Transport Properties of Aqueous Electrolyte Solutions (18) S. I. Yakubson, J . Phys. Chem. USSR, 21, 343 (1947). (19) V. A. Plotriikovand S. Yakubson, Z. Phys. Chem., 147, 227 (1930). (20) E. Y. Gorenbein, Univ. Etaf Kiev, Bull. Sci. Rec. Chim., 1, 101 (1935). (21) V. A. Plotriikov, I. A. Sheka, and V. A. Yankelevitch, J. e n . Chem. USSR, 3 , 481 (1933). (22) E. Y. Gonsnbein, J . Gen. Chem. USSR, 9, 2041 (1939). (23) E. Y. Gorenbein, J. Phys. Chem. USSR, 20, 547 (1946).
The Journal of Physical Chemistry, Vol. 83, No. 7, 1979
879
(24) E. Y. Gorenbein, J . Gen. Chem. USSR, 26, 2985 (1956). (25) E. Y. Gorenbein, Ukr. Khim. Zhur., 25, 173 (1959). (26) See, for example, M. H. Cohen in “Electrons in Fluids”, J. Jortner and N. R. Kestner, Ed., Springer Verlag, Berlin, 1973, p 207. (27) Z. Stein and E. Gileadi, manuscript In preparation. (28) A. Reger, Ph.D. Thesis, Tel-Aviv University, Tel-Aviv, 1978. (29) H. Cordes and H. Rottger, 2.Electrochem., 63, 1030 (1959).
Transport Properties of Aqueous Electrolyte Solutions. Temperature and Concentration Dependence of the Conductance and Viscosity of Concentrated Solutions of Tetraalkylammonium Bromides, NH,Br, and LiBr Antonlo Lo Surdo” Rosenstiei School of Marine and Atmospheric Science, University of Miami, Miami, Florida 33 149
and Henry E. Wirth Department of Chemistry. Syracuse University, Syracuse, New York 13210 (Received March 1, 1978; Revised Manuscript Received September 5, 1978)
The equivalent conductance, A, and absolute viscosity, 11, of concentrated (1I m Isaturation) aqueous solutions of tetraalkylammonium bromides, R4NBr (where R = Me, Et, n-Pr, and n-Bu), NH4Br, and LiBr have been determined, respectively, from specific conductance, and kinematic viscosity, v, measurements in the temperature range 5 5 t “C 5 65. Assuming these solutions behave as “fused salt solutions”, an attempt has been made to account for the temperature dependence of A and 7 according to the free volume theories of Cohen and Turnbull, Williams et al., Bueche, and Adam and Gibbs. The results indicate that the temperature dependence of the concentrated solutions can be explained by the WLF equation log uTg(7‘)[orlog bT1(T)]= -Clg(T - Tg)/(C2g + T - T J . The rate process theory of Eyring has been used to explain the conductance-viscosity product, All. Indications are found that cation-anion and cation-cation interactions play a predominant role in the R4NBr solutions and conceivably may give rise to aggregation or “associated species” in these systems.
e,
1. Introduction
Transport properties (conductance, viscosity, diffusion, etc.) of aqueous electrolytes are usually studied to obtain information on ion-solvent and ion-ion interaction^.'-^ Since ion-solvent interactions are predominant at infinite dilution, investigations4 of tetraalkylammonium halides in H 2 0 and DzOas well as other solvents have been carried out a t low coincentrations. For the concentration range 1 5 rn 5 saturation, and over the temperature range 5 5 t “C 5 65, there is no systematic study of the conductance and viscosity of aqueous solutions of R4NBr, NH4Br, and LiBr. Using Fuoss-Onsager conductance equations1 and the Jones-Dole viscosity equation: Kay et al.3p6-10concluded from the ratio of Walden product in D20 to water that (i) the Et4N+ion has very little effect on the water structure, (ii) the Me4N+ion is a structure breaker (has a net effect of breaking dlown water structure), and (iii) Pr4N+ and Bu4N+ ions are structure makers (have a net effect of making more structure around the ions). Similar classification of ions as water-structure breakers and waterstructure makers have been made re~ently.l’-~~ The use of these terms is, in general, ambiguous because little is known about the structure being broken and/or made. However, these classifications are in agreement with thermodynamic data.13-21 For Concentrated aqueous solutions there are no adequate theories of conductance and viscosity. Existing hydrodynamic theories1s2>22-2s are rarely valid a t concen-
trations greater than 0.1 M. The equation of Robinson et a1,25,26
(1) has been found to represent the conductivity of completely dissociated electrolytes up to 6 M. In this equation B1= 8.20 x 1 0 5 / ( ~ ~ ) 3 / 2B~ , = 82.5/a(6~)1/2,~ ~ ~ =1 50.29BC1/2/(tT)1/2= KU, q o / q is the inverse of the relative viscosity, and F is a constant whose numerical value is given elsewhere.26 While eq 1 correctly relates the viscosity and conductance of a solution, the introduction of the reciprocal relative viscosity term evades the basic problem of dealing with the cooperative mechanism which must control all the mass transport processes at the molecular A detailed discussion of the general limitations of the hydrodynamic approach is given elsewhere.% Consequently, eq 1 provides little additional information concerning factors which determine the absolute magnitude of electrolytic conductance. In previous s t ~ d i e s ~it+was ~ ~ suggested that cationanion (hydrophobic-hydrophilic) and cation-cation (hydrophobic-hydrophobic) interactions may give rise to “micelles” or aggregated ions in concentrated aqueous solutions of quarternary ammonium bromides. In this communication, we are reporting experimental results of
0022-365417912083-0879$0 1,0010 0 1979 American Chemical Society
1
2
880
The Journal of Physical Chemistry, Vol. 83, No. 7, 1979
the conductance and viscosity of concentrated (1 I: m 5 saturation) solutions of R4NBr,NH,Br, and LiBr over the temperature range 5-65 "C. Assuming these solutions behave as "fused salt solutions" an attempt has been made to account for the temperature dependence of the conductance and viscosity data according to the free volume theories of Cohen and T ~ r n b u l l Williams ,~~ et B ~ e c h eAdam , ~ ~ and G i b b ~and , ~ ~the rate process theory of E ~ r i n g .The ~ ~ results suggest that the temperature dependence of the concentrated solutions can be described by the WLF equation.34 2. Experimental Section Materials. Tetramethylammonium bromide, tetraethylammonium bromide, tetra-n-propylammonium bromide, and tetra-n-butylammonium bromide (Eastman) were recrystallized twice from suitable organic liquid mixtures and were dried under vacuum at 70-80 "C for a t least 48 h. Their purity was better than 99.9%. The procedures used for the purification and analysis of these salts have been described p r e v i ~ u s l y . Ammonium ~~~~~ bromide (Fisher Analytical reagent) and lithium bromide (Fisher purified) were used without further purification. Stock solutions were prepared using doubly distilled water and their concentrations determined by a modified Volhard's method.39 Solutions of known molalities were prepared by weight dilutions, applying vacuum corrections in all cases. Procedure. The resistances were measured with a conventional bridge (Leeds and Northrup) constructed and modified from plans of Edelson and Fuoss40by Orra4IThe bridge resistance decade box (General Radio) was calibrated in situ against National Bureau of Standards certified resistors, using a Leeds and Northrup four dial resistance box, by a substitution method. A HewlettPackard audio oscillator, connected to a 115 V constant voltage transformer (Sola), provided the necessary sinusoidal ac potential needed to operate the bridge. The null point was determined with an all-purpose Heath-Kit oscilloscope and a tuned amplifier (General Radio) which also served as a frequency filter. The detailed procedures are discussed elsewhere.38 The conductance cells were constructed of Pyrex glass, and were of simple Jones and B ~ l l i n g etubular r ~ ~ type. The platinum electrodes (1cm in diameter) were separated by an average distance of 7.8 cm, and were platinized to minimize polarization effect^.^^-^^ The cells were calibrated against 0.1D and 1.OD (where D denotes demal concentration) standard KC1 solut i o n ~ ,using ~ ~ ,the ~ ~specific conductance22 [L(O.lD) and t(l.OD)] from 0 to 25 "C: L(0.lD) X lo6 = 7137.60 + 208.3125 + 0.99077t2 0.006964t3 (2)
+
+
L(l.OD) X lo6 = 65176 1732.11t 4.58t2 (3) Several cell constants ( K )were determined at 5,15, and 25 "C using K = RL(O.1D) and K = RL(1.OD) (4) where R is the resistance (0) of the standard solutions. The results are summarized by cell I K X lo4 = 274382 - 1.03449t (f0.009 av dev) (5) cell I1 K x lo4 = 480387 - 15.5020t (f0.022 av dev) (6) Assuming the cell constants do not vary appreciably with temperature, linear extrapolations of K to higher tem-
A. Lo Surdo and H. E. Wirth
peratures were made as needed using eq 5 and 6. The viscosities were measured with four suspended-level Cannon-Ubbelohde viscometers (No. 25,75, 150, and 200) obtained from Cannon Instrument Co., and were mounted on brass frames to maintain their vertical position in a constant temperature water bath. The thermostated bath system46was controlled to f0.005 "C or better at each temperature. The viscometers were calibrated with NBS certified viscosity standards. The range of the viscometers constants ( t i ) was from 2.236 X to 113.1 X low3cSt s-*. The kinematic viscosity, ut = t i i t , was determined from the efflux (7,)time (s) of the solutions at the temperature t. 3. Results The specific conductance (I;,) and kinematic viscosity (ut) of concentrated (1m to saturation) aqueous solutions of Me4NBr, Et4NBr, n-Pr4NBr, n-Bu4NBr, NH4Br, and LiBr have been determined38at 10-deg intervals between 5 and 65 "C and represented by the equations L, = -to X t # t 2 + at3 (7)
+ +
and In ut = In A
+ B/T + C / P
(8)
where t and T are, respectively, the temperatures in degrees centigrade and Kelvin. The values of Lo,x,#, and w (given in Table 147), and In A , B, and C (given in Table 11)47are those evaluated from the experimental data by least-squares methods. The values of and ut obtained from eq 7 and 8 at 5-deg intervals between 5 and 65 "C were used to calculate the equivalent conductance (A) and absolute viscosity (Q) of the above electrolytes. The values of Lt are reliable to f l . O X cm-l ohm-' for ( ~ - B U ) ~ N B ~ and f3.7 X cm-l ohm-l for the remaining R4NBr. For NH4Br and LiBr values of Lt are reliable to f1.5 X cm-l ohm-l. The equivalent conductances (A) given in Table I11 were calculated from the concentration ( C ) ,in equivalents per liter, and the specific conductance ( L )of the solutions a t the same temperature using the equation A =L x 1031~ (9)
e,
The densities of the solutions were measured with a Vycor pycnometer described by Wirth and Lo Surdo,& and have been reported e l ~ e w h e r e .The ~ ~ molal concentration (rn) was converted to the molar concentration ( C ) as needed using the equation 103m rnd C= (10) 1 + 0.001mM 103/d0 m 4 v
+
where d and do are the densities of the solution and water at the temperature t , is the apparent molal volume, and M is the formula weight of the solute. The A's calculated from eq 9 at constant molality were fitted to At = A. x't + $'t2 + w't3 (11)
+
The coefficients of these equations, tabulated in Table IV,47were obtained from least squares. Values of At are reliable to k0.005 cm2 equiv-I ohm-l for (n-Bd4NBrand k0.008 cm2 equiv-' ohm-l for (n-Pr),NBr. For the remaining electrolytes the uncertainty is f0.06 cm2 equiv-l ohm-l. The absolute viscosities (Q), given in Table V, were determined from the kinematic viscosities (uJ and densities (d,) of the solutions at the same temperature, t , using the equation Q = vtdt (12)
The Journal of Physical Chemistry, Vol. 83, No. 7, 1979 081
Transport Properties of Aqueous Electrolyte Solutions
TABLE 111: -
Equivalent Conductancesu as a Function of Temperature and Concentration
t,“C
5.0
15.0
25.0
35.0
45.0
55.0
65.0
m
A
A
A
A
A
A
A
(n-Bu),NBr
i.ooalo
12.2620 4.0157 2.2829 1.5008 1.0822
18.67200 7.01340 4.12290 2.71000 1.61260 0.97032
26.4220 10.9780 6.6373 4.4749 2.6098 1.6825 1.1041
1.oo a1o
I. 7.09 10
3.ooao 5.0 0 0’0 8.00080
5.5997 2.9257 1.5672
24.6530 9.2735 5.2098 2.9365
33.6130 14.1660 8.4868 5.0409
1.0000 3.0000 5.0000 7.0000 9.9773
28.8160 14.1980 7.9058 4.7192 2.3773
38.6560 20.1 170 11,9980 7.5556 4.1929
49.9430 27.1420 16.9020 11.2060 6.7232
1.1326 3.0000 5.0000
42.6810 31.3500 24.0880
55.1130 40.6900 30.9310
68.7010 50.7590 38.5520
1.0000 3.0000 5.0000 8.0000
76.7940 74.9400 72.0130
95.7160 90.8360 85.4850
115.8200 107.3600 99.6880 87.2010
1.0000 3.0000 5.0000 7.0000
49.7040 38.8490 30.9760 24.3810
63.1800 48.8530 38.6580 30.2760
77.9060 59.6090 46.9 24 0 36.6900 24.6040
3.0 0010 5.00 00 7.0000 10.0000 13.0 0 00 16.OOClO
35.3760 15.8640 9.8349 6.7902 4.0699 2.7167 1.8306
45.3980 21.624 0 13.7 240 9.6508 5.9891 4.0797 2.8347
56.3520 28.2120 18.3140 13.0520 8.3636 5.7781 4.1248
68.1010 35.5810 23.6140 16.9880 11.1900 7.8185 5.7090
55.1710 27.1930 17.7710 11.3480
67.4930 35.1170 23.654 15.496
80.6570 43.8440 30.2830 20.2720
76.0070 44.0950 29.2360 20.8790 13.8880
90.360 53.818 36.712 26.865 18.501
105.3100 64.2360 45.0910 33.5940 23.7900
98.6370 72.7790 55.7220
114.6300 84.5770 65.0680
131.0600 96.7990 74.7860
158.4500 141.6600 129.1800 111.1500
180.4000 159.0900 143.9300 122.6500
202.4000 176.4900 158.3000 134.2600
110.1500 82.9630 64.8000 50.6150 34.1920
127.1800 95.3520 74.2090 57.8990 39.3360
144.4900 108.0800 83.7980 65.2430 44.6650
( n-Pr ) ,NBr 43.8320 20.1740 12.6940 7.8535
(Et),NBr 62.4640 3 5.168 0 22.6410 15.6540 9.9581
(Me),NBr 83.2690 61.4810 46.8490
NH, Br 136.8300 124.3600 114.3500 99.4430
LiBr
10.000~0 a
93.6430 71.0140 55.6710 43.5080 29.2700
In cm2 ecpiv- I ohm-’.
The densities were taken from previous For Concentrated solutions the values of 17 are believed reliable to 3t0.2 CPfor n-Bu4NBr and h0.05 CPfor n-Pr,NBr; for lower concentrations the uncertainty t(7) is approximately f0.05 cP. For the remaining electrolytes ~ ( 7 is) better than f0.05 cP. 4. Discussion
Recently it has become apparent that a fresh approach is needed in dealing with transport properties of highly concentrated electrolyte solutions and “ionic F u o s ~ ,predicted ~ that progress in this field must come from the fused end of the concentration scale. Lacking a working thleory for fused salts, attempts have been made to account .for the temperature dependence of “ionic liquids”, by treating mass transport behavior in anhydrous fused salts.5o Two viewpoints have been accepted: the free volume theory33,35,36 (which considers mass transport to be a function primarily of the free volume in the liquid or solution), arid the rate process theory37 (where mass transport is treated as an activated process with an activation energy barrier over which a molecule or ion must go in moving from one equilibrium position to the next). The free volume theory of Cohen and T ~ r n b u l has l~~ been applied with remarkable success by Moynihan4*and by Angel150-52in their treatment of the transport properties of fused salts, “glass” forming mixtures, and highly concentrated solutions and mixtures of “glass” forming salts. Eyring’s rate process theory has been utilized by Nightir1gale,6~and by Miller and D ~ r a in n ~the~ study of the transport of highly concentrated (10 M) electrolyte so-
lutions. Since the viscosity coefficient, when determined over a sufficiently wide temperature range, is not linearly related to the reciprocal of the absolute temperature, viscous flow may not be a simple activated process. Free Volume Theory of Conductance and Viscosity. Two empirical equations commonly used to describe the temperature dependence of fused salts and “glass” forming systems are the modified Arrhenius e q u a t i ~ n ~ O - ~ ~ D, AT, ... = Do, ... exp[-K*/(T - To*)] (13) and the equation of Williams, Landell, and Ferry34p55@ for polymers systems (henceforth called the WLF equation) log ~ T @ (=T )
In these equations, K* is the activation energy; To*‘is a constant interpreted as the (i) theoretical (equilibrium) glass transition temperature or (ii) temperature a t which the free volume molecular or ionic migration becomes impossible, and the configurational entropy of the liquid (or solution) van is he^;^^"^ T is the absolute temperature; T, is the experimental glass transition temperature (e.g., the temperature at which a change of slope occurs in the volume vs. temperature plot of a “quasistatic” volume expansion measurement); and C l g and Czg are constants pertaining to T9‘ The value of Tg, determined by conventional means, is expected to be somewhat higher than To*due to the long relaxation time encoun-
882
The Journal of Physical Chemistry, Vol. 83, No. 7, 1979
A. Lo Surdo and H. E. Wirth
TABLE V : Absolute Viscosities ( q ,cP) as a Function of Temperature and Concentration t, “ C 5.0 15.0 25.0 35.0 45.0 m R R 9 9 9
55.0
65.0
9
9
1.340 3.490 6.220 9.480 15.500 23.100 32.800
1.060 2.600 4.480 6.650 10.500 15.100 21.100
0.882 2.040 3.400 4.930 7.560 10.400 14.400
1.080 2.460 4.250 7.560
0.872 1.870 3.090 5.300
0.728 1.480 2.370 3.950
1.870 3.230 5.280 9.580
0.822 1.470 2.440 3.820 6.560
0.685 1.190 1.920 2.890 4.740
0.583 0.986 1.550 2.260 3.600
0.810 1.070 1.430
0.674 0.891 1.190
0.572 0.755 1.000
0.495 0.651 0.863
0.708 0.701 0.718 0.774
0.595 0.602 0.624 0.680
0.510 0.525 0.550 0.606
0.449 0.465 0.492 0.547
0.807 0.993 1.220 1.510 2.170
0.670 0.831 1.020 1.270 1.830
0.569 0.709 0.878 1.100 1.580
0.491 0.615 0.764 0.957 1.380
(12-Bu),NBr
1.oooo 3.0000 5.0000 7.0000 10.0000 13.0000 16.0000
5.62 22.50 47.90 82.90
3.56 12.20 25.10 42.00 76.10 126.60
2.420 7.520 14.600 23.600 41.300 66.200 99.100
1.0000 3.0000 5.0000 8.0000
3.71 14.00 32.40 75.60
2.53 8.06 16.90 36.10
1.820 5.060 9.820 19.500
1.0000 3.0000 5.0000 7.0000 9.9773
2.24 4.83 9.99 19.60 46.10
1.66 3.37 6.49 11.80 25.10
1.270 2.460 4.470 7.680 14.900
1.0000 3.0000 5.0000
1.66 2.14 2.90
1.26 1.65 2.23
0.998 1.310 1.770
1.0029 3.0142 5.0312 8.0076
1.39 1.26 1.22
1.08 1.01 1.00
0.862 0.833 0.840 0.895
1.0000 3.0000 5.0000 7.0000 10.0000
1.66 1.96 2.34 2.86
1.26 1.52 1.84 2.25
0.996 1.210 1.480 1.820 2.620
1.750 4.950 9.190 14.400 24.400 37.700 54.700
(n-Pr),NBr 1.370 3.420 6.220 11.600
(Et), NBr 1.010
(Me),NBr
NH, Br
LiBr
- 4c
(Et)nNBr
- 50
+
-60
I
- ac
- 9c I -20
I
I -10
I
I 0
I
I 10
I
I 20
I
I 30
I
I 40
Figure 1. Plot of ( T - To)llog ar,( T ) VS. ( T - To)K for Et,NBr at m = 3, 5 and 7, and ( T - T,)/log bra( T ) vs. ( T - To)K for tetra-n-butylammonium bromide at m = 1, 3, and 5.
tered in its measurement. It can be shown%that eq 13 and 14 are equivalent and that they can be theoretically
justified from the free volume theories of Cohen and T ~ r n b u l lB, ~~~e c h e and , ~ ~Adam and G i b b ~ . ~ ~
The Journal of Physical Chemistry, Vol. 83, No. 7, 1979
Transport Properties of Aqueous Electrolyte Solutions
The WLF'Equation. The familiar empirical form of the (eq 14) is given by WLF 1% ar,(T) = -17.44(T - Tg) (15) 51.6 + T - Tg log b T g ( T ) = where aTp(T')[or bT ( T ) ] = 7(T)/7(Tg) is the ratio of the relaxation times at t8e temperature T and Tg.57It has been shown experimentally that the empirical constants Clg = 17.44 and C z g = 51.6 (e.g., eq 15) can accurately describe the temperature behavior of great many polymers and nonpolymers near Tg34*55,56 The equation is valid over the temperature range Tg5 T 5 (Tg+ 100 "C) and has been theoretically derived by Cohen and T u r n b u l P and by Adam and G i b b ~ A . ~detailed ~ discussion concerning these theories and derivation of the WLF equation has been given by Lo surd^.^^ For clarity of the subject matter discussed below, we express eq 14 in the following form log a T o ( T ) = -Cl0(T - To) (16) Czo + T - To log b T o ( T ) = where
A, and d are, respectively, the absolute viscosity, equivalent conductance, and density of the solution at the temperature T; qo, A,, and do are the corresponding quantities at To;and Clo and Czo are properties of the particular system at To. According to eq 16 a plot at ( T - To)/log aT,,(T), or ( T - To)/log bT,(n, vs. ( T - To)should give a straight line. From the slope S and the intercept i one then obtains the coefficients C: = -1/S and C? = 7,
i/S. Shown in Figure 1are plots of ( T - To)/log aTo(T)and (T - To)/log b,,,(T) vs. ( T - To)for three concentrations of Et4NBr axid n-Bu4NBr, respectively. The reference temperature was arbitrarily chosen as To = 298.15 K. Three quasi-parallel lines are obtained for each salt. Similar plots were obtained from conductance and viscosity data for all the salts studied in the concentration range 1m to saturation. In view of these results, it is suggested that the temperature dependence of the conductance and viscosity (mass transport) of aqueous solutions of R4NBr, NH4Br, and LiBr may be described by the WLF equation. Experimental Parameters of the WLF Equation. The relationships between the coefficients Cl0, Czo,and Toof eq 16, and Clg, Czg, and Tgof the WLF equation (eq 14) are given by the e q u a t i o n ~ ~ ~ ~ ~ ~
Clg = C1OCp0/(C2O
+ Tg- To)
(20)
and
czg = czo+ Tg- To
(21) where af,,= (1/2.303c10c20)is the thermal expansion of the free volume; /(To)= (1/2.303C?), and f(Tg)= (1/2.303C1g) are the fractional free volumes (e.g., the ratio of free, V,,
883
TABLE VI: Values of T, and Constants for
viscosity m
T,
-
c*, (n-Bu,)NBr 12.37 15.65 17.36 20.16 24.1 5 24.07 24.64 (n-Pr), NBr 15.76 14.39 15.54 18.01
1.0000 3.0000 5.0000 7.0000 10.0000 13.0000 16.0000
195.64 199.16 200.25 197.58 193.20 200.17 202.07
1.0000 3.0000 5.0000 8.0000
175.01 198.79 204.73 205.80
1.0000 3.0000 5.0000 7.0000 9.9773
146.85 162.92 174.82 178.57 193.03
1.0000 3.0000 5.0000
149.68 144.50 139.27
1.0000 3.0000 5.0000 8.0000
155.52 134.61 129.89 127.32
20.03 19.36 19.33 21.46 19.95 Me,NBr 17.71 18.57 19.37 N H, Br 14.58 17.79 16.94 15.69
1.0000 3.0000 5.0000 7.0000 10.0000
145.41 137.92 134.50 138.51 139.16
Li Br 18.43 19.58 20.39 18.15 18.35
conductance
-
T, 194.19 202.13 201.74 195.80
12.59 12.43 14.26 17.39
199.52 195.74
2l.35 21.93
175.34 195.34 192.96 207.42
14.74 13.73 15.37 14.07
152.44 166.87 173.97 183.79 195.86
16.75 17.23 16.87 16.86 15.95
154.46 157.70 139.78
15.29 14.54 18.81
150.32 138.99 124.80 148.36
13.77 13.93 15.22 13.45
149.42 140.70 138.61 134.59 124.23
14.88 16.02 16.78 16.69 19.43
(Et ),NBr
to occupied, V,, volumes) at the temperatures Toand Tg, respectively; and CIo, C; and Clg, C2g are constants pertaining to To and T,. The values of Tg,Clg, and C2g for R4NBr, NH4Br, and LiBr were calculated from these equations and are listed in Table VI. The average value of afofor these solutions was found to be 1.4 X deg-l (for the viscosity) and 1.5 X deg-' (for the conductance). Individual values of cyfo vary from 1.0 X to 2.0 X deg-I for both conductance and viscosity. Since ClgCzg = C?C$ 56 these afovalues correspond to afgfor the electrolyte solutions. In contrast, for polymer systems the "universal" value cyfg = f(Tg)/C2g= (2.303clgc2g)-' = 4.8 X deg-' (individual values of afgrange from -2 X lo4 to -1 X deg-1).56 The fractional free volume f(To) calculated from the viscosity data was in good agreement with that calculated from the conductance data. In general, f ( T o )and afodecreased with increasing concentrations for Et,NBr, Pr4NBr, and Bu4NBr, the greatest decrease occurring for the larger quaternary ammonium bromides. For Me4NBr, NH4Br, and LiBr f ( T o )and ajo did not change appreciably with concentration. To obtain a value of T gfor R4NBr, NH4Br, and LiBr, we assume the following: (1) if crystallization (or precipitation) does not occur, in principle, any liquid or solution would go through a glass transition on cooling;33and (2) a t Tg all substances have the same fractional free volume f(Tg)= 0.025 f 0.003 (i.e., the experimental value found for polymers and polymer solution^).^^ If these assumptions are accepted, then the values of Tg,Clg, and Czgfor the solutions investigated may be calculated using
004
The Journal of Physical Chemistry, Vol. 83, No. 7, 1979
eq 19-21. The results are listed in Table VI. For a given salt solution at fixed concentrations approximately equal values of T are obtained from the conductance and viscosity data [Table VI). These results suggest that the same molecular motion is responsible for the viscosity and conductance of R4NBr, NH4Br, and LiBr, and that this motion stops at Tg.The experimental Tgis characterized by f ( T J = 0.025, whereas the theoretical Tg is defined by f ( T g )= 0,33or by the vanishing configurational entropy.36 The increasing order in Tg at fixed concent,rations for the salts studied was found to be Bu4NBr I Pr4NBr I Et4NBr L Me4Br I NH4Br I LiBr from both viscosity and conductance data (Table VI). The values of C 2 g of the WLF equation for R4NBr, NH,Br, and LiBr (Table VI) were calculated from eq 21. Since we assume f ( T J = 0.025, it follows38that Clg = 17.44 (Le., “semiuniversal” constant found for polymer systems), and, therefore, need not be calculated from eq 20; it compares with Clg = [2.303f(To)]-’ = (2.303 X 0.025)-’ = 17.4. In contrast to Czg = 51.6 for polymers, the average values of Czg for the electrolyte solutions are 18.5 for viscosity and 15.9 for conductance; individual values vary from 12.4 to 24.6 for viscosity, and from 12.4 to 21.9 for conductance (Table VI). This discrepancy between Czg = 51.6 and those calculated for the salt solutions is probably due to (i) the large differences in the coefficients of thermal expansion of free volume ( ~ r f o ) ,and ~ ~ (ii) the fact that we cannot assume f ( T g = ) 0.025 for the electrolyte solutions, although such an assumption is intuitively reasonable. Activation Energies. In Table VI1 we compare the activation energies calculated from the WLF and Arrhenius equations at 25 “C. The WLF apparent activation energies for the conductance, AHAia, and viscosity, AHVa, were calculated from the equation
AHha =
AH,* = where \k = aTp(T)or bTJT). The corresponding Arrhenius activation energies were calculated from
and
assuming AH* is invariant with temperature (i.e., aAH*/aT = 0). In these equations the subscripts 7 and A refer to the AH’S calculated from the absolute viscosity (7) and equivalent conductance (A) data; R and T are the gas constant and absolute temperature, respectively; and Clg and Czg are the coefficients of the WLF equation corresponding to the glass transition temperature Tg. For each system, and for each set of data (conductance or viscosity) at fixed concentrations the values of Clg, Czg, and T g(listed in Table VI) were used in calculating the AH’S. It should be noted that for electrolyte solutions the coefficients C l g and C z g may not necessarily correspond to the “semiuniversal” constants found for polymer systems. For a given set of data, viscosity or conductance, at fixed concentrations for the salts studied the activation energies calculated from the WLF and Arrhenius equations agree to within 10%. This agreement is surprising in view of the fact that the Arrhenius equation procedure is based on an incorrect assumption. The same agreement in the AH’S
A. Lo Surdo and H. E. Wirth
TABLE VII: Activation Energies (kcal mol“) at 25 ’C viscosity conductance
m
AH^*^
AHVa
AHA*
a
A H A ~
(n-Bu),NBr 1.0000 3.0000 5.0000 7.0000 10.0000 13.0000 16.0000
6.226 8.054 8.843 9.405 10.000 10.630 11.360
1.0000 3.0000 5.0000 8.0000
5.377 7.531 8.794 9.962
1.0000 3.0000 5.0000 7.0000 9.9113
4.374 5.183 6.126 1.103 8.464
1.0000 3.0000 5.0000
3.927 3.829 3.902
1.0000 3.0000 5.0000 8.0000
3.700 3.224 2.928 2.759
1.0000 3.0000 5.0000 7.0000 10.0000
3.951 3.747 3.614 3.529 3.576
6.650 8.449 9.211 9.813 10.280 11.460 12.000
5.599 7.133 7.596 8.056 8.320 9.157 9.448
10.520 10.060
5.052 6.818 7.812 8.632
5.521 1.172 7.503 9.089
4.223 4.909 5.561 6.381 1.516
4.503 5.543 6.016 6.947 8.094
3.621 3.622 3.655
4.292 4.294 4.251
3.143 2.763 2.566 2.559
3.141 3.299 3.037 3.581
3.464 3.289 3.208 3.195 3.252
3.943 3.711 3.829 3.644 3.688
6.566 7.498 8.260 8.605
(n-Pr),NBr 5.796 8.292 9.286 10.490
(Et),NBr 4.841 5.747 6.739 7.654 9.049
(Me),NBr 4.550 4.442 4.325
NH,Br 4.186 3.839 3.504 3.200
LiBr 4.462 4.297 4.271 4.074 4.140
a Activation energy calculated from the Arrhenius equation. Activation energy calculated from the WLF equation. Subscripts q and A refers to the viscosity and conductance data, respectively.
was obtained at other temperatures. In general, the activation energies (1)decreased with increasing temperatures, and increased with increasing concentrations for n-Bu4NBr, n-Pr4NBr, and Et,NBr; (2) decreased with increasing temperatures and concentrations for NH4Br; and (3) decreased with increasing temperatures, and decreased first and then increased with increasing concentration for Me4NBr and LiBr. For all the systems studied in the temperature range 5 I t “C I 65, the activation energies calculated from the viscosity (AH,) data, at fixed concentrations and temperatures, were approximately 0.6 kcal mol-l greater than those calculated from the conductance ( M Adata ) (Table VII). We speculate that this difference in activation energies between the viscosity and conductance data may be attributed to various ion-ion interactions giving rise to “aggregation” in solution, and can be explained according to theories of fused ~ a l t s . ~ ~ , ~ @ ~ ’ In viscous flow single ions and “aggregated species” are constrained to move together and the ease of such a flow is determined mainly by the resistance provided by the less mobile ions (“aggregates”). Electrical conductance, however, is assumed to occur primarily by the migration of the more mobile ions. The resistance to ionic migration may be considered to arise from the conventional activation energy b a r r i e r ~ , 3 ~or, from ~ ~ *the ~ ~requirement that some critical free volume be available to an ion before migration becomes possible.33 The applied potential in
Transport ProFierties of Aqueous Electrolyte Solutions
conductance lowers the activation energy barrier for the ions to move (or jump) forward into neighboring “holes”. The fact that AH, > AH,, is observed suggests that the opposing potential energy barrier is greater for the sheering stress encountered in viscous flow than it is for the electrical potential gradients encountered in electrical conduction. These findings are consistent with those found for “ionic liquids” (e.g., Ca(N03)2.4H20and NazSz03.5Hz0) by M ~ y n i h a n . ~ ~ Concentration Dependence of A and qr. In recent studies it was s u g g e ~ t e d that ~ ~ - the ~ ~ concentration dependence of the apparent molal volume and solubility of benzene in concentrated (1 5 m i: saturation) aqueous solutions of R4NBr could be explained by “micelle” or “aggregate” formation. These “aggregates” (formed by the overlap and (eventual disruption of hydration cospheres of ions) may increase or decrease the water structure in the vicinity of their large hydrophobic surfaces,6g and are compatible with infinite dilution studies concerned mainly with ion-solvent interactions. Since ion-ion interactions predominate at higher concentrations, conceivably various cation-anion (hydrophobic-hydrophilic), cation-cation (hydrophobic-hydrophobic), and multiplets interaction could give rise to “aggregation” or “associated species” linked electrostatically and/or “hydrophobic forces”. The importance of all possible ionic interactions in solution (e.g., +-, ++, --, and various triplets and higher multiplets) have been discussed by Friedman’s cluster theories.1g~zo,60 Various types of ion pairs61 may be possible within these “aggregates”, e.g., (1)solvent-separated ion pairs (pairs of ions separated by more than one water molecule), ( 2 ) solvent-shared ion pairs (pairs of ions separated by one water molecule), and (3) contact ion pairs (with no covalent bond). These ion pairs and aggregates may be short lived and are difficult to detect experimentally. However, in view of the present results that mass transport can be explained by the free volume theories of “fused salts” and polymer systems, it is of interest to see if the concentration dependence of A and the relative viscosity (vr) for R4NBr could be explained in terms of aggregation. Conductance. Plotted in Figure 2 is the concentration dependence of the equivalent conductance (A) of R4NBr as a function of temperature. Similar plots of A vs. C1lz for NH4Br aind LiBr are shown in Figures 3 and 4.47 A increases with increasing temperature and decreases with increasing concentration. For the larger R4NBr, A varies very slowly with temperature and concentration. When contrasted with the equivalent conductance at infinite dilutiong8J0 the observed curves for R4NBr fall off rapidly indicating aggregation. Since theoretical conductance equations are lacking at high ionic strengths (concentrations), a meaningful estimation of the degree of dissociation (a)or association (0 = 1 - a) for the R4NBr systems cannot be made at this time. Using a crude first approximation in estimating a suggest that (Y (1)increases with increasing temperature and (2) decreases with increasing concentrations, and alkyl group chain length.38 Viscosity. The extended Jones-Dole5 equation for the relative viscoiity (11,) of dilute electrolyte solutions = 7/70 = 1 + A,C1” + B,C D,C2 (25)
+
[where 7 is the viscosity of the solution of molar concentration (C) and rlo the viscosity of water (solvent)] has been used to dietermine the viscosity B, and D, coefficients of simple electrolytes and tetraalkylammonium halides.9@ The A coefficient is a constant depending on the longrange 6oulorn bic interactions between the and
The Journal of Physical Chemistry, Vol. 83, No. 7, 1979 885
can be calculated from the ionic equivalent conductance at infinite dilution.66 The B, and D, coefficients are adjustable parameters and are related to the size of the ions and ion-solvent and ion-ion interactions, respectively.62 Assuming the relative viscosity equations derived by Einstein6’ (for spherical colloidal suspensions) and T h o m a P (for high volume fraction dispersions) are applicable to solutions of hydrophobic solutes and inorganic salts, the quantities (B, - 2.5 X 1 0 - 3 4 ~ 0and ) D, X 10.05 X 104(~vo)z have been suggested to quantify the structural effect of solute-solvent and solute-solute interactions, respectively.62 The B, coefficients have also been divided into ionic contribution^.^^^^ The results indicate that the Me4N+ion i s a structure breaker, the Et4N+ion has very little effect on the water structure, and Pr4N+and Bu4N+ ions are structure maker^.^^^^ For concentrated (0-4 m) solutions of R4NBr over the temperature range 15-35 “C, Eagland and Pilling70derive equations for V, (“the effective volume of the flowing unit”) using the relative viscosity equations of Thomas,68 Vand,’l and Breslau and Miller.72 The authors found that, for Et4NBr, Pr4NBr, and Bu4NBr, V, decreased to a minimum with increasing concentration, and Me4Br showed no minimum in V, with concentration. The results were interpreted in terms of hydrophobic hydration in agreement with Kay’sginterpretation of the B, coefficients for R4NBr. The relative viscosity, qr = 7/v0, of the solutions was calculated from the absolute viscosity (7) given in Table I1 and the viscosity of water (qo) obtained from Robinson and Stokes.25 The molal concentration (m)was converted to the molar concentration (C) as needed using eq 10 and the density data published p r e v i ~ u s l y .The ~ ~ results are plotted in Figure 5. Shown in Figure 5 are plots of (7, - l)/C1lz vs. C1l2for R4NBr, NH4Br, and LiBr at several temperatures. The relative viscosities increase sharply with increasing concentrations for Et4NBr, n-Pr4NBr, and n-Bu4NBr;Me4NBr shows virtually no change with concentration and temperature, and LiBr shows a gradual increase with concentration. Below 45 “C NH4Br shows a decrease and then an increase in relative viscosity with concentration. At 45 “C and above, the viscosity of NH4Br shows a gradual increase with concentration. The relative viscosities of Et4NBr, n-Pr4NBr, and n-Bu4NBr decrease with increasing temperatures, whereas the relative viscosities of Me4NBr, NH4Br, and LiBr increase with increasing temperature. The steep rise in the relative viscosity occurs at -2 M for the larger tetraalkylammonium bromides and shifts to lower concentrations with decreasing temperatures (Figure 5). For Me4NBr the upswing in viscosity is expected to occur at much higher concentrations and is precluded by the onset of saturation. In contrast, Eagland and Pilling70 observe minima in the “effective volume” (V,) at 1 M for the larger R4NBr, and no minimum in V , for Me4NBr. The temperature effects are to increase or decrease qr, and to shift slightly the concentration where the upswing in qr (Figure 5) or the minimum in V , occurs. The .observation of a sharp increase in the relative viscosity at -2 M for R4NBr is compatible with the formation of aggregate^"'^ by the overlapping hydration cospheres of ions.59,74~75The number and kindci of “aggregated ions” may increase with concentration forming more compact larger single species favoring a more suitable close packing in solution. The packing density would approach that for molecules in organic crystals ( ~ 0 . 7 ) ~ ~ or organic solutes in water (which vary from 0.57 to 0.59
-
886
The Journal of Physical Chemistry, Vol. 83, No. 7, 1979
A. Lo Surdo and H. E. Wirth
IO0 -
I10
100
t
c
55 90-
55
70 -
45
80 45
-t
35 E
I
60
E
c ?
70
25
35
-
-
5=
50
5
40-
25
EI D
..
15
I
I5
4
30
50
-
5
30
70- t°C 65
-
t
60
--
50
-
7
40-
5
30-
=E
c7
-B d
55
45
-
35
-
25
20-
15
10 -
0I
1
I
I
10
I
I
I
I
I
I
I
15
Tetra-n-propylammonium bromide
Flgure 2. Plots of the temperature and concentration dependence of the equivalent conductance for n-Bu,NBr, n-Pr,NBr, Et,NBr, and Me4NBr.
for hydrocarbons, alcohols, and carboxylic and 0.61 for amines78). The packing density for random packing spheres is 0.634.79At concentrations where close packing may occur, an abrupt increase (change) in viscosity would be expected (Figure 5). The state of aggregation is expected to change with temperature and would manifest itself in a strong temperature dependence of the relative viscosity. This effect could be either positive or negative. In general, an increase in dissociation of the “aggregates” is expected with increasing temperatures. If this was the only effect, a negative temperature coefficient would be observed for the relative viscosity, as is the case for the larger tetraalkylammonium bromides. Similarly, the degree of solvation is expected to decrease with increasing temperature. Therefore, for highly solvated ions one would also expect a negative temperature coefficient for the relative viscosity.
The converse is observed for Me4NBr, NHIBr, and LiBr. Rate Process Theory of A and q. Walden’s22,80 empirical conductance-viscosity rule is given by AOqO= constant, where Ao is the limiting equivalent conductance of an electrolyte and qo is the viscosity of the homogeneous medium. This rule follows from Stokes law.22 For concentrated solutions of R4NBr, NH4Br, and LiBr, we define the conductance-viscosity product Aq where A and 17 are, respectively, the equivalent conductance and viscosity of the solution of concentration m at the temperature ( t ) . It has been found that Aq # constant = f(m,T) (26)
It is observed that the product Aq (a) decreases with increasing temperatures and increases with increasing concentrations for Bu4NBr, Pr4NBr, and Et4NBr; (b) decreases with increasing temperature, and decreases and
Transport Properties of Aqueous Electrolyte Solutions 160
.
140
-
I
75“
7 0.0
I
I
I
I
120
(n-BuI4NBr
60.0 0
(n-Pr)4NBr I
(Et),NBr o
(Me),NBr
8
LiBr
-
100
-
0
-
”4Br
-I60
-
140
-
120
- 100
500
40 0
I
77/70-I c1/2
50/
30 0
i
20.0
10.0
/25O
- 0
5”
0
08
IO
12
1.4
16
18
112
Flgure 5. Plot of (q/qo - l)/C”’ vs. C1I2for Bu4NBr, Pr4NBr, Et4NBr, Me4NBr, NH,Br, and LiBr at several temperatures.
then increases with increasing concentration for Me,NBr; and (c) decrleases with increasing temperature and concentration for NH4Br and LiBr. Assuming the conductance and viscosity of an electrolyte may be considered as a rate process, these results follow from Eyring’s absolute rate theory.37 In a purely formal way the conductance and viscosity of the electrolytes may be represented by37981J’2
A=-
VA2l3F exp(-AGA* /RT) RT
(27)
and 7 =
hN
- exp(AG,*/RT)
v,
where AGA* and AG,* are the free energy of activation for the conductance and viscous flow, respectively; V , and V, are the molar volumes of the moving species; F is the Faraday constant; and N , h, R, and T have their usual meaning. If it may be assumed that the viscosity and conductance proceed by the same m e ~ h a n i s m and , ~ ~ that the free energy of activation and the moving species are the same in both processes (i.e., V,, = V , = V , and AG,* = AGA* = A(;*), then
where A is a constant. Equation 29 is in agreement with that of Miller.81 The observed decrease in hq with increasing temperature may be qualitatively described using eq 29 since this product is reciprocally related to the absolute temperature, T. The increase in AT with increasing concentration for Bu4NBr, Pr4NBr, and Et4NBr is consistent with the idea of aggregation. Since a t high concentration penetration of Br- ions, H20 molecules, and alkyl groups into the space between the chains of the larger R4N+ions may occur, the
total volume occupied by the “aggregates” (favoring a more suitable close packing in solution) would be less than the volume occupied by the dissociated species. Since A? a l / V / 3the Walden’s product would increase with concentration. The converse would be expected for completely dissociated simple electrolytes (NH4Br and LiBr) since V would increase with concentration. In summary, the results presented here suggest that (i) the temperature dependence of the transport properties (conductance and viscosity) of concentrated solution of R4NBr,NH,Br, and LiBr can be explained by the “WLF” equation; (ii) the same molecular motion is responsible for the viscosity and conductance of the salt solutions investigated; and (iii) the concentration and temperature dependence of the conductance-viscosity product can be explained by the rate process theory of Eyring. Indications are also found that cation-anion (hydrophobic-hydrophilic) and cation-cation (hydrophobic-hydrophobic) interactions play a predominant role in the R4NBr solutions and conceivably may give rise to aggregation or “associated species”. It is suggested that the structure of concentrated aqueous solutions of R4NBr is different from that of dilute solutions and that of normal electrolytes. This structure difference is not necessarily in disagreement with studies at infinite dilution which are mainly concerned with ion-solvent interactions.
Acknowledgment. The authors acknowledge the support of the Office of Saline Water, Grant No. 14-010001-623, for this study. A. Lo Surdo also acknowledges the support of the Office of Naval Research (N0001475-(2-0173) and the Oceanographic Section of the National Science Foundation (OCE73-00351-A01) for their support during the preparation of the manuscript. Supplementary Material Available: Three tables containing the least-squares coefficients for the temperature dependence of the specific conductance (Table I), kinematic viscosity (Table 11))and equivalent conductance
000
The Journal of Physical Chemistry, Vol. 83, No. 7, 1979
(Table IV) of R4NBr (where R = Me, Et, Pr and Bu), NH,Br, and LiBr for the concentration range 1 5 m I saturation in water; and two figures containing plots of I vs. C1I2for NH4Br (Figure 3) and LiBr (Figure 4) over the temperature range 5 I t " C I 65 (8 pages). Ordering information is available on any current masthead page.
References and Notes (1) R. M. Fuoss and F. Accascina, "Electrolytic Conductance", Interscience, New York, 1959. (2) R. H. Stokes and R. Mills, "Viscosity of Electrolytes and Related Properties", Pergamon Press, New York, 1965. (3) R. L. Kay, Adv. Chem. Ser. No. 73, 1 (1968). (4) For an extensive bibliography list, see ref 38. (5) G. Jones and M. Dole, J. Am. Chem. Soc., 51, 2950 (1929). (6) R. L. Kay and D. F. Evans, J . Phys. Chem., 69, 4216 (1965). (7) D. F. Evans and R. L. Kay, J . Phys. Chem., 70, 366 (1966). (8) R. L. Kay and D. F. Evans, J . Phys. Chem., 70, 2325 (1966). (9) R. L. Kay, T. Vtuccio, C. Zawoyski, and D. F. Evans, J. Phys. Chem., 70, 2336 (1966). (10) D. F. Evans, G. P. Cunningham, and R. L. Kay, J . Phys. Chem., 70, 2974 (1966). (11) H. Frank and W.-Y. Wen, Discuss. Faraday Soc., 24, 113 (1957). (12) F. J. Millero, "Biophysical Properties of Skin", H. R. Elden, Ed., Wiley, New York, 1971. pp 329-376. (13) W.-Y. Wen, A. Lo Surdo, C. Jolicoeur, and J. Boileau, J. Phys. Chem., 80, 466 (1976). (14) W.-Y. Wen and U. Kaatzee, J . Phys. Chem., 81, 177 (1977). (15) A. Lo Surdo, W.-Y. Wen, C. Jolicoeur, and J.-L. Fortier, J . Phys. Chem., 81, 1813 (1977). (16) A. Lo Surdo, J . Solution Chem., in press. (17) A. Lo Sur&, W.-Y. Wen, and C. Jolicoeur, J. Solution Chem., in press. (18) A. S. Levine and R. H. Wood, J . Phys. Chem., 77, 2390 (1973). (19) C. V. Krishnan and H. L. Friedman, J. Phys. Chem., 74, 2356 (1970). (20) C. V. Krishnan and H. L. Friedman, J. Solution Chem., 2, 37 (1973). (21) C. Jolicoeur and G. Lacroix, Can. J. Chem., 51, 3051 (1973). (22) H. S. Harned and B. B. Owen, "The Physical Chemistry of Electrolyte Solutions", Reinhold, New York 1958. (23) L. Onsager and R. M. Fuoss, J . Phys. Chem., 36, 2689 (1932). (24) R. A. Robinson and R. H. Stokes, J. Am. Chem. Soc., 76, 1991 (1954). (25) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions", Butterworths, London, 1959. (26) B. F. Wishaw and R. H. Stokes, J. Am. Chem. Soc., 76, 2065 (1954). (27) C. A. Angell, J . Phys. Chem., 70, 3988 (1966). (28) S. B. Brummer and G. J. Hills, Trans. Faraday Soc., 57, 1816, 1823 (196 1). (29) H. E. Wirth and A. Lo Surdo, J . Phys. Chem., 72, 751 (1968). (30) A. Lo Surdo and H. E. Wirth, J . Phys. Chem., 76, 130 (1972). (31) A. Lo Surdo and H. E. Wirth, J. Phys. Chem., 76, 1333 (1972). (32) H. E. Wirth, J. Phys. Chem., 71, 2922 (1967). (33) M. H. Cohen and D. Turnbull, J . Chem. Phys., 31, 1164 (1959). (34) M. Williams, R. Landel, and J. Ferry, J. Am. Chem. SOC.,77, 3701 (1955). (35) J. Bueche, J. Chem. Phys., 30, 748 (1959). (36) G. Adam and J. H. Gibbs, J. Chem. Phys., 43, 139 (1965). (37) S. Gladstone, K. J. Laidler, and H. Eyring, "The Theory of Rate Processes", McGraw-Hill, New York, 1941. (36) A. Lo Surdo, R.D. Dissertation, Syracuse University, Syracuse, N.Y., 1970. (39) N. H. Furman, "Standard Methods of Chemical Analysis", Vol. 1, Van Nostrand, Princeton, N.J., 1966, pp 242, 329, 330. (40) D. Edelson and R. M. Fuoss, J . Chem. Educ., 27, 610 (1950). (41) C. H. Orr, Ph.D. Dissertatlon, Syracuse University, Syracuse, N.Y., 1953.
A. Lo Surdo and H. E. Wirth (42) G. Jones and D. M. Bollinger, J . Am. Chem. Soc., 57, 280 (1935). (43) G. Kortum and J. O'M Bockris, "Textbook of Electrochemistry", Vol. 2, Elsevier, New York, 1951, p 562. (44) T. Shedlovsky, "Techniques of Organic Chemistry", Vol. 1, A. Weissberger, Ed., Interscience, New York, 1959, part 4, p 3028. (45) B. E. Conway and R. G. Barradas, "Chemical Physics of Ionic Solutions", Wiley, New York, 1966. (46) H. E. Wirth and A. Lo Surdo, J . Chem. Eng. Data, 13, 226 (1968). (47) Available as supplementary material. See the paragraph at the end of text regarding supplementary material. (48) C. T. Moynihan, J. Phys. Chem., 70, 3399 (1966). (49) R. M. Fuoss, Chem. Rev., 17, 27 (1935). (50) C. A. Angell, J . Phys. Chem., 68, 218, 1917 (1964); 69, 399, 2137 (1965); 70, 2793, 3988 (1966). (51) C. A. Angell, J . Nectrochem. Soc., 112, 1224 (1965). (52) C. A. Angell, J . Chem. Phys., 43, 2899 (1965). (53) E. R. Nightingale, Jr., J . Phys. Chem., 66, 894 (1962). (54) M. L. Miller and M. Doran, J . Phys. Chem., 60, 186 (1956). (55) M. L. Williams, J . Phys. Chem., 59, 95 (1955). (56) J. D. Ferry, "Viscoelastic Properties of Polymers", Wiley, New York, 1961, Chapter 11. (57) M. Ilavsky and J. Hasa, Collect. Czech. Chem. Commun., 32, 4161 (1967). (58) The experimental value of C,g = 51.6 for polymers and polymer solutions is obtained for af = 4.8 X deg-'. For the electrolyte solutions a, = 1.54 X deg-'. (59) W.-Y. Wen, "Water and Aqueous Solutions", R. A. Horne, Ed., Wiley, New York, 1972. (60) H. L. Friedman, "Ionic Solution Theory", Wiley-Interscience, New York, 1962. (61) F. J. Millero, "The Sea: Ideas and Observations on Progress in the Study of the Seas", E. D. Goldberg, Ed., Wiley, New York, 1977. (62) J. E. Desnoyers and G. Perron, J . Solution Chem., I, 199 (1972). (63) H. Falkenhagen and H. Dole, Phys. Z . , 30, 611 (1929). (64) H. Falkenhagen, Phys. Z . , 32, 745 (1931). (65) H. Falkenhagen and E. L. Vernon, Phil. Mag., 14, 537 (1932). (66) H. Falkenhagen and E. L. Vernon, Phys. Z., 33, 140 (1932). (67) A. Einstein, Ann. Phys., 19, 289 (1906); 34, 591 (1911). (68) D. G. Thomas, J. Colloid Sci., 20, 267 (1965). (69) M. Kaminskv. Discuss. Faraday Soc.. 24. 171 11957). i70j D. Eagland and G. Piiling, J . PAYS. Chem., 76, 1902 (1972). (71) J. Vand, J . Phys. Chem., 52, 277 (1948). (72) B. R. Breslau and I.F. Miller, J . Phys. Chem., 74, 1056 (1970). (73) The same marked increase in the relative viscosity is usually observed for concentrated polymer solutions and polyelectrolytes, see ref 56 and R. M. Fuoss and V. P. Strauss, Ann. N . Y . Acad. Sci., 51, 836 (1949). (74) R. W. Gurney, "Ionic Processes in Solutions", McGraw-Hill, New York, 1954. (75) W.-Y. Wen and S. Saito, J . Phys. Chem., 68, 2639 (1964). (76) E. J. King, J . Phys. Chem., 73, 1220 (1969). (77) W. L. Masterton, J . Chem. Phys., 22, 1830 (1954); R. Kobayashi and D. L. Katz, Ind. Eng. Chem., 45, 440 (1953). (78) R. E. Verrall and B. E. Conway, J . Phys. Chem., 70, 3961 (1966); B. E. Conway, R. E. Verrall, and J. E. Desnoyers, Trans. Faraday Soc., 62, 2738 (1966); S.D. Hamann and S.C. Lim, Aust. J. Chem., 7, 329 (1954). (79) G. D. Scott, Nature (London), 165, 68 (1960); J. D, Bernal and J. L. Finney, Discuss. Faraday Soc., 43, 62 (1967): W. C. Duer, J. R. Greenstein, G. B. Oglesby, and F. J. Miilero, J . Chem. Educ., 54, 139 (1977). (80) P. Walden, Z . Phys. Chem., 55, 207, 246 (1906); P. Walden and H. Vlich, ibid., 107, 219 (1923). (81) M. L. Miller, J . Phys. Chem., 60, 189 (1956). (82) W. Good, Electrochim. Acta, 9, 203 (1964). (83) This is suggested by the fact that both the viscosity and conductance data give the same approximate values of Tgand activation energies.
