MPa, (ii) the 200 psi capsule
between 0.1323 and 1.4449 MPa, and (iii) the 500 psi cap-
sule between 1.1510 and 2.2959 MPa. The saturation pres-
sure of the binary mixture of liquid deuterium sulfide and
liquid deuterium oxide was measured using the 500 psi cap-
sule. The pressure of the deuterium sulfide solutions in deu-
terium oxide with D-ice was measured using the 16 psi
capsule.
conversion has a root mean squared bias of less than
0
.0003°C in the range zero to 40°C, of slightly smaller mag-
Experimental method
Late in 1963 the 200 psi gauge was used for our initial
measurements of the pressure. Approximately 90 cm deute-
nitude than the accuracy of our most precise measurements.
All temperatures and equations are based on the units degree
Celsius (ITS-90), with (t°C + 273.15) = T K.
3
rium oxide liquid (l ) was placed in the titanium cell and,
1
Temperatures were measured on the (IPTS-48) scale using
a standardized 25 ohm platinum resistance thermometer with
a Leeds and Northrup G-2 Mueller bridge, nanovolt ampli-
fier, and galvonometer (11). Resistances were measured to
within 1 × 10 ohm, corresponding to about 0.0001°C. The
resistance at the triple point of water was checked regularly
using Jarrett triple-point cells, by Trans-Sonics Incorporated,
maintained in an insulated ice-packed chest (14). The ther-
mostat temperature was controlled to within 0.001°C and
was measured with the platinum resistance thermometer
mounted in a cavity in a submerged stainless-steel block lo-
cated within the rapidly recirculating water of the thermostat
bath. The temperature difference between the titanium
thermowell and the stainless-steel block was measured by a
with continuous stirring, was thoroughly degassed using the
vacuum system. The thermostat was set at about 5°C, and
deuterium sulfide from its storage cylinder was admitted to
give a gas (g) pressure of about 100 psig in the cell. Rapid
formation of solid deuterium sulfide D-hydrate (h) ensued as
shown by a steady drop in pressure. After about 16 h, when
–
5
it was evident that the three-phase (hl g) equilibrium had
1
been attained, data sets of 14–37 pairs of pressure–tempera-
ture measurements were made over periods of 2–5 days: the
determinations reported are the means of these data sets. The
thermostat temperature was then raised by about 1°C and the
measurement procedure repeated. In 1965, when the pres-
sure exceeded 1.4449 MPa the 200 psi gauge was replaced
by the 500 psi gauge. Temperature was increased
incrementally, with further additions of deuterium sulfide to
maintain the D-hydrate phase at higher pressures, up to the
temperature of the quadruple point Q(hl l g), about 30.77°C,
1
0-junction copper-constantan thermocouple with the off-
balance signal detected by a nanovolt amplifier and
galvonometer. With this arrangement the temperature of the
stirred liquid sample within the reaction cell could be readily
determined with a precision of 0.0005°C.
1
2
above which the solid deuterium sulfide D-hydrate (h) be-
came unstable and decomposed into its two liquid
©
1998 NRC Canada

1
122
Can. J. Chem. Vol. 76, 1998
Table 1. Vapor pressure of mixed liquids deuterium oxide and deuterium sulfide.
P(l l g)
Temperature
°C)
1 2
Difference
(%)
Error on calculated
pressure(%)
(
Observed (MPa)
Calculated (MPa)
3
3
3
3
3
3
2
2
2
2
2
2
2
2
2
2
2
1
1
3.003
2.984
1.981
1.503
0.983
0.505
9.959
8.930
7.916
7.850
6.853
5.862
4.877
3.874
2.859
1.881
0.887
9.866
8.905
2.4500
2.4494
2.3924
2.3656
2.3380
2.3123
2.2831
2.2274
2.1746
2.1708
2.1210
2.0702
2.0208
1.9730
1.9242
1.8772
1.8310
1.7860
1.7428
2.4501
2.4490
2.3929
2.3664
2.3379
2.3119
2.2825
2.2277
2.1747
2.1712
2.1201
2.0701
2.0212
1.9724
1.9237
1.8778
1.8318
1.7855
1.7427
–0.003
0.017
–0.019
–0.035
0.003
0.017
0.028
–0.016
–0.005
–0.019
0.041
0.010
0.010
0.009
0.008
0.008
0.007
0.007
0.006
0.006
0.006
0.006
0.006
0.006
0.007
0.008
0.009
0.010
0.011
0.012
0.006
–0.022
0.031
0.022
–0.031
–0.043
0.024
0.004
components, liquid deuterium oxide (l ) and liquid deute-
rium sulfide (l2).
equilibrium measurements of the (hs l g) system with the
1
1 1
thermostat temperature controlled so that (i) the stirred D-hy-
drate (h) was neither forming nor decomposing, as shown by
a constant observed pressure and (ii) the stirred D-ice (s1)
was neither freezing nor melting, as shown by a zero signal
from the 10-junction thermocouple. To confirm equilibrium
conditions the impressed thermostat temperature was brack-
eted, with decreasing temperature differences, slightly above
and slightly below the temperature of the stirred reactor at
the quadruple point for a period of 15 days.
In our final study in 1966 the (s1l1g) system was measured
at preselected total pressures of deuterium sulfide. The equi-
librium temperature for the (s1l1g) system was measured di-
rectly for a period of 2 days, by bracketing the thermostat
temperature to equal the thermowell temperature, so that the
D-ice (s1) was in equilibrium (neither freezing nor melting)
with the stirred deuterium oxide (l1) saturated with deute-
rium sulfide (g) at the pre-defined total pressure. Table 3
lists the total pressures and temperatures found for the
(s1l1g) equilibrium.
At higher temperatures, where the three-phase (l l g) sys-
1
2
tem was stable, total equilibrium pressures were determined
for the stirred, mutually saturated, partially miscible liquids.
Measurements began at highest temperatures ~33°C, and
data sets of exactly 18 equilibrium pressure–temperature
measurements were collected for each temperature at inter-
vals of 2–3 days. The temperature was decreased and the
process repeated. In this manner the equilibrium pressure
was most rapidly attained by the removal of super-saturation
from the two liquid phases: attainment of equilibrium from
lower temperatures and from undersaturated conditions re-
quired up to 7 days. The (l l g) equilibrium was also mea-
1
2
sured with continuous stirring below the quadruple point in
the metastable region down to 18.9°C: below this tempera-
ture the stirred, two-liquid system spontaneously reformed
the stable deuterium sulfide D-hydrate. Three high tempera-
tures were finally remeasured for the (l l g) system to check
1
2
the hysteresis and reproducibility of the 500 psi gauge. Equi-
librium total pressures for the mutually saturated deuterium
oxide and deuterium sulfide liquids are listed in Table 1.
All pressures and temperatures listed as determinations
for the various equilibria are the mean values of the sets of
repeated single measurements. All regression equations have
been evaluated using the method of least squares (15). Stan-
dard error, abbreviated to SE, is to be understood to mean
the statistical estimate of the standard error.
In 1966, to define the (hl g) system at lower temperatures
1
with better accuracy, the 16 psi gauge was used (11), the
stirred reactor temperature was reduced to 7.961°C, and
some deuterium sulfide was removed so that excess solid D-
hydrate did not impede the stirrer. Again data sets of exactly
1
8 equilibrium pressure–temperature measurements were
collected at each temperature over periods of 3–4 days: the
mean values are reported. The temperature was decreased
and the process repeated down to 2.798°C. The seven mea-
surements listed between 3.383 and 2.798°C are metastable
relative to freezing of D-ice. Table 2 lists the equilibrium
pressures for deuterium sulfide D-hydrate.
Equation of state
Following our earlier work (11, 12) gas-phase imperfec-
tions have been represented by the Redlich–Kwong equation
of state (16), using the extension to mixtures by Spear et al.
(17). The a22 and b22 parameters used for deuterium sulfide
vapor are those derived from the high temperature (h.t.)
measurements from –30 to +30°C (11): the a11 and b11 for
The pressure and temperature of the invariant lower qua-
druple point Q(hs l g) were determined directly from
1
1
©
1998 NRC Canada

Clarke and Glew
1123
Table 2. Pressure of deuterium sulfide D-hydrate with deuterium oxide liquid.
P(hl g)
Temperature
°C)
1
Difference
(%)
Error on calculated
pressure (%)
(
Gauge
500
w1/2
Observed (MPa)
Calculated (MPa)
3
3
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
0.666
0.462
9.940
9.883
9.375
8.945
8.932
8.378
7.967
7.967
7.957
6.985
6.869
6.845
5.873
5.853
5.000
4.879
4.862
3.997
3.003
1.961
0.980
9.971
8.981
7.972
6.972
5.968
4.987
3.963
3.383
2.975
2.381
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.5
0.5
0.5
0.4
0.4
0.5
0.2
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.282
0.162
0.078
0.054
0.04
0.04
1
2.2959
2.2338
2.0903
2.0763
1.9476
1.8461
1.8431
1.7244
1.6425
1.6408
1.6400
1.4638
1.4449
1.4406
1.2903
1.2862
1.1702
1.1548
1.1510
1.0482
0.9411
0.8419
0.7585
0.6821
0.6149
0.5537
0.4991
0.4500
0.4070
0.3664
0.3452
0.3311
0.3116
0.2990
0.2813
0.2703
0.2438
0.2238
0.19899
0.19907
0.19798
0.17952
0.17883
0.16111
0.16002
0.14728
0.14610
0.13231
0.13148
0.12481
0.12364
0.12353
0.12227
0.12109
0.11994
0.11872
0.11746
0.11629
2.2953
2.2348
2.0902
2.0752
1.9472
1.8469
1.8440
1.7245
1.6419
1.6419
1.6399
1.4640
1.4446
1.4406
1.2899
1.2870
1.1701
1.1546
1.1524
1.0481
0.9410
0.8417
0.7585
0.6821
0.6150
0.5538
0.4993
0.4502
0.4069
0.3664
0.3452
0.3311
0.3115
0.2990
0.2811
0.2700
0.2435
0.2236
0.19874
0.19872
0.19798
0.17922
0.17887
0.16071
0.16003
0.14694
0.14612
0.13206
0.13145
0.12482
0.12363
0.12351
0.12226
0.12109
0.11994
0.11873
0.11748
0.11632
0.027
–0.046
0.003
0.053
0.017
–0.043
–0.048
–0.002
0.041
–0.065
0.003
–0.014
0.021
–0.002
0.031
–0.065
0.003
0.017
–0.126
0.011
0.005
0.017
–0.005
0.001
–0.012
–0.017
–0.033
–0.029
0.012
–0.003
–0.004
0.012
0.021
0.010
0.063
0.115
0.021
0.018
0.013
0.013
0.011
0.011
0.011
0.011
0.010
0.010
0.010
0.008
0.007
0.007
0.005
0.005
0.004
0.003
0.009
0.005
0.007
0.008
0.009
0.010
0.010
0.010
0.010
0.010
0.010
0.010
0.010
0.010
0.010
0.010
0.012
0.015
0.024
0.033
0.044
0.044
0.008
0.044
0.007
0.044
0.007
0.044
0.007
0.044
0.006
0.005
0.004
0.004
0.004
0.005
0.005
0.005
0.006
0.007
500
500
500
500
500
500
500
500
500
500
500
200
200
200
500
500
200
500
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
16
11.980
11.379
1
9
9
7
7
7
6
6
5
5
5
5
4
3
3
3
3
3
3
3
2
2
2
0.983
.977
.144
.998
.997
.961
.993
.974
.936
.895
.068
.014
.032
.987
.485
.392
.383
.284
.190
.097
.998
.895
.798
0.136
0.117
0.129
0.180
–0.002
0.167
–0.022
0.246
–0.007
0.229
–0.016
0.191
0.024
–0.003
0.007
0.009
0.004
0.004
0.000
–0.003
–0.019
–0.021
200
16
200
16
200
16
200
16
16
16
16
16
0.04
1
0.04
1
0.04
1
0.04
1
1
1
1
1
16
16
16
16
1
1
1
1
16
1
©
1998 NRC Canada

1
124
Can. J. Chem. Vol. 76, 1998
Table 3. Freezing point of deuterium oxide solutions of deuterium sulfide.
t(s l g)
P(s l g)
1 1
Difference
(°C)
Error on calculated
temperature (°C)
1
1
(
MPa)
Observed (°C)
Calculated (°C)
0
0
0
0
0
0
0
0
0
0
0
0
0
.00066
.00242
.00563
.01552
.02836
.04150
.05402
.06655
.08341
.08408
.09313
.10542
.12364
—
3.8125
3.8064
3.7954
3.7615
3.7176
3.6725
3.6297
3.5867
3.5290
3.5267
3.4957
3.4536
3.3912
—
0.00047
0.00047
0.00045
0.00040
0.00035
0.00031
0.00029
0.00029
0.00033
0.00033
0.00037
0.00042
0.00052
3.8061
3.7967
3.7614
3.7160
3.6741
3.6291
3.5866
3.5285
3.5264
3.4953
3.4540
3.3917
–0.00029
0.00132
–0.00018
–0.00157
0.00158
–0.00062
–0.00015
–0.00045
–0.00026
–0.00034
0.00039
0.00055
l1
deuterium oxide vapor are those derived for the solubility
measurements (12).
where G * is the molar Gibbs energy of pure liquid deute-
1
rium oxide at its saturation vapor pressure p °, and where f °
is its saturation fugacity, and G ° is the standard molar
1
1
g
1
Gibbs energy of gaseous deuterium oxide at unit pressure.
Method of evaluating compositions of aqueous and
gaseous phases
The iterative process used to evaluate the intensive prop-
erties of the liquid deuterium oxide solution and of the bi-
nary gaseous phase at equilibrium with deuterium sulfide is
similar in principle but different in method from that briefly
For pure liquid deuterium oxide at a total pressure P(>p °)
1
l1
the molar Gibbs energy G (P, 1) is
1
l1
l1
l1
[4]
G1 (P, 1) = G1 * + (P − p1 °)V1
l1
=
G * + RT ln f (Poynting)
1
1
outlined for the solubility (12). Modern values (i) for p °,
1
the saturation vapor pressure of deuterium oxide, are from
l1
l1
where f1(Poynting) = exp ((P – p1°)V1 /RT) is the Poynting
Hill and MacMillan (18) and (ii) for V , the molar volume
1
l1
pressure coefficient, and V1 is the molar volume of the liq-
of liquid deuterium oxide, are from Kell (19), evaluated with
proper allowance for the difference of the IPTS-48 and the
IPTS-68 scales of temperature.
uid.
For dilute solutions of deuterium sulfide in deuterium ox-
ide with mole fraction x1 of deuterium oxide at pressure P
the molar Gibbs energy for deuterium oxide is taken as
l1
Consider the equilibrium evaporation at a total pressure P
and temperature T of 1 g molar mass of deuterium oxide
l1
from its liquid solution with mole fraction x1 deuterium ox-
l1
l1
l1
l1
[
5]
G1 (P, x1 ) = G1 (P, 1) + RT ln x1
ide into its binary gas phase with mole fraction y deuterium
1
oxide as formally represented by the reaction equation:
where the liquid is assumed to obey Raoult’s law.
The sum of eqs. [3]–[5] gives
[
1]
D O(l )
º
D O(g)
2
1
2
l1
l1
og
og
l1
[
6a]
G1 (P, x1 ) = G1
+ RT ln f1 °
P, x1
P, y1
l1
l1
g
l1
G1 (P, x1
)
G1 (P, y1 )
+RT ln f (Poynting) + RT ln x
1
1
The molar Gibbs energy for deuterium oxide in the liquid
l1
l1
l1
l1
l1
g
[6b] G1 (P, x1 ) = G1 + RT ln [ f1 °⋅f1 (Poynting)⋅x1 ]
and in the gas phases are defined as G (P, x ) and G (P,
1
1
1
y1), respectively. For the system in thermodynamic equilib-
rium at constant T and P the molar Gibbs energy of deute-
rium oxide is the same in both the liquid and the gas phases
so that
expressing the molar Gibbs energy of deuterium oxide
l1
l1
l1
G (P, x ) at P and x in eq. [6a] in terms of the molar
1
1
1
Gibbs energy for the pure liquid at its saturation vapor pres-
sure with fugacity f °, plus the Poynting molar Gibbs energy
1
l1
l1
g
change with activity coefficient f (Poynting), plus the
1
[
2]
G1 (P, x1 ) = G1 (P, y1 )
Raoult-law molar Gibbs energy change with activity coeffi-
l1
cient x . Alternately eq. [6b] expresses the same molar
1
For the equilibrium evaporation of pure deuterium oxide
with x1 = 1, y = 1, and P = p °, eq. [2] yields the relations:
Gibbs energy in terms of the fugacity product within the
square brackets.
l1
1
1
The Redlich–Kwong equation of state for gas mixtures
(12, 16, 17) provides an independent expression for the
fugacity f of deuterium oxide at mole fraction y in a gas
l1
l1
g
[
3]
G1 ( p ° , 1) = G * = G1 ( p ° , 1)
1 1 1
1
1
g
=
G ° + RT ln f °
1 1
mixture with deuterium sulfide at total pressure P. Under
©
1998 NRC Canada

Clarke and Glew
1125
Table 4. Properties of gas and liquid phases in the (l l g) equilibrium.
1
2
Temperature
°C)
f °
f2
f1
y1
(× 103)
x2l1
(× 103)
x3l1
(× 106)
x1l2
(× 103)
2
(
(MPa)
(MPa)
(MPa)
3
3
3
3
3
3
2
2
2
2
2
2
2
2
2
2
2
1
1
3.003
2.984
1.981
1.503
0.983
0.505
9.959
8.930
7.916
7.850
6.853
5.862
4.877
3.874
2.859
1.881
0.887
9.866
8.905
2.0306
2.0298
1.9883
1.9687
1.9475
1.9281
1.9061
1.8652
1.8253
1.8228
1.7842
1.7463
1.7092
1.6719
1.6346
1.5992
1.5638
1.5279
1.4945
2.0039
2.0034
1.9626
1.9434
1.9234
1.9049
1.8837
1.8433
1.8047
1.8020
1.7653
1.7280
1.6914
1.6558
1.6193
1.5842
1.5494
1.5152
1.4824
0.00435
0.00435
0.00410
0.00399
0.00387
0.00376
0.00364
0.00342
0.00322
0.00321
0.00302
0.00284
0.00267
0.00251
0.00236
0.00221
0.00208
0.00195
0.00183
4.11
4.10
3.90
3.81
3.71
3.62
3.52
3.34
3.17
3.16
3.01
2.86
2.72
2.58
2.45
2.33
2.21
2.10
1.99
28.85
28.85
28.90
28.92
28.96
28.99
29.03
29.09
29.16
29.16
29.26
29.33
29.42
29.53
29.63
29.72
29.84
29.98
30.10
4.1
4.1
4.1
4.0
4.0
4.0
4.0
3.9
3.9
3.9
3.8
3.8
3.7
3.7
3.6
3.6
3.5
3.5
3.4
13.1
13.0
12.9
12.8
12.3
12.1
11.8
11.8
11.3
11.4
10.6
10.5
10.4
9.6
9.3
9.4
9.2
8.3
8.1
l1
these conditions the molar Gibbs energy for deuterium oxide
The x ′ is used with the ionization constant for deuterium
2
g
l1
in the gas phase G (P, y ) is given by
sulfide in deuterium oxide (12) to evaluate x ′, the dis-
1
1
3
solved mole fraction of the deuterium sulfide anion. In the
g
og
[
7]
G1 (P, y ) = G
+ RT ln f1
l1
1
1
first approximation x ′, the solution mole fraction of deute-
1
l1
l1
l1
rium oxide, is given by (1 – x ′– 2x ′) = x ′.
2
3
1
Returning to the equilibrium of the binary aqueous phase
with the binary gaseous phase, eqs. [6b] and [7] are substi-
tuted into eq. [2] to obtain the equilibrium relationship
The fugacity of deuterium oxide evaluated for the
l1
compressed solution using eq. [6b] is [f °⋅ f (Poynting)⋅x ′],
1
1
1
which is greater than the fugacity f ′ evaluated from the
1
l1
Redlich–Kwong equation using y ′. The reason that the R–K
1
[
8]
f = [ f °⋅f (Poynting)⋅x
]
1
1
1
1
fugacity f ′ is too small is because our first approximation of
1
y1′, using partial pressures, is too small: thus, in our second
where the fugacity f of deuterium oxide from the Redlich–
1
approximation we multiply y ′ by a converging factor greater
Kwong equation is equal to the saturation fugacity f ° of the
1
1
than unity.
pure liquid corrected for the effects of pressure and of solu-
l1
In the second approximation the gas-phase mole fraction
tion mole fraction. The equilibrium values for f and x are
1
1
of deuterium oxide y ′′ at total pressure P is taken as
obtained by successive approximations to evaluate eq. [8] as
follows.
As a first approximation the gas-phase mole fraction of
1
l1
[
10]
y ′′ = y ′[ f °⋅f (Poynting)⋅x ′] / f1 ′
1
1
1
1
1
deuterium oxide y ′ at total pressure P is taken as
1
giving the second
sequence of approximations,
l1
l1
l1
y ′′→ V′′→ f ′′ , f ′′→ x ′′ , x3 ′′→ x1 ′′→ y ′′[ f °⋅f
1
1
2
2
1
1
1
[
9]
y ′ = p °/P
l1
1
1
(
Poynting)⋅x1 ′′]͞f ′′ = y (3rd approximation), and so on.
1 1
with p ° evaluated from the equation of Hill and MacMillan
The approximations converge rapidly to give equilibrium
values after six cycles of iteration, satisfying eq. [8] within
the limits of single precision arithmetic.
1
(
18). This y ′ is used at P and T in the Redlich–Kwong (R–
1
K) equation for gas mixtures (12, 16, 17) to obtain V′ the
molar volume of the gas mixture, and thence to evaluate the
first approximations f ′ and f ′ for the R–K fugacities of deu-
Liquid D2O – liquid D2S – gas (l1l2g) equilibrium
Table 1 presents 19 determinations of P(l1l2g), the satura-
tion vapor pressure of the partially miscible liquids deute-
rium oxide and deuterium sulfide between 33.003 and
18.905°C, together with calculated values from the best (21)
representative equation
1
2
terium oxide and of deuterium sulfide, respectively. This f2′
is used with the Henry’s law solubility constant (12) and its
l1
Poynting correction to evaluate x ′, the mole fraction of
2
undissociated deuterium sulfide dissolved in deuterium ox-
ide.
The Poynting correction for the deuterium sulfide solute
[
11] ln P(l l g) = 7.95368 − 2160.7 / T
1 2
l1
l1
is f (Poynting) = exp ((P – p °)V /RT), where V is the
2
1
2
2
partial molar volume of deuterium sulfide in deuterium ox-
ide. Values of V2 for deuterium sulfide are estimated from
the measurements for hydrogen sulfide in water by Barbero
et al. (20).
with P(l l g) in MPa and absolute temperature T in Kelvin.
1 2
l1
The percentage differences between observed and calculated
pressures, shown in the fourth column, indicate a SE of
0.025% on a single determination: this precision properly
©
1998 NRC Canada

1
126
Can. J. Chem. Vol. 76, 1998
Table 5. Properties of gas and aqueous phases in the (hl g) equilibrium.
1
3
x2l1 (× 103)
x3l1 (× 106)
Temperature (°C)
f2 (MPa)
f1 (MPa)
y (× 10 )
1
3
3
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
9
9
7
7
7
6
6
5
5
5
5
4
3
3
3
3
3
3
3
2
2
2
0.666
0.462
9.940
9.883
9.375
8.945
8.932
8.378
7.967
7.967
7.957
6.985
6.869
6.845
5.873
5.853
5.000
4.879
4.862
3.997
3.003
1.961
0.980
9.971
8.981
7.972
6.972
5.968
4.987
3.963
3.383
2.975
2.381
1.980
1.379
0.983
.977
.144
.998
.997
.961
.993
.974
.936
.895
.068
.014
.032
.987
.485
.392
.383
.284
1.8946
1.8527
1.7539
1.7441
1.6530
1.5796
1.5774
1.4899
1.4284
1.4271
1.4265
1.2911
1.2764
1.2730
1.1539
1.1506
1.0564
1.0438
1.0406
0.9555
0.8651
0.7800
0.7074
0.6401
0.5802
0.5250
0.4753
0.4303
0.3905
0.3527
0.3329
0.3197
0.3013
0.2895
0.2727
0.2622
0.2371
0.2180
0.19422
0.19429
0.19324
0.17549
0.17483
0.15773
0.15668
0.14436
0.14322
0.12985
0.12904
0.12256
0.12142
0.12131
0.12009
0.11895
0.11782
0.11664
0.11541
0.11427
0.00380
0.00375
0.00364
0.00363
0.00352
0.00343
0.00343
0.00332
0.00324
0.00324
0.00323
0.00305
0.00303
0.00303
0.00285
0.00285
0.00271
0.00269
0.00268
0.00254
0.00239
0.00224
0.00211
0.00198
0.00186
0.00174
0.00163
0.00153
0.00143
0.00134
0.00129
0.00125
0.00120
0.00117
0.00112
0.00109
0.00102
0.00096
0.00089
0.00089
0.00089
0.00083
0.00083
0.00077
0.00077
0.00072
0.00072
0.00067
0.00067
0.00064
0.00064
0.00064
0.00063
0.00063
0.00062
0.00062
0.00062
0.00061
3.65
3.62
3.55
3.54
3.49
3.46
3.46
3.42
3.41
3.41
3.41
3.39
3.38
3.38
3.39
3.39
3.40
3.40
3.41
3.43
3.47
3.52
3.57
3.64
3.71
3.78
3.87
3.95
4.04
4.14
4.20
4.24
4.30
4.34
4.40
4.44
4.56
4.65
4.79
4.79
4.80
4.92
4.93
5.05
5.07
5.17
5.19
5.31
5.32
5.39
5.41
5.41
5.42
5.43
5.45
5.46
5.48
5.49
28.74
28.25
27.11
27.00
25.93
25.05
25.02
23.97
23.23
23.21
23.20
21.53
21.35
21.30
19.80
19.75
18.54
18.38
18.33
17.21
15.99
14.82
13.80
12.83
11.95
11.12
10.35
9.640
8.998
8.372
8.038
7.813
7.496
7.289
6.993
6.806
6.348
5.990
5.534
5.536
5.513
5.165
5.148
4.805
4.780
4.526
4.499
4.216
4.196
4.054
4.029
4.027
4.000
3.975
3.950
3.923
3.896
3.870
4.0
3.9
3.8
3.8
3.7
3.6
3.6
3.5
3.4
3.4
3.4
3.3
3.2
3.2
3.1
3.1
2.9
2.9
2.9
2.8
2.6
2.5
2.4
2.2
2.1
2.0
1.9
1.8
1.7
1.6
1.6
1.6
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.2
1.1
1.1
1.1
1.1
1.0
1.0
1.0
1.0
0.93
0.93
0.93
0.92
0.92
0.91
0.91
0.90
0.90
.190
.097
.998
.895
.798
©
1998 NRC Canada

Clarke and Glew
1127
Table 6. Properties of gas and aqueous phases in the (s l g) equilibrium.
1
1
Temperature
°C)
f2
f1
y1
(× 103)
x2l1
(× 103)
x3l1
(× 106)
(
(MPa)
(MPa)
3
3
3
3
3
3
3
3
3
3
3
3
.8061
.7967
.7614
.7160
.6741
.6291
.5866
.5285
.5264
.4953
.4540
.3917
0.00176
0.00497
0.01484
0.02762
0.04067
0.05306
0.06544
0.08204
0.08270
0.09158
0.10363
0.12142
0.00066
0.00066
0.00066
0.00066
0.00065
0.00065
0.00065
0.00065
0.00065
0.00064
0.00064
0.00064
273.0
117.0
42.6
23.4
16.0
12.3
10.0
7.98
7.92
7.16
6.33
5.41
0.058
0.163
0.487
0.908
1.338
1.748
2.159
2.711
2.733
3.030
3.432
4.029
0.11
0.19
0.32
0.44
0.54
0.61
0.68
0.76
0.76
0.80
0.86
0.93
l2
corresponds with the 0.030% accuracy of the 500 psi gauge
11). The parameter –2160.7 has SE 1.2 K. The fifth column
Combination of our 19 estimates of f /x for deuterium
1 1
l2
(
oxide in deuterium sulfide with five estimates of f /x for
1 1
shows the SE on the pressure calculated from eq. [11].
water in hydrogen sulfide, derived from the direct phase
analyses of x1 between 40 and 105°C by Carroll (22), gives
the best representative equation
l2
The vapor pressure of the mixed liquids, P(l l g), is less
1
2
than that of pure deuterium sulfide (11), p °, and the ratio of
2
pressures in this temperature range is best represented by
l2
[
13] ln [ f ͞x ] = 9.0634 − 3102͞T
1
1
[
12] ln [P(l l g) / p °] = −0.09553 + 25.7 / T
1 2 2
for the Henry’s law constant of deuterium oxide in liquid
deuterium sulfide with SE of 3.6% on a single determination
where p ° has been evaluated using eq. [2] from ref. 11 and
2
has a SE of 0.027%. The combined SE on an observed sin-
gle ratio of pressure is 0.037%, and the parameter 25.7 has
SE 1.7 K.
between 33 and 19°C: the parameter –3102 has SE 67 K. At
l2
2
5°C the Henry’s law constant H1 for deuterium oxide in
deuterium sulfide is 0.261 with SE 0.0022 MPa, that evalu-
ated from ref. 6 for water in hydrogen sulfide is 0.261 with
At 25°C the computed ratio of P(l l g)/p ° is 0.99074 with
1
2
2
SE 0.000088 and 17 degrees of freedom; this gives the devi-
ation (1 – 0.99074), a student t ratio of 106, which confirms
SE 0.0073 MPa.
The temperature dependence of x , the saturation mole
l2
1
that P(l l g)/p ° is significantly less than unity at a very high
1
2
2
fraction of deuterium oxide in liquid deuterium sulfide be-
tween 33 and 19°C, is best represented by
level of probability.
Table 4 presents values for the intensive properties of the
equilibrium (l l g) phases under the conditions of Table 1.
Values in columns three to seven are, respectively, for the
l2
1
2
[14] ln x1 = 2.7474 − 2182͞T
fugacities f of deuterium sulfide and f of deuterium oxide,
2
1
with SE of 4.6% on a single determination: the parameter
−2182 has SE 70 K. At 25°C x1 for deuterium oxide in deu-
for the gas-phase mole fraction y of deuterium oxide, for
1
l2
l1
the mole fractions x of undissociated deuterium sulfide
and x3 of deuterium sulfide anion in the liquid deuterium
2
l1
terium sulfide is 0.0103 with SE 0.00011, that evaluated
from (6) for water in hydrogen sulfide is 0.0119 with SE
oxide phase l . In column eight the saturation mole fraction
1
l2
l2
0.00034: the difference 0.0016 of x1 is significant.
x1 of deuterium oxide in the liquid deuterium sulfide phase
l has been evaluated as (1 – (f /f °)), using fugacities as-
2
2 2
suming the deuterium sulfide solvent obeys Raoult′s law.
Column two provides the required Redlich–Kwong fugacity
f2° for pure deuterium sulfide at its saturation vapor pressure
p2° (11).
D2S D-hydrate – liquid D2O – gas (hl1g) equilibrium
Table 2 presents 58 equilibrium determinations of P(hl1g),
the saturation vapor pressure of deuterium sulfide D-hydrate
in contact with liquid deuterium oxide between 30.666 and
The saturation solubility x1l2 of deuterium oxide in liquid
2
.798°C. The seven determinations below 3.392°C are in
metastable equilibrium.
deuterium sulfide l is best discussed in terms of the Henry’s
2
l2
l2
law constant, H1 = f /x MPa, for transfer of deuterium
The second column denotes the pressure gauge used, data
marked 500, 200, and 16 used the 500 psi, 200 psi, and 16
psi gauges, respectively. The third column gives the square
root of the weights used to combine the data from the vari-
ous gauges into a properly weighted least-squares regression
of the logarithm of pressure as a function of temperature.
1
1
oxide from phase l into the gas phase. Comparison of our
2
l2
1
9 estimates of f /x1 for deuterium oxide in liquid deute-
1
l2
rium sulfide with 27 similar estimates of f /x for water in
1
1
liquid hydrogen sulfide, derived from the vapor pressure
l2
data of Scheffer (6), shows that f /x for deuterium oxide in
1
1
deuterium sulfide and for water in hydrogen sulfide are
equal within experimental error at the same temperature be-
tween 33 and 19°C.
The fourth column lists the observed P(hl g), the fifth
1
gives P(hl g) calculated from the best model of the form
1
(21)
©
1998 NRC Canada

1
128
Can. J. Chem. Vol. 76, 1998
D-Ice – liquid D O – gas (s l g) equilibrium
[
15a] ln P(hl g) = b0 + b1⋅u1 + b2⋅u2 + b3⋅u3
1
2
1 1
Table 3 presents 11 determinations of t(s l g), the equilib-
rium temperature of D-ice with a deuterium oxide solution
1
1
+
b4⋅u4 + b5⋅u5 + b6⋅u6
which is mathematically equivalent to
15b] ln P(hl g) = A + B͞T + C ln T + DT + ET
saturated with deuterium sulfide at total pressure P(s l g) be-
1 1
tween 0.00242 and 0.10542 MPa. The final row presents the
2
[
temperature t(hs l g) determined at the total pressure
1
1 1
P(hs l g) 0.12364 MPa. The third column shows calculated
FT 3 + GT 4
1 1
+
temperatures from the representative equation
and which required seven parameters for a proper represen-
tation of the 58 data. The percentage differences between
observed and calculated pressures, shown in the sixth col-
umn, yield an overall SE of 0.013% for a single determina-
tion of unit weight with 51 degrees of freedom. The seventh
column shows the percentage error on the pressure estimated
from the weighted regression model.
[16] t(s l g) = 3.81473 − 3.4258 P(s l g)
1
1
1 1
(0.00047) (0.0067)
with t(s l g) in °C and P(s l g) in MPa: the SEs are shown
1
1
1 1
in parenthesis below the parameters. Differences between
observed and calculated temperatures, shown in the fourth
column, indicate a SE of 0.00090°C on a single temperature
determination, with 10 degrees of freedom. The fifth column
shows the SE estimate on the temperature evaluated from
eq. [16].
The first row of Table 3 shows an estimated triple-point
temperature of 3.8125 with SE 0.00047°C: this disagrees
significantly with our first direct measurement of the triple-
point at 3.800 with SE 0.0005°C in a preliminary experi-
ment in 1963. We suggest in that first experiment, where we
were unaware of the need to bracket the thermostat tempera-
ture both above and below the stirred reactor temperature,
we unwittingly had applied a “too large” cooling differential
to the stirred reactor, and that had caused the negative bias
The 14 residuals using the 16 psi gauge indicate a SE of
.013%, the 19 residuals at highest pressure using the 200
0
psi gauge indicate a SE of 0.018%, and the 14 residuals at
highest pressure using the 500 psi gauge indicate a SE of
0
.039%. Comparison of these SE estimates with the gauge
accuracies (11) shows that (i) the data at low pressure are
properly represented with SE 0.013% and a 0.020% accu-
racy of 16 psi gauge calibration, (ii) the data at intermediate
pressure with SE 0.018% are somewhat more precise than
the 0.030% accuracy of 200 psi gauge calibration, and
(
iii) the high-pressure data with SE 0.039% are slightly more
variable than the 0.030% accuracy of 500 psi gauge calibra-
tion.
The six temperature variables u1–u6 in eq. [15a] are de-
fined in ref. 21 with x = (T – 298.15)/298.15, and the param-
eters b0–b6 with their (SEs) are b0 = 0.157129 (0.000090),
b1 = 33.0126 (0.010), b2 = 232.179 (1.2), b3 = 5590.55
−
0.0125°C on the observed temperature. We note that the 12
determinations presented in Table 3 were made at the end of
our study in 1966, with more experience and with tempera-
ture bracketing, and therefore probably with less bias.
Table 6 presents values for the intensive properties of the
(
=
84), b4 = 121 174 (5900), b5 = 1 619 360 (130 000), and b6
8 860 000 (890 000). We note that the deuterium sulfide D-
equilibrium l and g phases under the conditions of Table 3.
1
hydrate pressures properly define six temperature parameters
b1–b6 at 25°C, that all parameters are positive with no alter-
nation of sign, and that the value of the least significant pa-
rameter b6 could arise by pure chance at a probability level
Upper quadruple point Q(hl l g)
1 2
The upper quadruple point Q(hl l g) is the invariant four-
1 2
phase point at the highest temperature where the D-hydrate
can coexist in equilibrium with a gas phase: it is located at
the cut of the two univariant three-phase curves (hl g) and
1
5
of less than one in 10 times.
Regression of the 58 data, each assumed equally probable
with unit weight, (i) gave an unrealistic poor fit of the 14
most accurate determinations at low pressure by the 16 psi
gauge and (ii) indicated an unrealistic high SE estimate of
1
(
l l g). The (hl g) curve has been defined by the upper 14
1 2 1
determinations using the 500 psi gauge between 25.000 and
0.666°C and indicated a SE of 0.042% on a single pressure
3
determination with 10 degrees of freedom. The (l l g) curve
has been defined by eq. [11]. The quadruple-point tempera-
0
.057% for a single determination, but (iii) still required a
1 2
seven-parameter model (21) with b1–b6 all positive and
highly significant.
ture t(hl l g) is 30.770 with SE 0.0043°C and the quadruple-
1 2
point pressure P(hl l g) is 2.3263 with SE 0.00018 MPa.
The requirement of a seven-parameter model together
with the unusually large positive values of b1–b3 show that
1 2
Comparison of Q(hl l g) for deuterium sulfide D-hydrate
1 2
with that for hydrogen sulfide hydrate, reported by Scheffer
the P(hl g) data contain information of significant composi-
1
(
6) at 29.5°C and at 2.24 MPa, shows a difference of tem-
tion change with temperature for deuterium sulfide D-hy-
drate between 2.8 and 30.7°C.
perature of 1.27°C and a difference of pressure of 0.09 MPa.
Table 5 presents values for the intensive properties of the
equilibrium l and g phases under the conditions of Table 2.
Lower quadruple point Q(hs l g)
1
1 1
l1
l1
The values listed under f , f , y , x , and x have the same
The lower quadruple point Q(hs l g) is the invariant four-
2
1
1
2
3
1 1
meaning as in Table 4.
The saturation vapor pressure P(hl g) of deuterium sulfide
D-hydrate is about 88% of that for hydrogen sulfide hydrate
phase point at the lowest temperature where the D-hydrate
coexists in stable equilibrium with a liquid deuterium oxide
phase: it is located at the cut of the two univariant three-
phase curves (hl g) and (s l g). The (hl g) curve has been
1
(
6, 7) at the same temperature. This ratio of P(hl g) is simi-
1
1
1 1
1
lar to the ratio of 81% exhibited by the Structure I
cyclopropane D-hydrate relative to its cyclopropane hydrate
defined by the lower 10 determinations using the 16 psi
gauge between 3.987 and 2.798°C and indicated a SE of
0.0072% on a single pressure determination with 8 degrees
(
23) at the same temperature between 6 and 16°C.
©
1998 NRC Canada

Clarke and Glew
1129
of freedom. The (s l g) curve has been defined by eq. [16].
4. F.T. Selleck, L.T. Carmichael, and B.H. Sage. Ind. Eng. Chem.
1
1
The lower quadruple-point temperature t(hs l g) has been
44, 2219 (1952).
1
1
5
6
. R. de Forcrand and P. Villard. Compt. Rend. 106, 849 (1888).
. F.E.C. Scheffer. Proc. R. Acad. Sci. Amsterdam, 13, 829
evaluated at 3.3912 with SE 0.00057°C and the quadruple-
point pressure P(hs l g) at 0.12363 with SE 0.000002 MPa.
1
1
(
1911).
. F.E.C. Scheffer and G. Meyer. Proc. R. Acad. Sci. Amsterdam,
1, 1338 (1919).
The lower quadruple point, determined directly, has given
7
the temperature t(hs l g) at 3.3917 with SE 0.00090°C and
1
1
2
the pressure P(hs l g) at 0.12364 with SE 0.000011 MPa.
1
1
8
9
. F.T. Barr and W.P. Drews. Chem. Eng. Progr. 56(3), 49 (1960).
. J.S. Drury. Progr. Nucl. Energy, 4, 308 (1961).
Comparison of Q(hs l g) for deuterium sulfide D-hydrate
1
1
with that for hydrogen sulfide hydrate evaluated by Scheffer
and Meyer (7) at –0.4°C and at about 0.094 MPa, indicates a
difference of temperature of 3.79°C and of pressure of about
1
0. D.N. Glew, H.D. Mak, and N.S. Rath. Can. J. Chem. 45, 3059
1967).
1. E.C.W. Clarke and D.N. Glew. Can. J. Chem. 48, 764 (1970).
(
1
1
1
0
.030 MPa. The ratio of P(hs l g) for deuterium sulfide D-
1 1
2. E.C.W. Clarke and D.N. Glew. Can. J. Chem. 49, 691 (1971).
3. R.N. Goldberg and R.D. Weir. Pure Appl. Chem. 10, 1545
hydrate relative to hydrogen sulfide hydrate at their quadru-
ple points is equal to that 1.31 ratio exhibited by Structure I
cyclopropane D-hydrate (23) relative to cyclopropane hy-
drate at their quadruple points.
(
1992).
1
1
4. R.J. Berry. Can. J. Phys. 37, 1230 (1959).
5. N.R. Draper and H. Smith. Applied regression analysis. 2nd
ed. John Wiley & Sons, Inc., New York. 1981.
1
1
6. O. Redlich and J.N.S. Kwong. Chem. Rev. 44, 233 (1949).
7. R.R. Spear, R.L. Robinson, Jr., and K.C. Chao. Ind. Eng.
Chem. Fundam. 8, 2 (1969).
We wish to thank Dr. Howard K. Rae of Atomic Energy
of Canada Limited for his assistance in obtaining isotope
analysis for our deuterium oxide sample. This work was
supported in part by grants under the National Research
Council of Canada, Industrial Research Assistance Program,
for 1963–1966.
18. P.G. Hill and R.D.C. MacMillan. Ind. Eng. Chem. Fundam. 18,
412 (1979).
19. G.S. Kell. J. Phys. Chem. Ref. Data, 6, 1109 (1977).
20. J.A. Barbero, K.G. McCurdy, and P.R. Tremaine. Can. J.
Chem. 60, 1872 (1982).
2
1. E.C.W. Clarke and D.N. Glew. Trans. Faraday Soc. 62, 539
1966).
(
2
2. J.J. Carroll. Ph.D thesis, University of Alberta, Edmonton,
1990.
1
2
3
. D.N. Glew. Can. J. Chem. 38, 208 (1960).
. D.N. Glew. J. Phys. Chem. 66, 605 (1962).
. R.H. Wright and O. Maass. Can. J. Res. 6B, 94 (1932).
23. D.R. Hafemann and S.L. Miller. J. Phys. Chem. 73, 1392,
(1969); 73, 1398 (1969).
©
1998 NRC Canada