J. Chem. SOC., Faraday Trans. 1 , 1982, 78, 2095-2100 Heats of Dilution of Aqueous Solutions of Sodium Tetraphenylboron at 25 OC BY THELMA M. HERRINGTON* AND ELSPETH L. MOLE Department of Chemistry, University of Reading, Reading RG6 2AD Received 8th June, 1981 The heats of dilution of aqueous solutions of sodium tetraphenylboron are determined at 25 "C. The microcalorimeter was first tested by determining the heat of dilution of sodium chloride. The temperature dependence of the solute-solute attraction, after subtracting the Debye-Hiickel contribution, was compared with that of other electrolytes and non-electrolytes. In studies of the physico-chemical behaviour of the tetraphenylborate ion, it has been found that very different behaviour is observed compared with other quaternary ions of similar size (e.g.Bu,N+, Ph,P+); these include enthalpies of transfer,' conductivity measurements2 and n.m.r. ~tudies.~ The apparent molar volumes of aqueous sodium tetraphenylboron solutions have been determined between 0 and 60 OC by Millero4 and also by Jolicoeur and Philip;5 the latter authors also found that the apparent molar heat capacity of sodium tetraphenylboron showed a marked temperature dependence compared with Ph,P+ and Bu,N+, which are only weakly temperature dependent. The observed temperature dependence, however, was less than that found earlier by Subramanian and Ahluwalia.6 The relative magnitudes of solute-solute and solute-solvent interactions have been studied for non-electrolytes using rigorous statistical mechanical theorie~.~ In dilute solution up to 0.1 mol kg-l, if the Debye-Huckel electrostatic contribution is subtracted from a thermodynamic parameter, e.g.In y, then the remainder is linear in the molality as it would be for a non-electrolyte. It was decided to determine the heats of dilution and to compare these data with our previous treatment of non-electrolytes. * EXPERIMENTAL MATERIALS The sodium tetraphenylboron was purified by the method of Skinner and FUOSS;~ finally it was recrystallized three times from conductivity water, dried and stored under argon. All solutions were prepared using once distilled but previously deionized water, which had a conductance of < 1 x S cm-l. Solutions were made up by weight and buoyancy corrections applied to give a precision of & 0.1 mg.T H E CALORIMETER The microcalorimeter and the method of operation have been described previously.8 The aqueous solution of sodium tetraphenylboron, NaBPh,, was contained in a sealed pipette and diluted with water in the outer vessel. The temperature rise was monitored by a thermistor a.c. bridge. Heat was evolved on dilution and compensated for by the cooling effect of frigistors. Once experience had been gained of the heat liberated on dilution, compensation was arranged so as to minimise cooling corrections. The heat of opening of the pipette valves was found to 20952096 HEATS OF DILUTION OF AQUEOUS SOLUTIONS be negligible. The accuracy of the calorimeter was tested by determining the enthalpies of dilution of sodium chloride solutions and comparing the results with those of Gulbransen and Robin~on.~ Unfortunately, the number of dilutions that could be performed with sodium tetraphenylboron was limited by its solubility.RESULTS The results of both the sodium chloride and the sodium tetraphenylboron dilutions were analysed by first subtracting the Debye-Huckel contributions. The molar enthalpy of dilution is equal to the difference in the apparent molar enthalpy of the solution on dilution from an initial molality, mI, to a final molality, mF. Thus if H , is the value of the heat function for a quantity of solution containing one mole of solute at a molality m, then (1) AH$' = HF , -HI , = A4H2 = A4L2 (2) d d T where Hm = -2RT2-[lny+(l -#)I for a 1 : 1 electrolyte.* Let us define a standard enthalpy function by As the solutions are dilute (0.1 mol kg-l), the Debye-HuckellO values for ySt and bst (4) are used, then In yst = - arni/(l+ mi) where and a = (2nNp,)4 (e2/411&k~)t. (9) From Sylvester and PitzeP C is 1.947 kJ mol-l.The experimental data for sodium chloride were compared with those obtained by Gulbransen and Robin~on.~ Their results in the form of A H 2 l - A H z were plotted against Am; this plot is linear up to Am = 0.1 mol kg-l, so that a smoothed value of AH$," could be obtained to compare with our own values. Our experimental results are compared with those of Gulbransen and Robinson in table 1; the agreement is satisfactory . The heat of dilution of sodium tetraphenylboron solutions is much greater than that of sodium chloride between the same two molalities; heat is evolved on dilution.The results for sodium tetraphenylboron are given in table 2, as also are values for A H 2 and AH$' -AH:. Let the activity coefficient of the solute in this molality range be represented by In y = In ySt + mm then, if the plot of (AHZl-AHg) against Am is a straight line, the slope is -RT2(8m/aT). For sodium chloride the value obtained for au/aT is 2.04 x mol-1 kg K-l. For sodium tetraphenylboron the plot is also a straight line * See Glossary of Symbols on p. 2099.T. M. H E R R I N G T O N AND E. L. MOLE 2097 TABLE HEATS OF DILUTION OF AQUEOUS SODIUM CHLORIDE SOLUTIONS AT 25 O C 0.099 82 0.004 62 272 270 10 0.100 25 0.005 37 262 252k 15 0.101 38 0.005 11 267 270 & 8.2 0.100 03 0.004 33 276 264+ 10 0.099 25 0.006 38 247 243 & 7.2 From ref. (9).TABLE 2.-HEATS OF DILUTION OF AQUEOUS SODIUM TETRAPHENYLBORON SOLUTIONS AT 25 OC ~~ -(AH$' - AH$) rn'/mol kg-l rnF/moi kg-' -AP;/J mol-' -AHE1/J mol-1 /J mol-l 0.024 76 0.001 26 200 1464&33 1264f33 0.025 20 0.001 27 209 1477Ifr 13 1268f 13 0.025 14 0.001 24 209 1515+25 1306 & 25 0.020 03 0.000 96 190 1188f25 998 k 25 0.001 10 203 1381 +25 11 78 + 25 0.023 046 _~ __ ~ ~ _ _ _ ____ ____ and hence aw/aT is -7.22 x lo-, mol-l kg K-I. An interpretation of ao/aTmay be found from the theory of dilute solutions of non-electrolytes. DISCUSSION From theoretical considerations12 the Gibbs energy of a solution of mole ratio of solute to solvent m may be written _ _ - - G / N l k T = ~ ~ / k T + ~ ~ ~ / k T - m + m l n r n + ~ A , , ~ 2 f ~ B , 2 , r n 3 + .. . (1 1) where the coefficients A,, etc. are functions of temperature and pressure only, then the apparent molar enthalpy is given by 4H, = H P - RT2[~(2A2,/L1T)pMIrn+~(c?B,2,/c?T),M~m2.. .I. 4H2 = H P +xrn + yrn2 -+ . . . . (12) (13) For sodium tetraphenylboron, let us denote the non-electrolyte contribution to the apparent molar enthalpy by 4HP, then as it was found, as discussed above, that AHp/Am (where Am = mF-rnl) was a constant over the range of molalities investi- gated, the apparent relative heat content of the solutions due to the non-electrolyte (14) contribution is given by 4Lp =xm and the partial relative molar enthalpies of solute, Lp, and of solvent, Lp, are given Lp = 2xm (15) Lp = -Xrn2M1. (16) For simplicity eqn (13) will be written in the form by2098 Then HEATS OF DILUTION OF AQUEOUS SOLUTIONS "P/J mol-1 = 5.335 x lo3 (m,/mol kg-l) LF/J mol-l = 10.67 x lo3 (rn,/mol kg-l) Lp/J mol-1 = - 96.11 (m,/mol kg-l),. (17) (18) (19) Now from eqn (1 1) for a 1 : 1 electrolyte 21nyo = A , , ~ + B , 2 2 ~ 2 + .. . . (20) Thus from eqn (10) and (20), co = A2,M1/2 and the value of (aA,,/aT), is obtained from the heats of dilution since According to the theory of McMillan and Mayer13 for a solution of a solute in a solvent, the osmotic pressure, ll, is given by I l / k T = n+Bz,n2+B,*,,n3+ . . . (23) (24) where n is the number density of the solute. From eqn (16) and (19) of Garrod and Herringtonl, A,,v; = 2B,*,0-2~p+kT~ where B,*,O = - b:,. From KelP4 the molar volume of water at 25 OC is 18.07 cm3 mol-1 and (au;/aT), is 4.56 x cm3 mol-1 K-l.The critical compilation of Bradley and Pitzer15 was used for the compressibility of water 1O1lh-/(N m-2)-1 = 51.5-0.343(t/'C)+ 3.63 x (t/°C)2. The value of (aA2,/i3T>, is given by the heats of dilution. From determination of the osmotic coefficient16 at 25 OC, co = - 1.84 kg mol-l. Millero4 has determined the apparent molar volumes of aqueous solutions of sodium tetraphenylboron in the temperature range 0-60 "C; his data give (av$+/aT), at 25 OC as 0.33 cm3 mol-1 K-l. These figures give for the temperature dependence of B&!' for sodium tetraphenylboron N(aB:,O/aT), = - 72.6 cm3 mol-1 K-l. at 25 OC B:; can be considered to be composed of an attractive and a repulsive contribution from the intermolecular forces, thus B:: = S+q5A (26) where S is the repulsive and q5* the attractive contribution.If a hard-sphere model is assumed then the temperature dependence of B,*,O is that of the attractive contri- bution. In table 3 values of N(8q5A/ii?T)p are compared with those for tetrabutyl- ammonium chloride, sodium chloride, hexamethylenetetramine, sucrose and urea. For tetrabutylammonium chloride aw/aTwas taken as - 8.10 x mol-1 kg K-l,17 (avF/aT), is 0.275 cm3 mol-1 K-l14 and w = -0.032 kg mo1-l.18 For sodium chloride our own data for heat of dilution were used for aco/aT; from ref. (19) (o is 0.29 kg mol-1 and (c?vp/aT), is 0.073 cm3 mol-1 K-1.20 The values for hexa- methylenetetramine, sucrose and urea were taken from ref. (8). It can be seen thatT.M. HERRINGTON AND E. L. MOLE 2099 TABLE 3.-TEMPERATURE DEPENDENCE OF THE ATTRACTIVE CONTRIBUTION TO THE SOLUTE-SOLUTE INTERACTION COEFFICIENT, THE SOLUTE-SOLUTE VIRIAL COEFFICIENT B,*,O AND SOLUTE-SOLVENT VIRIAL COEFFICIENT B:: sodium tetraphenylboron 72.6 - 1570 275 tetra bu t ylammonium chloride 7 . 8 6 262 293 sucrose 0.56 285 210 urea -0.51 1 43 sodium chloride - 2.20 307 16 hexame th ylene te tramine 1 . 5 8 338 110 the solute-solute attraction increases with temperature for sodium tetraphenylboron, tetrabutylammonium chloride, hexamethylenetetramine and sucrose, but decreases for sodium chloride and urea. In sucrose and urea, attractive forces between the molecules may include hydrogen bonding. It has been suggested4 that the large tetraphenylboron anions behave like the large tetraalkylammonium cations in the solute-solute interactions, but like the chloride ion in their solute-solvent interactions.From eqn (24) the solute-solute virial coefficients, Btt, can be calculated. The apparent molar volume of sodium tetraphen- ylboron at infinite dilution at 25 O C is 276.4 cm3 m ~ l - l , ~ for tetrabutylammonium chloride 294.3 cm3 mol-l 21 and for sodium chloride 16.6 cm3 mo1-1.20 Values for NB,*,o are given in table 3 for these salts and also for hexamethylenetetramine, sucrose and urea.8 Sodium tetraphenylboron alone has a large negative value. Solute-solvent interaction can be calculated from apparent molar volume data. (27) From eqn (69) Of ref' (12) byl = -,,?++TK. Values for NB:: (where BT: = -by1) are also given in table 3 for the above solutes.It can be seen that sodium tetraphenylboron and tetrabutylammonium chloride have very similar values for BTF, which, if we assume comparable hard-sphere molar volumes, implies similar solute-solvent interaction. GLOSSARY OF SYMBOLS Superscript denotes the non-electrolyte contribution to the thermodynamic state function X 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 partial molar enthalpy of solute at infinite dilution apparent molar enthalpy Boltzmann's constant partial relative molar enthalpy of solvent partial relative molar enthalpy of solute apparent relative molar enthalpy molar ratio of solute to solvent ( N 2 / N l ) molality of solute - bE2 - by12100 Ml N , N2 n N R S T Lf U Q Y Er n P W & K 4 4* Pl PZ co ' C HEATS OF DILUTION OF AQUEOUS SOLUTIONS molar mass of solvent in kg mol-l number density of solute Avogadro's constant number of molecules of solvent number of molecules of solute gas constant repulsive contribution to the configuration integral absolute temperature molecular volume of pure solvent partial molecular volume of solute at infinite dilution activity coefficient of solute on molality scale rationalized permittivity relative permittivity isothermal compressibility of water osmotic pressure density of water in kg per unit volume osmotic coefficient attractive contribution to the configuration integral chemical potential of solvent chemical potential of solute non-electrolyte interaction coefficient V.Krishnan and H. L. Friedman, J . Phys. Chem., 1971, 75, 3606. J. F. Skinner and R. M. Fuoss, J . Phys. Chem., 1964, 68, 1882. J. F. Coetzee and W. R. Sharpe. J . Phys. Chem., 1971, 75, 3141. F. J. Millero, J. Chem. Eng. Dam, 1970, 15, 562. C. Jolicoeur and P. R. Philip, J . Solution Chem., 1975, 4, 3. S. Subramanian and J. C. Ahluwalia, J . Phys. Chem., 1968, 72, 2525. T. M. Herrington and E. L. Mole, J . Chem. Soc., Furuday Trans. I , 1982, 78, 213. J. E. Garrod and T. M. Herrington, J . Chem. SOC., Faraduy Trans. I , 1981, 77, 2559. E. A. Gulbransen and A. L. Robinson, J . Am. Chem. SOC., 1934, 56, 2637. L. F. Sylvester and K. S. Pitzer, J . Phys. Chem., 1977, 81, 1822. J. E. Garrod and T. M. Herrington, J . Phys. Chem., 1969, 73, 1877. l 3 W. G. McMillan and J. E. Mayer, J. Chem. Phys., 1945, 13, 276. G . S. Kell and E. Whalley, Philos. Trans. R . Soc. London, Ser. A , 1965, 258, 565. D. J. Bradley and K. S. Pitzer, J . Phys. Chem., 1979, 83, 1599. lo P. Debye and E. Hiickel, Phys. Z . , 1923, 24, 185. l 6 T. M. Herrington and C. Taylor, to be published. l 7 S. Lindenbaum, J . Phys. Chem., 1966, 70, 814. l9 R. A. Robinson and R. H. Stokes, Electrolyte Solutions (Butterworths, London, 1959). 2o L. A. Dunn, Truns. Furuday Soc., 1968, 64, 2951. I * B. E. Conway, R. E. Verrall and J. E. Desnoyers, Trans. Faraday Soc., 1966, 62, 2739. S. Lindenbaum and G. E. Boyd, J. Phys. Chem., 1964, 68, 91 1. (PAPER 1 /9 19)