An experimental investigation on the influence of NaCl on the solubility of CO2 in (water + phenol)

An experimental investigation on the influence of NaCl on the solubility of CO2 in (water + phenol)

Fluid Phase Equilibria 385 (2015) 248–257 Contents lists available at ScienceDirect Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e...

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Fluid Phase Equilibria 385 (2015) 248–257

Contents lists available at ScienceDirect

Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d

An experimental investigation on the influence of NaCl on the solubility of CO2 in (water + phenol) Jianzhong Xia 1, Michael Jödecke 2 , Álvaro Pérez-Salado Kamps, Gerd Maurer * Department of Mechanical and Process Engineering, University of Kaiserslautern, P.O. Box 30 49, Kaiserslautern D-67653, Germany

A R T I C L E I N F O

A B S T R A C T

Article history: Received 21 August 2014 Received in revised form 29 October 2014 Accepted 3 November 2014 Available online 6 November 2014

New experimental results are presented for the solubility and the partial molar volume of carbon dioxide in an aqueous solution of phenol and sodium chloride at temperatures of about (314, 354 and 395) K and pressures up to about 10 MPa. The composition of the solvent – expressed as molality in water – is about 0.5 mol/(kg H2O) for phenol and 1 mol/(kg H2O) for sodium chloride. The experimental work is a continuation of investigations on the influence of organic components and strong electrolytes on the solubility of carbon dioxide in water. It extends a data base for developing and testing thermodynamic models to describe the solubility of gases in salt-free and salt-containing aqueous solvents mixed with organic compounds. The experimental results are compared to predictions and correlations from a thermodynamic model which combines a model for the solubility of CO2 in aqueous solutions of NaCl with a model for the solubility of CO2 in aqueous solutions of phenol. The prediction results reveal a reasonable agreement. As in a previous investigation – with N,N-dimethylformamide instead of phenol as the organic solvent component – adjusting a ternary parameter for interactions between the three solutes (i.e. CO2, NaCl, and phenol) results in a correlation that allows to describe the new experimental data within experimental uncertainty. ã 2014 Published by Elsevier B.V.

Keywords: Gas solubility Partial molar volume Carbon dioxide Phenol Sodium chloride Aqueous electrolyte solutions Mixed solvents

1. Introduction Prediction as well as correlation methods for gas solubility phenomena in aqueous solutions are required for many applications for example, in the chemical, pharmaceutical, and oil related industries. The development of such thermodynamic models is still a demanding task in fluid phase equilibrium thermodynamics, in particular when electrolytes are present in the liquid phase. Thermodynamic models can only be developed and tested when sufficient and reliable experimental gas solubility data is available. The present publication extends previous reports of the principal investigator’s group on experimental and modelling work on the physical as well as on the chemical solubility of single gases and binary gas mixtures in pure solvents as well as in solvent mixtures (for example, Jödecke et al. [1]). The work presented here is an extension of investigations (both experimental and theoretical) on the physical solubility of gases in (salt-free and salt-containing) binary solutions of water and an organic solvent. In particular, it is an extension of recent work on the solubility of CO2 in salt-free and

* Corresponding author. Tel.: +49 631 205 2410; fax: +49 631 205 3835. E-mail address: [email protected] (G. Maurer). 1 Current address: Shanghai Baosteel Chemical Co., Ltd., Shanghai 200942, PR China. 2 Current address: BASF SE, Ludwigshafen 67056, Germany. http://dx.doi.org/10.1016/j.fluid.2014.11.002 0378-3812/ ã 2014 Published by Elsevier B.V.

salt-containing aqueous solutions of the single organic components methanol, acetone [2–8], and N,N-dimethylformamide [1,9,10] as well as on the solubility of CO2 in phenol [11] and in aqueous solutions of phenol [12]. New experimental results are reported for the solubility of carbon dioxide in an aqueous solution of NaCl (molality of NaCl in water 1 mol/(kg H2O)) that also contains phenol (molality of phenol in water 0.5 mol/(kg H2O)) at three temperatures (314 K, 354 K, and 395 K) at pressures up to about 10 MPa. The experimental investigations were performed by applying the synthetic gas solubility method using a constant volume high pressure cell. The experiments yield – as a side product – also the density of the liquid mixture. The experimental results are used to determine Henry’s constant and the partial molar volume of CO2 in the aqueous solvent mixture. The experimental results for the solubility pressure as well as the evaluation results for Henry’s constant are compared with prediction results. Predictions were made by combining a model for the solubility of CO2 in aqueous solutions of NaCl on one side with a similar model for the solubility of CO2 in aqueous solutions of phenol on the other side. Both models are extensions of Pitzer’s expression for the Gibbs excess energy of aqueous electrolyte solutions [13,14]. The model treats phenol, NaCl, and CO2 as solutes in the solvent water. That extension requires parameters for binary and ternary interactions between the solute species in water. Some of those parameters are already available from the previous investigations on the solubility

J. Xia et al. / Fluid Phase Equilibria 385 (2015) 248–257

Nomenclature A Aw aCO2 ;solv

ai B BG,MX Bi,j b Ci,j,k Cl– CO2 fi f2(I) f3(I) H2O I i i, j, k ðm;0Þ

kH;i;W ðm;0Þ

kH;i;solv ðm;ps

solv kH;i;solv

Þ

MX M+ Mi mi mi;solv ~ solv m m0 m0solv N Nexp Na+ NaCl p psi pssolv R T V V m;W V1 m;i;W V1 m;CO2 ;solv

vsolv X

parameter Debye–Hückel parameter for water molality based activity of CO2 in the solvent that is normalized according to Henry’s law for the solubility of CO2 in the solvent activity of component i in liquid phase parameter 2nd osmotic virial coefficient for interactions between gas G and electrolyte MX 2nd virial coefficient for interactions between i and j constant (b = 1.2) 3rd virial coefficient for interactions between i,j, and k chloride ion carbon dioxide fugacity of component i function of ionic strength I in Eq. (18) function of ionic strength I in Eq. (18) water ionic strength on the molality scale experimental data point solute species Henry’s constant for the solubility of component i in pure water (on the molality scale) at zero pressure Henry’s constant for the solubility of component i in the solvent (on the molality scale) at zero pressure Henry’s constant for the solubility of component i in the solvent (on the molality scale) at the saturation pressure of that solvent electrolyte cation relative molar mass of component i divided by 1000 molality of solute i in water molality of solute i in the solvent (water + phenol + NaCl) mass of solvent (water + phenol + NaCl) in viewcell 1 mol/(kg water); the solvent is water 1 mol/(kg solvent); the solvent is (water + phenol + NaCl) number of data points number of experimental data points sodium ion sodium chloride pressure saturation pressure of component i saturation pressure of the solvent (water + phenol + NaCl) universal gas constant absolute temperature cell volume molar volume of water partial molar volume of solute i infinitely diluted in water partial molar volume of CO2 infinitely diluted in the solvent (water + phenol + NaCl) specific volume of the solvent (water + phenol + NaCl) anion

yi Z zi

249

vapour phase mole fraction of component i compressibility factor number of electric charges on species i

Greek letters constant (a = 2) binary parameter for interactions between solutes i and j in water binary parameter for interactions between solutes i bð1Þ i;j and j in water mean relative deviation between experimentally Dx determined and calculated property x Gi;j;k third osmotic virial coefficient for interactions between species i, j and k ðmÞ activity coefficient of solute i (on the molality scale) in gi water activity coefficient of solute i (on the molality scale) in g ðmÞ i;solv the solvent (water + phenol + NaCl) ’i vapour phase fugacity coefficient of component i mi;j;k ternary parameter for interactions between solutes i, j, and k in water n+ stoichiometric factor for cation M in MX n stoichiometric factor for anion X in MX

a bð0Þ i;j

Subscripts Cl– chloride ion correl correlation result CO2 carbon dioxide exp experimental result G gas G i, j, k solute species Na+ sodium ion MX electrolyte m molar property max maximum min minimum pred prediction result pure pure component solv solvent mixture (water + phenol + NaCl) W water Superscripts (m,0) on the molality scale at zero pressure (m, pssolv ) on the molality scale at pssolv L liquid phase s saturation property V vapour phase 1 at infinite dilution

of CO2 in (a) pure water and in aqueous solutions of NaCl (Rumpf et al. [15] and Pérez-Salado Kamps et al. [6]) and (b) aqueous solutions of phenol (Jödecke et al. [12]). In addition, the model for the solubility of CO2 in aqueous solutions of (phenol and NaCl) requires binary and ternary parameters for interactions between phenol and NaCl in water as well as ternary parameters for interactions between all solutes (i.e. CO2, NaCl, and phenol) in water. When these additional parameters are neglected the combined model allows to predict the pressure that is required to dissolve CO2 in the liquid mixture. The prediction results are compared with the experimental data. Furthermore, the new experimental gas solubility data are used to determine a single ternary parameter for interactions between CO2, NaCl, and phenol. Introducing that parameter results in a correlation that allows to describe the new experimental results for the solubility pressure within experimental uncertainty.

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Table 1 Sample description. Chemical

CAS No.

Purity (mass fraction)

Relative molar mass

Supplier

CO2 Phenol NaCl H2O

124-38-9 108-95-2 7647-14-5 7732-18-5

0.99995 0.995 0.995

44.01 94.11 58.44 18.015

Messer-Griesheim GmbH, Ludwigshafen, Germany Merck GmbH, Darmstadt, Germany Merck GmbH, Darmstadt, Germany University of Kaiserslautern, Germany

Table 2a Experimental results (and standard uncertainties) for the solubility of CO2 (1) in (water (2) + phenol (3) + NaCl (4)) at (313.7  0.1) Ka . m3 = (0.497  0.001) mol/(kg H2O) m4 = (0.975  0.002) mol/(kg H2O) p MPa

m1 mol=ðkg H2 OÞ 0.0532  0.0008 0.192  0.001 0.289  0.002 0.421  0.002 0.569  0.003 0.715  0.004 0.853  0.005 1.006  0.005 1.13  0.01

0.279 0.967 1.49 2.25 3.19 4.19 5.35 6.85 8.86

        

0.001 0.009 0.01 0.01 0.01 0.02 0.02 0.02 0.02

~ solv V=m dm3 =ðkg solventÞ 0.9431 0.9425 0.9509 0.9504 0.9539 0.9643 0.9600 0.9716 0.9653

2.2. Materials and sample pretreatment Details (CAS-No, purity, relative molar mass, and supplier) of all materials are listed in Table 1. Carbon dioxide was used without further purification. Phenol was degassed under vacuum. Deionized water was degassed by vacuum distillation. Sodium chloride was also degassed under vacuum. The solvent mixture (about 1 kg) was gravimetrically prepared. 3. Results and discussion 3.1. Experimental results for the solubility of CO2 in an aqueous solution of (phenol + NaCl)

The apparatus realizes the principles of the synthetic gas solubility method, i.e. in an experiment the pressure p is measured that is required to dissolve at a pre-set temperature T a known amount of CO2 in a known amount of solvent mixture in a high-pressure, constant-volume cell. The equipment also allows to determine a volumetric property (the ratio of cell volume V to the ~ solv ). Details of the equipment used as well as amount of solvent m on the experimental procedure applied have been reported before (for example, Rumpf [16], Rumpf and Maurer [17], Xia et al. [4], and Pérez-Salado Kamps et al. [18]). In recent publications [1,9] we reported details such as, for example, the experimental procedures and the experimental uncertainties. That information also holds for the present work and is thus not repeated.

The solubility of carbon dioxide (component 1) in a solvent mixture of water (component 2), phenol (component 3), and NaCl (component 4) was measured at three temperatures T = (313.7, 354.4, and 395.0) K and total pressures p up to 9.42 MPa. The molalities of phenol and NaCl in the liquid phase were m3 = 0.497 mol/(kg H2O) and m4 = 0.975 mol/(kg H2O), respectively. The experimental results are given in Table 2a (for T = 313.7 K), Table 2b (for T = 354.4 K) and Table 2c (for T = 395.0 K). The gas solubility is expressed treating water as the only solvent component and all other components as solutes, i.e. the composition of the liquid mixture that coexists with the vapour phase is given in terms of molality (mi where i = 1, 3, 4), that is the amount of substance i (the number of moles of component i) per kilogram of water (component 2). Furthermore the ratio of cell volume V to the ~ solv of the solvent mixture (of water, phenol, and NaCl) mass m which was determined as a side-product (cf. Jödecke et al. [1]) is also given in those tables. The experimental uncertainty of that ratio is estimated to about 0.7%. The experimental total pressure p is plotted in Fig.1 against the ratio of molality of carbon dioxide m1 to m0 (where m0 = 1 mol/(kg H2O)). Fig. 1 reveals a purely physical gas solubility behaviour. The solubility of CO2 in that particular aqueous solution of (phenol + NaCl) decreases with

Table 2b Experimental results (and standard uncertainties) for the solubility of CO2 (1) in (water (2) + phenol (3) + NaCl (4)) at (354.4  0.1) Ka .

Table 2c Experimental results (and standard uncertainties) for the solubility of CO2 (1) in (water (2) + phenol (3) + NaCl (4)) at (395.0  0.1) Ka .

a

~ solv :  0.7%. Estimated relative standard uncertainty for V=m

2. Experimental arrangement and materials 2.1. Apparatus and method

m3 = (0.497  0.001) mol/(kg H2O)

m3 = (0.497  0.001) mol/(kg H2O)

m4 = (0.975  0.002) mol/(kg H2O)

m4 = (0.975  0.002) mol/(kg H2O)

m1 mol=ðkg H2 OÞ

p MPa

0.0548  0.0008 0.156  0.001 0.221  0.002 0.321  0.002 0.430  0.003 0.526  0.003 0.637  0.003 0.738  0.003 0.806  0.004

0.534  0.014 1.45  0.01 2.03  0.01 3.01  0.01 4.17  0.02 5.37  0.02 6.69  0.02 8.18  0.02 9.34  0.02

a

~ solv V=m dm3 =ðkg solventÞ 0.9693 0.9736 0.9800 0.9801 0.9938 0.9816 0.9949 0.9957 0.9979

~ solv :  0.7%. Estimated relative standard uncertainty for V=m

m1 mol=ðkg H2 OÞ 0.0569  0.0008 0.138  0.001 0.182  0.001 0.264  0.002 0.347  0.002 0.428  0.003 0.510  0.003 0.594  0.002 0.676  0.003 a

p MPa 0.855 1.80 2.33 3.35 4.43 5.57 6.72 8.00 9.42

        

0.004 0.01 0.01 0.01 0.01 0.02 0.02 0.02 0.02

~ solv V=m dm3 =ðkg solventÞ 1.0085 1.0115 1.0098 1.0132 1.0152 1.0166 1.0196 1.0232 1.0246

~ solv :  0.7%. Estimated relative standard uncertainty for V=m

J. Xia et al. / Fluid Phase Equilibria 385 (2015) 248–257

[(Fig._1)TD$IG]

Fig. 1. Experimental results for the total pressure p above solutions of CO2 (1) + H2O (2) + phenol (3) + NaCl (4) plotted versus m1/m0 where m1 is the molality of CO2 in the liquid phase (in mol/(kg H2O)) and m0 = 1 mol/(kg H2O) (m3 = 0.497 mol/(kg H2O), m4 = 0.975 mol/(kg H2O)): T = 313.7 K (&), T = 354.4 K (*), T = 395 K ().

[(Fig._2)TD$IG]

251

increasing temperature. For example, at a total pressure of 5 MPa, the molality of dissolved carbon dioxide decreases from 0.79 to 0.50 to 0.39 when the temperature increases from 314 K to 354 K to 395 K. Fig. 2 demonstrates the influence of either phenol (calculation results using the method by Jödecke et al. [12]) or NaCl (calculation results using the method described by Rumpf et al. [15]) on the solubility of CO2 in the aqueous solvent. Fig. 2 shows the difference between the pressure that is required to dissolve the same amount (per kg water) of CO2 in either an aqueous solution of phenol (m3 = 0.497 mol/(kg H2O)) or in an aqueous solution of NaCl (m4 = 0.975 mol/(kg H2O)) or in the aqueous solution of phenol and NaCl (m3 = 0.497 mol/(kg H2O) and m4 = 0.975 mol/(kg H2O)) that was the solvent in the work presented here, on one side and in pure water on the other side. The presence of sodium chloride results in an increased solubility pressure (“salting-out” of CO2 by NaCl) whereas phenol increases the solubility of CO2, i.e. phenol reduces the pressure that is required to dissolve CO2 – that phenomenon is sometimes called “salting-in”. The absolute differences between the solubility pressures increase with increasing temperature for both single solutes, i.e. for NaCl as well as for phenol. For the particular solvent investigated in the present work, the influence of NaCl is higher than the influence of phenol. Therefore, at all investigated temperatures the pressure required to dissolve a certain amount of CO2 (expressed as the molality of CO2 in water) is slightly higher than the pressure that is required to dissolve the same amount of CO2 in pure water. With the exception of three experimental results (at 314 K and the highest molalities of CO2) the pressure that is required to dissolve CO2 in the investigated solvent of (water + NaCl + phenol) is less than 0.5 MPa higher than the pressure that is required to dissolve CO2 in pure water. ~ solv plotted versus Fig. 3 shows the experimental results for V=m m1; solv =m0solv  m1; solv is the molality of CO2 in the solvent mixture of (H2O + phenol + NaCl) (in mol/(kg solvent)), and m0solv = 1 mol/(kg solvent). m1,solv is related to the molality of CO2 m1 in water by: m1;solv 1   ¼  m4  m1 3 1þ m M 0 3 þ m0 M4 m

(1)

where Mk is the relative molar mass of component k divided by 1000.

[(Fig._3)TD$IG]

Fig. 2. Influence of phenol (3) and NaCl (4) on the solubility of CO2 (1) in water (2) (m3 = 0.497 mol/(kg H2O), m4 = 0.975 mol/(kg H2O)): (a) T = 313.7 K, (b) T = 354.4 K, (c) T = 395 K; symbols: exp. results for solvent (water + phenol + NaCl); full curves: correlation results for solvent (water + NaCl) [15] dashed curves: correlation results for solvent (water + phenol) [12]; dashed dotted curves: predictions from Model II for solvent (water + phenol + NaCl).

Fig. 3. Evaluation of the volumetric data to determine the partial molar volume of CO2 (1) at infinite dilution in solvent (water (2) + phenol (3) + NaCl (4)) (m3 = 0.497 mol/(kg H2O), m4 = 0.975 mol/(kg H2O)).

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J. Xia et al. / Fluid Phase Equilibria 385 (2015) 248–257

Table 3 Evaluation of the experimental results for Henry’s constant on the molality scale ðm;pssolv Þ

ðm;0Þ

kH;CO2 ;solv ( kH;CO2 ;solv ) and the partial molar volume V 1 m;CO2 ;solv of CO2 in an aqueous solvent of phenol (3) (m3 = 0.497 mol/(kg H2O)) and NaCl (4) (m4 = 0.975 mol/(kg H2O)) and specific volume of the solvent Vsolv. ðm;ps

Þ

V1 m;CO2 ;solv cm3 =mol

V solv cm3 =g

kH;COsolv 2 ;solv MPa

where Nmax = Nexp and Nmin = 2 for the evaluations at 313.7 K, Nmin = 3 for the evaluations at 354 K and 395 K. For all three temperatures Df 1 is lower than 0.8%. To estimate the influence of the assumption on the vapour phase on the evaluated Henry’s constant, a second method (Method B) was applied to determine Henry’s constant of CO2 in the solvent mixture. In that method the fugacity of CO2 in Eq. (2) is L

from solubility pressure Method A T K

exp.

313.7 354.4 395.0

5.274 9.500 13.50

replaced by the fugacity of CO2 in the liquid phase f 1 which is calculated from the extended Henry’s law for CO2 in water using a model for the activity aCO2 of CO2 in the liquid phase.  1  V m;CO2 ;W ðTÞp L ðm;0Þ aCO2 f 1 ¼ f 1 ¼ kH;CO2 ;W ðTÞexp (5) RT

pred.

Method B

Df 2 /% 0.4 0.6 0.8

exp. 5.325 9.394 12.01

Df 1 /% 0.4 0.2 0.1

5.358 9.441 12.05

0.941 0.969 1.006

28 40 29

ðm;0Þ

where kH;CO2 ;W ðTÞ, V 1 m;CO2 ;W ðTÞ, and aCO2 are Henry’s constant of CO2

As already observed in previous investigations, a linear ~ solv and m1; solv =m0solv is observed for relationship between V=m all investigated temperatures. No comparison with literature data is possible, as to the best of our knowledge no experimental results neither for the solubility of CO2 in aqueous solutions of phenol and NaCl nor for the volumetric properties of such mixtures are available in the open literature. 3.2. Henry’s constant of CO2 in the solvent mixture 3.2.1. Evaluation of gas solubility data ðm;ps

Þ

Henry’s constant on the molality scale kH;COsolv for the 2 ;solv solubility of CO2 in the solvent mixture (i.e., the particular aqueous solution of phenol and sodium chloride) was determined by extrapolating at a contant temperature T the ratio of fugacity f1 and dimensionless molality m1; solv =m0solv to zero: ðm;ps

Þ

ðTÞ ¼ kH;COsolv 2 ;solv

f 1 ðT; pÞ lim 0 ðm1; solv =m0solv Þ!0ðm1; solv =msolv Þ

(2)

The extrapolation by Eq. (2) gives Henry’s constant at the saturation pressure pssolv of the aqueous solution of phenol and sodium chloride. Two procedures were applied to determine the fugacity of CO2: Method A treats the vapour phase as pure CO2. The fugacity of pure CO2 was calculated from the experimental results for temperature T and solubility pressure p from the equation of state by Span and Wagner [19] via the software package Thermofluids [20]. This assumption is a good approximation as long as the temperature is sufficiently low and the pressure is sufficiently high, i.e. it is best at 313.7 K and the highest pressures and it is weakest at 395 K and the lowest pressures. Nevertheless it was used here for all experimental (T, p) pairs. A linear relation between f 1 ðT ¼ const:; pÞ=ðm1; solv =m0solv Þ and m1;solv =m0solv holds over the complete investigated range of gas molalities. Thus, the extrapolation was performed by a linear regression: " # ! m1; solv f 1 ðT ¼ const:; pÞ (3) ¼AþB m0solv m1;solv =m0solv correl

where

ðm;ps Þ . A = kH;COsolv 2 ;solv

For the evaluations for 313.7 K the experimen-

tal results at the lowest pressure and for 354.4 K and 395 K, those at the two lowest pressures were neglected. The results are given in Table 3 together with the average relative differences: ! N max X f 1;correl  f 1;exp Df 1 100 ¼ abs (4) 1 þ Nmax  Nmin i¼N % f 1;exp min

i

at zero pressure in water, the partial molar volume of CO2 at infinite dilution in water, and the molality based activity of CO2 in the liquid phase, respectively, and R is the universal gas constant. ðm;0Þ

kH;CO2 ;W and V 1 m;CO2 ;W are available from previous investigations. They are given in Table A1 in the Appendix A. The activity of CO2 is expressed as aCO2 ¼

m1 ðmÞ g m0 1

(6) ðmÞ

where m0 = 1 mol/(kg H2O) and g 1 is the activity coefficient of CO2 on the molality scale which is normalized according to Henry’s law with water being the solvent (i.e. the reference state is a hypothetical one molal solution of solute i in pure water at temperature and pressure of the real solution where the solute experiences the same interactions as at infinite dilution in water). The activity coefficient of CO2 is calculated from an extension of Pitzer’s expression [13,14] for the excess Gibbs energy of aqueous electrolyte solutions: X  mj  ð0Þ X X  mj mk  ðmÞ lng 1 ¼ 2 b þ 3 mCO2 ;j;k (7) CO2 ;j m0 m0 m0 j j k

bð0Þ CO2 ;j and mCO2 ;j;k are binary and ternary parameters for interactions in water between CO2 on one side and all solute species on the other side. These interaction parameters are ð0Þ

ð0Þ

symmetrical (for example, bCO2 ;j = bj;CO2 ) and they depend only on temperature. All parameters for interactions between dissolved CO2 are ð0Þ

neglected (bCO2 ;CO2 = mCO2 ;CO2 ;CO2 = 0). All parameters for interactions between CO2 on one side and sodium and/or chloride ions on the other side are available from a previous investigation (see, for example, Pérez-Salado Kamps et al. [6], Rumpf et al. [15]) and all parameters for interactions between CO2 on one side and phenol on the other side are available from Jödecke et al. [12]. However, no parameters mCO2 ;j;k are available for ternary interactions between CO2, phenol (i.e. j = phenol), and sodium chloride (i.e. k = Na+ or Cl–). Therefore, these parameters had to be neglected in that evaluation. In the evaluation all experimental results were used, i.e. Nmin = 1 and Nmax = Nexp. The evaluation results from Eq. (2) with f1 from the right-hand side of Eq. (5) are also given in Table 3 together with the corresponding values for Df 1. For all three

temperatures Df 1 is lower than 0.4%, i.e. it is smaller than the corresponding deviation that was observed in the evaluation from Method A. ðm;ps

Þ

The numerical values for kH;COsolv from both evaluation 2 ;solv methods agree within about 1% for 314 K and 354 K, but deviate by about 10% for 395 K. The approximation of Method A (the vapour is assumed to be pure CO2) is too crude at 395 K – indeed the model described below (cf. Section 4.4) reveals that the mole

J. Xia et al. / Fluid Phase Equilibria 385 (2015) 248–257

fraction of CO2 in the vapour phase at 395 K is between 0.75 and 0.96 (at the lowest and highest investigated pressure, respectively), whereas at 314 K (354 K) the mole fraction of CO2 in the vapour phase increases from 0.97 to 0.99 (0.90 to 0.99). 3.2.2. Comparison with predictions As no literature data for the solubility of CO2 in aqueous solutions of (phenol + NaCl) are available, no comparison with other experimental results is possible. However, combining the models that are available for the description of the solubility of CO2 in an aqueous solution of phenol (Jödecke et al. [12]) and in aqueous solutions of NaCl (Rumpf et al. [15])) allows to predict Henry's constant for the solubility of CO2 in an aqueous solution of (phenol + NaCl). The fugacity of CO2 in the liquid phase can be expressed also by the following equation where the solvent is an aqueous solution of (phenol + NaCl):  1  V m;CO2 ;solv ðTÞðp  pssolv Þ ðm;ps Þ L aCO2 ;solv f 1 ¼ kH;COsolv ðTÞexp (8) 2 ;solv R T where aCO2 ;solv is the molality based activity of CO2 in the solvent that is normalized according to Henry’s law for the solubility of CO2 in that solvent (i.e. the aqueous solution of (phenol + NaCl): aCO2 ;solv ¼

m1;solv ðmÞ g m0solv 1;solv

(9)

Combining Eqs. (5), (6), (8), and (9) gives ðm;ps

Þ

kH;COsolv 2 ;solv ðm;0Þ

kH;CO2 ;W

 1  ðmÞ s V m;CO2 ;W p  ðV 1 m1 g 1 m;CO2 ;solv ðp  psolv ÞÞ ¼ exp RT m1;solv g ðmÞ

1;solv

(10) As the left hand-side of Eq. (10) does not depend on the amount of dissolved CO2, the right-hand side of Eq. (10) does not depend either. For example, with a vanishing amount of dissolved CO2 (molality m1 ! 0) in an aqueous solution of phenol (molality m3) and sodium chloride (molality m4), the pressure p above the ðmÞ

aqueous solution of phenol and NaCl reduces to pssolv , g 1;solv reduces ðmÞ

ðmÞ

to 1, and g 1 reduces to g 1 ðm1 ¼ 0; m3 ; m4 Þ. Thus, with Eq. (1) one finds: ðm;ps

Þ

kH;COsolv 2 ;solv ðm;0Þ

kH;CO2 ;W

 1   V m;CO2 ;W pssolv  m m ðmÞ 1 þ 30 M3 þ 40 M4 g 1 ðm1 ¼ exp RT m m ¼ 0; m3 ; m4 Þ (10a)

Neglecting the Krichevsky–Kasarnovsky correction gives ðm;ps Þ kH;COsolv 2 ;solv ðm;0Þ kH;CO2 ;W

3.3. Volumetric properties and Henry’s constant at zero pressure The experimental results for the ratio of the cell volume V to the ~ solv were used to mass of the solvent (water + phenol + NaCl) m determine the partial molar volume of CO2 at infinite dilution in that solvent V 1 m;CO2 ;solv . As described by Kumełan et al. [22], at low gas concentrations in the solvent the following relation holds for ~ solv : the influence of the amount of dissolved CO2 on V=m 1

~ solv V=m v 1 m1;solv V m;CO2 ;solv ¼ solv þ cm3 =g cm3 =g 1000 m0solv cm3 =mol

(11)

where vsolv is the specific volume of the solvent. ~ solv and As shown in Fig. 3, the linear relation between V=m m1;solv =m0solv holds over the whole investigated range of gas molalities. Therefore, vsolv and V 1 m;CO2 ;solv were determined from a linear regression. The results are given in Table 3. The estimated uncertainties are 0.4% for vsolv and 5 cm3/mol for V 1 m;CO2 ;solv. As expected, the partial molar volume of CO2 in that particular aqueous solution of phenol and NaCl is positive, i.e. dissolving CO2 results in an expansion of the volume of the liquid phase. The numerical values for V 1 m;CO2 ;solv in that particular solvent have the same order of magnitude (about 20 to 50 cm3/mol) as in other aqueous solutions of organic solvents (for example N,N-dimethylformamide) without as well as with a strong electrolyte [1,9,10] but also as in some ionic liquids [21–23]. For the particular solvent investigated here, no literature data are available for comparison. Henry’s constant of CO2 in the solvent at zero pressure can be calculated from Henry’s constant of CO2 at saturation pressure of the solvent and the partial molar volume of CO2 in the solvent:   s V1 ðm;ps Þ ðm;0Þ m;CO2 ;solv psolv (12) kH;CO2 ;solv ¼ kH;COsolv exp  2 ;solv RT

The correction is small and no information on the influence of NaCl on the saturation pressure of an aqueous solution of phenol is available. Therefore, the correction is done here by replacing the saturation pressure of the solvent pssolv ðm3 ; m4 Þ by the saturation pressure of the salt-free solution pssolv ðm3 ; m4 ¼ 0Þ. That pressure was taken from the correlation of Jödecke et al. [12]. The exponential correction factor in Eq. (12) is about 0.9992, 0.9993, and 0.9982 at 314 K, 354 K, and 395 K, respectively, i.e. the correction can be neglected and ðm;0Þ

ðm;ps

Þ

kH;CO2 ;solv  kH;COsolv 2 ;solv

(13)

is a very good approximation.

 m m4  ðmÞ ¼ 1 þ 30 M3 þ 0 M4 g 1 ðm1 ¼ 0; m3 ; m4 Þ m m

(10b)

4. Modelling of gas solubility 4.1. Models

ðmÞ 1 ðm1

g ¼ 0; m3 ; m4 Þ may be calculated from Eq. (7), where j and k stand for phenol, sodium ions, and chloride ions, but not for CO2. Using the set of parameters described above (i.e. also setting mCO2 ; phenol; Naþ = mCO2 ; phenol; Cl = 0, cf. below) allows to predict the ðm;ps

Þ

for the solubility of CO2 molality based Henry’s constant kH;COsolv 2 ;solv in an aqueous solution of (phenol + NaCl). The prediction results are given in Table 3. The deviations from the results of the evaluation of the experimental results for the solubility pressure with Method B are less than 0.6%, i.e. the deviations are smaller ðm;ps

Þ

than the estimated experimental uncertainty of kH;COsolv (that 2 ;solv amounts to about 1%).

253

Several methods might be applied for correlating the solubility of CO2 in aqueous solutions of (phenol + NaCl). These methods can differ in the selection of the solvent and in the treatment of the liquid and/or vapour phases. As the fractions of CO2, phenol, and NaCl in the aqueous solutions are small, we consider these components as solutes and water as the solvent. Therefore, the solubility of CO2 in the aqueous solutions is described by combining the extended Henry’s law for CO2  1  V m;CO2 ;W p ðm;0Þ V aCO2 ¼ f CO2 kH;CO2 ;W exp (14) RT

254

J. Xia et al. / Fluid Phase Equilibria 385 (2015) 248–257

and phenol  1  V m;phenol;W p ðm;0Þ V aphenol ¼ f phenol kH;phenol;W exp RT

(15)

with the extended Raoult’s law for water   V m;W ðp  psW Þ V psW ’sW exp aW ¼ f W R T

(16)

ðm;0Þ

kH;i;W is Henry’s constant of solute i in pure water on the

molality scale at zero pressure and V 1 m;i;W is the partial molar volume of solute i in water at infinite dilution. ai is the activity of V

component i in the liquid phase and f i is the fugacity of component i in the vapour phase. The saturation pressure, the fugacity coefficient and the molar liquid volume at saturation of pure water are abbreviated by psW, ’sW , and V m;W , respectively. These properties were taken from previous publications, for example from Jödecke et al. [12]. They are given in the Appendix A (Tables A1–A3). The liquid phase is treated by applying an extension of Pitzer’s equation for the excess Gibbs energy of aqueous electrolyte solutions. That method was already used above (cf. Method B – in the section on the evaluation of the experimental results to determine Henry’s constant of CO2 in the solvent mixture). At low temperatures and high pressures the amounts of phenol and water in the vapour phase are small and are neglected. That assumption was already described above (Method A in the section on Henry’s constant of CO2 in the aqueous solution of (phenol + NaCl)). In that case Eq. (14) reduces to  1  V m;CO2 ;W p ðm;0Þ V aCO2 ¼ f CO2 ;pure ðT; pÞ kH;CO2 ;W exp (14a) RT and Eqs. (15) and (16) are not considered further. Combining the treatment of the liquid phase with this assumption on the vapour phase is called Model I. At higher temperatures and low pressures the presence of water and phenol in the vapour phase cannot be neglected. Then, the vapour phase is treated as a ternary gas mixture and its properties are described by the virial equation of state that is truncated after the 3rd virial coefficient. The combination of the treatment of the liquid phase with that assumption on the vapour phase is called Model II. 4.2. Details of the description of the liquid phase The description of the liquid phase is a combination of modelling means that were used before, for example, on the solubility of CO2 in aqueous solutions of (N,N-dimethylformamide and a strong electrolyte) [9,10] and in aqueous solutions of phenol [12]. The method is described here in detail. The activity of a volatile solute component i (i.e. i = CO2 and phenol) is ai ¼

mi ðmÞ g m0 i

(17)

The solutes are CO2, phenol as well as sodium and chloride ions. The activity coefficient of a solute species i is calculated from an extension of Pitzer’s expression [13,14] for the excess Gibbs energy of aqueous electrolyte solutions: " pffiffi # pffiffi 2 I ðmÞ 2 pffiffi þ lnð1 þ b IÞ lng i ¼ A’ zi 1þb I b X mj  ð0Þ ð1Þ þ2 ½bi;j þ bi;j f 2 ðIÞ

0 m j XX mj mk  ð1Þ  f 3 ðIÞz2i b m0 m0 j;k j k   XX mj mk  þ3 mi;j;k (18) m0 m0 j k where Aw is the Debye–Hückel parameter for water, zi is the ð0Þ

ð1Þ

number of electrical charges on species i, and bi;j , bi;j , and mi;j;k are binary and ternary parameters for interactions between solute species i, j, and k in water. The interaction parameters are ð0Þ

ð0Þ

symmetrical (for example, bi;j = bj;i ) and they depend only on temperature. I is the ionic strength on the molality scale:   1X m j 2 z I¼ 2 j m0 j

(19)

f2 and f3 are functions of the ionic strength: f 2 ðIÞ ¼

  pffiffi pffiffii 2 h 1  1 þ a I exp a I 2 a I

(20)

    pffiffi 1 pffiffi 2 (21) 1  1 þ a a I exp  a I þ I 2 a2 I2 b and a are constants (b = 1.2; a = 2). The activity of the solvent (i.e. water) follows via the Gibbs– Duhem equation from the activity coefficients of the solutes i, j and k: 2 pffiffiffiffi XX mj mk  ð0Þ pffiffi I3  4 pffiffi þ lnaW ¼ MW 2A’ bj;k þ bð1Þ expða I j;k 0 0 m m 1þb I j k # X  mj  XXX  mi  mj  mk  m þ (22) þ2 i;j;k m0 m0 m0 m0 i j j k

f 3 ðIÞ ¼

2

The Debye–Hückel parameter Af of water was calculated using the correlation of Bradley and Pitzer [24]. Numerical values for Aw are given in the Appendix A in Table A2.The method requires parameters for interactions between all solute species in water. For interactions between CO2 these parameters are neglected ð0Þ

ð1Þ

(bCO2 ;CO2 = bCO2 ;CO2 = mCO2 ;CO2 ;CO2 = 0). For interactions between phenol on one side and phenol or CO2 on the other side these parameters were adopted from Jödecke et al. [12]. For interactions between the ionic species sodium and chloride the parameters were taken from Silvester and Pitzer [25] (cf. also Pérez-Salado Kamps [26]). For interactions between CO2 on one side and sodium

Table 4 Comparison between calculation results and experimental data for the solubility of CO2 in an aqueous solution of (phenol + NaCl). Prediction

T K

mCO2 ;phenol;Naþ

314 354 395

0 0 0

a

Correlation Model I

Model IIa

DmCO2

Dp

%

1.0 2.0 4.6

%

1.9 3.3 1.9

Considering only data points where the compressibility factor Z > 0.7.

Model IIa

Model I DmCO2

mCO2 ;phenol;Naþ –0.0018 –0.0028 0.0079

%

0.2 1.6 2.5

Dp

mCO2 ;phenol;Naþ –0.0015 –0.0048 –0.0028

%

1.2 1.3 1.3

J. Xia et al. / Fluid Phase Equilibria 385 (2015) 248–257

chloride ions on the other side these parameters were adopted from Rumpf et al. [15] (cf. also Pérez-Salado Kamps et al. [7]). As no experimental information is available on the influence of NaCl on the volatility of phenol in aqueous solutions, all parameters between phenol on one side and sodium chloride ions on the other side were neglected. All non-neglected parameters that were taken from the literature are given in the Appendix A in Tables A3 and A4. For an application to describe the thermodynamic properties of the liquid phase of the system (CO2 + water + phenol + NaCl) there remain only two unknown ternary interaction parameters: mCO2 ; phenol; Naþ and mCO2 ; phenol; Cl . However, as the sodium chloride is dissolved in water, mNaþ = mCl and only the sum of both parameters has an influence on the vapour–liquid equilibrium. Therefore, one of these parameters can be chosen arbitrarily (here mCO2 ; phenol; Cl = 0) and there remains only a single adjustable parameter: mCO2 ; phenol; Naþ . 4.3. Model I Model I combines the treatment of the liquid phase discussed in the preceding section with the assumption that the vapour phase is pure CO2. The fugacity of pure carbon dioxide was calculated – as in Section 3.2.1 – from the equation of state by Span and Wagner [19] via the software package Thermofluids [20]. Setting the only remaining adjustable parameter mCO2 ; phenol; Naþ = 0 allows to predict the solubility of CO2 in the aqueous solution of (phenol + NaCl). The results are shown in Table 4. The average relative deviation between the experimental results for the molality of CO2 in the liquid phase and the prediction results

Dm CO2 %

¼

  N max X mCO2 ;pred  mCO2 ;exp 100 abs 1 þ Nmax  Nmin i¼N mCO2 ;exp i

(23)

min

is 1.0% (at 314 K with Nmin = 2), 2.0% (at 354 K with Nmin = 3), and 4.6% (at 395 K with Nmin = 3). At 314 K the prediction results agree well with the experimental data, but the deviations get larger when the temperature increases and at 395 K Dm CO2 is beyond the experimental uncertainty. As already discussed above, Model I is only a good approximation at low temperatures and high pressures. Therefore, at 354 K and 395 K the comparison does not include the two lowest pressures (i.e. Nmin = 3). The deviations can be reduced by adjusting mCO2 ; phenol; Naþ . The results are also

shown in Table 4. The mean deviation Dm CO2 can be reduced to 0.2% (for 314 K), 1.6% (for 354 K), and 2.5% (for 395 K). The resulting values for the adjusted parameter mCO2 ; phenol; Naþ are small, but as they also have to compensate for the assumption that the vapour phase is pure CO2, they do not reveal a simple influence of temperature. 4.4. Model II Model II treats the liquid phase just as Model I, but the vapour phase is a ternary mixture (CO2 + water + phenol) whose properties are calculated with the virial equation of state that is truncated after the third virial coefficient. The fugacity of component i in the vapour phase then is: f i ¼ yi p’i V

(24)

where yi and ’i are the mole fraction and the fugacity coefficient, respectively of component i in the vapour phase. Therefore, Model II allows to calculate the composition of the vapour phase. That method is adopted from a previous publication on the solubility of CO2 in aqueous solutions of phenol (Jödecke et al. [12]). Since all details (such as, for example, the methods to determine the virial coefficients and details of the calculation procedure) were adopted

255

from that publication, only the virial coefficients are given in Table A5 in the Appendix A. Again, setting the only remaining adjustable parameter mCO2 ; phenol; Naþ = 0 allows to predict the solubility of CO2 in the aqueous solution of (phenol + NaCl). The results are shown in Table 4. The average relative deviation between the experimental results for the solubility pressure and the prediction results is expressed by ! max ppred  pexp Dp 100 NX ¼ abs (25) % Nmax i¼1 pexp i

The truncated virial equation is not a good approximation to describe the properties of the vapour phase at high pressures. Thus, the comparison was restricted to those data points where the calculation results for the compressibility factor Z of the vapour phase was above an arbitrarily selected limit: Z > 0.7. This limit allowed to consider all experimental results at 395 K, whereas at 354 K (314 K) one (two) data points were excluded, i.e. in Eq. (25) Nmax = 8 for 354 K and Nmax = 7 for 314 K. The prediction results for the solubility pressure give for the average relative deviation Dp = 1.9% (for 314 K), 3.3% (for 354 K), and 1.9% (for 395 K). The mean deviation Dp can be reduced to about 1% (1.1% for 314 K, 1.6% for 354 K, and 1.3% for 395 K) when the ternary parameter mCO2 ; phenol;Naþ is adjusted. The largest deviations are observed at each temperature for the lowest pressure. If these data points are not taken into account, Dp reduces to 0.6% (for 314 K) and 1.1% (for 354 K and 395 K). The numerical values for the adjusted parameter mCO2 ; phenol; Naþ are small. They are given in Table 4. The numerical values for mCO2 ; phenol; Naþ adjusted using Model II deviate slightly from those determined using Model I, as they depend on the model version that is applied. The prediction results for the vapour phase mole fraction of phenol vary between 0.0004 < yphenol < 0.0051 and those for the vapour phase mole fraction of water for 314 K between 0.003 < yW < 0.028 and for 395 K between 0.04 < yW < 0.25. These prediction results (in particular those for phenol) are preliminary, as (due to the lack of experimental data) all parameters for interactions between phenol on one side and NaCl on the other side in the liquid phase had to be neglected. 5. Conclusions The influence of a strong electrolyte on the solubility of a gas in aqueous solutions of organic solvents is of interest in many processes in the chemical and related industries. The present work extends the rather limited experimental data base for that phenomenon by reporting new experimental data for the influence of sodium chloride on the solubility of carbon dioxide in aqueous solutions of phenol at three temperatures (314 K, 354 K, and 395 K) and pressures up to nearly10 MPa.Onlyasingleaqueoussolventwasinvestigated(1 mol NaCl/(kg water) and 0.5 mol phenol/(kg water)). The experimental results confirmthe expectation thatasCO2 is“salted-out” by NaCl, but “salted-in” by phenol, the influence of NaCl on the solubility of CO2 in water is partially compensated by the influence of phenol. The experimental results are described using an extension of Pitzer’s model for the excess Gibbs energy of aqueous electrolyte solutions. When the model combines the models for the solubility of CO2 in (water + phenol) on one side and in (water + NaCl) on the other side – which both are available from previous investigations – predictions for the combined influence of phenol and NaCl on the solubility of CO2 in water are possible. However, the quality of the prediction results also depends on the model that is chosen to represent the properties of the vapour phase. Replacing the vapour phase mixture by pure CO2 results in good predictions for the solubility of CO2 in the aqueous solution of (phenol + NaCl) at (low temperatures + high pressures). Vice versa,

256

J. Xia et al. / Fluid Phase Equilibria 385 (2015) 248–257

considering the vapour to be a ternary mixture and assuming that the fugacities in the vapour phase can be approximated by the truncated virial equation of state, gives reasonable predictions at (high temperatures + low pressures). In both cases the agreement between experimental data and calculations results can be improved when a single ternary parameter for interactions between CO2, phenol, and sodium chloride in the liquid phase is adjusted. However, as the prediction results already give a reasonable agreement with the experimental data, it is concluded, that reliable predictions for the simultaneous influence of an organic solute and an electrolyte solute on the solubility of a nonreacting gaseous solute in water are possible, but only when the models used to describe the properties of the liquid and the vapour phases as well as the model parameters are carefully selected. Also some volumetric properties were obtained as a side product of the experimental investigations on the gas solubility. These data were used to determine the partial molar volume of carbon dioxide at infinite dilution in the investigated aqueous solutions of (phenol + NaCl). In accordance with previous investigations on the solubility of CO2 in aqueous as well as in nonaqueous solvents, the new results confirm that dissolving CO2 expands the volume of the solvent. As far as can be stated at this moment of time, the influence of such solvents on the partial molar volume of CO2 is small and (30–50) cm3/mol can be used to estimate the volume expansion of a liquid phase caused by dissolved CO2 at around ambient temperature. Nevertheless we recommend further experimental and modelling work to confirm and extend the results of the present investigation. Acknowledgements

Table A3 ðm;0Þ

Phenol in water: Henry’s constant on the molality scale at zero pressure kH;phenol;W , partial molar volume of phenol at infinite dilution

V1 m;phenol;W ,

and parameters

for interactions between phenol on one side and phenol or CO2 on the other side. ðm;0Þ

T K

314 354 395

kH;phenol;W

V1 m;phenol;W

kPa

cm3 = mol

0.161 1.38 6.42

89.1 92.1 95.5

bð0Þ phenol; phenol

bð0Þ CO2 ; phenol

0.303 0.238 0.194

–0.0738 –0.0870 –0.1005

mCO2 ;CO2 ;phenol

–0.0105 –0.0105 –0.0105

Table A4 Parameters for interactions in water between sodium and chloride ions and between CO2 on one side and sodium and/or chloride ions on the other sidea . T K

bð0Þ  Naþ Cl

ð1Þ bNa þ ;Cl

314 354 395

0.0861 0.0989 0.1018

0.2778 0.3089 0.3443

mNaþ ;Naþ ;Cl

bð0Þ CO2 ;Naþ

mCO2 ;Naþ ;Cl

–0.0000763 –0.0009280 –0.001379

0.1052 0.0943 0.0937

-0.0028388 -0.0028388 -0.0028388

a Parameters for interactions between a gas G and an electrolyte MX (= Mnþ Xn ) are sometimes given as osmotic virial coefficients for interactions between G

ð0Þ

ð0Þ

and MX: second virial coefficient: BG;MX = nþ bG;Mþ + n bG;X and third virial coefficients: GG;MX;MX ¼ ðn Þ mG;Mþ ;Mþ þ 2n n mG;Mþ ;X þ ðn Þ mG;X ;X  ; GG;G;MX ¼  þ nþ mG;G;Mþ þ n mG;G;X resulting in: BCO2 ; NaCl ¼ bð0Þ CO2 ; Naþ , GCO2 ;NaCl;NaCl ¼ mCO2 ;Na ;Cl and GCO2 ;CO2 ;NaCl ¼ 0. þ 2

 2

þ 

Table A5 Virial coefficients for the ternary system CO2 (1) + water (2) + phenol (3). j!

2nd virial coefficient Bi,j/(cm3/mol)

i#

1

The experimental part of this work was supported by the German Government (BMBF Grant-No. 01/RK9808/8) and co-sponsored by Siemens-Axiva GmbH & Co. KG, Lurgi Energie und Entsorgung GmbH, Lurgi Oel Gas Chemie GmbH, Degussa AG, Bayer AG, and BASF AG. Funding and cooperation is gratefully acknowledged.

T/K 1 2 3

313.8 354.4 395.0 313.8 354.4 395.0 –109.1 –82.1 –62.3 –162.5 –128.1 –103.3 –954 –557 –365

Appendix A.

T/K C1,1,1

2

3 313.8 354.4 395.0 –294 –226.7 –178.2 –461 –336 –255 –4477 –2867 –1945

3rd virial coefficient C1,1,1/(cm6/mol2) 313.8 4464

354.4 3842

395.0 3351

See Tables A1–A5 References Table A1 Solubility of CO2 in water: Henry’s constant on the molality scale at zero pressure ðm;0Þ

kH;CO2 ;W and partial molar volume of CO2 at infinite dilution V 1 m;CO2 ;W . V1 m;CO2 ;W cm3 = mol

ðm;0Þ

T K

kH;CO2 ;W MPa

313.8 354.4 395.0

4.29 7.82 10.12

22.89 25.90 26.20

Table A2 Properties of water: Debye–Hückel parameter Af and saturation properties (vapour pressure psW , molar liquid volume V sW and fugacity coefficient ’sW ). T K

314 354 395

Aw

0.4034 0.4389 0.4880

psW kPa

7.62 49.8 210.6

V sW cm3 =mol 18.16 18.55 19.03

’sW

0.9994 0.9959 0.9836

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