Vapor−Liquid−Solid Phase Transitions in Aqueous Sodium Sulfate

J. Chem. Eng. Data 2000, 45, 1133-1138

1133

Vapor-Liquid-Solid Phase Transitions in Aqueous Sodium Sulfate and Sodium Carbonate from Heat Capacity Measurements near the First Critical End Point. 1. Sodium Sulfate Ilmutdin M. Abdulagatov,*,†,‡ Boris A. Mursalov,† and Vasilii I. Dvoryanchikov† Institute for Geothermal Problems of the Dagestan Scientific Center of the Russian Academy of Sciences, 367030 Makhachkala, Shamilya 39 A, Dagestan, Russia

Heat capacities at constant volume and composition are reported for aqueous sodium sulfate for three compositions, 1 mass %, 5 mass %, and 10 mass %, respectively, and along 19 isochores, from 250 kg‚m-3 to 1073 kg‚m-3 in the temperature range from 350 K to 670 K. In the range from 630 K to 650 K, many of these isochores display two features in the heat capacity as a function of the temperature: one peak or step when solid salt first precipitates and, on further heating, a λ-shaped peak when the vapor- or liquid-phase disappears. In Part 2 of this paper, these features will be interpreted.

Introduction There has been growing interest in aqueous solutions at near-critical and supercritical conditions due to their importance in supercritical water oxidation (SCWO) technology. SCWO technology is an emerging technology for the destruction of civilian and military hazardous wastes. One of the important applications of SCWO for waste treatment is in the handling of solids which can be present at high temperatures and high pressures. Sodium sulfate is one of the most commonly encoutered salts in prospective applications of SCWO. Development of effective strategies for applying SCWO technology to the destruction of hazardous materials requires knowledge of the thermodynamic properties of aqueous salt solutions near the critical point. This paper presents new isochoric heat capacity data for aqueous sodium sulfate at temperatures up to 670 K. Sodium sulfate, or Glauber salt, was a mainstay of the German chemical and pharmaceutical industry in the 19th century. The salt has a complex phase diagram. Above 250 °C, however, in the range of declining solubility of interest here, the solid salt exists in dehydrated form only. The solid phase extends above the critical point of water; thus, cutting off the saltwater critical line in a critical end point. This so-called Type-2 solid-liquid-vapor phase behavior, typical for sodium sulfate, sodium carbonate (Abdulagatov et al.1), and many other salts poorly soluble in water, will be described in more detail in Valyashko et al.,2 Part 2 of this series. Interest in sodium sulfate was reactivated recently because the salt is formed, and found to clog the reactor tubes, during the process of SCWO of sulfur-containing organic waste, when caustic is added for neutralization. Armellini and Tester3 (MIT) studied the kinetics of salt deposition under near-critical conditions. Salt deposition from aqueous sodium sulfate was studied in a collaboration.3,4 At the Dagestan Scientific Center of the Russian Academy of Sciences, the heat capacity Cvx of aqueous sodium * To whom correspondence should be addressed. † Institute for Geothermal Problems of the Dagestan Scientific Center of the Russian Academy of Sciences. E-mail: [email protected]. ‡ Present address: National Institute of Standards and Technology, Boulder, CO 80303. E-mail: [email protected].

Table 1. Typical Ramp Rates for Some Isochores at Density G F/kg‚m-3 697.8 537.6 537.6 490.0

rate/K‚s-1 (heating and cooling) from 6.07 × 10-4 from 7.15 × 10-4 from 5.77 × 10-4 from 3.45 × 10-4

to 7.55 × 10-4 to 8.97 × 10-4 to 7.27 × 10-4 to 11.79 × 10-4

sulfate has been measured in two or three coexisting phases at constant overall volume V and mass fraction x. Although some of the results have appeared in print before (Abdulagatov et al.5), the comprehensive set of 19 isochores at three compositions is included here for the first time. Many of these isochores show two characteristic features. In a heating run, first a step or peak appears when solid salt begins to drop out of solution. Some runs were taken both in the heating and the cooling mode. At a higher temperature, either the liquid or the vapor phase disappears, with a characteristic λ-shaped peak for those isochores that are close to the critical density for the solution. In the present paper, the data are presented. In a followup paper, Valyashko et al.,2 Part 2 in this series, an interpretation is given of the features in the data, and a comparison is made with data from the literature. Experimental Section Measurements of the isochoric heat capacity of sodium sulfate and sodium carbonate solutions were made in a spherical high-temperature, high-pressure adiabatic calorimeter, of a design pioneered by Amirkhanov et al.6 The present calorimeter has been described in a recent paper in this journal (Abdulagatov et al.7), and additional detail is given by Mursalov et al.8 The spherical vessel is constructed of heat- and corrosion-resistant 1X18H9T stainless steel and has a volume of 101.45 cm3. The contents of the vessel are stirred prior to measurement. Heat capacities are measured in a ramping heating mode; occasionally, a cooling mode is used. The ramp rate is varied, to make sure that the heat capacity does not depend on the ramp rate. Some typical optimal ramp rates are given in Table 1. The papers by Abdulagatov et al.7 and Mursalov et al.8 contain a detailed analysis of all sources of uncertainty likely to affect the determination of Cvx, with

10.1021/je0001227 CCC: $19.00 © 2000 American Chemical Society Published on Web 10/04/2000

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Journal of Chemical and Engineering Data, Vol. 45, No. 6, 2000

Table 2. Experimental Values of the Heat Capacities Cvx along Isochores in Aqueous Sodium Sulfate T K

Cvx kJ‚

kg-1‚K-1

T K

585.29 585.46 585.64 585.82 585.98 629.02 629.19 629.38 629.54 629.68 629.87 630.05

6.231 6.759 6.650 6.667 6.443 8.972 8.868 8.963 8.867 13.406 10.350 10.297

630.22 631.24 631.41 631.59 646.41 646.58 646.75 646.92 647.08 647.26 647.43 647.60

588.44 588.61 588.79 588.96 589.14 630.56 630.73 630.90 631.24 631.41 631.59

5.528 5.560 5.753 5.772 5.775 8.024 8.086 8.021 8.012 8.017 8.012

631.76 631.93 632.10 632.27 632.44 632.61 632.78 647.02 647.26 647.43 647.60

583.71 583.88 584.06 584.23 584.41 624.75 624.92 625.09 625.26 625.43 631.07 631.14 631.41 631.59 631.76 631.93 632.10 632.27 632.44 632.61 632.78 632.95 633.12

5.502 5.331 5.331 5.333 5.332 7.397 7.383 7.417 7.327 7.322 7.891 7.887 7.799 7.885 7.881 7.848 7.902 7.881 7.830 7.825 7.907 11.473 9.464

633.29 633.46 633.73 634.66 634.83 635.00 635.17 635.34 635.51 646.92 647.09 647.26 647.43 647.60 647.78 647.95 648.12 648.29 648.46 648.63 649.14 649.31 649.48

630.05 630.22 630.39 630.56 630.73 632.95 633.12 633.29 633.46 634.15C 634.32C 634.49C 634.49 634.66 634.66C

6.394 6.521 6.447 6.540 6.344 6.400 6.396 6.399 6.403 6.740 7.067 7.305 6.797 6.741 7.307

591.24 591.41 591.58 591.76 592.93 593.10 599.42 599.59 599.77

5.024 4.974 5.046 5.025 5.025 4.980 5.261 5.217 5.221

Cvx kJ‚

T

Cvx

K

kJ‚ kg-1‚K-1

647.78 647.95 648.12 648.29 648.63 648.80 648.97 649.31 665.65 665.82 665.99

6.079 5.972 4.473 4.485 4.042 4.119 4.120 4.054 3.410 3.275 3.276

647.78 647.95 648.12 648.29 648.46 648.63 648.80 648.97 649.14 649.31 649.48

16.085 16.073 6.255 5.577 5.235 5.144 4.972 5.086 5.257 5.173 5.085

649.65 649.82 649.99 650.16 652.71 652.88 653.05 653.22 653.39 653.56 653.73 653.89 654.06 654.23 667.01 667.18 667.35 667.52 667.69 667.86 668.32 668.55

4.569 4.570 4.570 4.595 4.049 4.049 4.031 4.061 4.061 3.964 4.052 3.966 4.096 4.097 3.337 3.340 3.253 3.328 3.298 3.124 3.327 3.251

7.422 6.872 6.757 7.613 7.675 9.003 9.184 7.734 7.735 8.095 8.019 7.857 7.908 8.070

636.02 637.39 637.56 637.73 637.90 638.07 638.41 638.58 639.75 639.92 662.75 662.92 663.09 663.26

8.077 7.852 7.851 7.912 7.813 7.807 3.170 3.108 3.111 3.106 2.927 2.954 2.906 2.931

5.280 5.175 3.036 2.798 2.846 2.846 2.977 2.992 2.999

602.19 602.37 602.54 602.71 610.49 610.66 610.83 611.01 611.18

2.999 3.020 3.000 3.019 2.956 2.977 2.976 2.978 2.978

kg-1‚K-1

1 mass % Na2SO4 F ) 250.1 kg‚m-3 10.294 10.340 10.341 10.237 13.323 13.577 13.705 13.620 13.520 10.300 9.033 7.135 F ) 309.9 kg‚m-3 8.089 8.509 12.225 9.270 9.228 9.280 9.275 13.437 14.043 14.638 15.235 F ) 361.9 kg‚m-3 8.935 9.088 9.088 9.195 9.125 9.110 9.253 9.254 9.340 12.520 12.829 14.084 13.983 15.345 16.178 8.749 5.817 5.353 5.177 4.779 4.737 4.740 4.743

F ) 521.3 kg‚m-3 634.83C a 634.83 635.00 635.00C 635.17C 635.17 635.34 635.34C 635.51C 635.51 635.68 635.68C 635.85C 635.85 F ) 664.0 kg‚m-3 599.94 600.11 600.46 600.63 600.81 600.98 601.15 601.33 602.02

Journal of Chemical and Engineering Data, Vol. 45, No. 6, 2000 1135 Table 2. (continued) T K

492.17 492.36 492.55 492.74 492.93 493.13 493.32

Cvx kJ‚

kg-1‚K-1

4.457 4.432 4.408 4.495 4.451 3.586 3.630

T K

493.51 493.70 493.89 494.08 494.27 494.46 494.65

Cvx kJ‚

kg-1‚K-1

1 mass % Na2SO4 F ) 860.5 kg‚m-3 3.364 3.311 3.234 3.180 3.312 3.188 3.234

T

Cvx

K

kJ‚ kg-1‚K-1

494.84 513.32 513.52 513.70 513.88 514.07 514.26

3.185 3.279 3.234 3.236 3.283 3.261 3.304

644.71 644.72C 644.80C 644.88 644.89C 645.05 645.17 645.39 645.56 647.09 647.26 647.43 647.60 647.77

3.476 3.386 3.449 3.199 3.509 3.145 3.199 3.199 3.145 3.208 3.292 3.292 3.248 3.173

608.93 609.11 609.28 609.45 609.63 609.97 610.14 610.32 610.49 637.37 637.54 637.71 638.23 643.01 643.18

5.143 5.168 5.068 5.080 5.091 12.519 6.613 6.565 6.517 7.961 7.810 7.980 7.962 8.567 8.633

5 mass % Na2SO4 F ) 490.0 kg‚m-3 643.35 8.829 643.52 8.913 643.69 8.687 643.86 8.996 644.03 8.719 C 644.11 7.687 644.20C 8.074 644.20 7.507 644.29C 9.129 644.37 6.607 644.38C 3.581 644.46C 3.506 644.54 3.201 C 644.55 3.377 C 644.63 3.386

607.56 607.73 607.90 608.07 608.94 609.80 609.97 610.32 610.49 610.66

4.682 4.828 4.643 4.627 4.850 4.851 4.854 4.798 4.790 11.605

611.01 611.18 611.52 611.87 612.04 612.21 615.31 615.48 615.65 616.00

F ) 674.7 kg‚m-3 6.468 6.419 6.397 6.352 6.400 6.342 6.565 6.679 6.504 2.836

616.17 616.69 616.86 617.54 617.72 631.93 632.10 632.44 632.61

2.873 2.871 2.814 2.754 2.749 3.049 3.050 2.979 3.015

460.35 460.55 460.74 460.94 461.14 461.34

3.383 3.352 3.409 3.268 2.793 2.853

461.53 461.73 462.12 462.32 462.52 462.72

F ) 925.9 kg‚m-3 3.049 2.802 2.821 2.727 2.610 2.798

480.57 480.77 480.96 481.16 481.36

2.711 2.760 2.645 2.718 2.743

590.54C 590.71C 590.89C 591.06C 591.41C 591.58C 591.58 591.76 591.76C 591.93C 591.93 592.11 592.11C 592.28C 592.28

4.371 4.368 4.370 4.337 4.335 5.383 4.441 4.366 5.264 5.441 4.484 4.428 5.520 5.570 5.146

10 mass % Na2SO4 F ) 537.6 kg‚m-3 592.46 9.639 592.46C 5.660 C 592.63 5.602 592.63 6.466 C 592.81 5.735 592.98C 5.686 593.33 5.968 593.50 6.050 593.68 5.930 593.85 6.123 594.03 6.178 640.55 7.631 640.62 7.882 640.79 7.885 640.96 7.855

641.30 641.48 641.65 641.82 641.99 642.16 642.33 642.50 642.67 642.84 643.18 643.35 643.52 643.69

7.865 8.012 8.166 8.477 8.318 8.315 8.313 8.155 7.907 7.482 2.978 2.978 2.976 2.951

591.24C 591.41C 591.58C 591.76C 591.93 591.93C 592.11C 592.11 592.28 592.28C 592.46 592.46C 592.63C 592.81 592.81C 592.98C

4.765 4.744 4.862 4.884 4.411 4.883 5.072 4.430 4.393 5.560 4.406 5.592 5.643 4.367 5.589 5.591

619.26 619.43 619.60 619.78 619.95 620.12 631.59 631.76 631.93 632.10 632.27 632.78 640.45 640.62 640.79

6.385 6.119 3.422 2.692 2.690 2.642 2.717 2.763 2.716 2.835 2.726 2.751 2.721 2.671 2.670

593.15C 593.33C 593.50C 593.68 593.68C 593.85C 594.20 594.37 594.55 594.72 594.90 618.58 618.75 618.92 619.09

F ) 697.8 kg‚m-3 5.570 5.454 5.981 5.732 5.546 5.837 5.841 5.912 5.868 5.954 5.933 6.517 6.486 6.503 6.428

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Journal of Chemical and Engineering Data, Vol. 45, No. 6, 2000

Table 2. (continued) T K

Cvx kJ‚

kg-1‚K-1

T K

Cvx kJ‚

kg-1‚K-1

T

Cvx

K

kJ‚ kg-1‚K-1

10 mass % Na2SO4 589.66 589.84 590.01 590.19 591.58C 591.76C 591.93C 591.93 592.11 592.11C 592.28C 592.46C 592.46 592.63C 592.81C 592.81

4.398 4.399 4.381 4.397 4.188 4.117 4.226 4.395 4.396 4.262 4.404 4.833 4.395 5.116 5.259 4.327

F ) 774.2 kg‚m-3 592.94C 592.98 593.03 593.15 593.33 593.33C 593.50C 593.50 593.68 593.68C 593.85C 593.85 594.03C 594.20C 594.20 602.54

5.324 4.403 4.396 4.398 4.402 5.407 5.402 4.400 4.405 5.544 5.535 13.420 5.550 5.554 5.982 6.053

602.71 602.89 603.06 603.23 603.41 603.58 603.75 603.93 604.10 604.27 604.46 604.62 604.79 604.96 605.14

6.032 6.027 6.025 5.979 5.984 3.565 2.497 2.440 2.557 2.439 2.678 2.678 2.681 2.681 2.678

476.59 476.78 476.98 477.17 477.36 477.56 477.95 478.14 478.33 478.53 574.90 575.07 575.25 575.78

3.636 3.643 3.642 3.627 3.660 3.661 3.632 3.658 3.693 3.663 4.244 4.157 4.199 4.237

F ) 796.2 kg‚m-3 589.14 589.31 589.49 589.84 590.36 590.71 590.89 591.06 593.85 594.03 594.20 594.55 595.42 595.59

4.383 4.381 4.402 4.350 4.393 4.353 4.340 4.353 5.652 5.690 5.697 5.839 5.858 5.900

596.64 596.81 597.16 597.85 598.03 598.38 598.72 598.90 599.42 613.25 613.42 613.59 613.77

5.930 5.935 5.996 5.875 5.787 6.024 2.734 2.733 2.729 2.697 2.697 2.738 2.697

587.21 587.38 587.56 587.73 587.91 588.09 588.26 588.44 588.96 589.14 589.31 589.49 589.83

4.402 4.267 4.265 4.213 3.035 2.782 2.731 2.832 2.731 2.683 2.685 2.736 2.625

F ) 830.7 kg‚m-3 590.01 590.19 590.36 590.53 590.71 590.89 591.06 591.24 605.83 606.00 606.18 606.35

2.625 2.736 2.687 2.688 2.686 2.735 2.684 2.735 2.739 2.688 2.791 2.688

606.52 606.70 607.04 607.21 607.39 607.56 607.91 608.08 608.25 608.42 608.60 608.77

2.791 2.639 2.746 2.746 2.599 2.701 2.647 2.728 2.674 2.667 2.662 2.672

476.81 476.01 476.20 476.39 476.59 476.98 527.80 527.98 528.17

3.952 3.958 3.953 3.953 3.977 3.941 4.042 4.000 3.947

F ) 844.8 kg‚m-3 528.54 578.60 578.78 579.13 579.31 579.66 579.75 579.84 580.01

4.088 4.346 4.344 4.323 4.351 4.330 2.640 2.702 2.696

580.54 580.72 581.07 581.42 597.33 597.82 598.03 598.20

2.665 2.638 2.657 2.666 2.557 2.583 2.568 2.589

514.82 515.00 515.19 515.37 515.56 515.94 516.12

4.006 4.023 3.997 4.020 3.985 3.960 3.972

F ) 936.3 kg‚m-3 516.50 516.68 516.87 517.05 517.24 517.98 518.17

3.974 2.891 2.860 2.879 2.880 2.888 2.874

518.36 534.42 534.45 534.97 535.15 535.33

2.905 2.840 2.827 2.829 2.791 2.816

467.62 467.82 468.02 468.21 468.41 468.60 468.80

3.968 3.984 4.007 4.000 3.944 3.964 3.917

F ) 989.2 kg‚m-3 468.99 469.38 469.58 469.67 477.65 477.95 478.14

3.954 3.001 3.007 2.985 2.977 3.014 2.978

478.33 478.53 488.15 488.35 488.73 488.92

2.716 2.996 2.960 2.994 2.995 2.953

Journal of Chemical and Engineering Data, Vol. 45, No. 6, 2000 1137 Table 2. (continued) T

Cvx

K

kJ‚

kg-1‚K-1

T K

Cvx kJ‚

kg-1‚K-1

T

Cvx

K

kJ‚ kg-1‚K-1

10 mass % Na2SO4 F ) 774.2 kg‚m-3

a

383.06 383.28 383.50 383.71 383.93 384.15

3.768 3.796 3.823 3.821 3.743 3.746

F ) 1059.0 kg‚m-3 384.37 384.58 384.80 385.02 385.24 385.45

352.56 352.79 353.02 353.25 353.47 353.70

3.887 3.890 3.905 3.909 3.859 3.877

F ) 1072.5 kg‚m-3 353.93 354.16 354.39 354.85 355.08 355.30

3.716 3.528 3.476 3.395 3.367 3.363

385.67 385.89 385.27 385.48 385.70 385.92

3.380 3.372 3.366 3.362 3.379 3.371

3.867 3.885 3.594 3.568 3.550 3.539

355.54 356.22 356.45 356.67 357.13

3.554 3.527 3.536 3.572 3.517

Values of isochoric heat capacities obtained on cooling are indicated by a superscript C.

allowance for the propagation of uncertainty from temperature and heat measurement, as well as from not strictly isochoric conditions of the process. The uncertainty in Cvx measurements arises from two general types of uncertainties: measurement uncertainties and nonmeasurement uncertainties. Measurement uncertainties were associated with uncertainties that exist in the measured quantities (m, ∆Q, ∆T, and C0) contained in the working equation

Cv )

{

1 ∆Q - C0 m ∆T

}

(1)

where m is the mass of the sample in the calorimeter, ∆Q is the amount of heat released by the internal heater, C0 is the heat capacity of the empty calorimeter, and ∆T is the temperature change resulting from the addition of an amount of heat ∆Q. Nonmeasurement uncertainties were associated with deviations of actual experimental conditions from the mathematical model used to derive the equation for computing the heat capacity. The relative uncertainties in measured quantities are δ(∆Q) ) 0.08%, δ(∆T) ) (0.02 to 0.05) K depending on the magnitude of ∆T, δm ) 0.01%, and δ(C0) ) (0.5 to 1.5)% depending on the temperature range. The temperature was determined with an uncertainty not exceeding 10 mK. The major sources of nonmeasurement uncertainties are: (1) the nonisochoric behavior of the apparatus (deviations of the system from a constant volume) during heating, (2) the nonadiabatic conditions of the system, and (3) stray heat flows through the calorimeter not controlled by the semiconductor layer, for example, parasitic flows caused by spurious temperature differences. The correction related to the nonisochoric behavior during heating is about 0.5 to 1.0% of the total magnitude of the heat capacity. The possible supply or removal of heat through the layer of the thermoelement caused by the imperfect adiabatic behavior of the calorimetric system was estimated from the relation

∆T ∆Q ) λ Sτ d

the heat losses ∆Q for this time were 0.2 J or 0.02% of the total heat supplied to the system. The heat losses through the areas of the calorimeter that are not controlled by the thermoelement (the well for the internal heater or the resistance thermometer) do not exceed 4 × 10-4 J. The heat loss through the capillary used to fill the calorimeter with the sample is 0.003 J. Heat losses through the inlet and outlet wires of the internal heater were 0.066 J, and those through the wires of the temperature sensor were 0.0016 J. The heat flow through all uncontrolled areas was 0.27 J or 0.06% of the total amount of heat supplied to the system. On the basis of detailed analysis, all sources of uncertainties likely to affect the determination of Cv were 1 to 1.5% in the liquid phase, 2 to 3% in the vapor phase, and 4 to 5% near the critical point. The uncertainty of the phase transition temperature measurements is about 0.01 to 0.02 K. All original temperature data, as well as the experimental Cvx data themselves, have been corrected for conversion from IPTS-68 to ITS-90 temperature scales (Rusby9). At temperatures below 400 K the correction of Cvx is only 0.0008%, orders of magnitude below the experimental uncertainty. For temperatures approaching 670 K, the Cvx correction reached up to 0.027%, still well below the experimental uncertainty. Heat capacity data for aqueous sodium sulfate were obtained for three compositions, 1 mass %, 5 mass %, and 10 mass %, respectively, and along 19 isochores from 250 kg‚m-3 to 1073 kg‚m-3, in the temperature range from 350 K to 670 K. The data are listed in Table 2. The column heading lists the average density of the isochore, which are equal to the mass of solution divided by the volume of the calorimeter at ambient conditions. Most data were obtained in a heating ramping mode. Those obtained in a cooling ramping mode are marked with a superscript C in Table 2. The data for sodium carbonate, which will be referred to in Part 2 of this series, were published in Abdulagatov et al.1

(2)

where λ ≈ 2.09 W‚m-1‚K-1 is the thermal conductivity of the semiconductor layer (cuprous oxide), S is the surface area of the cuprous oxide layer, d is the thickness of the cuprous oxide layer, and ∆T ≈ 10-4 K is the temperature difference between inner and outer calorimetric vessels. The average time of one measurement was τ ) 300 s, and

Phase Transitions on Isochoric Heating Plots of some typical isochores are shown in Figure 1. It is clear that several effects are taking place when the sodium sulfate solution is heated isochorically. Two peaks or jumps are often found. The first peak or jump, at the lower temperature, is associated with the appearance of the solid phase. The second peak or jump accompanies the

1138

Journal of Chemical and Engineering Data, Vol. 45, No. 6, 2000 sented. The data extend over a sizable range in density and temperature around the critical point of water. The isochoric heat capacity as a function of temperature may show one or two jumps or spikes, which are indicative of the appearance or disappearance of solid or fluid phases, as explained by Valyashko et al.,2 Part 2 of this series. Literature Cited

Figure 1. (a and b) Typical Cvx behavior as a function of temperature along isochores for two choices of overall concentration and density.

disappearance of the vapor or liquid phase. The phase behavior will be fully explored and explained, and the phase boundaries delineated, in Valyashko et al.,2 Part 2 of this series. Conclusions A set of constant-volume, constant-overall-composition heat capacity data for aqueous Na2SO4 solutions is pre-

(1) Abdulagatov, I. M.; Dvoryanchikov, V. I.; Mursalov, B. A.; Kamalov, A. N. Heat capacity at constant volume of H2O + Na2CO3 solutions near the critical point of pure water. J. Solution Chem. 1999, 28, 871-889. (2) Valyashko, V. M.; Abdulagatov, I. M.; Levelt Sengers, J. M. H. Vapor-Liquid-Solid Phase Transitions in Aqueous Sodium Sulfate and Sodium Carbonate from Heat Capacity Measurements near the First Critical End Point. 2. Phase Boundaries. J. Chem. Eng. Data 2000, 45, 1139. (3) Armellini, F. J.; Tester, J. W. Precipitation of sodium chloride and sodium sulfate in water from sub- to supercritical conditions: 150 to 550 °C, 100 to 300 bar. J. Supercrit. Fluids 1994, 7, 147-158. (4) Hodes, M. S.; Smith, K. A.; Hurst, W. S.; Bowers, W. J., Jr.; Griffith, P.; Sako, K. Measurements and analysis of solubilities and deposition rates in near-supercritical, aqueous, sodium sulfate and potassium sulfate solutions. In preparation for J. Supercrit. Fluids. (5) Abdulagatov, I. M.; Dvoryanchikov, V. I.; Mursalov, B. A.; Kamalov, A. N. Measurements of the heat capacity at constant volume of H2O + Na2SO4 in near-critical and supercritical water. Fluid Phase Equilib. 1998, 150, 525-535. (6) Amirkhanov, Kh. I.; Stepanov, G. V.; Alibekov, B. G. Isochoric Heat Capacity of Water and Steam; Amerind Publ. Co.: New Delhi, 1974. (7) Abdulagatov, I. M.; Dvoryanchikov, V. I.; Kamalov, A. N. Heat capacity at constant volume of pure water in the temperature range 412-693 K at densities from 250 to 925 kg m-3. J. Chem. Eng. Data 1998, 43, 830-838. (8) Mursalov, B. A.; Abdulagatov, I. M.; Dvoryanchikov, V. I.; Kamalov, A. N.; Kiselev, S. B. Isochoric heat capacity of heavy water at subcritical and supercritical conditions. Int. J. Thermophys. 1999, 20, 1497-1528. (9) Rusby, R. L. The conversion of thermal reference values to the ITS-90. J. Chem. Thermodyn. 1991, 23, 1153-1161.

Acknowledgment I.M.A. acknowledges the hospitality of the Division of Physical and Chemical Properties at NIST and the advice and encouragement of Dr. J. Magee. Received for review April 27, 2000. Accepted August 22, 2000. The experimental work was supported by INTAS Grant No. INTAS-96-1989.

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