J . Chem. SOC., Faraday Trans. 1, 1982, 78, 3409-3415 Osmotic and Activity Coefficients of Aqueous Solutions of Sodium Tetraphenylboron at 0 and 25 O C BY THELMA M. HERRINGTON* AND CHRISTINE MARY TAYLOR Department of Chemistry, The University of Reading, Whiteknights, Reading RG6 2AD Received 1st April, 1982 The osmotic coefficient of the solvent and the activity coefficient of the solute for aqueous solutions of sodium tetraphenylboron have been determined at 0 and 25 OC. The solute-solute interaction left after subtracting the Debye-Huckel contribution for the electrostatic forces indicates ion pairing. The large tetraphenylborate ion shows singular behaviour in its physico-chemical properties compared with other quaternary ions of similar size (e.g. 44A~+, 44P+ and Bu4N+).Skinner and FUOSS~ found that the limiting conductances of B& and Am,BuN+ are nearly equal but that there is an unexplained difference in behaviour at dilutions less than infinite; the former ion has a positive coefficient in the conductance function while the latter has a negative one. The n.m.r. spectra of B4h in water of Coetze and Sharpe2 indicate specific solute-solvent effects; the chemical shift of the water hydroxy proton showed that the orientation of water molecules by B4; is very different from that of I$~As+ and 44P+. Krishnan and Friedman3 found that in both water and methanol the solvation enthalpy of 44A~+ is close to that of four benzene molecules, whereas the solvation enthalpy of B4; shows a large extra negative contribution. Jolicoeur and Philip4 found that the temperature dependence of the heat capacity of the tetraphenylborate ion was considerably greater than that of d4P+ and Bu4N+.However, Millero5 determined the apparent molar volumes of aqueous sodium tetraphenylboron solutions between 0 and 60 OC and found that the deviations of the apparent molar volumes from the limiting law were large and negative; this behaviour is similar to that of tetra-alkylammonium salts. There has long been speculation as to whether the unusual properties of the tetraphenylborate anion could be the result of ion pairing. Covington and Tait6 analysed their conductivity data at 25 OC in terms of two models, one of which indicated extensive ion pairing. However, further spectroscopic studies7 failed to confirm this.Millero5 has suggested that because of the similarities of the deviations of the apparent molar volumes of NaB4, and Bu4NBr aqueous solutions, similar types of ion-ion interactions are responsible in both systems. He points out that as it is usually considered that some type of cationsation interaction is responsible for the large negative deviations of the Bu4NX solutions, by analogy the negative deviations of the NaB4, solutions might be attributed to anion-anion interactions. This work is an attempt to explain why the large B4; anion confers similar behaviour to the large R4N+ cation for some physico-chemical properties but not others, and to what extent considerations of ion pairing are relevant. It was decided to obtain equilibrium thermodynamic data for aqueous solutions of sodium tetra- phenylboron at 0 and 25 OC and to analyse them in terms of an electrolyte plus a non-electrolyte contribution.Sodium tetraphenylboron is soluble up to 0.15 molal at 34093410 OSMOTIC A N D ACTIVITY COEFFICIENTS OF AQUEOUS NaB4, 25 OC. In these dilute solutions, if the Debye-Huckel electrostatic contribution is subtracted from In y, then the remainder is linear in the molality as for a non-electrolyte. The recent theory of Pitzer8 was also used to calculate the electrostatic contribution. The non-electrolyte contribution can then be analysed using rigorous statistical- mechanical t h e ~ r i e s . ~ EXPERIMENTAL FREEZING-POINT MEASUREMENTS The freezing-point depressions were measured with a model 3R osmometer (Advanced Instruments Inc.).The solution is supercooled and the formation of ice crystals initiated by a vibrating probe. Heat of fusion is liberated and the sample temperature rises to its freezing point. To obtain reproducible results, care must be taken to exclude dust, centre the thermistor probe and keep the temperature of the freezing bath constant. The freezing point could be read to 0.1 x K; at least ten readings were taken at each molality and the standard deviation varied from 0.2 to 0.5 at the highest molality. The instrument was calibrated with sodium chloride solutions over the same freezing-point range and the calibration was checked before and after each run. The overall accuracy in the freezing point depression of the sodium tetraphenylboron solutions is & lop4 K.VAPOUR-PRESSURE MEASUREMENTS If a drop of solution and a drop of solvent are suspended side-by-side in aconstant-temperature enclosure saturated with solvent vapour, a differential mass transfer occurs between the two drops and the vapour phase. This transfer cmses a temperature difference between the two drops which is proportional to the vapour-pressure lowering.1o. l1 The drops are formed on two thermistor beads mounted in opposite arms of a resistance bridge, so that the temperature difference is measured as a change in resistance. The calibration constant for the instrument was determined using sodium chloride solutions of known molality against water as a reference. For the sodium tetraphenylboron solutions a solution of sodium chloride of known molality and closely matching vapour pressure was used, so that only a small correction to an accurately known osmotic coefficient needs to be determined.MATERIALS The sodium tetraphenylboron (B.D.H. Ltd) was purified by the method of Skinner and FUOSS.~ All solutions were prepared using once distilled but previously deionized water; it had a conductance of 1 x lop6 Rpl cm-l. Solutions were made up by weight and buoyancy corrections applied to give a precision of kO.1 mg. RESULTS OSMOTIC COEFFICIENT AT 0°C The freezing-point apparatus was calibrated using aqueous sodium chloride solutions of accurately known molality. The freezing-point data of Scatchard and Prentiss12 were smoothed using Debye-Hiickel theory13 [eqn (Al) and (A3) of the Appendix]: these smoothed values of the osmotic coefficient were used for calibration (table 1).Values for the osmotic coefficient of aqueous sodium tetraphenylboron solutions were calculated at 0 O C using the equation 4 = 812 x 1.8606 m. These values for the osmotic coefficient were smoothed by both the Debye-Hiickel and Pitzer methods (see the Appendix) to give the smoothed values for the osmotic * A glossary of symbols is given in the Appendix.T. M. HERRINGTON AND C. M. TAYLOR 341 1 TABLE 1 .-SMOOTHED VALUES OF THE OSMOTIC COEFFICIENT FOR AQUEOUS SODIUM CHLORIDE SOLUTIONS AT 0 AND 25°C rnlmol kg-* 4 (0 "C) 4 (25 "C) 0.0100 0.0300 0.0500 0.0700 0.0900 0.1 100 0.1300 0.1500 0.969 0.952 0.944 0.938 0.935 0.932 0.930 0.929 0.968 0.95 1 0.943 0.938 0.935 0.932 0.93 1 0.930 TABLE 2.-sMOOTHED VALUES OF THE OSMOTIC COEFFICIENT OF THE SOLVENT AND ACTIVITY COEFFICIENT OF THE SOLUTE FOR AQUEOUS SOLUTIONS OF SODIUM TETRAPHENYLBORON AT 0 AND 25 O C 0 O C 25 "C m/mol kg-l In Y Y 4 In Y Y 0.0100 0.0300 0.0500 0.0700 0.0900 0.1100 0.1300 0.1500 0.975 0.967 0.967 0.969 0.974 0.979 0.985 0.992 -0.093 -0.136 -0.155 -0.164 -0.168 -0.168 -0.166 -0.161 0.912 0.873 0.856 0.848 0.845 0.845 0.847 0.851 0.918 - 0.228 0.796 0.888 - 0.306 0.736 0.862 -0.374 0.688 0.646 0.813 - 0.496 0.610 0.791 -0.550 0.577 0.769 - 0.603 0.547 0.836 - 0.437 coefficient of the solvent and the activity coefficient of the solute, y , recorded in table 2.(The smoothed values of 4 and y were the same by both methods to the number of figures given.) The values of cu found were cu(Debye-Huckel) = 1.03 kg mol-l and w(Pitzer) = 1.18 kg mol-l.OSMOTIC COEFFICIENTS AT 25 O C The Mechrolab 30 1 vapour-pressure osmometer was calibrated using the same sodium chloride solutions as for the freezing-point apparatus. The osmotic coefficients for aqueous sodium chloride solutions were required at molalities of < 0.15 mol kg-l: the activity coefficient of the solute is accurately known at these low molalities from electromotive-force measurements. The data of Brown and McInnes14 and of Longworth15 were smoothed using eqn (A 2) and (A 4) of the Appendix. The values of the osmotic coefficient used for calibration are given in table 1. The experimental values for the osmotic coefficient of aqueous sodium tetraphenyl- boron solutions were smoothed in the same manner as the results at 0 O C .Smoothed values of the osmotic coefficient of the solvent and the activity coefficient of the solute are given in table 2. It was found that co(Debye-Hiickel) = - 1.84 kg mol-l and w(Pitzer) = - 1.69 kg mol-l.3412 OSMOTIC AND ACTIVITY COEFFICIENTS OF AQUEOUS NaB4, DISCUSSION From theoretical considerations16 the Gibbs energy of a solution of mole ratio of solute to solvent r i may be written G / N l k T = ,u:/kT+rn,u~/kT-m+inln Eii+$A22m2+&22m3+ .... (2) According to the theory of McMillan and Mayer,17 for a solution of a solute in a solvent the osmotic pressure, n, is given by n/kT= n+B,*nn2+B,*,,n3+ . . . . ( 3 ) Hill1* has shown that the coefficients A,, etc. may be related to the coefficients I?,*, etc. For example (4) A,, V: = 2B:: - VF + by1 where B,*,O = - b:,, the solute-solute cluster integral.Now b:l, the solute-solvent cluster integral, is related to the partial molecular volume of solute at infinite dilution by16 For aqueous solutions of sodium tetraphenylboron let us denote the non-electrolyte contribution to the solute activity coefficient by In y*, then from eqn (2) in dilute by, = -@+kTu. ( 5 ) solution 2In y* = A , , i ~ + B , , , i ? i ~ f .... Thus from eqn (A 2) and (6) o = A,, M1/2, and from eqn (4) and ( 5 ) NB,*,O = A,, V,O/2+ V?-RTu/2. (7) Values for the solute-solute virial coefficient B,*,O were calculated from the values obtained for o. The critical compilation of Bradley and Pitzerlg was used for the compressibility of water. For water Vy is 18.02 cm3 mo1-1 at 0 OC and 18.07 cm3 mol-l at 25 OC.,O The apparent molar volume of sodium tetraphenylboron at O°C is 267.2 cm3 mol-l and at 25 O C 276.4 cm3 ~ 0 I - l .~ Values for NB,*,O are given in table 3 using both the Debye-Huckel and Pitzer values for o. Different values are obtained for the non-electrolyte contribution depending on which theory is used for the electrostatic forces. As the values are of the same order of magnitude only the Debye-Huckel method was used for comparison with other electrolytes. Data for aqueous solutions of sodium chloride and aqueous solutions of sucrose in table 3 are from ref. (9) and (21). The values for NB,*,O for sodium tetraphenylboron are very different from those of sucrose and sodium chloride; at 0 OC NB,*,O is large and positive and at 25 O C large and negative for sodium tetraphenylboron, whereas it is not markedly temperature dependent for either sucrose or sodium chloride.BZ: can be considered to be composed of an attractive and a repulsive contribution from the intermolecular forces, thus B,*,O = S+@* ( 8 ) where S is the repulsive and (DA the attractive contribution. If a hard-sphere model is assumed for the repulsive contribution, then the temperature dependence of B:: is that of the attractive. contribution. In table 3 values of N(a@*/aT),, obtained from heat-of-dilution datag for sodium tetraphenylboron are compared with those for sodium chloride and sucrose. If the repulsive contribution to NB,*,O is constant then the negative value at 25 OC implies that the attractive contribution increases markedly with increasing temperature, and this is supported by the large negative value forT.M. HERRINGTON AND C. M. TAYLOR 341 3 TABLE 3.-sOLUTE-SOLUTE VIRIAL COEFFICIENT B::, SOLUTE-SOLVENT VIRIAL COEFFICIENT B::, AND TEMPERATURE DEPENDENCE OF THE SOLUTE-SOLUTE INTERACTION COEFFICIENT NB,*,0/cm3 mol-l NB,*,O - N(i3DA/aT), NB,*p species T/K Debye-Hiickel Pitzer /cm3 mol-l /cm3 mol-l K-' /cm3 mol-l NaB4, NaB44 NaCl NaCP sucroseb sucrosea Bu,NCl B u N C 1 273.15 298.15 - 2 7 3 . 1 5 2 9 8 . 1 5 2 7 3 . 1 5 298.15 273.15 2 9 8 . 1 5 - - 266 1 3 0 0 1 4 5 0 1570 - 1420 72.51" 275 1 2 232 307 - 2.20 1 6 3 3 0 - 205 - - 28 5 0.56 2 1 0 - 287 262 7.86 2 9 3 - - - - - - - - - - - - - a Data from ref. (9); * Data from ref. (21). N(a@*/a T ) p .Thus on this model ion pairing in sodium tetraphenylboron solutions should be appreciable at 25 O C . The small negative value of N(a@*/aT), for sucrose is consistent with the slight decrease in NB,*,O with increasing temperature and shows that the attractive force between two sucrose molecules is not highly temperature dependent. From our analysis for sodium chloride w(0 "C) = 0.22 kg mol-1 and w(25 "C) = 0.29 kg mol-l: V p values for sodium chloride were taken from Dunn22 and the values for NB,*,O are given in table 3. The increase in NB,*,O with temperature for sodium chloride is consistent with the small positive value for N(&DA/dT),, indicating that the solute-solute attraction decreases with increasing temperature. It has been suggested5 that the behaviour of the apparent molar volume of sodium tetraphenylboron solutions indicates that this electrolyte behaves like the tetra- alkylammonium chlorides in its ion-ion interactions and like sodium chloride in its ion-water interactions.From eqn ( 5 ) values for the solute-solvent virial coefficient B;r,O = --byl can be calculated. Data are given for tetrabutylammonium chloride in table 3 . 9 3 23 Sodium tetraphenylboron and tetrabutylammonium chloride have similar values for NB,*P, which implies similar solute-solvent interaction, if we assume comparable hard-sphere molar volumes, but very different values for their solute-solute interactions. Sodium chloride has considerably smaller values for NBT,O consistent with a smaller hard-sphere repulsive force. For all three electrolytes the solute-solvent attractive forces decrease with increasing temperature.Friedman and co-w~rkers~~ have analysed the thermodynamic properties of aqueous solutions of tetra- alkylammonium halides using ion-pair correlation functions. The models that best fit the data show that + - ion pairing is of considerably greater importance than + + or - - ion pairing. However, all types of ion pairing contribute to thermodynamic and conductance data and our analysis makes no attempt to distinguish between them. CONCLUSION Analysis of the non-electrostatic interaction between solute molecules in aqueous solutions of sodium tetraphenylboron using the McMillan-Mayer interaction coeffi- cients for the solute-solute cluster integral indicates considerable ion pairing at 25 O C , decreasing rapidly with decreasing temperature.The trend of the osmotic-coefficient data obtained at 0 and 25 *C is in agreement with our measurements of the heat of3414 OSMOTIC AND ACTIVITY COEFFICIENTS OF AQUEOUS NaB4, dilution at 25 0C.9 In the same temperature range the solute-solvent interaction decreases slightly. The solute-solute behaviour of the large tetraphenylboron anion is quite different from that of the large tetrabutylammonium cation, whereas their solute-solvent interactions are similar. The similar negative deviations of the apparent molar volumes of NaB4, and Bu,NBr aqueous solutions come in fact from the non-electrolyte term linear in the molality and reflect the pressure derivative (i3A22/i3p)T. From eqn (4) and (5)’ A,, reflects both solute-solute and solute-solvent interaction : it seems plausible that the pressure dependence of the similar solute-solvent interaction dominates this term.There has been considerable speculation6* as to whether or not ion pairing occurs in sodium tetraphenylboron aqueous solutions at 25 OC. A recent coilductance study by Schiavo el al.25 concludes that ‘ion pairing’ is not negligible for sodium tetraphenylboron solutions at 25 OC. Ion-pairing constants have also been found for a range of other solvents. APPENDIX DATA SMOOTHING Standard values for the osmotic coefficient of solvent tjSt: and the activity coefficient of solute, ySt, are defined using electrolyte theory and the experimental values of the osmotic or activity coefficient are fitted to the equations tj-tjSt = om12 (A 1) (A 2) In y-ln ySt = om.Two expressions for the standard values were used. (a) Based on Debye-Huckel theory:I3 1 - @t = abP3 m-l[ 1 + bm: - (1 + bm;)-l- 2 In (1 + bmj)] In ySt = -am:( 1 +bm$)-l. (A 3) (A 4) At 0 OC, a = 1.132 kgi mol-a and at 25 OC, a = 1.173 kg’ mol-i; b = 1 .O kgi mol-4 (b) Based on the theory of Pitzer? 1 - qPt = A, mi( 1 + bm;)-’ In ySt = -A, mi( 1 + brni)-l - 2A, In (1 + bmi)/b (A 5 ) (A 6) where A , = a13 and b = 1.2 k& mol-4. G k iTi m MI n N GLOSSARY OF SYMBOLS Pitzer electrostatic parameter solute-solute virial coefficient (Bzf = - b;,) solute-solvent virial coefficient (B1*p = - byl) cluster integral for two molecules of solute in pure solvent cluster integral for one molecule of solute and one of solvent in pure solvent Gibbs energy Bol tzmann’s constant mole ratio of solute to solvent (N2/N1) molaiity of solute in mol kg-l molar mass of solvent in kg mol-1 number density of solute Avogadro’s constant number of molecules of solvent number of molecules of soluteT.M. HERRINGTON AND C. M. TAYLOR 3415 gas constant repulsive contribution to the cluster integral absolute temperature partial molecular volume of solvent molecular volume of pure solvent molar volume of pure solvent partial molecular volume of solute at infinite dilution partial molar volume of solute at infinite dilution De bye-Hiickel electrostatic parameter activity coefficient of solute on the molality scale non-electrolyte contribution to the solute activity coefficient osmotic pressure osmotic coefficient attractive contribution to the configuration integral isothermal compressibility of solvent molecular chemical potential of pure solvent molecular chemical potential of the solute at infinite dilution non-electrolyte solute-solute interaction parameter freezing point depression J.F. Skinner and R. M. Fuoss, J. Phys. Chem., 1964, 68, 1882. * J. F. Coetze and W. R. Sharpe, J . Phys. Chem., 1971, 75, 3141. C. V. Krishnan and H. L. Friedman, J. Phys. Chem., 1971, 75, 3606. C. Jolicoeur and P. R. Philip, J. 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A, 1965, 258, 565. 22 L. A. Dunn, Trans. Faraday SOC., 1968, 64, 2951. 23 W-Y. Wen, in Structure and Transport Processes in Water and Aqueous Solutions, ed. R. A. Horne 24 P. S. Ramanathan, C. V. Krishnan and H. L. Friedman, J . Solution Chem., 1972, 1 , 237. 25 S. Schiavo, R. M. Fuoss and G. Marrosu, J. Solution Chem., 1980, 9, 563. L. G. Longsworth, J. Am. Chem. SOC., 1932, 54, 2741. T. M. Herrington and C. P. Meunier, J. Chem. SOC., Furaday Trans. 1, 1982, 78, 225. (Wiley, New York, 1970), chap. 15. (PAPER 2/557)