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Effect of pressure on the solid-liquid phase equilibria in (water + sodium sulfate) system
163
Fluid Phase Equilibria, 76 (1992) 163-173 Elsevier Science Publishers B.V., Amsterdam
Effect of Pressure on the Solid-Liquid Phase Equilibria in (Water + Sodium sulfate) System
Y.Tanaka”,
S.Hada”,
a Department Rokkodai,
T.Makita”,
of Chemical
Nada-ku,
bAdvanced Separation
and M.Moritok?
Engineering,
Kobe
University
Kobe 657, Japan Systems
Department,
New Business
Development
Group
Kobe Steel Ltd., Kobe 651, Japan
Keywords: high pressure, sulfate, water
solid-liquid
phase equilibrium,
solubility,
sodium
ABSTRACT The effect of pressure on the phase diagram of (Hz0 + Na2S04) system has been investigated at temperatures from 263 to 343 K and pressures up to 500 MPa. This system forms an intermolecular compound Na$Oa.lOH,O. The sodium sulfate decahydrate has an incongruent melting point at 305.5 The present study was undertaken to obtain K at atmospheric pressure. extensive and accurate data concerning the effect of pressure on two kinds of solid-liquid phase equilibria, namely, the solubility curve and the incongruent melting point (peritectic point) of Na$S04.10HzO. The solid-liquid equilibrium measurements were performed by the direct visual observation of the crystal growth and disappearance using a high-pressure optical vessel. The uncertainties in measurements of temperature, pressure, and composition are within 0.1 K, 0.5 MPa and 0.001 mole fraction, respectively. It was found that both the solubility curve and the incongruent melting temperature of NazSOs. 10HsO decrease with increasing pressure. The solid-liquid coexistence curves were correlated by an empirical equation.
INTRODUCTION High pressure crystallization has been recognized as a new separation and purification process to obtain high purity of products and low energy consumption. Accurate knowledge of high-pressure solid-liquid phase equilibria 037%3812/92/$05.00
0 1992 Elsevier Science Publishers B.V. All rights reserved
164
plays important roles in the design of systems for high pressure crystallization processes. However, multicomponent solid-liquid phase equilibria have rarely been investigated under high pressure. For this reason, the authors have reported the effect of pressure on the solid-liquid phase equilibria in several organic binary systems (Nagaoka and Makita, 1987a, b, 1988a, b, 1989). The present work extends the investigation to (Hz0 + Na2S04) system. As shown in Fig.1, (water + sodium sulfate) system forms an intermolecular compound Na2SO*.lOH20 with an incongruent melting point. Ice separates from the aqueous sodium sulfate solutions along the curve AE, which represents the compositions of liquids in equilibrium with ice, and so this curve is regarded as giving the freezing points of the solutions. On the other hand, EG is the solubility curve of NazS04-10H20, since sodium sulfate decahydrate is in equilibrium with aqueous solutions that are saturated with this salt. The freezing point and the solubility curves meet at E, the eutectic point, where both ice and sodium sulfate decahydrate deposit from solution at 271.9 K; this is the lowest temperature at which an aqueous solution of sodium sulfate can exist at atmospheric pressure.
320
c
L
L-l L+ Na$O,
G
305.53 K
H
.F Ice t Na$O, ~10H,O I 60 40 0 20 Weight Percent of Na2SOL
fig. 1 Solid-liquid phase equilibria of (Hz0 + Na2SOI, ) system at atmospheric
pressure
165
The sodium sulfate decahydrate decomposes completely at 305.5 K (below its melting point) into its constituents, giving pure anhydrous sodium sulfate and a solution of composition G ; the sodium sulfate decahydrate cannot be in equilibrium with a liquid having the same composition as itself. The compound is then said to have an incongruent melting point or peritectic point. At the peritectic temperature the decahydrate and anhydrous salts are in equilibrium with saturated solution ; there are thus two solid phases and one liquid, and so the condensed system is invariant at fixed pressure. Along the curve EG solid Na2S04.10H20 separates, but along BG the solid phase consists of NasS04. It should be noted that this curve slopes to the left, indicating that the solubility decreases with increasing temperature. The present study was undertaken in order to obtain extensive and accurate data for the effect of pressure on two kinds of solid-liquid phase equilibria in this system as follows : (a) the solubility curve of Na&04-10HzO (line EG) (b) the incongruent melting line of Na2S04.10Hz0 (line GCH) The pressure effects on the phase diagram are discussed based on the experimental results. The equilibrium composition of the solid-liquid coexistence curve is correlated with the equilibrium pressure and temperature by an empirical equation.
EXPERIMENTAL The solid-liquid equilibrium measurements were performed by direct visual observation of the phase transition in a high-pressure optical vessel. Vl
ii
,E
D E F
_L -_
C
I~/
\ &.I4
J K
Fig.2
Schematic diagram of the apparatus
High Pressure Optical Vessel Thermostat Thermocouple Strain Gauge Intensifier Displacement Meter Oil Pump Exchanger Pressure Indicator Pressure Indicator Temperature Indicator Displacement Indicator 3-Pen Recorder Sample Inlet 0 Sample Outlet
166
The apparatus and experimental procedures were almost the same as those used in the previous work (Nagaoka and Makita (1987a)). The schematic diagram of the apparatus is shown in Fig.2. The sample solution of a known composition was introduced in the equilibrium vessel (A), which was immersed in a liquid bath (B) thermostatically controlled within f0.05 K. The pressure was applied to the sample by means of a pressure intensifier (E) and an oil pump (G). The phase transition across the solubility curve EG of Na2S04. lOHg0 can be determined from the complete disappearance of a solid phase by direct visual observation when the pressure of the system is increased gradually at a constant temperature. At first, the temperature of a solution with a known composition between 0.006 and 0.056 mole fraction was lowered to atmospheric pressure where the crystal of Na2S04.10HzO appeared, and then the pressure was increased at a given constant temperature stepwise by 1 MPa for every 20 minutes near the melting pressure on the liquidus where the solid phase completely disappeared. The phase transition across the incongruent melting line GCH of Na#Os. 10HzO was determined from the first appearance of a liquid phase in the homogeneous solid mixture of crystalline Na$Oh and Na$SOd. lOHz0 of a known composition which was sealed in a small transparent polyethylene bag. The solid mixtures with compositions of 0.113 and 0.160 mole fractions of Na2S04 were selected arbitrarily as typical mixtures between C and H. The mixtures were compressed using ethanol as a pressure medium at a given constant temperature gradually to the incongruent melting pressures where the liquid phase appeared initially in the solid phase. Pressure was measured with a calibrated digital gauge with a strain sensor (D) within an uncertainty less than 410.5 MPa. Temperature was measured with a copper-constantan thermocouple (C) within an uncertainty of f0.05 K. The samples used were obtained from commercial sources. The purities of anhydrous sodium sulfate and decahydrate should be better than 99.0%. The anhydrous sodium sulfate was used after desiccation by heating. The aqueous solution and solid mixture were prepared by weighing. The uncertainty of composition is within 0.001 mole fraction.
EXPERIMENTAL Effect of pressure
Changing
RESULTS
AND
DISCUSSIONS
on the solubility curve of Na:,SC&- 1OHzO
the composition
of aqueous sodium sulfate solution from 0.006
167
to 0.056 mole fraction, the solid-liquid equilibrium pressure and temperature have been measured. The experimental results are given in Table 1 together with the solubility data of Na$Oh. lOHz0 at atmospheric pressure cited from the literature (Int.Crit.Tables). The equilibrium pressure and temperature are plotted in Fig.3 for each solution. Each curve has a negative gradient. The higher pressure region above the equilibrium line denotes a homogeneous liquid phase, while the portion below each line represents a region where the solid (Na$SOb. lOH20) and the liquid coexist. Each line is found to behave almost linearly against temperature, although the melting pressure decreases with increasing temperature along curves for solutions above 0.037 mole fraction. The melting temperature at a given pressure can be read from Fig.3 along each line by graphical interpolation. In Fig.4 the melting temperatures at round pressures thus obtained are plotted against composition of the solution. It should be noted that the equilibrium temperature at a constant composition decreases with increasing pressure. Figure 4 shows the variation of the solubility curve of Na$04.10Hz0, EG in Fig.1, with increasing pressure. Although each isobar apparently approaches the eutectic point E at atmospheric pressure with decreasing composition of Na2S04, the true behavior
Mote Fraction of Sodium
fig. 3
Melting pressure Na2SOs-10HnO
Fig. 4
Effect of pressure
vs. temperature
diagram for the solubility
on the solubility
of Na2SOI,-1OH20
Sulfate
of
168
of each isobar near the eutectic point is unknown. According to the experimental data of Bridgman (1911) concerning the effect of pressure on the equilibrium curve of ice I and water, the melting temperature of ice I decreases by about 10 K for each 100 MPa increase in pressure. Judging from these data, each isobar mentioned above may decrease steeply near the eutectic composition as shown in Fig.4 by dotted lines which are estimated theoretically.
E#ect of pressure on the incongruent
melting line of Na#O4-1OH20
The effect of pressure on the incongruent melting temperature of the sodium sulfate decahydrate, the line GCH in Fig.1, has been investigated. Using two kinds of solid mixtures of NasS04 and NasS04.10Hz0 containing TABLE 1 Solid-liquid
equilibrium T(K)
X=
data for the solubility
Pm (MPaI
0.006
273.2 273.3b
0.008
275.7 277.2 277.Bb
255.8 108.1 0.1
0.010
278.2 280.7 281.3b
260.1 59.5 0.1
0.014
278.2 280.7 283.2 286.1b
436.1 300.8 143.7 0.1
a b c
of Na2SQ.10H20 Pm WW
T(K)
0.022
285.7 288.2 290.7 292.0b
341.4 222.5 74.3 0.1
0.037
293.2 295.7 298.2 299. lb
406.7 346.2 247.4 0.1
0.052
301.2 303.2
aoa.ob
378.6 215.3 0.1
303.2 304.2 305.3b
322.1 228.3 0.1
0.056
Mole fraction of Na2S04 Interpolated from literature values The equilibrium pressure determined has an uncertainty f 1 MPa due to the stepwise variation of pressure
TABLE 2 Incongruent x= 0.113
a b
96.3 c 0.1
X
curve
melting temperature
T (I0 305.2 304.2 303.2
P (MPa) 126.gb 280.4 365.1
of Na2SOc-10H20 under X
0.160
T
-
of
high pressure
(K)
305.2 304.2 303.2
Mole fraction of NanSOb The equilibrium pressure determined has an uncertainty it 1 MPa due to the stepwise variation of pressure
P (MPa) 126.5 280.6 364.5 of
169 308
306-
07
I
;
1
,
o al MPa l lOOMPa n MOMPa 0 ZOOMPa DUlOMPa _
Mole Fraction of Sodium Sulfate Fig.5
Effect of pressure Na2S04 10H20
on the incongruent
melting temperature
on
0.113 and 0.160 mole fraction of Na2S04, the incongruent melting pressure was measured at 305.2, 304.2 and 303.2 K. The incongruent melting pressures obtained at each composition are given in Table 2. By means of graphical interpolation the incongruent melting temperatures at round pressures were obtained. The pressure dependences of the incongruent melting line are shown in Fig.5 as well as the melting line at atmospheric pressure cited from literature (Int.Crit.Tables). Each incongruent melting line at high pressure is parallel to that at 0.1 MPa and decreases with increasing pressure. The liquid-Na2S04-Na$04* lOHz0 triple point G at each constant pressure has been determined as an intersecting point of the solubility curve EG and the incongruent melting line GCH by graphical extrapolation. The temperature and composition of the triple point G shift gradually with increasing pressure. The incongruent melting temperature decreases monotonically with increasing pressure from 305.5 K at 0.1 MPa to 302.7 K at 400 MPa with a negative curvature. The composition decreases slightly, almost linearly with increasing pressure from xr=O.O59 at 0.1 MPa to 0.057 at 400 MPa. The shifts of the triple point temperature and composition are found to be expressed as a function of pressure as follows :
Mole Fraction Fig.
6
Equilibrium of Na2SOr
of Sodium Sulfate
pressure * 10H20
vs.
composition
diagram
for
the
solubility
Tp = 305.53 - 6.286 x 10-4P - 1.594 x 10-5P2
(1)
z9 = 5.93 x 1O-2 - 5.23 x 10-6P - 1.42 x lo-‘P2
(2)
where Tp is in K and P is in MPa. Correlation of the solubility curve of Na2S04-10H20
under high pressure
To correlate the solubility curves of Na2S04.10H20 under high pressure the equation previously proposed by Nagaoka and Makita (1988) for organic binary systems was applied :
TABLE 3 Empirical coefficients
lo-’ B (MPa) 278.2 283.2 288.2 293.2 298.2 303.2
5.435 3.065 3.106 3.782 4.922 8.671
in Eq. (4)
C (cm3 mole-‘) -2.053 -3.446 -3.170 -2.411 -1.713 -0.877
bo ( - )
lo3 bl (MPa-’ )
Mean dev. (%)
Max.dev. (%)
-4. a24 -4.486 -4.109 -3.740 -3.400 -3.017
0.8876 1.464 1.323 0.9889 0.6908 0.3479
0.44 0.07 0.27 0.62 0.93 0.32
0.45 0.10 0.48 1.20 1.44 0.57
e2
273
273
283
Temperature(K)
Fig. 7
Temperature dependence8 of B and C in Eq. (4)
Fig.8
Temperature dependences of b. and bl in Eq.(4)
znxp,T)
=
2
293
f@mpefatureo()
{C(T)[P - B(T)] + D(T)[P2- B(q2]}
(3)
where z(P,T) is the mole fraction of Na2S04, P is the pressure in MPa, T in K, and B, C, and D are the temperature-dependent coefficients, respectively. The relations between the equilibrium pressure and logarithm of the composition are illustrated along isotherms in Fig.6. It is found that a linear relation holds satisfactorily for each isotherm within the uncertainty of the experiment. This means that the coefficient D is substantially negligible in the composition range between 0.005 and 0.06 mole fraction of Na2SOb. Thus Eq.(3) is reduced to a linear equation in pressure as follows :
is the temperature
lnx - -(P -i$?
- B(T)] = h)(T) + bl(T) - P
(4
The coefficients B,C, b,-,and bl were determined by least squares fitting. The coefficients obtained are given in Table 3 together with the mean and the maximum deviations of the experimental data from Eq.(4). The variations of the coefficients with temperature are shown in Figs.7 and 8. Judging from these figures, the coefficients bo and bl change more simply and systematically than B and C above 288.2 K. Therefore bo and bl were correlated with temperature by linear equations in T as follows :
172 c&(T)
=
-24.9504
+ 0.072318T
bl(T) = 19.901 x 1O-3 - 6.4468 x 10-5T
(5) (6)
where the applicable range of temperature is between 288.2 K and 303.2 K. Here, the coefficients B and C are not satisfactorily expressed by polynomials in the reciprocal of temperature, as used previously by Nagaoka and Makita (1988a) for organic binary systems. Equations (4), (5) and (6) can reproduce the experimental P-T-x data above 285.7 K in Table 1 with a mean deviation of 2.4% and the maximum of 7.6%.
CONCLUSIONS The effects of pressure on the solubility curve and the incongruent melting temperature of Na2S04+10H20 in (Hz0 + Na$OJ) system were investigated in a high-pressure optical vessel. Concerning the solubility curve of Na$l04.10H20, the equilibrium temperature at a constant composition decreases with increasing pressure. The equilibrium composition was satisfactorily correlated with temperature and pressure by means of Eqs.(4), (5) and (6) in a temperature range from 288 to 303 K. The incongruent melting temperature of Na$S04.10HzO is found to decrease with increasing pressure. The variation of the incongruent melting temperature with pressure can be expressed by Eq.(l). Although we tried to investigate the effect of pressure on the solubility curve of NazS04, BG in Fig.1, by means of the same procedure employed for the solubility curve of Na2SO.+.lOHsO, we could never observe the growth and disappearance of Na2S04 crystal. The manual control of pressure and the visual observation may be unsuitable for investigation of the solubility curve of Na#04 since the solubility curve is too steep. REFERENCES Bridgman,P.W., 1911. Water in the Liquid and five Solid Forms under Pressure. Proc.Am.Acad.Arts Sci., 47 : 441. International Critical Tables, 1928. Vo1.4, McGraw-Hill, New York, p.236. Nagaoka,K., and Makita,T., 1987a. Solid-Liquid Phase Equilibria of Benzene + Cyclohexane System Under High Pressures. Int.J.Thermophys., 8 : 415. Nagaoka,K., and Makita,T., 1987b. Solid-Liquid Phase Equilibria of (o-Methylnaphthalene + /3-Methylnaphthalene) and (Chlorobenzene
173
+ Bromobenzene) Systems Under High Pressures. Int.J.Thermophys., 8: 671. Nagaoka,K., and Makita,T., 1988a. Solid-Liquid Phase Equilibria of Benzene + 2-Methyl-2-Propanol System Under High Pressures. Int.J.Thermophys., 9 : 61. Nagaoka,K., and Makita,T., 1988b. Effect of Pressure on the SolidLiquid Phase Equilibria of (Carbon Tetrachloride + p-Xylene) and (Carbon Tetrachloride + Benzene) Systems. Int.J.Thermophys., 9 : 535. Nagaoka,K., Makita,T., Nishiguchi,N., and Moritoki,M., 1989. Effect of Pressure on the Solid-Liquid Phase Equilibria of Binary Organic Systems. Int.J.Thermophys., 10 : 27.
Fluid Phase Equilibria, 76 (1992) 163-173 Elsevier Science Publishers B.V., Amsterdam
Effect of Pressure on the Solid-Liquid Phase Equilibria in (Water + Sodium sulfate) System
Y.Tanaka”,
S.Hada”,
a Department Rokkodai,
T.Makita”,
of Chemical
Nada-ku,
bAdvanced Separation
and M.Moritok?
Engineering,
Kobe
University
Kobe 657, Japan Systems
Department,
New Business
Development
Group
Kobe Steel Ltd., Kobe 651, Japan
Keywords: high pressure, sulfate, water
solid-liquid
phase equilibrium,
solubility,
sodium
ABSTRACT The effect of pressure on the phase diagram of (Hz0 + Na2S04) system has been investigated at temperatures from 263 to 343 K and pressures up to 500 MPa. This system forms an intermolecular compound Na$Oa.lOH,O. The sodium sulfate decahydrate has an incongruent melting point at 305.5 The present study was undertaken to obtain K at atmospheric pressure. extensive and accurate data concerning the effect of pressure on two kinds of solid-liquid phase equilibria, namely, the solubility curve and the incongruent melting point (peritectic point) of Na$S04.10HzO. The solid-liquid equilibrium measurements were performed by the direct visual observation of the crystal growth and disappearance using a high-pressure optical vessel. The uncertainties in measurements of temperature, pressure, and composition are within 0.1 K, 0.5 MPa and 0.001 mole fraction, respectively. It was found that both the solubility curve and the incongruent melting temperature of NazSOs. 10HsO decrease with increasing pressure. The solid-liquid coexistence curves were correlated by an empirical equation.
INTRODUCTION High pressure crystallization has been recognized as a new separation and purification process to obtain high purity of products and low energy consumption. Accurate knowledge of high-pressure solid-liquid phase equilibria 037%3812/92/$05.00
0 1992 Elsevier Science Publishers B.V. All rights reserved
164
plays important roles in the design of systems for high pressure crystallization processes. However, multicomponent solid-liquid phase equilibria have rarely been investigated under high pressure. For this reason, the authors have reported the effect of pressure on the solid-liquid phase equilibria in several organic binary systems (Nagaoka and Makita, 1987a, b, 1988a, b, 1989). The present work extends the investigation to (Hz0 + Na2S04) system. As shown in Fig.1, (water + sodium sulfate) system forms an intermolecular compound Na2SO*.lOH20 with an incongruent melting point. Ice separates from the aqueous sodium sulfate solutions along the curve AE, which represents the compositions of liquids in equilibrium with ice, and so this curve is regarded as giving the freezing points of the solutions. On the other hand, EG is the solubility curve of NazS04-10H20, since sodium sulfate decahydrate is in equilibrium with aqueous solutions that are saturated with this salt. The freezing point and the solubility curves meet at E, the eutectic point, where both ice and sodium sulfate decahydrate deposit from solution at 271.9 K; this is the lowest temperature at which an aqueous solution of sodium sulfate can exist at atmospheric pressure.
320
c
L
L-l L+ Na$O,
G
305.53 K
H
.F Ice t Na$O, ~10H,O I 60 40 0 20 Weight Percent of Na2SOL
fig. 1 Solid-liquid phase equilibria of (Hz0 + Na2SOI, ) system at atmospheric
pressure
165
The sodium sulfate decahydrate decomposes completely at 305.5 K (below its melting point) into its constituents, giving pure anhydrous sodium sulfate and a solution of composition G ; the sodium sulfate decahydrate cannot be in equilibrium with a liquid having the same composition as itself. The compound is then said to have an incongruent melting point or peritectic point. At the peritectic temperature the decahydrate and anhydrous salts are in equilibrium with saturated solution ; there are thus two solid phases and one liquid, and so the condensed system is invariant at fixed pressure. Along the curve EG solid Na2S04.10H20 separates, but along BG the solid phase consists of NasS04. It should be noted that this curve slopes to the left, indicating that the solubility decreases with increasing temperature. The present study was undertaken in order to obtain extensive and accurate data for the effect of pressure on two kinds of solid-liquid phase equilibria in this system as follows : (a) the solubility curve of Na&04-10HzO (line EG) (b) the incongruent melting line of Na2S04.10Hz0 (line GCH) The pressure effects on the phase diagram are discussed based on the experimental results. The equilibrium composition of the solid-liquid coexistence curve is correlated with the equilibrium pressure and temperature by an empirical equation.
EXPERIMENTAL The solid-liquid equilibrium measurements were performed by direct visual observation of the phase transition in a high-pressure optical vessel. Vl
ii
,E
D E F
_L -_
C
I~/
\ &.I4
J K
Fig.2
Schematic diagram of the apparatus
High Pressure Optical Vessel Thermostat Thermocouple Strain Gauge Intensifier Displacement Meter Oil Pump Exchanger Pressure Indicator Pressure Indicator Temperature Indicator Displacement Indicator 3-Pen Recorder Sample Inlet 0 Sample Outlet
166
The apparatus and experimental procedures were almost the same as those used in the previous work (Nagaoka and Makita (1987a)). The schematic diagram of the apparatus is shown in Fig.2. The sample solution of a known composition was introduced in the equilibrium vessel (A), which was immersed in a liquid bath (B) thermostatically controlled within f0.05 K. The pressure was applied to the sample by means of a pressure intensifier (E) and an oil pump (G). The phase transition across the solubility curve EG of Na2S04. lOHg0 can be determined from the complete disappearance of a solid phase by direct visual observation when the pressure of the system is increased gradually at a constant temperature. At first, the temperature of a solution with a known composition between 0.006 and 0.056 mole fraction was lowered to atmospheric pressure where the crystal of Na2S04.10HzO appeared, and then the pressure was increased at a given constant temperature stepwise by 1 MPa for every 20 minutes near the melting pressure on the liquidus where the solid phase completely disappeared. The phase transition across the incongruent melting line GCH of Na#Os. 10HzO was determined from the first appearance of a liquid phase in the homogeneous solid mixture of crystalline Na$Oh and Na$SOd. lOHz0 of a known composition which was sealed in a small transparent polyethylene bag. The solid mixtures with compositions of 0.113 and 0.160 mole fractions of Na2S04 were selected arbitrarily as typical mixtures between C and H. The mixtures were compressed using ethanol as a pressure medium at a given constant temperature gradually to the incongruent melting pressures where the liquid phase appeared initially in the solid phase. Pressure was measured with a calibrated digital gauge with a strain sensor (D) within an uncertainty less than 410.5 MPa. Temperature was measured with a copper-constantan thermocouple (C) within an uncertainty of f0.05 K. The samples used were obtained from commercial sources. The purities of anhydrous sodium sulfate and decahydrate should be better than 99.0%. The anhydrous sodium sulfate was used after desiccation by heating. The aqueous solution and solid mixture were prepared by weighing. The uncertainty of composition is within 0.001 mole fraction.
EXPERIMENTAL Effect of pressure
Changing
RESULTS
AND
DISCUSSIONS
on the solubility curve of Na:,SC&- 1OHzO
the composition
of aqueous sodium sulfate solution from 0.006
167
to 0.056 mole fraction, the solid-liquid equilibrium pressure and temperature have been measured. The experimental results are given in Table 1 together with the solubility data of Na$Oh. lOHz0 at atmospheric pressure cited from the literature (Int.Crit.Tables). The equilibrium pressure and temperature are plotted in Fig.3 for each solution. Each curve has a negative gradient. The higher pressure region above the equilibrium line denotes a homogeneous liquid phase, while the portion below each line represents a region where the solid (Na$SOb. lOH20) and the liquid coexist. Each line is found to behave almost linearly against temperature, although the melting pressure decreases with increasing temperature along curves for solutions above 0.037 mole fraction. The melting temperature at a given pressure can be read from Fig.3 along each line by graphical interpolation. In Fig.4 the melting temperatures at round pressures thus obtained are plotted against composition of the solution. It should be noted that the equilibrium temperature at a constant composition decreases with increasing pressure. Figure 4 shows the variation of the solubility curve of Na$04.10Hz0, EG in Fig.1, with increasing pressure. Although each isobar apparently approaches the eutectic point E at atmospheric pressure with decreasing composition of Na2S04, the true behavior
Mote Fraction of Sodium
fig. 3
Melting pressure Na2SOs-10HnO
Fig. 4
Effect of pressure
vs. temperature
diagram for the solubility
on the solubility
of Na2SOI,-1OH20
Sulfate
of
168
of each isobar near the eutectic point is unknown. According to the experimental data of Bridgman (1911) concerning the effect of pressure on the equilibrium curve of ice I and water, the melting temperature of ice I decreases by about 10 K for each 100 MPa increase in pressure. Judging from these data, each isobar mentioned above may decrease steeply near the eutectic composition as shown in Fig.4 by dotted lines which are estimated theoretically.
E#ect of pressure on the incongruent
melting line of Na#O4-1OH20
The effect of pressure on the incongruent melting temperature of the sodium sulfate decahydrate, the line GCH in Fig.1, has been investigated. Using two kinds of solid mixtures of NasS04 and NasS04.10Hz0 containing TABLE 1 Solid-liquid
equilibrium T(K)
X=
data for the solubility
Pm (MPaI
0.006
273.2 273.3b
0.008
275.7 277.2 277.Bb
255.8 108.1 0.1
0.010
278.2 280.7 281.3b
260.1 59.5 0.1
0.014
278.2 280.7 283.2 286.1b
436.1 300.8 143.7 0.1
a b c
of Na2SQ.10H20 Pm WW
T(K)
0.022
285.7 288.2 290.7 292.0b
341.4 222.5 74.3 0.1
0.037
293.2 295.7 298.2 299. lb
406.7 346.2 247.4 0.1
0.052
301.2 303.2
aoa.ob
378.6 215.3 0.1
303.2 304.2 305.3b
322.1 228.3 0.1
0.056
Mole fraction of Na2S04 Interpolated from literature values The equilibrium pressure determined has an uncertainty f 1 MPa due to the stepwise variation of pressure
TABLE 2 Incongruent x= 0.113
a b
96.3 c 0.1
X
curve
melting temperature
T (I0 305.2 304.2 303.2
P (MPa) 126.gb 280.4 365.1
of Na2SOc-10H20 under X
0.160
T
-
of
high pressure
(K)
305.2 304.2 303.2
Mole fraction of NanSOb The equilibrium pressure determined has an uncertainty it 1 MPa due to the stepwise variation of pressure
P (MPa) 126.5 280.6 364.5 of
169 308
306-
07
I
;
1
,
o al MPa l lOOMPa n MOMPa 0 ZOOMPa DUlOMPa _
Mole Fraction of Sodium Sulfate Fig.5
Effect of pressure Na2S04 10H20
on the incongruent
melting temperature
on
0.113 and 0.160 mole fraction of Na2S04, the incongruent melting pressure was measured at 305.2, 304.2 and 303.2 K. The incongruent melting pressures obtained at each composition are given in Table 2. By means of graphical interpolation the incongruent melting temperatures at round pressures were obtained. The pressure dependences of the incongruent melting line are shown in Fig.5 as well as the melting line at atmospheric pressure cited from literature (Int.Crit.Tables). Each incongruent melting line at high pressure is parallel to that at 0.1 MPa and decreases with increasing pressure. The liquid-Na2S04-Na$04* lOHz0 triple point G at each constant pressure has been determined as an intersecting point of the solubility curve EG and the incongruent melting line GCH by graphical extrapolation. The temperature and composition of the triple point G shift gradually with increasing pressure. The incongruent melting temperature decreases monotonically with increasing pressure from 305.5 K at 0.1 MPa to 302.7 K at 400 MPa with a negative curvature. The composition decreases slightly, almost linearly with increasing pressure from xr=O.O59 at 0.1 MPa to 0.057 at 400 MPa. The shifts of the triple point temperature and composition are found to be expressed as a function of pressure as follows :
Mole Fraction Fig.
6
Equilibrium of Na2SOr
of Sodium Sulfate
pressure * 10H20
vs.
composition
diagram
for
the
solubility
Tp = 305.53 - 6.286 x 10-4P - 1.594 x 10-5P2
(1)
z9 = 5.93 x 1O-2 - 5.23 x 10-6P - 1.42 x lo-‘P2
(2)
where Tp is in K and P is in MPa. Correlation of the solubility curve of Na2S04-10H20
under high pressure
To correlate the solubility curves of Na2S04.10H20 under high pressure the equation previously proposed by Nagaoka and Makita (1988) for organic binary systems was applied :
TABLE 3 Empirical coefficients
lo-’ B (MPa) 278.2 283.2 288.2 293.2 298.2 303.2
5.435 3.065 3.106 3.782 4.922 8.671
in Eq. (4)
C (cm3 mole-‘) -2.053 -3.446 -3.170 -2.411 -1.713 -0.877
bo ( - )
lo3 bl (MPa-’ )
Mean dev. (%)
Max.dev. (%)
-4. a24 -4.486 -4.109 -3.740 -3.400 -3.017
0.8876 1.464 1.323 0.9889 0.6908 0.3479
0.44 0.07 0.27 0.62 0.93 0.32
0.45 0.10 0.48 1.20 1.44 0.57
e2
273
273
283
Temperature(K)
Fig. 7
Temperature dependence8 of B and C in Eq. (4)
Fig.8
Temperature dependences of b. and bl in Eq.(4)
znxp,T)
=
2
293
f@mpefatureo()
{C(T)[P - B(T)] + D(T)[P2- B(q2]}
(3)
where z(P,T) is the mole fraction of Na2S04, P is the pressure in MPa, T in K, and B, C, and D are the temperature-dependent coefficients, respectively. The relations between the equilibrium pressure and logarithm of the composition are illustrated along isotherms in Fig.6. It is found that a linear relation holds satisfactorily for each isotherm within the uncertainty of the experiment. This means that the coefficient D is substantially negligible in the composition range between 0.005 and 0.06 mole fraction of Na2SOb. Thus Eq.(3) is reduced to a linear equation in pressure as follows :
is the temperature
lnx - -(P -i$?
- B(T)] = h)(T) + bl(T) - P
(4
The coefficients B,C, b,-,and bl were determined by least squares fitting. The coefficients obtained are given in Table 3 together with the mean and the maximum deviations of the experimental data from Eq.(4). The variations of the coefficients with temperature are shown in Figs.7 and 8. Judging from these figures, the coefficients bo and bl change more simply and systematically than B and C above 288.2 K. Therefore bo and bl were correlated with temperature by linear equations in T as follows :
172 c&(T)
=
-24.9504
+ 0.072318T
bl(T) = 19.901 x 1O-3 - 6.4468 x 10-5T
(5) (6)
where the applicable range of temperature is between 288.2 K and 303.2 K. Here, the coefficients B and C are not satisfactorily expressed by polynomials in the reciprocal of temperature, as used previously by Nagaoka and Makita (1988a) for organic binary systems. Equations (4), (5) and (6) can reproduce the experimental P-T-x data above 285.7 K in Table 1 with a mean deviation of 2.4% and the maximum of 7.6%.
CONCLUSIONS The effects of pressure on the solubility curve and the incongruent melting temperature of Na2S04+10H20 in (Hz0 + Na$OJ) system were investigated in a high-pressure optical vessel. Concerning the solubility curve of Na$l04.10H20, the equilibrium temperature at a constant composition decreases with increasing pressure. The equilibrium composition was satisfactorily correlated with temperature and pressure by means of Eqs.(4), (5) and (6) in a temperature range from 288 to 303 K. The incongruent melting temperature of Na$S04.10HzO is found to decrease with increasing pressure. The variation of the incongruent melting temperature with pressure can be expressed by Eq.(l). Although we tried to investigate the effect of pressure on the solubility curve of NazS04, BG in Fig.1, by means of the same procedure employed for the solubility curve of Na2SO.+.lOHsO, we could never observe the growth and disappearance of Na2S04 crystal. The manual control of pressure and the visual observation may be unsuitable for investigation of the solubility curve of Na#04 since the solubility curve is too steep. REFERENCES Bridgman,P.W., 1911. Water in the Liquid and five Solid Forms under Pressure. Proc.Am.Acad.Arts Sci., 47 : 441. International Critical Tables, 1928. Vo1.4, McGraw-Hill, New York, p.236. Nagaoka,K., and Makita,T., 1987a. Solid-Liquid Phase Equilibria of Benzene + Cyclohexane System Under High Pressures. Int.J.Thermophys., 8 : 415. Nagaoka,K., and Makita,T., 1987b. Solid-Liquid Phase Equilibria of (o-Methylnaphthalene + /3-Methylnaphthalene) and (Chlorobenzene
173
+ Bromobenzene) Systems Under High Pressures. Int.J.Thermophys., 8: 671. Nagaoka,K., and Makita,T., 1988a. Solid-Liquid Phase Equilibria of Benzene + 2-Methyl-2-Propanol System Under High Pressures. Int.J.Thermophys., 9 : 61. Nagaoka,K., and Makita,T., 1988b. Effect of Pressure on the SolidLiquid Phase Equilibria of (Carbon Tetrachloride + p-Xylene) and (Carbon Tetrachloride + Benzene) Systems. Int.J.Thermophys., 9 : 535. Nagaoka,K., Makita,T., Nishiguchi,N., and Moritoki,M., 1989. Effect of Pressure on the Solid-Liquid Phase Equilibria of Binary Organic Systems. Int.J.Thermophys., 10 : 27.