Osmotic and activity coefficients of sodium sulphate in water from 150 to 250 C

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1 Osmotic and activity coefficients of sodium sulphate in water from 150 to 250 C OM N. BHATNAGAR AND A. N. CAMPBELL Deprrrrinet~t of Chetnistry, Utziversity of Mnnitoba, Witztiipeg, Mntz., Catlndn R3T 2N2 Received October 22, 1981 OM N. BHATNAGAR and A. N. CAMPBELL. Can. J. Chem. 60, 1754 (1982). Osmotic and activity coefficients of sodium sulphate in aqueous solution have been determined at temperatures up to 250 C, at solute concentration from 0.3 In to saturation, by measurements of vapour pressure using a newly designed high pressure cell. A precision pressure transducer is used in this cell for pressure measurement. Certain thermodynamic quantities have been calculated from the activity coefficients. OM N. BHATNAGAR et A. N. CAMPBELL. Can. J. Chem. 60, 1754 (1982). Operant a des temperatures allant jusqu'i 250 C et des concentrations allant de 0,3 tn a la saturation, on a determine les coefficients depression osmttique et d'activite du sulfate de sodium en solution aqueuse, en mesurant la pression de vapeur a I'aide d'une nouvelle cellule a haute pression de conception rtcente. On a utilise un transducteur de pression de precision dans cette cellule pour mesurer la pression. On a calculc certaines quantitks thermodynamiques partir des coefficients d'activite. [Traduit par le journal] Introduction The problems of corrosion and scale formation in steam generators are widespread and are of great concern to industry (1, 2). Knowledge and understanding of thermodynamic properties of aqueous electrolyte solutions at elevated temperatures are helpful in attempts to solve these problems. Moreover, the thermodynamic data are of interest to the oil industry for understanding the problem of secondary recovery in oil wells. Some work on the thermodynamic properties of electrolyte solutions at elevated temperatures has been reported in the last few years (3-13,22). In a previous paper (4) we reported the osmotic and activity coefficients of sodium sulphate from 50 to 150 C. Recently, Ragers and Pitzer (23) have reported heat capacities of aqueous sodium sulphate solutions from 30 to 200 C. They have used their data to calculate a number of thermodynamic properties, such as osmotic and activity coefficients. In this paper, we report the osmotic and activity coefficients of sodium sulphate in water from 150 to 250 C, and at concentrations from 0.3 tn to saturation using a newly designed vapour pressure cell. Experimental VAPOUR PRESSURE CELL Electrical cable Copper Metallic Seal h Pressure Temperature FIG. 1. High temperature vapour pressure cell. Our method consists in the determination of vapour pressure. The pressure transducer is mounted on the Cap (B) as shown In order to extend our work beyond 150 C it was necessary to in Fig. 1. A pressure-tight seal is made by using a silver metallic design a vapour pressure cell that could withstand high pressure seal between transducer and the cap. The cap is screwed on to and in which the pressure could be measured without visual the lower part of the cell (A). The sealing edge inside the cap observation. presses on to the copper metallic seal, providing a pressure-tight The design of the cell is shown in Fig. 1. The cell is made from seal. The Swagelok connections and high-temperature high- 316 stainless steel, machined from a solid 9cm diameter rod. pressure valve serve to introduce and degas the solutions. The inside of the cell, which is a cavity of 2.5cm diameter and Before performing an experiment, the cell is assembled as locm deep, was plated with gold to protect it from corrosion. shown in Fig. 1. It is attached to a helium leak detector through The pressure is measured using a pressure transducer, specially the high-pressure high-temperature valve, and the system is made for high temperature work by Kaman Science Corporation checked for any leaks. A sample of liquid is then introduced into (P.O. Box 7463, Colorado Springs, CO 80933, U.S.A.). the cell through the opening "C", and the end is sealed with a /82/ $01.OO/O National Research Council of Canada/Conseil national de recherches du Canada

2 BHATNAGAR AND CAMPBELL 1755 Swagelok plug. The sample is degassed several times after freezing in an acetone and solid C02 mixture, through the high-temperature high-pressure valve. After degassing, the cell is placed in the constant temperature oil bath. The pressure readings are measured as millivolt output from the transducer. By using a calibration curve provided by the manufacturer, the pressure at each temperature can be obtained readily. The system was tested using triply distilled water and 1 tn NaCl solution; our values of osmotic coefficients of NaCl were within 1% of the literature values (8). By knowing the vapour pressures of water and those of the solutions, the values of AP, the vapour pressure lowerings, were evaluated for each concentration, in the temperature range of 150 to 250"C. Analytical grade sodium sulphate was used to make the solutions. The concentrations of solutions were determined after each experiment by gravimetric analysis of the sample as barium sulphate (14). The temperature of the bath was measured by a platinum resistance thermometer. The saturation concentration values were taken from the literature (20). Results and discussion The osmotic coefficients were calculated using the following equation (8): ['I loo '=vmm1rt [RT In (PolP) M ~ vmvx [ = - IZ~ZxIA4 +- [PMx'O' + PMx"' exp (-ct11'2)] bi1i2 v where ZM and Zx are the positive and negative ionic charges in electronic units. I is the ionic strength, A4 is the Debye-Hiickel coefficient for osmotic functions, VM and vx are the numbers of ions of each type in the formulae, and v = vm + vx. PMX'O' and PMx"' account for various short range interactions between M and X and for cosphere overlap effect, CMx$ accounts for triple ion interaction and is of importance at high concentration. The parameters ct and b are given values of 2 and 1.2 respectively for the present calculations and are treated as temperature independent (17). The Debye-Hiickel coefficient A+ is given by where 4 is the osmotic coefficient, R the gas constant, T the absolute temperature, v the number of ions resulting from the ionization of one molecule, m the molality, M, the molecular weight of water, and Po and P the vapour pressures of pure water and solution respectively. The first term in the brackets gives the osmotic coefficient at low pressures, the second term gives the correction for deviations of the vapour from the perfect gas law, while the third term is a reasonable approximation for the isothermal compression of the solution from its own vapour pressure to that of liquid water. The term 5 was calculated from the equations of Smith, Keyes and Gerry (15). The molar volume of pure water, VIO(l) and Po were calculated using the equations in ref. 15. In our calc~lations~~~(1) is used instead ofll(l) for the partial mold volume of water because under these conditions the difference is negligible. The osmotic coefficients calculated from eq. [I] were fitted to the recently developed equations of Pitzer (16). These equations are semiempirical but they are quite successful in predicting the thermodynamic properties of electrolyte solutions up to 6 M (17-19) and can be applied to any valence type compounds. Pitzer's equations for osmotic and activity coefficients are given below: tn 22(~M~X)312 v where No is the Avogadro number, p, is the density of water at temperature T, D is the static dielectric constant of water, k is the Boltzmann's constant, and e is the electronic charge. The experimental values of 4 and m were used to evaluate PMX'O), PMX'I), and CMx$ which, in turn, were used to calculate mean ionic activity coefficients, y,t, using eq. [3]. As reported earlier (4) the possibility of HSO,- ion formation was considered but it was

3 1756 CAN. J. CHEM. VOL. 60, 1982 TABLE 1. Osmotic and activity coefficients of sodium sulphate in water Temp. ("C) 117 (mollkg) AP (Torr) + Y TABLE 2. Parameters for eqs. [2] and [3] Temp. ("C) P,x'O' PMX"' CMXQ f found to be insufficient to cause any change in the final results. The values of m, AP, 4, and y+ are given in Table 1. The values of PMX(0), PMX('), and C,,@ for various temperatures are given in Table 2. The smoothed values of m, 4, and y+ are given in Table 3. The values of osmotic coefficients, determined from present and previous work (4), at 150 C, are compared in Fig. 2. The activity coefficients at 150 C obtained from this work are compared with our previous results (4) and with those reported by Rogers and Pitzer (23). In general the agreement is good. Since the activity coefficients have been calculated up to saturation concentrations at each temperature the standard TABLE 3. Smoothed values of osmotic and activity coefficients Temp. ("C) Molality + Y f OOO OOO free energy change, AGO, can be calculated from the following equations: [5] AGO= -RTlnK for Na2S04 [6] AGO = -RT In Ksp = -RT In [2m+ y+12[m-y+] where K,, is the solubility product constant and /n+ and ~n- refer to analytical molalities of Na+ and SO4'- respectively. The values of log Ksp calculated from eq. [6] were fitted to a polynomial equation of the following form 2 [7] logksp=a +A, (f) +A, (f) Using a least-squares programme for polynomial

4 BHATNAGAR AND CAMPBELL MOLALITY (rn) MOLALITY (rn) FIG. 2. Osmotic and activity coefficients of sodium sulphate in water at 150 C. 0 data from ref. 4; from present work. TABLE 4. Parameters for eq. [7] Parameter Value curve fitting, values of A, A,, and A, were evaluated and these are given in Table 4. The Van't Hoff equation can be written as Differentiations of eq. [7] with respect to 1/T and subsequent substitution in eq. [8] give the values of AH0, the standard change in enthalpy at a given temperature. From the values of AGO and AH0 the values of AS0 were evaluated. The values of K,,, AGO, AH0, and AS0 are given in Table 5. The values of yk can also be used to calculate relative partial mold heat capacity,t,. The osmotic and activity coefficients decrease data from ref. 23; e data with increasing temperature and reach a minimum at approximately 225 C; beyond this temperature they increase again. For each temperature, the osmotic coefficients decrease with increasing concentration and pass through a minimum at about 1 mold. Marshall (21) has reported the thermodynamic data on the Na,SO,-H,O system from 300 to 350 C, but our results cannot be compared with those of Marshall because anhydrous sodium sulphate undergoes an allotropic change, from rhombic to monoclinic, at 241 C. Marshall's work throughout is in a temperature range where sodium sulphate is in the monoclinic form. Our P,,(O) values are in good agreement with those reported by Rogers and Pitzer (23), considering that their values refer to a different concentration range from ours. Our CMx+ values show a similar trend, with respect to change in temperature, to those of Rogers and Pitzer (23) but the numerical values are different. The variation with temperature of the P,,(') values reported by us show a minimum at 200 C, but Rogers and Pitzer (23) report no such minimum and we find this quite puzzling. Recently, Homes and Mesmer (24) have reported PMX(O), PMx"', and CMX+, for SrCl, and TABLE 5. The values of Ks, and other thermodynamic functions of Na,SO, in water AGO AH0 AS0 Temp. ("C) KSD kcal mol- ' kcal mol-i cal mol-i deg x 10-I 1 SO x lo-' x lo-' x~o-' x lo-'

5 1758 CAN. J. CHEM. VOL. 60, 1982 BaCl,, from isopiestic measurements. They have found a minimum in P,,' values of SrC1, and BaC1, below 100 C. Acknowledgements We want to thank Atomic Energy of Canada Ltd., Chalk River, Ontario, for the financial support of this project. 1. P. V. BALAKRISHNAN. 41st International Water Conference. Pittsburgh, PA. October 20-22, R. C. MURRAY and J. W. COBBLE. 41st International Water Conference. Pittsburgh, PA. October 20-22, H. F. HOLMES and R. E. MESMER. J. Chem. Thermodyn. 13, 131 (1981) N. BHATNAGAR and A. N. CAMPBELL. Can. J. Chem. 59, 123 (1981). 5. A. N. CAMPBELL and 0. N. BHATNAGAR. Can. J. Chern. 57, 2542 (1979). 6. H. F. HOLMES, C. F. BAES, and R. E. MESMER. J. Chem. Therrnodyn. 10, 983 (1978). 7. C. LIU and W. T. LINDSAY, JR. J. Solution Chem. 1, 45 (1972). 8. C. LIU and W. T. LINDSAY, JR. J. Phys. Chem. 74, 341 (1970). 9. E. R. GARDNER. Trans. Faraday Soc. 65,91 (1969). 10. E. R. GARDNER, P. J. JONES, and H. J. DENORDWALL. Trans. Faraday Soc. 59, 1994 (1963). 11. H. F. HOLMES, C. F. BAES, and R. E. MESMER. J. Chem. Thermodyn. 11, 1035 (1979). 12. B. A. SOLDANO and P. B. BIEN. J. Chem. Soc. A, 1825 (1966). 13. C. M. C~lssand J. W. COBBLE. J. Am. Chem. Soc. 86,5385 (1964). 14. J. M. KOLTHOFF, E. B. SANDELL, E. J. MECHAN, and S. BRUCKENSTEIN. Qualitative chemical analysis. 4th ed. The MacMillan Company, New York, NY L. B. SMITH, F. G. KEYES, and H. T. GERRY. Proc. Am. Acad. Arts Sci. 69, 137 (1934). 16. K. S. PITZER. J. :Phys. Chem. 77, 268(1973). 17. K. S. PITZER and G. MAYORGA. J. Phys. Chern. 77, 2309 (1973). 18. K. S. PITZER and G. MAYORGA. J. Solution Chem. 3, 539 (1974). 19. L. F. SILVESTER~~~ K. S. PITZER. J. Phys. Chem. 81,1822 (1977). 20. W. C. SCHROEDER, A. GABRIEL, and E. P. PARTRIDGE. J. Am. Chern. Soc. 57, 1539 (1935). 21. W. L. MARSHALL. J. Inorg. Nucl. Chern. 37, 2155 (1975). 22. S. LIKKE and L. A. BROMLEY. J. Chern. Eng. Data, 18, 189 (1973). 23. P. S. G. ROGERS and K. S. PITZER. J. Phys. Chem. 85, 2886 (1981). 24. H. F. HOLMES and R. E. MESMER. J. Chern. Thermodyn. 13, 1025 (1981).

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