Electrolyte Viscosities in Sulfolane References a n d Notes (1) H. S. Frank and M. W. Evans, J. Chem. Phys., 13,507 (1945). (2) W. Kauzmann, Adv. Protein Chem., 14, 1 (1959). (3) M. A. Rougvie and R. S. Bear, J. Am. Leather Chem. Assoc., 48, 735 (1953). (4) G. N. Ramachandran and R. S. Chandrasekharan, Biopolymers, 6, 1649 (1968). (5)A. Yonath and W. Traub, J. Mol. Biol., 43, 461 (1969). (6) H. J. C. Berendsen, J. Chem. Phys., 36, 3297 (1962). (7) R. E. Dehl and C. A. J. Hoeve, J. Chem. Phys., 50, 3245 (1969). (8) G. E. Chapman and K. A. McLauchlan, Proc. R. Soc. London, Ser. 6, 173, 223 (1969). (9) G. E. Chapman, S. S. Danyluk, and K. A. McLauchlan, Proc. R. Soc. London, Ser. 6, 178, 465 (1971). (IO) B. M. Fung and P. Trautmann, Biopolymers, 10, 391 (1971). (11) B. M. Fung and M. M. Slegel, Biochem. Biophys. Acta, 278, 185 (1972). (12) B. M. Fung and S. C. Wei, Biopolymers, 12, 1053 (1973). (13) C. Migchelsen and H. J. C. Berendsen, J. Chem. Phys., 59, 296 (1973). (14) C. A. J. Hoeve and P. C. Lue, Biopolymers, 13, 1661 (1974). (15) D. Eisenberg and W. Kauzmann, "The Structure and Properties of
749
(16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30)
Water", Oxford University Press, New York, N.Y., 1969, Chapter 3. D. Eisenberg and W. Kauzmann, ref 15, Chapter 4. H. S. Frank and W. Y. Wen, Discuss. Faraday Soc., 24, 133 (1957). G. Nemethy and H. A. Scheraga, J. Chem. Phys., 38, 3382 (1962). G. E. Walrafen, "Water, A Comprehensive Treatise", Vol. 1, F. Franks, Ed., Plenum Press, New York, N.Y., 1972, Chapter 5. M. Falk and 0. Knop, "Water. A Comprehensive Treatise". Vol. 2, F. Franks, Ed., Plenum Press, New York, N.Y., 1973, Chapter 2. J. A. Pople, Proc. R. Soc. London, Ser. A, 205, 163 (1951). D. W. Davison, ref 20, Chapter 3. Y. S. Touioukian and E. H. Buyco, "Specific Heat, Nonmetalllc Solids, Thermophysical Properties of Matter", Vol. 5, IFVPlenum, New York, N.Y., 1970. I. Yannas, J. Macromol. Sci. Rev. Macromol. Chem., C 7, 49 (1972). A. R. Haly and J. W. Snaith, Biopolymers, 10, 1681 (1971). W. F. Harrington and P. H. von Hippel, Adv. Protein Chem., 16, 1 (196 1). A. Rich and F. H. C. Crick, J. Mol. Biol., 3, 483 (1961). H. Susi, J. S. Ard, and R. J. Carroll, Biopolymers, I O , 1597 (1971). J. M. Cassel, Biopolymers, 4, 989 (1966). J. M. Cassel and R. G. Christensen, Biopolymers, 5,431 (1967).
Electrolyte Viscosities in Sulfolane at 30, 40, and 50
O C
Antonio Sacco,* Giuseppe Petrella, and Maurizio Castagnolo lnstltute of Physical Chemistry, University of Bari, 70 126 Bari, ltaly Revised Manuscript Received December 1, 1975)
(Received May 28, 1975;
Publication costs assisted by the University of Bari
Viscosities of iAmsBuNBPh4, iAmsBuN1, NaBPh4, Bu4NC104, Bu4N1, BudNBr, Bu4NC1, LiC104, NaC104, KC104, RbC104, and CsC104 in sulfolane were determined at 30,40, and 50 "C. Data were analyzed by the Jones-Dole equation. The B coefficients obtained were separated in the ionic contributions B*, assuming that B ~ A ~ ~ =BBBph4~ N += & A ~ ~ B ~ N The B ~ B* ~ ~ values / ~ . were discussed in terms of Einstein's equation. This analysis shows that cations are solvated, as opposed to all anions and iAmsBuN+ and Bu4N+. Some comments are made on the temperature dependence of the B* coefficients.
Introduction Study of the transport properties of electrolytic solutions gives very useful information about ion-solvent interactions. One method employed for these investigations is to study the solution viscosity. Most viscometric measurements have been carried out on aqueous systems, whereas not much data on ions in nonaqueous solvents are available in the literature. In the present paper the viscosities of solutions of several electrolytes in sulfolane at 30, 40, and 50 "C are reported. Sulfolane is a dipolar aprotic solvent of high dipole moment and intermediate dielectric constant ( p = 4.8 D and t = 43.3 a t 30 "C). In recent years much interest has been shown in this solvent, which possesses many useful properties for electrochemical studies. Particularly conductometric datal have shown the existence of specific ion-solvent interactions. Viscosimetric measurements were performed in order to obtain more information about these effects. Experimental Section Materials. Commercial sulfolane (Shell Co.) was purified as described by Desbarres, Pichet, and Benoit2 and
then distilled three times over sodium hydroxide pellets under reduced pressure mmHg). Water content in the final product, detected by the Karl Fisher method, was less thed 0.007 wt %. Sulfolane densities and viscosities at 30, 40, and 50 "C are 1.26227, 1.25346, 1.24464 g/cm3 and 0.1029,0.07946,0.06304 P, respectively. The same values at 30 "C are reported by Fernandez-Prini and Prue.la Triisoamylbutylammonium tetraphenylboride (TABBPh4) was prepared and purified following the method suggested by Coplan and Fuoss3 (mp 275 "C). Sodium tetraphenylboride (NaBPh4) (Fluka puriss. p.a.) was recrystallized three times from acetone and then dried in vacuo at 80 "C for 3 days. Triisoamylbutylammonium iodide (TABI) was obtained and purified by the method described by Coplan and Fuoss3 (mp 119 "C). Tetrabutylammonium perchlorate (C. Erba R.S.) was purified by recrystallization from ether-acetone mixtures, followed by drying in vacuo for 48 h at room temperature (mp 213 "C). Tetrabutylammonium iodide (C. Erba R.S.) was dissolved in a minimum amount of acetone and then ether was added. The resulting crystals were removed by filtration. The Journal of Physical Chemistry, Vol. 80, No. 7, 1976
750
A.
This procedure was repeated three times and the salt was dried a t 90 "C under reduced pressure. Tetrabutylammonium bromide (C. Erba R.S.) was recrystallized three times from ethyl acetate and dried in vacuo a t 56 "C (mp 118 OC). Tetrabutylammonium chloride (K&K Laboratory) was recrystallized from acetone by the addition of ether. All manipulations of this salt owing to its extreme hygroscopic nature were carried out in a drybox through which dry nitrogen was passing. Lithium perchlorate (Fluka purum), sodium and potassium perchlorates (Fisher Laboratory Chemicals), and rubidium and caesium perchlorates (K & K Laboratory) were recrystallized several times from water-methanol mixtures (1:l) and dried at 150 "C in a vacuum oven for 4 days. A stock solution for each salt was prepared by weight and working solutions in the concentration range 0.01 < M < 0.08 were obtained by weight dilution. All weights were corrected to vacuum. Apparatus. An Ubbelohde suspended bulb level viscometer (Jena Glaswerk Schott Gen-Mainz) was used for all measurements. Two photocells (Hewlett-Packard Co.) were attached to the viscometer approximately a t the etched lines. The viscometer and lamp photocell assemblies were coupled by a Hewlett-Packard Auto-Viscometer, Model 5901B, which provided automatic influxing in preparation for the efflux measurements and digital display of efflux time in milliseconds. The measurements were made in a viscometric water thermostat (Herzog-Berlin); the control was within f0.01 "C and the temperature monitored by a NBS certified platinum resistance thermometer in conjunction with a G2 Mueller Bridge (L & N Co.). Viscometer calibration was made with aqueous solutions of sucrosd (Fisher certified ACS) a t 15, 20, and 25 "C using viscosity and density values reported in l i t e r a t ~ r e . ~ Kinematic viscosities (cSt) were converted to absolute viscosities (cP) using density values obtained by a DMA 02C densimeter manufactured by Anton Paar K.G.;6 reproducibility was found to be f l X g/ml. The densities p of working solutions were obtained from p
= po
+ 9m
where m is the concentration in moles per kilogram of solution, po is the solvent density, and t9 is an empirical constant determined by density measurements on the most concentrated solution studied for each salt.
Results The viscosities were calculated from L
= Kt -(1) t where q is the absolute viscosity, p is the density, t the flow time, and K and L are characteristic viscometer constants. The values of K and L , obtained by calibration, were 0.03004 cSt/s and 0.64 cSt s, respectively. Molar concentrations c and the values of (q/qo - l)/&, where q/qo is the relative viscosity of solution, are listed in Tables I, 11, and 1116for each salt at 30, 40, and 50 "C, respectively. For TABBPh4 and NaBPh4, a t all temperatures are included data for two runs performed using different samples of solvent and salt. q/p
The Journal of Physical Chemistry. Vol. 80, No. 7,1976
Sacco, G. Petrella, and M. Castagnolo
Experimental data were analyzed by Jones-Dole equation? (q/qo -
I)/& = A
+ B&
(2)
where A and B are characteristic parameters for the solvent and the electrolyte. The viscosity A coefficient depends on ion-ion interactions and can be calculated if limiting ionic equivalent conductances and solvent physical properties are known.8 Theoretical A coefficients calculated a t 30 "C by conductometric datalb+ are reported in Table IV for all salts studied. Viscosity B coefficient is an experimental constant related to ion-solvent interactions. Experimental values of (q/qo - l)/& were plotted against &, as shown in Figures 1 and 2 a t 30 "C. As may be seen, the points show linear trends for all salts, except for TABBPh4, NaBPh4, NaC104, BudNBr, and Bu4NI a t c 0.07 M. These points, which show positive deviations from linearity, were excluded in all calculations. By the least-squares method negative A values were calculated as intercept of the (q/qo - l)/& vs. & plots, and this result is without physical significance. The same behavior was observed by Kay and co-workers in waterg and by Yao and Bennion in DMSO.1° According to the Yao and Bennion treatment, B coefficients were calculated as slopes of the straight lines, obtained by the least-squares method, with intercept forced close to theoretical A values. Theoretical A values at 40 and 50 OC cannot be calculated because conductometric data a t those temperatures are lacking. So, supposing that A coefficients have a weak temperature dependence as observed for many so1vents,10-12 the values calculated a t 30 "C were used at 40 and 50 O C . Viscosity B coefficients are summarized in Table IV together with their standard deyiations. Ionic B+ coefficients were obtained as suggested by Krumgal'z13 assuming BTAB+= BBph4- = B(TABBPh4)/2. The hydrodynamic equivalence in sulfolane at 30 OC of TAB+ and BPh4- i s also shown by the same mobilities found by Zipple on the basis of the transference numbers of Della Monica and co-workers.lb The ionic B+ coefficients at 30, 40, and 50 OC are reported in Table v.
-
Discussion As may be seen in Figures 1 and 2 the Jones-Dole equation holds good in sulfolane in the range of concentrations investigated, with the exceptions of TABBPh4, NaBPh4, NaC104, BucNBr, and Bu4NI at c 0.07 M. The internal consistency of our data can be shown by the good agreement between the B value obtained experimentally for TAB1 a t 30, 40, and 50 OC (0.99, 0.89, and 0.80, respectively) and that obtained on adding ionic B+ coefficients of TAB+ and I- derived from the sequence TABBPh4, NaBPh4, NaC104, Bu4NC104, and Bu4NI (0.99, 0.89, and 0.79 at 30,40, and 50 "C, respectively). Viscosity coefficients for cations and for BPh4- are all positive and very high. On the contrary the other anions show very low B- values; particularly C1- at 30 O C , and C104- a t all temperatures, show small negative B- values. Ionic B* viscosity coefficients can be analyzed on the basis of Einstein's equation14 4~ Rrt3N B+ = 2.5-(3) 3 1000
-
-
where R+ is the radius of the ion assumed as a rigid sphere, N is Avogadro's number, and 2.5 is the shape factor for a
75 1
Electrolyte Viscosities in Sulfolane Table I V Theoretical A Coefficients at 30 "C and E Coefficients in Sulfolane at 30,40, and 50 "C Salt TABBPh4 NaBPh4 NaC104 Bu4NC104 Bu~NI Bu4NBr Bu4NCl
1.90 f 0.01" 2.25 f 0.03n 1.13 f 0.01 0.72 f 0.01 0.83 f 0.01 0.85 f 0.01 0.78 f 0.02 0.99 f 0.02 1.00 f 0.02 1.04 f 0.01 0.97 f 0.01 0.84 f 0.01
TABI LiC104 KC104 RbC104 csc104 a
B40 'C
B30 "C
1.68 f O.Ola 2.01 f 0.03n 1.12 f 0.01 0.64 f 0.01 0.74 f 0.01 0.75 f 0.02 0.69 f 0.02 0.89 f 0.02 0.95 f 0.02 0.98 f 0.01 0.90 f 0.01 0.80 f 0.01
1.90 f 0.02b 2.24 f 0.04b
A3'
B50 "C 1.50 f O.Ola 1.84 f 0.03n 1.05 f 0.01 0.57 f 0.01 0.65 f 0.01 0.69 f 0.01 0.63 f 0.02 0.80 f 0.02 0.93 f 0.01 0.93 f 0.01 0.86 f 0.01 0.75 f 0.01
1.68 f O.Olb 2.01 f 0.03b
'theor
0.0177 0.0112 0.0135 0.0181 0.0183 0.0188 0.0189 0.0213 0,0109 0.0118 0.0114 0.0111
1.50 f 0.01* 1.83 f 0.02b
*
Run a. Run b.
0
'
/'
o TABBPh,
I-1
I
I
I
0
Bu~NCIO, 0
LICIO,
o NaCIO, a KCIO,
o NaBPh,
BTABI Bu,N I Bu,NBr A Bu,NCI
1
1
0.1
c1/2
0.2
1
I
0.3
- I)/& vs. & for TABBPh4, NaBPh4, TABI, Bu4NI, Bu4NBr, and Bu4NCl in sulfolane at 30 O C .
Figure 1. (qlqo
sphere. By eq 3 R+ values at 30, 40, and 50 O C were calculated and are shown in Table V together with crystallographic radii, rc, and corrected Stokes radii at 30 O C , rcor, obtained by conductometric data. As can be seen in Table V, R+ values a t 30 "C for TAB+, BPhd-, and Bu4N+ are in reasonable agreement with the corrected Stokes and crystallographic radii. This result indicates that these ions are scarcely solvated in sulfolane and behave as spherical entities. On the contrary R+ values for Li+, Na+, K+, Rb+, and Cs+ are higher than crystallographic radii. This may be interpreted assuming that these ions are solvated in sulfolane by ion-dipole interactions. The observed order of B+ coefficients, Na+ > K+ > Li+ > Rb+ > Cs+, with the exception of Li+, shows that the obstruction to the solvent viscous flow increases with increase of the ion charge density and hence with the increase of the size of the hydrodynamic entity by solvation. Similar results have been obtained by conductometric measurements which show that Na+ ions have the higher solvation number ( h = 2) with respect to the other alkali cations.lC I t is interesting to observe that the behavior of Li+ appears anomalous also by conductometric data. In fact the order of Xo+s products, Li+ > Cs+ > Rb+ > K+ >
0.1
c1/2
0.2
0.3
Figure 2. (s/qo - I)/& vs. 6 for Bu4NC104, LiC104, NaC104, KC104,RbC104, and CsC104 in sulfolane at 30 O C .
Na+, shows that Li+, in spite of its higher charge density, has the highest mobility. However, it must be noted that Einstein's radii are much greater than the relevant corrected Stokes radii. This difference may be ascribed to the fact that the solvated cations lose their spherical size, so the shape factor higher than 2.5 should be inserted in Einstein's e q ~ a t i 0 n . l ~ Let us now consider the viscosity behavior of the anions. I- and Br- give a very small increase of the solvent viscosity. The B- value nearly equal to zero for C1- indicates that this ion does not affect the viscosimetric flow of sulfolane. The negative B- value for clod- in a scarcely associated solvent such as sulfolane is surprising, keeping in mind that negative B+ values were found only in solvents highly associated by hydrogen bonds.16 Analysis of B - values for these anions on the basis of Einstein's equation is not satisfactory because this equation is not valid for negative B+ values and in the range of low B* coefficients little changes in B+ give great changes in derived R* values. For example, in the case of I-, if we take for B- the values 0.03 instead of 0.04, the calculated ionic radius changes from 1.7 to 1.9 8. The Journal of Physical Chemistry, Vol. 80, No. 7, 1976
752
A. Sacco, G. Petrella, and M. Castagnolo
Table V: B* Ionic Coefficients and Ionic Radii ( R * )Calculated by Einstein's Equation at 30,40, and 50 "C;Crystallographic ( r c ) and Corrected Stokes Radii (reor) at 30 "C (&, r,, and reorin Angstroms)
TAB+ BPh4-
clodIBr-
c1-
Li+ Na+
K+ Rb+
cs+ Bu4N+
0.95 0.95 -0.07 0.04 0.06 -0.01 1.07 1.30 1.11 1.04 0.91 0.79
0.84 0.84 -0.05 0.05 0.06 0.00 1.00 1.17 1.03 0.95 0.85 0.69
0.75 0.75 -0.04 0.04 0.08 0.02 0.97 1.09 0.97 0.90 0.79 0.61
5.32 5.32
5.11 5.11
4.92 4.92
1.9 2.1
2.0 2.1
5.54 5.91 5.61 5.49 5.25 5.01
5.41 5.71 5.47 5.32 5.13 4.78
1.9 2.3 1.5 5.36 5.57 5.36 5.23 5.01 4.59
4.94 4.94 2.40 2.16 1.95 1.81 0.60 0.95 1.33 1.48 1.69 4.94
5.23 5.23 2.64 2.47 2.06 1.98 3.74 4.23 3.92 3.85 3.78 4.94
References I Ca n d 10. References ICa n d le.
I t is, however, interesting to observe that B- values calculated by eq 3 using corrected Stokes radii are: Bel- = 0.05; B B ~ =- 0.06; BI- = 0.10; Bc104- = 0.12. These values, with exception of BcQ-, are in fair agreement with experimental B - coefficients. In any case, the low values of B- coefficients found for the halide ions indicate that the interactions between anions and sulfolane dipoles are very weak and the sizes of hydrodynamic entities are small and close to that of bare ions. This result agrees perfectly with those obtained by conductometric measurements. Let us now consider the effect of the temperature on the viscous flow of the solutions. Only in the case of the anions C104-, I-, Br-, and C1- the changes of B- with the temperature are very small. On the contrary, other ions show a marked decrease of ionic B* coefficient with increase of the temperature, ranging between 10% in the case of Li+, and 20% in the case of Na+. This behavior is different from that observed in other nonaqueous solvents such as DMSO,1° MeOH,g CH&N,g and DMF,I7 in which very low dB*/dT coefficients were found. These results can be explained on the basis of the assumption that the influence of the ions upon the viscous process in sulfolane, a scarcely structured medium,18 may be ascribed mainly to the size of the particles. Greater temperature effects are observed in the case of large and unsolvated ions and in the case of small strongly solvated ions which form hydrodynamic entities larger than the molecular size of sulfolane. This may be interpreted by assuming that the increase of temperature reduces the obstruction to the viscous flow of sulfolane caused by the larger hydrodynamic entities.
The Journal of Physical Chemistry, Vol. EO, No. 7, 1976
Supplementary Material Auailable: Tables I, 11, and I11 (3 pages). Ordering information is available on any current masthead page.
References and Notes (1) (a) R. Fernandez-Prini and J. E. Prue, Trans. Faraday SOC., 62, 1257 (1966); (b) M. Della Monica, U. Larnanna, and L. Senatore, J. Phys. Chem., 72, 2124 (1968); (c) M. Della Monica and U. Larnanna, ibid., 72, 4329 (1968); (d) P. M. P. Eller and J. A. Caruso, Can. J. Chem., 51, 448 (1973): (e) A. P. Zipp, J. Phys. Chem., 5, 718 (1973); (f) M. Castagnolo and G. Petrella, Nectrochim. Acta, 19, 855 (1974). (2) J. Desbarres, P. Pichet, and R. L. Benoit, Electrochim. Acta, 13, 1899 (1968). (3) M. A. Coplan and R. M. Fuoss, J. Phys. Chem., 68, 1177 (1964). (4) R. H. Stokes and R. Mills, "Viscosity of Electrolytes and Related Properties", Pergarnon Press, Oxford, 1965, p 75. (5) 0. Kratky, H. Leopold, and H. Stabinger, Z. Angew. Phys., 27, 273 (1969). (6) See paragraph at end of text regarding supplementary material. (7) G. Jones and M. Dole, J. Am. Chem. SOC., 51,2950 (1929). (8) (a) H. Falkenhagen and M. Dole, Physik. Z.,30, 61 1 (1929); (b) L. Onsager and R. M.Fuoss, J. Phys. Chem., 36,2689 (1932). (9) R. L. Kay, T. Vituccio, C. Zawoyski, and D. F. Evans, J. Phys. Chem., 70, 2336 (1966). (10) N. P. Yao and D. N. Bennion, J. Phys. Chem., 75, 1727 (1971). (1 1) D. Feakins and K. G. Lawrence, J. Chem. SOC.A, 212 (1966). (12) Reference 4, p 3 1. (13) B. S. Krurngal'z, Russ. J. Phys. Chem., 47,956 (1973). (14) A. Einstein, Ann. Phys., 19, 289 (1906). (15) (a) G. B. Jeffery, Proc. R. SOC.London, Ser. A, 102, 161 (1922); (b) R. Sirnha, J. Phys: Chem., 44, 25 (1940). (16) (a) J. P. Bare and J. F. Skinner, J. Phys. Chem., 76, 434 (1972); (b) Ref 4, Chapter 4. (17) R. Gopal and P. P. Rastogi, Z. Phys. Chem. (Frankfurt am Main), 69, 1 (1970). (18) (a) U. Lamanna, 0. Sciacovelli, and L. Jannelli, Gazz. Chim. Ita/., 96, 114 (1966): (b) 0. Sciacovelli, L. Jannelli, and A. Della Monica, ibid., 98, 936 (1968); (c) U. Lamanna, 0. Sciacovelli, and L. Jannelli, ibid., 94, 567 (1964). '
