Journal of Molecular Liquids 177 (2013) 7–10Contents lists available at SciVerse ScienceDirect Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq Prediction of salting-out and salting-in constants Yizhak Marcus Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel a r t i c l e i n f o Article history: Received 10 June 2012 Accepted 14 September 2012 Available online 26 September 2012 Keywords: Setchenow constants Salting-out Salting in Ionic values Organic solutes a b s t r a c t An expression is established to predict the Setchenow salting constants of solid and liquid organic compounds from aqueous solutions by electrolytes. It employs the conventional standard partial molar volumes and the intrinsic molar volumes of the ions. It also uses properties for the non-electrolytes that are foreign to their aqueous solution behavior: their molar volumes and either the Kamlet/Taft polarity/polarizability indexes or the Hildebrand solubility parameters. The expression is tested on data not included in the correlations used to establish it. © 2012 Elsevier B.V. All rights reserved. 1. Introduction The solubility of non-electrolytes in aqueous salts solutions is of importance in several fields of chemistry, such as marine chemistry, recovery of synthesis products from aqueous solutions, and petroleum production. The observed quantities are generally correlated by means of the Setchenow equation [1]: logðsN0 =sN Þ ¼ kN;E cE ð1Þ Here sN0 and sN are the molar solubilities of the non-electrolyte (subscript N) in pure water and in a cE molar solution of the electrolyte (subscript E), and kN,E is the salting constant (the Setchenow constant). The latter is generally positive (for salting-out), but in certain cases it is negative (for salting-in). Eq. (1) is generally valid up to cE of the aqueous electrolyte of several mol L −1. It is of interest to be able to predict the value of kN,E for an arbitrary non-electrolyte and an arbitrary electrolyte from independent properties of these substances. Ni and Yalkowsky [2] did indeed propose a predictive expression for one electrolyte, namely sodium chloride, which is the main salt constituent of sea water. They applied it to Setchenow constants of 101 non-electrolytes at ambient temperatures with the expression: kN;E ¼ 0:114 þ 0:040logK Now ð2Þ Here logKNow is the logarithm of the distribution constant of the non-electrolyte between 1-octanol and water. The adjusted correla2 = 0.7717 and the standard error of tion coefficient squared is radj the fit is σfit = 0.041. The values correlated by this expression were E-mail address:
[email protected]. 0167-7322/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.molliq.2012.09.007 mostly gleaned from the review by Xie et al. [3] (for 20–25 °C) but included also data from other annotated sources. It should be noted, however, that the kN,E values for a given non-electrolyte and a given electrolyte in these sources have a considerable spread between those reported by various authors. This is seen, e.g., for the values reported for toluene and aqueous sodium chloride, ranging from 0.195 to 0.270 [3], from among which 0.210 was selected as representative. An even worse case is naphthalene salted out from aqueous sodium chloride, where the spread of the reported kN,E is from 0.213 to 0.620. No expression has so far been proposed to predict the salting properties of organic compounds by electrolytes other than sodium chloride. However, in the case of gaseous substances (subscript G) such predictions were proposed by Weisenberger and Schumpe [4] by means of the empirical expression: h kG;E ¼ ΣI ν I kG;I þ kG;25 þ hG t= CÞ–25 ð3Þ The index I pertains to the individual ions of the salting-out electrolyte E (including mixed electrolytes), kG,I is an ion specific parameter that is relatively independent of the temperature, and kG,25 and hG are gas specific parameters. Weisenberger and Schumpe reported conventional numerical values for the kG,I for many ions on the basis that kG,I(H +) conv = 0, shown in Table 1. In spite of the successful correlation by Eq. (2) for the salting of solid and liquid organic compounds by sodium chloride, a reservation may be made that it employs quantities, logKNow, already representative of the solution behavior of the non-electrolytes in water. Thus, it is not completely independent of the salting behavior it is supposed to predict. [3] reported the kPhH. rc [20] VI∞ conv [8] VIintr ΔVI kPhH. The expressions for these lines are as follows: kPhH.E ¼ 0:046–0:0065ΔV E kPhMe. Its operative quantity is the difference ΔVI between the conventional standard partial molar volume of the ion.9 −10.0 −22.3 6.084 0.2 −12.181 0.8 Y. (5) and (7).114 0. was used. the data being rather uncertain. though for the tetraalkylammonium bromides only qualitatively.5 −0.064 0. kPhMe. conv According to the additivity principle kPhH.207 0.1 −22.077 0.I could then be + conv established on the basis that kPhH.063 0.E ¼ 0:057–0:0087ΔV E n ¼ 30 2 radj ¼ 0:9635 σ fit ¼ 0:044 ð5Þ 2 n ¼ 27 r adj ¼ 0:9490 σ fit ¼ 0:048 ð6Þ kNphth.4 20.220 0.6 0.092 0.057 0. only Fig. 1.6 −10.004 0.213 0.027 0. again taking into account the voids in the hydration shell.056 0.169 0.2 −7.3 17. The salting-in of benzene and naphthalene by HClO4. The latter were calculated by the expression suggested by Mukerjee [9]: VIintr = 2522(1.100 0.230 26. shown in Table 1. the ionic radius.063 0. Of the several theoretical expressions relating the Setchenow constants to the properties of the ions.174 0.011 −0. VI∞ conv (based on VI∞ conv(H +) = 0).I [4] 0.370 −0.E values (PhH stands for benzene) at 25 °C for a large number of electrolytes.3 4.195 0.2 36.149 0. and CH3CO2−.9 34.102 0. (5) well. Plots of kN.6 13.379 0.585 0.138 0.4 275.E = ΣI νIkPhH.151 0. Me4NBr.004 0. it stands to reason that whatever is established for sodium chloride should be valid also for other electrolytes.054 0.9 24.5 −1.I calc Eq. For the poorly hydrated large ions. For the well hydrated SO42− anion the values suggested by Glueckauf [10].I expt [3.7 11.6 kG. VIintr.8 30.246 −0.054 0.E values (PhMe stands for toluene) tested for additivity from among the reported values that have considerable spreads.170 0. and Et4NBr noted by Xie et al.032 0. The plot of kPhH.240 0.075 I− SCN− NO3− ClO3− ClO4− HCO2− MeCO2− SO42− 0. ClO3−.075 0. Prediction of the salting properties of liquid and solid organic compounds The ionic kN.9 −18.019 −0.9 −1.3 −2.196 −0.2 17. and this should hold. such results quoted by them could be ascribed to the choice of the kPhMe.6] kPhH.9 4.I(H ) = 0.337 0. ΔVI is shown in Fig.002 0. However.075 0. Marcus / Journal of Molecular Liquids 177 (2013) 7–10 Table 1 Properties of ions and the Setchenow constants for the salting of benzene and of gases at 25 °C.E ¼ 0:008–0:0098ΔV E 2 n ¼ 25 r adj ¼ 0:9098 σ fit ¼ 0:071 ð7Þ 0.E.005 0. CsSCN. Conventional ionic salting constants for benzene (filled circles) and the difference between the experimental and calculated ones (from Eq.2 52. also for other solutes for which extensive data for various electrolytes are available.061 0.065 0. NO3−.5 −0.E.I .7 44. This expression takes care of the voids between the water molecules in the hydration shell of the ions and is appropriate for the monatomic ions but was also applied to NH4+. indeed the case for kPhH.009 0.092 0. (4). Conventional ionic values kPhH.6 149.1 214. the present treatment found the internal pressure/electrostriction approach of McDevit and Long [7] to be the most appropriate in a qualitative sense.0 55.9 89. 3.1 21. The resulting ionic values are shown in Table 1.373 −0.176 0.213rI) 3.112 The two tasks that were undertaken in the present study were to establish an expression to predict the salting properties of solid and liquid organic compounds by electrolytes other than sodium chloride and one that employs only data for the non-electrolyte foreign to its aqueous solution properties. assuming that no need for recognition of the voids exists.1 26.5 −1.072 0.5 9.E should be additive with regard to the ions.077 0.4 96. ΔVE = ΣI νIΔVI should produce straight lines.568 0.200 0.0 14. 2.2 61. [3] is corroborated by Eqs.0 26.021 −0.2 −5.I being additive for the three aromatic hydrocarbons tested.139 −0.3 −47. [6].8 10.103 0.143 0.E (Nphth stands for naphthalene).020 −0.0 0.004 0.7 −6.1 50. (1) is a proportionality with respect to the concentration of the electrolyte.6 77.183 −0.413 0.E vs.145 0.084 0.301 Ion + − 5. the polyatomic The fits become worse on going from benzene to toluene to naphthalene as do the qualities of the data (larger spreads in reported values) but the fits are still well acceptable.2 34.100 0. Therefore.076 0.135 0.7 −21. as well as for Cs + and I − the bare intrinsic volumes were used: VIintr = 2522rI3.8 24.I vs.2 35.7 26.148 0.6 1.7 1. where 2522 = (NA4π/3) for rI.232 0.018 0. For the tetraalkylammonium ions corresponding values are available from Desnoyers et al.2 −17.3 158.133 0. These values of VIintr as well as the conv resulting ΔVI values are shown in Table 1.049 SCN −. (8) nm cm3/mol cm3/mol cm3/mol L/mol L/mol L/mol Li Na+ K+ Rb+ Cs+ NH4+ Me4N+ Et4N+ Pr4N+ Bu4N+ Mg2+ Ca2+ Sr2+ Ba2+ F− Cl− Br− 0.9795 and a with an adjusted correlation constant squared radj standard error of the fit σfit = 0.5 23.8 8.9 −24. in nm and the resulting volume in cm 3 mol −1. The former values were taken from Millero [8]. The more accurate data for benzene salting-in by tetraalkylammonium bromides of Desnoyers et al.I conv ¼ ð0:045 0:006Þ–ð0:00538 0:00016ÞΔV I ð4Þ 2 = 0.013 0.024 −0.026 for n = 24 ions.5 137.069 0.3 10.217 0. also shown in Table 1.2 9. therefore.4 13.041 −0. and ClO4−. . HCO2−. empty triangles) plotted against the difference between the conventional ionic standard molar volume and the ionic intrinsic volume. Therefore.189 0.2 32. [5] concerning ionic non-additivity for the salting out of toluene.1 9.238 −0.7 −21.5 4.2 40. This is contrary to the assertion by Poulson et al.204 0. and its intrinsic volume. 1 to be expressed well by the straight line: kPhH. as is.3 12. [6] confirm the predictions by Eq.013 0.0 5.136 0.087 0. hence should be valid at infinite dilution.0 4.5 14.280 0.113 0. Xie et al.166 0.016 0.006 0.106 0. kN. LiSCN. and kNphth.163 0.167 0. including hydrochloric and conv perchloric acids. Prediction of the salting properties of electrolytes Eq.310 0.1 117.9 34. The following expression was derived: kN. The reversed ratio may be tentatively used to obtain approximate kG. the intrinsic molar volume of the ion. 2. say.5]. 4. it is only right that this should also be employed for the organic compound dependence. calculated from the group contributions. for which no data were shown in [4]. A combination of Eqs. As an alternative. Discussion A relationship exists between the ionic salting constants for liquid and solid organic compounds listed in Table 1 and the corresponding constants for gases reported by Weisenberger and Schumpe [4] for monatomic ions and ammonium. the LeBas volume. might be employed. the lower is their tendency to be salted-out for similar molar volumes. The following expression is derived: kN. Li+ and Mg2+.NaCl expt in Fig. are less well established. the Gibbs energies of hydration as might have been supposed. Other sets of volume data besides the LeBas volumes VLB. and the Kamlet– Taft polarity/polarizability index. or (12) would be achieved thereby. These are approximately proportional to the VLB values. perchlorate. The ratio kPhH.Epred ¼ 0:10–10 Fig.I values for the first members of the alkali metal and alkaline earth metal cations. However. (10) and (11) are the amino acids (glycine. The values of kN. VIintr.05. The values of kN. Marcus / Journal of Molecular Liquids 177 (2013) 7–10 the extensive data available [2. (with ΔVI = VI∞ conv − VIintr). VLB.I values for the tetraalkylammonium cations.g. (10) represent the experimental values to approximately the same accuracy as Eq. VLB [11].NaCl calc ¼ −0:030 þ 0:983kN.12± 0. are employed. KNow. VLB and δH. be rescued if another characteristic quantity of the compounds is additionally used.05 of these expressions. nitrate. δH). but as stated in the introduction. (2). The expression: kN.04 to ±0. One such approach. The Kamlet–Taft polarity/polarizability index π* [12. (4) and (10)) now permits the prediction of the salting properties of any arbitrary liquid and solid organic compound by any arbitrary electrolyte (or mixture of electrolytes) in terms of four independently known (or estimatable) quantities: the ionic conventional standard partial molar volume.NaCl expt − kN. (8) represent the experimental values to approximately the same accuracy as Eq. tyrosine. . 2 as are the difference values kN. It is noteworthy that both the kPhH. of the organic compounds may be employed instead of the π* parameters. Ni and Yalkowski [2] showed that this does not work well for the 101 compounds tested by them when the LeBas molar volumes. however. Notable outliers from Eqs. (4) and (8) (or of Eqs. This approach states that the Setchenow constant should be proportional to the molar volume of the organic compound. leucine. is sought here. are independent from the properties of the compounds in aqueous solutions. Calculated salting constants for organic solutes (filled circles) by sodium chloride and the difference between the experimental and calculated ones (empty triangles) plotted against the experimental salting constants.I and kG. the Hildebrand solubility parameters.NaCl calc ¼ −0:011 þ 1:050kN. the large alkali metal and halide ions (Cs+ and I −) do not conform to this relationship. and it is not expected that a significant improvement in the predictive value of Eqs.I could be derived for the lack of salting-out data. VLB and π*. The predictive expression using π* is: kN. It is noted that the higher the polarity of the compounds.NaCl calc are plotted against kN. (8).NaCl values were available. the two variables.NaCl calc for 64 compounds (not all of which are the same as those in Fig. Other values for the polarity or other quantities describing possible interactions of the organic compounds (e. (10). involving the octanol/water partition coefficients. However. Many of the δH values have been compiled [14].NaCl calc. namely ± 0. (2). This is due to the spread of the reported values commented on above.NaClcalc ¼ 0:01 þ ð0:0022 0:0001ÞV LB –ð0:16 0:01Þπ ð8Þ The two independent variables. are independent from the properties of the compounds in aqueous solutions. that is commensurate with the σfit = ±0. an expression independent from the properties of these compounds in water. VI∞ conv. others may be obtained from the vaporization enthalpies and molar volumes [15] or be computed from group contributions [16].3] for this salt need to be examined regarding the properties of the organic compounds to be salted-out (or -in). and it is known for 65 from among the compounds for which kN. are smaller than the subsequent members of the series and no direct relation exists of the salting constants with. also shown in Table 1. and sulfate.Y.I was reported [4] but no kPhH. The internal pressure/electrostriction approach of McDevit and Long [7] having been invoked for the electrolyte dependence.22 may be applied to the transition metal ions for which kG. (4) and (8). such as the experimental molar volumes at ambient temperatures (these are sensitive to differences among isomers). commensurate with the uncertainty of the data [3. such as thiocyanate. the Dimroth–Redichardt ETN or the Kamlet–Taft EPD/ HBA property β) are not available for as many compounds or have a similar effect on the salting properties as the π* or δH employed here. nor do so polyatomic anions.13] comes into mind in this connection. 2) are related to the experimental values by: kN. inherent in the values of KNow. Most of the solubility parameters are available for liquids. of these compounds was proposed by Ni and Yalkowski [2]. including those in mixed electrolytes) with stoichiometric coefficients νI.NaCl expt n ¼ 64 2 r adj ¼ 0:7625 ð11Þ σ fit ¼ 0:040 showing that the values calculated according to Eq.I = 1. those of solid organic compounds.NaCl calc ¼ 0:22 þ ð0:0022 0:0001ÞV LB –ð0:0155 0:001ÞδH ð10Þ Again. 9 –4 conv 0:94V LB –68π ΣI vI ΔV I ð12Þ The summation extends over all the ionic species (cations and anions. The principle involved can. The claimed mean uncertainty is somewhat larger than the standard errors of the fits in Eqs. and cysteine [2]) and long chain alkanes (dodecane and higher ones [3]). π* (or the Hildebrand solubility parameter.NaCl expt n ¼ 65 2 r adj ¼ 0:7467 ð9Þ σ fit ¼ 0:038 shows that the values calculated according to Eq.I/kG. δH. 20)ΣI vI cm3 mol−1 from 25 to 40 °C. Krishnan. Mackay. B 113 (2009) 10285. Xie. Joliceuour.22.20]. Lee. Deno.A.-L. are available for ambient temperatures in several compilations (e. N. others in an earlier paper by Masterton and Lee [24]. 1984. and the Kamlet–Taft polarity/polarizability index. N-methylacetamide. Desnoyers. the values of LeBas volume. 2) sodium nitrate. J. T.W.3] that were used for establishment of this expression but also for prediction of values not thus used.05 and +0. involving the properties of these substances that are independent (for the organic compounds) from their behavior in aqueous solutions. Shiu. Fedors. The Properties of Gases and Liquids. 1997. [8.T. The δH parameter for substances for which it had not been reported can be estimated according to prescriptions and group contributions provided by Fedors [16]. and N-methylpropanamide was reported by Krishnan and Friedman [18]. Y. Canadian Journal of Chemistry 43 (1965) 3232.E values (transformed from natural logarithms in [18] to decadic ones as in Eq. The π* index for substances for which it had not been reported can be estimated according to prescriptions in Ref. On the other hand. ether.A. but see additions and corrections to Ref. A. (12). since ΣI vIΔVIconv increases only by (0. . These kN. Journal of Solution Chemistry 3 (1974) 727. values of ΔVI may thus be estimated for a range of temperatures for applying Eq. The latter shows that none of the approaches tested: the McDevit and Long internal pressure/ electrostriction one [7] (examined by Deno and Spink [17] too). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] Fig.V. benzene. (12)) salting constants of chloroform (circles). HN. Millero.J. J.06± 0.M. hydrogencarbonate. M. have not been obtained for other than ambient conditions. VIintr. Chemical Reviews 75 (1975) 731. Bockris. McDevit.L. [12].F. Zeitschrift für Physikalische Chemie 4 (1889) 117. Marcus. 8) magnesium chloride.P. shown for 10 representative salts in Fig. CRC. however. Poulson. chlorobenzene (downward triangles) and anisole (squares) by: 1) ammonium nitrate. their molar masses divided by their densities (for the liquid ones and the undercooled molten solid ones). D. Journal of Physical Chemistry 67 (1963) 1347. Abboud.M. Kamlet. Journal of the American Chemical Society 74 (1952) 1773. chlorobenzene. Y. Boca Raton.L.23] and since the intrinsic volumes of the ions. these could then be employed for a range of temperatures. benzene (upright triangles).E 0/HN. 6) potassium chloride. R.C. are not expected to be appreciably temperature dependent.I. Talanta 48 (1999) 633. Poling. (12). π* [12. Y. McGraw-Hill. 82nd ed. Notario. This is accomplished by Eq. 9) ammonium sulfate. and 28 electrolytes.. International Journal of Pharmaceutics 254 (2003) 167.H. 5) lithium chloride.M. Friedman. These were obtained from the Henry's law coefficients. A review of the theoretical approaches to the salting-out and ‐in is not intended here.E to be measured accurately. Weisenberger. Marcus.40± 0. (8) is established in terms of the experimental molar volumes of the non-electrolytes. H. A set of Setchenow constants was reported more recently by Görgényi et al. B. It is noted that the increased temperature has little effect on the success of the predictions. C.E.13]. one [25] that modified an earlier electrostatic theory. J. R. Bowler-Reed. Masterton. Doherty. Differences between experimental and calculated (Eq. Marcus. Ch. J.E.10 Y. (12) within the uncertainties of the reported data and applied not only to correlations of the data in the databases [2. Journal of Physical Chemistry 98 (1994) 5807.05 as before. aldehydes and ketones) was reported by Deno and Spink [17].03 units (L mol−1). Laurence. VI∞ conv. J. C. Schumpe. If an expression such as Eq. Nicolet. Long. Handbook of Chemistry and Physics. Y. W. M. N. P.F. Lide. It should be noted. R. Yalkowsky. and iodide and the non-electrolytes methanol. Polymer Engineering and Science 14 (1974) 147. F. 1-propanol. It is the purpose of this paper to present a predictive expression for the Setchenow constants for arbitrary electrolytes and non-electrolytes.E. (2001/2). K. that the reported data [19] show unexplained reversals between the values for the sodium and potassium salts. VLB [11].J. Journal of Physical Chemistry 65 (1961) 740. M.F. (12) represented their kN. Journal of Physical Chemistry 74 (1970) 1776. none of the organic solutes being included in the correlations based on the data in [2.H. 4) ammonium chloride.. G. Marcus. H.E. and 10) potassium sulfate. Prausnitz. O'M. Harrington. New York. Marcus / Journal of Molecular Liquids 177 (2013) 7–10 A set of 16 Setchenow constants involving ammonium sulfate and oxygenated aliphatic compounds (alkanols. Dalati.-Y. 7) sodium chloride. J. Dewulf. Chemical Reviews 71 (1971) 147. The Journal of Physical Chemistry. M. the higher temperature being necessary because of the need for sufficient volatility of the organic compounds in order for HN. Y. Journal of Physical Chemistry B 116 (2012) 7232. The dashed lines are the 95% confidence limits of the values. ethanol.E = log(HN. Ni. Representation by Eq. hydrogen-phosphate. Marcus. Spink. (12) yielded calculated values differing from the experimental ones by −0.E expt − kN. Chemical Reviews 111 (2011) 2761. S. J. R. D. 3. S. (1)) within the limits of ±0. Drever. Transactions of the Faraday Society 47 (1951) 184. Abraham. and the scaled particle theory applied by Masterton and Lee [24] were significantly more successful in describing quantitatively the Setchenow constants for benzene by alkali metal halides than the present empirical correlation. Reis. Values at other temperatures are also available [8. Journal of Physical Chemistry 92 (1988) 5244. bromide. [8] in Ref. J.3]. New York. Setchenow. and dihydrogenphosphate salts [19] could not be predicted because no reasonable values for the intrinsic volumes of these anions could be estimated. Another set of 15 Setchenow constants involving sodium chloride. J. The predictive Eq. R. at 40 °C.M. Görgényi. [19] for four organic compounds: chloroform. 3rd ed. Ion Properties. [21]). AICHE Journal 42 (1996) 298. covering practically all the ions relevant to the salting behavior.10 as expected from the uncertainty reported above for Eq. Taft.E)/cE values are compared with the corresponding ones predicted from Eq. [3]. W. and anisole. (12). Glueckauf. Van Langenhove. These differences for 38 of the cases are within the range −0.R.E pred. Dekker. Mukerjee.-H. R.C. W. Chemosphere 65 (2006) 802. 3) potassium nitrate. Barton. Transactions of the Faraday Society 61 (1965) 914. W. Marine Environmental Research 44 (1997) 429. Refs.g. C. the Bockris et al. F. Pelletier. P. E. S.H.R. Héberger. ed. Values for the carbonate.. Conventional standard partial molar volumes of ions. some of these approaches are listed in the review by Xie et al. mainly for the carbonate and dihydrogenphosphate salts that ought not to occur when true proportionality of log(HN0/HN) to cE down to infinite dilution took place. A. Kitchenert. 3 as the differences kN.