Chemical Engineering Science 55 (2000) 4993}5001

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1 Chemical Engineering Science 55 (2000) 4993}5001 A further study of solid}liquid equilibrium for the NaCl}NH O system Xiaoyan Ji, Xiaohua Lu*, Luzheng Zhang, Ningzhong Bao, Yanru Wang, Jun Shi, Benjamin C. -Y. Lu Department of Chemical Engineering, Nanjing University of Chemical Technology, Nanjing , People's Republic of China Department of Chemical Engineering, University of Ottawa, Ontario, Canada K1N 6N5 Received 11 October 1999; received in revised form 25 March 2000; accepted 31 March 2000 Abstract Solid}liquid equilibrium (SLE) values were experimentally determined for the NaCl}NH O system in the temperature range from to K, using the #ow-cloud-point method (Zhang et al., 1998, Journal of Chemical and Engineering Data, 43, 32}37). A judicially selected equilibrium constant of NH Cl, which is consistent with the available literature values, was used to determine a new Pitzer interaction parameter for pure NH Cl. This new parameter, together with the Pitzer mixing parameters determined from correlating the experimental values obtained in this work and some of the literature values, could be used to extend SLE for this system from to K, satisfying the process simulation requirement involved in the production of soda Elsevier Science Ltd. All rights reserved. Keywords: Phase equilibria; Solubility; Solutions; Modelling; Model parameters; Mixing 1. Introduction Many authors have investigated the solubility of NaCl and NH Cl in H O for decades. One of the main reasons for studying this system is that it is a subsystem in the manufacturing of soda. Solubility values are available in some compilations (Linke & Seidell, 1965; Silcock, 1979). However, in order to substantiate the database for establishing a correlation of the temperature e!ect on solubility, more experimental values are desirable. In this work, the SLE values for the NaCl}NH O system were determined by the recently developed #ow-cloud-point method (Zhang, Gui, Lu, Wang, Shi & Lu, 1998). Data correlation is essential in process simulation. In this work, the Pitzer equation was adopted for this purpose. New Pitzer interaction parameters of pure NH Cl were obtained by using a judicially selected equilibrium constant for NH Cl, and the Pitzer mixing parameters were correlated using the experimental data together with some of the literature values. The capability of the * Corresponding author. address: xhlu@dns.njuct.edu.cn (X. Lu). correlated parameters for representing data from to K is established. 2. Determination of SLE data Sodium chloride (Guaranteed grade, purity '99.8%, Beijing Chemical Plant, Beijing) was dried in a vacuum dryer until a constant mass was reached. Ammonium chloride (Guaranteed grade, purity '99.8%, YuLing Chemical Plant, Shanghai) was dried in a vacuum desiccator at 0.01 kpa and K for 4 h. The deionized water was prepared by re-distillation in the presence of KMnO and its electrical conductivity was found to be (1.210 Ω cm. In the #ow-cloud-point method (Zhang et al., 1998), the temperature increments were made progressively smaller as the number and size of the existing crystals decreased. A series of experimental data could be measured rapidly by this method. The standard deviations in the experimental results were found to be in the range of 0.006}0.022 mol kg. The SLE values for the system of NaCl}NH O were determined herewith by this method from to K /00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S ( 0 0 )

2 4994 X. Ji et al. / Chemical Engineering Science 55 (2000) 4993} Results and discussion The experimental solubilities obtained at nine temperatures are listed in Table 1, reported on the solvent-free basis. A comparison of the solubilities of NH Cl in the NaCl}NH O system reported in the literature (Silcock, 1979) at K with our experimental results determined at the same temperature is depicted in Fig. 1, indicating that the experimental results obtained by the #ow-cloud-point method are consistent with the literature values. In actual process simulation concerning the NaCl} NH O system, temperature is generally within K. Consequently, the temperature range of concern is from to K. Cisternas and Rudd (1993) indicated that multiple saturation points play a very important role in fractional crystallization from solution. It is essential that a model used for solubility calculations, can also represent multiple saturation point. The calculation method for solubility of salt has been described previously (Ji, Feng, Lu, Zhang, Wang & Shi, 1999). It is a generalized and rapid method for obtaining the compositions of coexisting phases at equilibrium. However, the value of equilibrium constants must be known in advance. In addition, a suitable thermodynamic model is required for calculating the activity coe$cients of the liquid components. Considering the thermodynamics of electrolyte solutions, several models have been proposed in the literature for predicting solubility data. The model previously proposed by Lu et al. (Lu & Maurer, 1993; Lu, Zhang, Wang & Shi, 1996a,b) could predict the solubility for ternary systems, hence, it was "rst tested. In the prediction, the values of equilibrium constant K of NaCl and of NH Cl were taken from the literature (Lu et al., 1996a). A comparison of the predicted solubilities at the multiple saturation points at four temperatures with those available in the literature (Linke & Seidell, 1965) is presented in Table 2 (Case 1). Although the predicted values are in good agreement with the literature values at and K, the deviations increase as temperature increases. On the other hand, the predicted binary results are reasonable (Lu et al., 1996a). Because adjustable parameters are not available in the model, there is no way to improve the prediction for the ternary system. For this reason, there is a need to choose another model for representing the solubilities in this ternary system. Pitzer equation has been used to calculate solubility in numerous cases (Pabalan & Pitzer, 1991). Although its capability of prediction is poorer than that of the Lu and Maurer model, the calculated results could be more accurate if the parameters were correlated within the calculation range (Lu et al., 1996a). Consequently, the Pitzer equation was chosen in this work. Table 1 Experimental solubilities (mol kg) in the NaCl}NH O system K K K NH Cl NaCl NH Cl NaCl NH Cl NaCl K K K K K K Calculation of equilibrium constant K There are two possible reactions in the NaCl} NH O system, NaCl"Na#Cl (1) NH Cl"NH #Cl (2) and their equilibrium constants are designated as K for NaCl and K for NH Cl. The equilibrium constants should be known before any solubility calculations. It is known that changes in K values increase very rapidly with a small change in the chemical potentials of the equilibrium species, which should be veri"ed beforehand. Johnson, Oelkers and Helgeson (1992) have compiled and veri"ed, for the species of Na, Cl and NaCl, and NH, the standard-state chemical potentials, enthalpies of formation, and entropies at K, together with the temperature functions of their heat capacities. These

3 X. Ji et al. / Chemical Engineering Science 55 (2000) 4993} Fig. 1. Solubilities in the ternary NaCl}NH O system at K. Solid curve, calculated by the Pitzer equation (1991); experimental data:, Silcock (1979); #, This work. values are listed in Table 3 and were adopted in this work for the evaluation of K. The remaining consideration concerns K. Generally, there are three methods for obtaining equilibrium constants. In Method 1, they are calculated from the solubility of a single electrolyte in pure water, using an adequate model for describing the activity coe$cients (Lu et al., 1996a). In Method 2, they are calculated from the chemical potentials of the equilibrium species (Pabalan & Pitzer, 1991). In Method 3, they are calculated from the experimental data and the activity coe$cients of the components of the liquid (Staveley & Davies, 1995). The accuracy of the model used in Method 1 for describing the activity coe$cients a!ects the K values directly. In Method 2, the accuracy of K values is independent of the solubility data as well as the model used to describe the activity coe$cients, but the error in K increases rather rapidly with the error in the chemical potentials of the equilibrium species (Rafal, Berthold, Scrivner & Girse, 1994). In Method 3, accurate experimental data are required. Regardless of the method used, the calculated results should be consistent with each other if they are to be acceptable. Because it is usually di$cult to obtain adequate experimental activity coe$cients at various temperatures, Method 2 is generally "rst chosen to calculate the equilibrium constants. For the NaCl}NH O system, K has been reported by Lu et al. (1996a), which was calculated by Method 1 and listed in Table 4. Therefore, its accuracy would be a!ected by the accuracy of the activity coe$cients calculated by the model of Lu et al. (Lu & Maurer, 1993; Lu et al., 1996b). If the model parameters could not represent the activity coe$cients with su$cient accuracy up to K, the values of K calculated by Method 1 would deviate from the real value. In order to avoid this possibility, the value of K was recalculated by Method 2, which is independent of the thermodynamic model. Thermodynamic data for NH Cl have been reported by Barin and Knacke (1973). If these values were accurate, the value of K calculated by Method 2 at K should be close to the value obtained by Method 3. Although di!erent values of K at K, obtained by Method 3, have been reported in the literature (Harmer & Wu, 1972; Christov, Petrenko, Balarev & Valyashko, 1994; Staveley & Davies, 1995), the di!erences are small, implying that the calculated values by Method 3 are accurate. The values of K obtained from Methods 2 and Table 2 Comparison of multiple saturation point concentrations (Linke & Seidell, 1965) with those obtained from di!erent models at four temperatures K K K K NH Cl NaCl NH Cl NaCl NH Cl NaCl NH Cl NaCl Lit. data m Case 1 m RD 2.79% 4.87% 12.26% 21.76% Case 2 m RD 6.74% Case 3 m RD 0.51% 1.71% 2.01% 4.66% RD"0.5 m!m # m m!m m.

4 4996 X. Ji et al. / Chemical Engineering Science 55 (2000) 4993}5001 Table 3 Standard-state chemical potentials, enthalpies of formation, and entropies of species at K, and coe$cients of temperature functions for heat capacities Species!μ (J mol)! H (J mol) S (J mol K) C "a #a ¹#a /¹ (J mol K) Ref. a 10 a 10 a T (K) range Cl H N NH 79, , ! Na 261, , ! Cl 131, , ! ! NaCl 184, , NH Cl ! } , ,139 Moore (1976). Johnson et al. (1992). Callanan et al. (1980). Staveley and Davies (1995). This work. 3 are also listed in Table 4 for comparison. It is obvious that there is a signi"cant di!erence between the values obtained by these two methods. It appears that there is a need to reestablish the thermodynamic data for NH Cl. The heat capacities of NH Cl were reported by Callanan et al. (1980), and the entropy at K, by Staveley and Davies (1995). If the standard-state chemical potential of NH Cl at K is known, K could be calculated at various temperatures. The standard-state chemical potential of NH Cl at K reported by Moore (1976) has a value of! kj mol, corresponding to a ln K value of It varies signi"cantly from the values obtained by Method 3 as shown in Table 4, indicating the need for a new standard-state chemical potential of NH Cl at K. It was calculated in this work by means of μ "μ #μ #R¹ ln K (3) using the values of K at K obtained from Method 3. The values of the chemical potential thus obtained are close to each other. Hence, the value of ln K " reported by Staveley and Davies (1995) was chosen, because the thermodynamic properties of S and C adopted in this work were also reported by their group (Callanan et al., 1980; Staveley & Davies, 1995). The values of S and C are also listed in Table 3. The values of H reported in the table were obtained by H "μ #¹ (S!0.5S!2S!0.5S ). (4) Table 4 Equilibrium constant of NH Cl (Eq. (2)) at K Method ln K Ref. Lu et al. (1996a). Barin and Knacke (1973). Staveley and Davies (1995). Christov et al. (1994). Harmer and Wu (1972). In the calculation, the entropies of N,H were taken from Johnson et al. (1992) and that of Cl, from Moore (1976). All these values and the calculated results of μ and H of NH Cl are also listed in Table 3. It should be mentioned that the calculated μ value for NH Cl is close to the value of kj mol, reported by Moore (1976). The relative deviation is only 0.33%. This is another indication that a small di!erence in the chemical potential values causes a large deviation in the equilibrium constant. The calculated value of H is also close to the value of kj mol, reported by Barin and Knacke (1973), indicating that the calculation is reasonable. Using the thermodynamic data listed in Table 3, the equilibrium constants of NaCl and NH Cl were calculated at various temperatures, and correlated by ln K"; #; 1 ¹! #; ln ¹ #; (¹!298.15). (5)

5 X. Ji et al. / Chemical Engineering Science 55 (2000) 4993} Table 5 Temperature coe$cients of equilibrium constants of NaCl (K ) and NH Cl (K ) U U U U T (K) range 10 SD ln K ! ! } ln K ! ! ! } SD" 1 N!1 (ln K!ln K ), where N the number of temperature points. The values of the coe$cients and the correlated results are listed in Table Pitzer equation Lima and Pitzer (1983) described the Pitzer equation for activity coe$cient of a 1}1 electrolyte MX in a common-ion mixture with NX by ln γ "!A ( 1#bI # 2 b ln(1#bi) #I[B #y(b(!b( #θ )] #I 3 2 C( #y C(!C( #1 2 ψ # 1 2 y(1!y)ψ, (6) where B"2β#2β αi 2 [1!(1#αI) exp(!αi)], (7) B("β#β exp(!αi). (8) For the system considered in the work, the values of the empirical parameters b and α were taken to be 1.2 and 2.0 kg mol, respectively. A is the Debye}HuK ckel ( parameter for the osmotic coe$cient, whose value was obtained from the work of Pitzer (1991). θ and ψ are the mixing parameters. θ represents the di!erence in the interaction of unlike ions with charges of the same sign from an appropriate average for like ions. The ψ is similarly de"ned but for three ions with charges not all of the same sign. An analogous equation can be obtained for γ by transposing subscripts and replacing y with (1!y) Ionic interaction parameters of pure species Pitzer, Peiper and Bussey (1984) reported extensive thermodynamic data for NaCl, leading to a complete set of parameters valid in the temperature range from to K and with saturation pressure up to 100 MPa. The calculated solubilities of NaCl, using these parameters (Pitzer et al., 1984) and the equilibrium constant of this work listed in Table 5, are in excellent agreement with the data compiled by Linke and Seidell (1965). The maximum deviation of 0.6% was observed at K. Thiessen and Simonson (1990) have reported extensive thermodynamic data for NH Cl. Using their parameter values and the equilibrium constant selected in this work, the calculated solubilities of NH Cl in H O are much higher than the experimental values at higher temperatures (¹* K). This is because the existing ionic interaction parameters are only suitable up to mol kg. However, in the binary system, the solubility of NH Cl is much higher than this value at higher temperature. Therefore, it is necessary to obtain a new set of ionic interaction parameters of pure NH Cl, in order to calculate the ionic activity coe$cients up to saturation from to K. To our knowledge, the experimental ionic activity coe$cients at 0.1 MPa are available only at K for this system. In this work, the activity coe$cients calculated by the existing ionic interaction parameters of Thiessen and Simonson (1990) from to K were treated as the experimental values up to 6 mol kg. The new ionic interaction parameters of β, β and C were correlated based on the values of activity coe$cients up to saturation. The activity coe$cients of saturated solutions can be calculated using binary solubility data. The activity coe$cients up to 6 mol kg can be calculated by using their ionic interaction parameters. It should be mentioned that our experimental results compared satisfactorily with the literature values as depicted in Fig. 2. The mean value of the solubility (m) at each temperature was used to calculate the mean activity coe$cients at saturation by means of the equation γ " K (9) m in which the value of K is equal to K in this part of the consideration. The mean solubility data in the binary NH Cl}H O system and the corresponding activity coe$cients are listed in Table 6. The correlated values of β, β and C( at each temperature were "tted by the following equation: M(¹)"b #b ¹# b ¹ #b ln (¹) (10)

6 4998 X. Ji et al. / Chemical Engineering Science 55 (2000) 4993}5001 Table 6 Mean solubilities and mean activity coe$cients in the binary NH Cl}H O system, and standard deviations at 14 temperatures T (K) m (mol kg) γ SD SD" 1 N!1 (ln γ!ln γ ), where N, is the number of experimental data points. Fig. 2. Solubility of NH Cl in the binary NH O system. Solid curve, calculated by the Pitzer equation (1991); experimental data:,, Linke and Seidell (1965);, Scholder and Hendrich (1939);, Mohr (1898);, Restiano (1938); *, Labash and Lusby (1955);,Ye (1990); # This work. where M denotes β, β or C(, and the coe$cient values obtained are listed in Table 7. The ionic activity coe$cients obtained from using these correlations are compared favorably with the experimental values. The standard deviations obtained at 14 temperatures are included in Table The Pitzer mixing parameters The Pitzer mixing parameters have been determined for the NaCl}NH O system (Pitzer, 1991). However, the applicability of these parameters to saturated solutions is still unknown. When the solubilities in the ternary system at K were calculated using the existing Pitzer mixing parameter values and compared with the experimental data reported by Linke and Seidell (1965), the deviation at the multiple saturation point is large as shown in Table 2 (Case 2). Hence, there is a need to further correlate the Pitzer mixing parameters for calculating solubilities in the NaCl}NH O system. The mean ionic activity coe$cients, γ, were calculated from the SLE data available in the literature (Linke and Seidell (1965), values compiled by Silcock (1979)), together with those obtained in this work by Eq. (9). When the solid phase is NaCl, K is equal to K and m is the ionic mean molality of NaCl, otherwise K is equal to K and m is the ionic mean molality of NH Cl. Using these calculated values, a new set of Pitzer mixing-parameter values was regressed at K with θ "! and ψ "! by the least-squares method. The SLE values of the ternary system at other temperatures were predicted using the new set of parameter values. The agreement with the experimental values was good up to K. When the equilibrium temperature is higher than K, the deviations are more pronounced. The SLE could not even be predicted at K. Therefore, the values of θ and ψ should be further evaluated. In order to do so, the mean ionic activity coe$cients γ were calculated from the available experimental SLE values at all temperatures by Eq. (9), with θ taken to be a constant having the value at K. Then, ψ was regressed by the least-squares method, and correlated in terms of temperature by means of Eq. (10). The coe$cient values thus obtained are reported in Table 7. Then, the solubilities of the NH Cl}NaCl}H O system were calculated from to K with the newly established and correlated mixing parameters. The calculation results indicate good agreement with experimental values from to K. At K the deviations are slightly higher. A comparison of the calculated solubilities and the literature values, reported by Linke and Seidell (1965) and Restiano (1938), at three temperatures is depicted in Fig. 3, in which the maximum deviation (about 10%) occurred at K in the (NaCl) concentration. This is probably caused by the high ionic strength. A comparison of the calculated and the literature values (Linke & Seidell, 1965) at the

7 X. Ji et al. / Chemical Engineering Science 55 (2000) 4993} Table 7 Temperature coe$cients of β, β and C( of pure NH Cl, and Pitzer mixing parameters θ and ψ for the NH Cl}Na O system b 10b b b 10SD β ! ! β ! ! C(! ! θ! * * * * ψ! ! SD" 1 N!1 (M!M ) (M"β, β, C or ψ ), where N, the number of temperature points. Fig. 3. Solubilities in the ternary NaCl}NH O system at , and K. Solid curves: calculated by the Pitzer equation (1991), using correlated mixing parameters. Experimental data: K, Linke and Seidell (1965); and K, Restiano (1938). Fig. 4. Solubilities in the ternary NaCl}NH O system at and K. Solid curves: calculated by the Pitzer equation (1991), using correlated mixing parameters. Experimental data: This work. multiple saturation point is presented in Table 2 (Case 3). All the deviations at the point of multiple saturation are (5% for the four temperatures tested, and are much smaller than the other two cases included in the table. A comparison of the calculated solubilities with the experimental data determined in this work at and K is shown in Fig. 4, while the comparison made for data at K is included in Fig. 1. The good agreement obtained is an indication that the new set of Pitzer mixing-parameter values can represent the data, and the experimental values are consistent with the literature values. 4. Conclusions The SLE values for the system of NaCl}NH O at } K were determined using the method of #ow-cloud-point. The experimental results are consistent with the values available in the literature. In the application of the Pitzer equation for calculating solubilities to meet the need of process simulation, a new standard-state chemical potential of NH Cl at K was judicially obtained, and the resulting equilibrium constant of NH Cl at this temperature was found to be consistent with the literature values. A new set of Pitzer mixing-parameter values was correlated, making it

8 5000 X. Ji et al. / Chemical Engineering Science 55 (2000) 4993}5001 feasible to calculate the activity coe$cients for the NaCl} NH O system from } K up to saturation. Notation a }a Coe$cients of C A Debye}HuK ckel parameter for osmotic coe$cient ( b Empirical parameter of the Pitzer equation b }b Constant in Eq. (10) B, B( Parameters of the Pitzer equation C Standard-state heat capacity at constant pressure, J mol K C ~ Pitzer mixing parameter H Standard enthalpy of formation, J mol I Ionic strength on molality scale K Equilibrium constant K Equilibrium constant, Eq. (1) K Equilibrium constant, Eq. (2) m Molality of species, mol kg MX 1}1 electrolyte, the cation is M and the anion is X NX 1}1 electrolyte, the cation is N and the anion is X R Universal gas constant RD Relative deviation, Table 2. S Entropy at the standard state, J mol K SD Standard deviation ¹ Temperature, K ¹ Temperature at reference state ; }; Coe$cients, Eq. (5) y The ionic strength fraction of NX Greek letters α Empirical parameter of Pitzer equation β,β Pitzer interaction parameters of pure species γ Mean ionic activity coe$cient on molality scale θ,ψ Pitzer mixing parameters μ Standard-state chemical potentials Acknowledgements The authors thank the National Natural Science Foundation of People's Republic of China (No ), the National Natural Science Foundation of Jiangsu Province of People's Republic of China (BK 97124), the Outstanding Young Teacher Education Foundation of People's Republic of China, the Outstanding Youth of National Natural Science Foundation of People's Republic of China ( ) and the Alexander-von-Humboldt Foundation of Germany for "nancial support. References Barin, I., & Knacke, O. (1973). Thermochemical properties of inorganic substances. Spring: Berlin. Callanan, J. E., Weir, R. D., & Staveley, L. A. K. (1980). The thermodynamics of mixed crystals of ammonium chloride and ammonium bromide. II. An analysis of the heat capacity of ammonium chloride, ammonium bromide, and an approximately equimolar solid solution of these salts. Proceedings of the Royal Society of London A, 372, 497}516. Christov, Chr., Petrenko, S., Balarew, Chr., & Valyashko VI (1994). Calculation of the Gibbs energy of mixing in crystals using Pitzer's model. Journal of Solution Chemistry, 23, 795}812. Cisternas, L. A., & Rudd, D. F. (1993). Process design for fractional crystallization from solution. Industrial and Engineering Chemistry Research, 32, 1993}2005. Harmer, W. J., & Wu, Y. C. (1972). Osmotic coe$cients and mean activity coe$cients of uni-univalent electrolytes in water at 253C. Journal of Physical and Chemical Reference Data, 1, 1047}1100. Ji, X., Feng, X., Lu, X., Zhang, L., Wang, Y., & Shi, J. (1999). A generalized algorithm for solid}liquid equilibrium stage. Journal of Chemical and Industrial Engineering, 50, 743}750 (Chinese). Johnson, J. W., Oelkers, R. H., & Helgeson, H. C. (1992). Supcrt92: A software package for calculating the standard molal thermodynamic properties of minerals, gases, aqueous, and reactions from 1 to 5000 bar and 0 to 10003C. Computers and Geosciences, 18, 899}947. Labash, J. A., & Lusby, G. R. (1955). Cited in Silcock (1979), p. 364 (No. 2472). Lima, M. C. P., & Pitzer, K. S. (1983). Thermodynamics of saturated aqueous solutions including mixtures of NaCl, KCl and CsCl. Journal of Solution Chemistry, 12, 171}185. Linke, W. F., & Seidell, A. (1965). Solubilities of inorganic and metalorganic compounds (pp. 654}655, 666}667, 958}959). American Chemical Society: Washington, DC. Lu, X., & Maurer, G. (1993). Model for describing activity coe$cients in mixed electrolyte aqueous solutions. A.I.Ch.E. Journal, 39, 1527}1538. Lu, X., Zhang, L., Wang, Y., & Shi, J. (1996a). Prediction of activity coe$cients of electrolytes in aqueous solutions at high temperatures. Industrial and Engineering Chemistry Research, 35, 1777}1784. Lu, X., Zhang, L., Wang, Y., & Shi, J. (1996b). Simultaneous prediction of activity coe$cients and enthalpy for aqueous electrolyte solutions at high temperatures. Fluid Phase Equilibria, 116, 201}208. Mohr, Z., (1898), cited in Silcock (1979), p. 360 (No. 2462). Moore, W. J. (1976). Physical chemistry (p.111). Longman: London. Pabalan, R. T., & Pitzer, K. S. (1991). Activity coezcients in electrolyte solution (2nd ed.) (pp. 435}490). CRC Press: Boston. Pitzer K S., (1991). Activity coezcients in electrolyte solution (2nd ed.) (pp. 75}153). CRC Press: Boston. Pitzer, K. S., Peiper, J. C., & Busey, R. H. (1984). Thermodynamic properties of aqueous sodium chloride solutions. Journal of Physical and Chemical Reference Data, 13, 1}102. Rafal, M., Berthold, J. W., Scrivner, N. C., & Girse, S. T. (1994). Models for electrolyte solutions, (pp. 601}671). Marcel Dekker: New York. Restiano, S. (1938). Cited in Silcock (1979), p. 363 (No. 2470). Scholder, R., & Hendrich, G. (1939). Cited in Silcock (1979), p. 363 (No. 2469). Silcock, H. L. (1979). Solubilities of inorganic and organic compound (pp. 358}364). Pergamon Press: Oxford. Staveley, L. A. K., & Davies, N. J. (1995). The thermodynamics of mixed crystals of (ammonium chloride#ammonium bromide) IV. The excess Gibbs free energy, excess enthalpy, and excess entropy at the

9 X. Ji et al. / Chemical Engineering Science 55 (2000) 4993} temperature T" K and at T"0. Journal of Chemical Thermodynamics, 27, 787}799. Thiessen, W. E., & Simonson, J. M. (1990). Enthalpy of dilution and the thermodynamics of NH Cl (aq) to 523 K and 35 MPa. Journal of Physical Chemistry, 94, 7794}7800. Ye, T. (1990). Industry of soda (p. 527). Chemical Industry Press: Beijing. Zhang, L., Gui, Q., Lu, X., Wang, Y., Shi, J., & Lu, B. C. -Y. (1998). Measurement of solid}liquid equilibria by a #ow-cloud-point method. Journal of Chemical Engineering Data, 43, 32}37.