J. Chem. SOC., Faraday Trans. 1, 1982, 78, 2479-2481 Partial Molar Volumes, Partial Molar Expansibilities and Viscosity of Benzene Solutions of Tri-n-octylammonium Halides BY SPELA PALJK AND CVETO KLOFUTAR* J. Stefan Institute, E. Kardelj University of Ljubljana, 61000 Ljubljana, Yugoslavia Received 13th October, 198 1 The densities of benzene solutions of tri-n-octylammonium chloride, tri-n-octylammonium bromide and tri-n-octylammonium iodide up to 0.25 mol kg-' at 293.15, 298.15, 303.15, 313.15 and 323.15 K were measured. The partial molar volumes and partial molar expansibilities of the solutes were found to be independent of concentration, and the partial molar expansibilities were found to be equal for all the solutes investigated. For these systems viscosity measurements were also made and the viscosity coefficients B and D determined.In addition, the relative viscosity was interpreted on the basis of the theory of rate processes and regular solution theory, and thermodynamic functions of activation for viscous flow and the solubility parameters of the solutes investigated were calculated at 298.15 K. The conductance of a system which contains solute molecules as hydrogen-bonded ion pairs of relatively high dipole moment dissolved in a non-polar solvent suggests that even at highest dilution the dissociation of ion pairs to free ions and the formation of triplet ions can be negligible, and that the non-ideal behaviour of the system can be attributed to interactions among the solute molecules and, to a lesser extent, among the solute-solvent pairs.In the case of an aprotic solvent of low permittivity, the solvent effects may be considered ~nimportant.l-~ The aim of this work was to determine some volumetric and transport properties in such a system where ion pairs, due to the dipole-dipole interactions, undergo intensive aggregation processes, while the solvent effects are ignored. With this in mind the benzene solutions of tri-n-octylammonium halides were investigated at 293.15-323.15 K. The partial molar volumes and partial molar expansibilities of solutes and solvent, respectively, and the viscosity of these solutions were determined. The relative viscosity was interpreted on the basis of the viscosity coefficients B and D, and by rate process t h e ~ r y ~ ' ~ and regular solution The limiting values of thermodynamic functions of activation for viscous flow and the solubility parameters of the solutes were also calculated.In addition, the effects of the size of the halide ion and also the effects of aggregation of the investigated solutes on the values obtained are discussed. EXPERIMENTAL Tri-n-octylammonium chloride (TOAHCI), tri-n-octylammonium bromide (TOAHBr) and tri-n-octylammonium iodide (TOAHI) and their benzene solutions were prepared as in ref. (9) and (10). The densities of the investigated solutions at a definite temperature were determined as in ref. (1 1). 24792480 BENZENE SOLUTIONS OF TRI-n-OCTYLAMMONIUM HALIDES The viscosities of these solutions were determined with a Cannon-Fenske viscometer. The absolute viscosity values were calculated by means of the equationI2 where ql, is the absolute viscosity of the solution (kg rn-' s-,), d l , is the density of the solution (kg dm-9, t is the flow time(s) and C and E are constants characteristic of the viscometer.The viscometer constants C = 1.6061 x (& 5 x 10-lo) m2 s - ~ and E = 0.805 f0.069 m2 were determined by a least-squares fit to eqn (1) of the literature data for the absolute viscosity13 and densityI4 of water at the respective temperature. The temperature of the water bath was maintained to k0.05 K. RESULTS AND DISCUSSION The density determinations were made over the concentration range 0.0 1-0.25 mol kg-' at temperatures from 293.15 to 323.15 K. The density of the investigated solutions dl, is given by dl,2 = dl+ac (2) where dl is the density of the solvent (kg dm-3), c is the concentration of the solution (mol dm-3) and a is a constant characteristic of the solute and the temperature.The values of constant a of eqn (2) for the solutions investigated and the density of benzene at the temperatures studied are given in table 1. The values of dl obtained at 293.15, 298.15 and 303.15 K are close to values given in the literature.'* TABLE VALUES OF COEFFICIENT a OF EQN (2) AND THE DENSITY OF BENZENE, d,, IN THE TEMPERATURE RANGE FROM 293.15 TO 323.15 K T / K 293.15 298.15 303.15 313.15 323.15 ~~ ~ ~~ ~~ a/ kg mol-l solute TOAHCl 0.0035 f 0.0002 0.0053 f 0.0002 0.0057 k O.oOo3 0.0085 0.0002 0.01 10 & 0.0003 TOAHBr 0.041 5 f 0.0005 0.0432 & 0.0003 0.0444 k 0.0007 0.0475 & 0.0006 0.0500 f 0.0009 TOAHI 0.0850 & 0.0007 0.0856 f 0.0005 0.0869 If: 0.0007 0.0896 f 0.0008 0.0922 f 0.0007 solvent benzene 0.8796+_0.0001 0.8740+0.0001 0.8679 +_0.0001 0.8564f 0.0002 0.8448 k 0.0001 dJkg dmP3 The values of the coefficient of expansibility of the solutions investigated, al, 2, were calculated from15 a', = a, + bc where a, = -(6dl/6T)p/d, is the coefficient of expansibility of the solvent and b = - (&/a T)/d, is a constant.The coefficient of expansibility of benzene at 298.15 K, calculated from the density data for benzene given in table 1, is 0.001 33 +O.OOOOl K-l. In ref. (14) the value of a, for benzene in the temperature interval from 273.15 to 353.15 K is 0.001 38 K-l. The derivative aa/aTfor all solutions studied was found to be independent of the anion of the solute and is 0.00026_+0.00002 kg mol-l K-l.The apparent molar volume, q4G, for the solutes investigated is given by (4) 1 - dl 4V - - (M2-a)s. PALJK AND C. KLOFUTAR 248 1 where M , is the molecular weight of the solute (kg mol-l). From eqn (4) it follows that the apparent molar volume is independent of concentration and equal to the partial molar volume of the solute, c. At 298.15 K the following values of the apparent molar volume were obtained (dm3 mol-l) : 0,440 & 0.0002 (TOAHCl), 0.4478 +0.0004 (TOAHBr) and 0.4531 +0.0006 (TOAHI). The value of for TOAHCl is close to the value given in ref. (1 1). The apparent molar expansibility, 4E2, for the solutes investigated is given by15 By combining eqn (3) and (9, the apparent molar expansibility is expressed by the equation 4E2 = b+a, &.(6) From eqn (6) it is evident that the apparent molar expansibility is independent of the concentration and thus equal to the partial molar expansibility of the solute, g2. Furthermore, the values of the apparent molar expansibility for the solutes investigated are, within experimental error, equal and are 2.96 x dm3 mol-1 K-l at 298.15 K. The viscosity determinations were made in the same concentration and temperature ranges as the density measurements. The experimental data were analysed according to16 (7) qr=-= l+Bm+Dm2 (_+ 5 x V l , 2 71 where vr is the relative viscosity, v ~ , ~ is the absolute viscosity of the solution, ql is the absolute viscosity of the solvent and m is the concentration of the solutions (mol kg-l).Eqn (7) is valid for the concentration dependence of the relative viscosity of non-electrolytes. The viscosity coefficient B may be given by B = r n - 0 lim igr-lmDm2 In terms of the volume fraction, 42 = m c dl, eqn (7) can be given in the form The parameters B and D are characteristic for a given solute-solvent pair and include the solute-solvent and solute-solute interactions, respectively. The values of coefficients B and D, given in table 2 with the relevant errors, were obtained as the intercepts and slopes of the lines of plots (vr- l)/m against rn by the method of least squares. The values of the viscosity coefficients B and D for TOAHCl at 298.15 K are, within experimental error, equal to those determined previously.ll As can be seen from table 2, the coefficient B shows a slight dependence on the anion of the solute and the temperature.The temperature dependence of coefficient B is linear and nearly equal for the solutes investigated; the average value of dB/dT = 0.0043 f0.0004 kg mol-1 K-l. The positive value of dB/dTmay be due to changes of conformation structure of the alkyl chains in the alkylammonium ion. On the other hand, the coefficient D shows pronounced dependence on the nature of the anion of the solute, as well as on the temperature. The values of viscosity2482 BENZENE SOLUTIONS OF TRI-n-OCTYLAMMONIUM HALIDES TABLE 2.-vALUES OF COEFFICIENTS B AND D OF EQN (7) FOR THE INVESTIGATED TERTIARY n-OCTYLAMMONIUM HALIDES IN BENZENE SOLUTIONS AND THE ABSOLUTE VISCOSITY OF BENZENE, ql, IN THE TEMPERATURE RANGE FROM 293.15 TO 323.15 K T / K 293.15 298.15 303.15 B/kg mol-l D/kg2 moP2 B/kg mol-l D/kg2 mo1-2 B/kg mol-l D/kg2 mo1-2 solute TOAHCl 0.8940.01 1.56f0.07 0.91 f0.02 1.29f0.07 0.93f0.01 1.04f0.08 TOAHBr 0.95 2 0.05 3.08 f 0.20 0.97 f 0.04 2.73 f 0.12 1 .OO f 0.10 2.40 f 0.15 TOAHI 1.00f0.03 5.56f0.19 1.02f0.03 4.93fO.11 1.05f0.06 4.36f0.25 solvent kg m-l s-l benzene 0.647 f 0.001 0.599 f 0.002 0.558 f 0.002 313.15 323.15 B/kg mol-l D/kg2 mo1-2 B/kg mol-l D/kg2 mo1-2 T/K solute TOAHCl 0.98 0.02 0.52 & 0.10 1 .OO f 0.02 0.24 f 0.09 TOAHBr 1.04f0.09 1.60f0.30 1.09+0.10 0.80f0.30 TOAHI 1.09 4 0.05 3.16 f 0.30 1.13 f 0.06 1.96f 0.35 ql/ 1 0-3 kg m-l s-l solvent benzene 0.489 f 0.002 0.434 f 0.002 coefficient D of the investigated solutes at a definite temperature increase in the same order as their ability to form higher aggregates.The temperature dependence of coefficient D is linear, specific for each solute and negative: dD/dT (kg2 moF2 K-l) = - 0.045 & 0.002 (TOAHCI), - 0.076 0.005 (TOAHBr) and In fig. 1, the concentration dependence of the relative viscosity of benzene solutions of TOAHCl, TOAHBr and TOAHI at 298.15 K is shown. The concentration dependence of the relative viscosity of benzene solutions of TOAHI at the temperatures studied is shown in fig. 2. In fig. 1 and 2 the curves were drawn on the basis of eqn (7), using the coefficients B and D at definite temperatures from table 2. The values of the viscosity increment, u = B/r2dl, of the investigated solutes at 293.15 K are: 2.30 (TOAHCI), 2.42 (TOAHBr) and 2.52 (TOAHI).The viscosity increment u increases with increasing temperature; the average value of du/dT is 0.014 K-l for all the solutes investigated. From the values of the viscosity increment it may be assumed that the solute particles behave as spheres in a continuum.17 The values of the viscosity increment D/rEdy increase with increasing size of the anion and at 293.15 K are 10.43 (TOAHCl), 19.93 (TOAHBr) and 35.35 (TOAHI). Their temperature dependences are: d(D/ pi d:)/dT (K-l) = - 0.343 f0.002 (TOAHCI), - 0.49 & 0.01 (TOAHBr) and - 0.744 _+ 0.006 (TOAHI). Considering the theory of rate processes applied to viscous flow, the relative viscosity of a solution is given by5 - 0.120 & 0.005 (TOAHI). rr = - exp [(AG:, - AG,*)/RT] (2)s.PALJK AND C. KLOFUTAR 2483 1.500 1.400 1.300 77r 1.200 1.1 00 1.000 0.050 0.100 0.150 0.200 rnlmol kg-' FIG. 1 .-Concentration dependence of qr of benzene solutions of TOAHCl (O), TOAHBr (0) and TOAHI (A) at 298.15 K. where K, is the average molar volume and AG:, is the change of the average Gibbs free energy of activation for viscous flow of the solution, is the molar volume of the solvent, AG,* is the change of the Gibbs free energy of activation for viscous flow of the solvent, R is the gas constant and T is the absolute temperature. For dilute solutions eqn (7) can be give- as In v,. = Bm + Dm2. (1 1) Combining eqn (10) and (1 1), the following relation can be written6 where subscript 0 indicates the values at infinite dilution of the solute. on solute concentration, Since for the investigated systems the molar volume of solution is linearly dependent K , 2 = v;+(G- Q X , (13) where X2 is the mole fraction of the solute, the partial molar volume of solvent, c, is identical to its molar volume, = Ml/dl, where M, is the molecular weight of solvent (kg mol-I), and the partial molar volume of solute, <, is independent of =2484 BENZENE SOLUTIONS OF TRI-n-OCTYLAMMONIUM HALIDES 1.600 1.500 1.400 Qr 1.300 1.200 1.100 1.000 I I I I 1 u.u3u U.IUU u.13u U.LUU U.L3U rnlmol kg-' FIG.2.-Concentration dependence of qr of benzene solutions of TOAHI at 293.15 (O), 298.15 (A), 303.15 (O), 313.15 (0) and 323.15 K (m). concentration and equal to its volume at infinite dilution, i.e. for dilute solutions the approximation Xz = mM, can be made.= c, o. Furthermore, So, the first term of eqn (12) may be replaced by and the term (AG?, - AGr)o by W?, 2 - m > o = mM1 (A&, 0 - AP?,o) (15) where ApZo is the change of the partial molar Gibbs free energy of activation for viscous flow of the component i at infinite dilution. From eqn (14) and (15) it is seen that the first two terms on the right-hand side of eqn (12) are linearly dependent on molality. Therefore, these terms can be identified with the Bm term of eqn (12), relating only to the solute-solvent interactions, while the Dm2 term, related mainly to the solute-solute interactions, can be identified with f (m>* Consequently, the relation for the viscosity coefficient B can be given bys.PALJK AND C. KLOFUTAR 2485 Eqn (16) shows that the viscosity coefficient B also includes, besides the partial molar volumes, the contributions of changes of partial molar Gibbs free energy of activation for viscous flow of solvent and solute. TABLE 3.-vALUES OF Ap:, AT 293.15-323.15 K AND AS:, AND AR, AT 298.15 K FOR THE SOLUTES INVESTIGATED IN BENZENE SOLUTIONS ______~ ~~ T / K 293.15 298.15 303.15 313.15 323.15 298.15 298.15 A%, 0 A R , 0 solute Ap:, 0/104 J rnol-l /J rnol-1 K-' / lo4 J rno1-I - 3.7 TOAHCl 4.7 4.8 4.9 5.2 5.4 - TOAHBr 4.9 5.0 5.2 5.4 5.7 -285f5 - 3.5 - 3.3 TOAHI 5.1 5.2 5.3 5.6 5.9 - From the known values of the viscosity coefficient B, the partial molar volumes of solute and solvent at infinite dilution, the density of the pure solvent and the change of partial molar Gibbs free energy of activation for viscous flow of solvent, the change of partial molar Gibbs free energy of activation for viscous flow of the solute, Ap:, o, can be calculated.The values of Ap:, for the investigated solutes in the temperature range studied, together with the partial molar entropy, As:,,, and partial molar enthalpy, AP:, o, of activation for viscous flow at 298.15 K are given in table 3. The value of AG;" = Apl, of 9397 & 16 J mol-I was calculated from the relation 271 = w*/ G ) exp (AG;"/RT) (17) where h is Planck's constant and NA is the Avogadro constant, using the values of the density and absolute viscosity of benzene at the temperatures studied from tables 1 and 2. As can be seen from table 3, the partial molar entropy of activation for viscous flow of the solutes investigated, s:,o, calculated via was found to be negative and independent of the anion of the salt.The values of the partial molar enthalpy of activation for viscous flow of the investigated solutes, A@, o, were calculated from the Gibbs-Helmholtz relation As can be seen from table 3, the Ap:, values for all of the solutes studied are positive and show an increase with increasing size of the anion of the salt and with temperature. The Ap:, values are nearly five times greater than that of the pure solvent, indicating the formation of a less favourable transition state in the presence of solute.6 The AH:, values at 298.15 K are negative and increase with the size of the anion. by Through eqn (1 6) the temperature dependence of the viscosity coefficient B is given (20) dB M - dT = - ( E 2 , 0 - '1,o) ' 1 + ' 1 (E, 0 - <) -1 (ARz, 0 - AH;", 0) R T 22486 BENZENE SOLUTIONS OF TRI-n-OCTYLAMMONIUM HALIDES where El,, is the partial molar expansibility and AR,, is the partial molar enthalpy of activation for viscous flow of solvent at infinite dilution.From eqn (20) it is obvious that dB/dTdepends on three terms, i.e. the differences of partial molar expansibilities, the partial molar volumes and the partial molar enthalpies of activation for viscous flow of solute and solvent at infinite dilution. However, the contributions of the first and second terms of this equation are negligible compared with the third term and lie within the experimental error of dB/dT.Taking the ratio of the change of molar energy of vaporization, AEV, to the change of Gibbs free energy of activation for viscous flow as constant for solution or solvent, i.e. AEV/AG* 2 2.5,5 and the change of molar energy of vaporization of the solution, AE;,,,7 as AEY,2 = X1AEY+X2AE:-AEM (21) where AEM is the change in the energy of mixing of both components and for regular solutions given by (22) AEM = Wl K + x2 vz) (61 - 621, 41 #2 where & is the molar volume of the solute and 6, the solubility parameters of solvent and solute, are8 6, = (AEY/E)h and 6, = (AE,V/K)i, then the relative viscosity of solution is given byl8 On the basis of eqn (23) the solubility parameters for the investigated solutes in benzene solutions at 298.15 K were calculated by the method of least squares.The obtained values are: 6, (Ji dmd) = 0.57 (0.5818) (TOAHCI), 0.60 (TOAHBr) and 0.65 (TOAHI). From the above results we conclude that the nature of the anion affects neither the viscosity coefficient B nor the respective partial molar thermodynamic quantities at infinite dilution (e.g. & , o , p:,,, AS:,,, A@,,) of the solutes investigated. Since the partial molar volumes of solutes are independent of concentration, it may therefore be anticipated that the partial molar volume of i-meric species is i times the partial molar volume of the monomer. From the viscosity increment u it may be assumed that the molecules of the solutes investigated behave as spheres in a continuum. Furthermore, it was shown that the aggregation of similar ion pairs depends mainly on their dipole moments.', 4 r la Thereby, the effects of aggregation are visible in the viscosity coefficient D.Thus, the aggregation of solute molecules, and consequently the values of viscosity coefficient D, increase with increasing dipole moment of the simple ion pairs and decrease with increasing temperature. From the values of the solubility parameters of solutes, which are close to the value of the solubility parameter of the pure ~olvent,~ it follows that the investigated solutes are highly soluble in benzene. We thank Mrs J. Burger for her skilful technical assistance. We also thank the Slovene Research Community for financial support. C. A. Kraus, J. Phys. Chem., 1956, 60, 129. C. Klofutar, 5. Paljk and M. Zumer, J. Chem. SOC., Perkin Trans. 2, 1978, 292. C. Klofutar and s. Paljk, J. Chem. SOC., Faraday Trans. 1, 1979, 75, 825. C. Klofutar and 5. Paljk, J. Chem. SOC., Faraday Trans. I , 1981, 77, 2705.5. PALJK AND C. KLOFUTAR 2487 S. Glastone, K. J. Laidler and H. Eyring, The Theory of Rate Processes (McGraw-Hill, New York, 1941), p. 477. D. Feakins, D. J. Freemantle and K. G. Lawrence, J. Chem. Soc., Faraday Trans. 1, 1974, 70, 795. J. H. Hildebrand, J. M. Prausnitz and R. L. Scott, Regular and Related Solutions (Van Nostrand Reinhold, New York, 1970), pp. 8, 82 and 213. C. 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