The Effect of Solvent Structure on the Mobility of Symmetrical Ions in

MOBILITYOF SYMMETRICAL IONS IN AQUEOUS SOLUTION

2325

The Effect of Solvent Structure on the Mobility of Symmetrical Ions in Aqueous Solution

by Robert L. Kay and D. Fennel1 Evans Mellon Institute, Pittsburgh, Pennsylvania

16613

(Received February 6, 1966)

Conductance measurements are reported for Me4NBr, Et4NBr, Pr4NBr, BurNBr, Me4NI, Pr4NI,and Bu4NI in aqueous solutions at 45". Solvent structural influences on the limiting conductance of these large ions as well as on the alkali and halide ions in aqueous solution are investigated by considering the effect of temperature and pressure on the Walden product and by comparing their behavior in aqueous solution with that in nonaqueous solution. The mobility of the larger tetraalkylammonium ions is shown to be influenced to a considerable extent by the enforcement of water structure about their hydrocarbon chains. The same explanation applied to diffusion data for nonelectrolytes and dipolar ions accounts for the dependence of their Walden products on temperature and solvent. The possibility that solvent structural influences also cause the greater-than-normal decrease of the equivalent conductance with concentration for the tetraalkylammonium iodides is considered.

Introduction A recent investigation of the conductance of the tetraalkylammonium halides in aqueous solution at 10 and 2501 indicated that the limiting conductance of these large cations is influenced to a considerable extent by the formation of what have been called clathratelike structures of water about their hydrocarbon chains. It has been shown2 that such an assumption will explain the differences in the limiting Walden product for these ions in HtO and D20. Also, the concentration dependence obtained could best be explained by the assumption that they were slightly associated in aqueous solution and that the amount of association increased with increasing anion size. The purpose of this extension of the conductance measurements to 45" was to study both the limiting Walden product and the apparent association of these large tetraalkylammonium ions under conditions in which the amount of solvent structure has been reduced substantially. In the Discussion section, the hydrodynamic properties of both large and small symmetrical ions are investigated by comparing their behavior in aqueous and nonaqueous solutions and particularly by noting their temperature and pressure dependence. The investigation is also extended to nonelectrolytes and

dipolar ions. It was found that solvent structural effects were essential to any consistent explanation of transport properties of ions in aqueous solution at infinite dilution.

Experimental Section The conductance bridge, conductance cells, salt-cup dispensing device, and general techniques were the same as previously described1gas4with the exception of the constant-temperature bath. This was an insulated stainless steel tank containing 12 gallons of oil and fitted on top with a chamber which had a hinged Plexiglas cover. This chamber was heated to a temperature of 47" with two 100-w light bulbs so as to prevent condensation of the solvent in the salt-cup dispensing device. The change in the cell constant from 25 to 45", as calculated from the cell geometry and coefficients of expansion given by Robinson and stoke^,^ was found to be less than 0.01%. ~~

(1) D.F. Evans and R. L. Kay, J. Phys. Cltem., 70, 366 (1966). (2) R.L.Kay and D. F. Evans, ibid., 70,4216 (1965). ( 3 ) D.F. Evans, C. Zawoyski, and R. L. Kay, ibid., 69, 3878,4208 (1965). (4) J. L.Hawes and R. L. Kay, ibid., 69,2420 (1965).

Volume 70, Number 7 July 1966

2326

ROBERT L. KAYAND D. FENNELL EVANS

Temperature was controlled to 45 f 0.007” as determined by a calibrated platinum resistance thermometer. The purification procedures for the conductivity water and the salts have been adequately described elsewhere.l v 3

Results The density increments for the tetraalkylammonium bromide solutions, used to calculate the volume concentrations, were obtained from density measurements on 0.06 1cf solutions and were assumed to follow the relationship d = do t%, where do = 0.99024 at 45” and where 7iz is the concentration in moles per kilogram of solution. The 0 values were found to be: MerNBr, 0.039; EtrNBr, 0.036; PrdNBr, 0.027; BudNBr, 0.022. The corresponding values for the iodides were estimated by adding the iodide-bromide difference of 0.030 obtained from density measurements at both 10 and 25O.l The viscosity B coefficients were measured6 and found to be: Me4NBr, 0.11; Et4NBr, 0.30; PrrNBr, 0.64; Bu4NBr, 0.99. The corresponding values for the iodides were assumed to be 0.03 lower in keeping with the results found at 10 and 25’. The measured equivalent conductances, the corresponding concentration in moles per liter, and the solvent conductances are given in Table I. The data were analyzed by the Fuoss-Onsager conductance theory? in the form

+

A =

A0

- SC”’ + EC log C + (J - BAo)C

(1) and also, in the case of Pr4NIand Bu4N1, where association was detected, by A = &, - S(Cy)”’

+ ECy log Cy + (J - BAo)Cr

- KACTA.P

(2) The AA values in Table I are the difference between the measured A and that calculated by eq 1 or by eq 2 in the case of Pr4NI and Bu4NI. The conductance parameters in Table I1 were determined by a leastsquares computation using computer programs. a ** A dielectric constant e = 71.5l9 and a viscosity q = 0.5963 cpl0 were used for water at 45”. In Table 11, the standard deviations in each parameter, the standard deviations of the individual points u,,, and the values of J are given for convenience of computation. The limiting conductances for the tetraalkylammonium ions at 45” are given in Table 111. They were calculated using Xo(Br-) = 110.69 and ho(I-) = 108.76, which were obtained from the corresponding values a t 25” as quoted by Evans and Kay1 and the temperature-dependent equation of Harned and Owen.” The Journal of Physical Chemktw

Table I 10‘C

A

AA

MerNBr, lo7% = 9.021 171.64 18.025 169.90 27.756 168.53 38.001 167.33 46.982 166.44 59.365 165.34 68.416 164.62 78.396 163.89

1.5 0.05 -0.01 -0.02 -0.02 -0.01 0.00 0.00 0.02

EtJVBr, ~O’K,, = 7.677 155.06 18.812 152.87 26.150 151.86 37.251 150.56 43.986 149.88 54.455 148.92 65.171 148.05 78.792 147.03

1.3 0.08 -0.04 -0.03 -0.03 -0.02 -0.01 0.02 0.03

Pr4NBr, lo7%= 7.070 143.02 12.828 141.74 21.612 140.32 29.771 139.25 36.440 138.50

1.6 0.03 -0.02 -0.02 -0.01 0.02

Bu4NBr, ~O’K,, = 1 . 7 9.997 137.09 0.00 15.456 136.04 -0.01 21.553 135.09 -0.01 27.473 134.33 0.03 33.865 133.52 0.00 41.102 132.72 0.00 47.565 132.06 0.01

104c

A

AA

MeSJI, 1 0 7 = ~ 1.5 5.946 170.50 0.03 13.269 168.81 -0.01 Z.087 167.35 -0.02 29.232 166.40 0.00 37.168 165.46 0.00 43.543 164.78 0.00 53.256 163.84 0.00 61.667 163.10 0.01 PrdNI, 107~0= 5.071 141.56 10.888 140.01 16.667 138.91 23.767 137.75 29.931 136.89 37.755 135.87 44.892 135.06 52.972 134.20

1.4

BuaNI, l O ’ ~ 0 = 4.181 136.31 10.183 134.60 16.331 133.32 23.413 132.10 31.353 130.88 39.379 129.85 46.903 128.94 57.472 127.77

1.6 0.01 -0.02 -0.01 0.01 -0.02 0.01 0.01 -0.01

0.02 -0.04 0.00 0.00 0.02 -0.01 0.00 -0.01

The agreement in the cation conductances from the bromide and iodide salts is entirely satisfactory and indicates that the techniques employed here permit conductance measurements to be carried out a t elevated temperatures with almost the same precision as those a t 25”. (5) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” 2nd ed, Butterworths and Co. Ltd., London, 1959, p 97. (6) R. L. Kay, T. Vituccio, C. Zawoyski, and D. F. Evans, J. Phue. Chem., 70, 2336 (1966). (7) R. M. Fuoss and F. Accmcina, “Electrolytic Conductance,” Interscience Publishers, Inc., New York, N. Y., 1959. (8) R. L. Kay, J. Am. Chem. SOC.,82, 2099 (1960). (9) C. G. Malmberg and A. A. Maryott, J. Res. Natt. Bur. Std., 56, 1 (1956). (10) See ref 5, p 457. (11) H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” 3rd ed, Reinhold Publishing Corp., New York, N. Y., 1958, p 233.

MOBILITY OF SYMMETRICAL IONS IN AQUEOUSSOLUTION

2327

Table 11: Conductance Parameters for Aqueous Solutions at 45" Salt

d

Ao

KA

J

UA

Me4NBr EtdNBr Pr4NBr BQNBr

175.67 f 0.02 158.64f0.03 146.45i0.03 141.19 i 0 . 0 2

2.04 f 0.04 1.98 f 0.08 1.8 f 0 . 1 2.02 f 0.07

0.03 0.04 0.03 0.02

167.4 152.5 128.0 144.9

Me4NI

173.79 f 0.01

1.59

* 0.03

0.02

124.7

Pr4NI

144.48f0.02 144.56 f 0.03"

0.40 f0.05 5 i25

3 A 15

0.03 0.02

-72.9 368.0

138.94i0.03 139.07 i0.02"

0.10 f 0.02 6 1"

5.0 f 0.8"

0.05 0.02

-75.4 453.4

BQNI

*

" Equation 2.

Discussion (1) Walden Product. Alkali Halides. Before dis-

Table 111 : Limiting Cation Conductances in Aqueous Solution a t 45" Br -

Me4N+ EtrN Pr4N + BurN +

64.98 47.95 35.76 30.50

+

1-

Av

65.03

65.01 47.95 35.78 30.40

35.80 30.31

cussing the Walden product for the tetraalkylammonium ions, it is necessary to review the known results for smaller, univalent, symmetrical ions. These have been collected in Table IV along with data for the quaternary ammonium ions in all solvents for which precise transference numbers or for which data on a

Table IV : Limiting Ion Conductances" Ion

Li + Na + K+ c s+ Me4N EtaN + Pr4N+ BurN + ~ h 4 +N i-Am,BuN + +

Fc1-

Hi0 (459b

Ha0

Ha0

(25°)b

(100)b

DIO'

CHaOH'J

CzHsOH'

58.02 73.83 103.61 107.56

38.66 50.20 73.55 77.29

26.37 34.93 53.08 56.50

41.62 61.40 64.44

39.55 45.17 52.44 60. 83h

17.07 20.30 23.55 26.46'

65.01 47.95 35.78 30.40

44.42 32.22 23.22 19.31 17.38' 20.67d

30.93 21.90 15.33 12.56

36.61' 26.44' 18.84' 15.62'

68.73 60.5 46.08 38.94 34.8 36.6

30. O l k 29. 53k

52.36 56.45 62.78

21.87 24. Ozk 26.13'

55.32' 76.39 78.22 76.98

108.96 110.69 108.76

BrI-

54.33 56.15 55.39

44.79 62.83 64.67 63.79'

19. l g l

CHaNOz"

CHaCN"

54.50 47.60 39.14 34.07

94.15 84.64 70.28 61.36 58.13

62.70 62.94

98.7 100.74 102.69

" Solvent viscosities, in centipoises, used to obtain Walden products are: Ha0 (25"), 0.8903; HzO(lo'), 1.306; DzO, 1.096; CH30H, This work and ref 1 and 8. H. M. Daggett, E. J. Bair, and C. A. Kraus, 0.5445; CZH~OH, 1.084; CHZNOZ, 0.627; CHaCN, 0.341. J. Am. Chem. SOL, 73,799 (1951); J. F. Skinner and R. M. FUOSS, J. Phys. Chem., 68,1882 (1964). ' C. G. Swain and D. F. Evans, J. Am. Chem. Soc., 88,383 (1966). R. L. Kay and D. F. Evans, J. Phys. Chem., 69,4216 (1965). The split into ionic conductances is discussed in detail in ref 3. Ir R. L. Kay and J. L. Hawes, J. Phys. Chem., 69,2787 (1965). The ionic conductances for the alkali and halide ions are based on the transference data of J. R. Graham and A. R. Gordon, J. Am. Chem. SOC.,79,2350 (1957), and the conductance data of J. R. Graham, G. S. Kell, and A. R. Gordon, ibid., 79,2352 (1957), aa recalculated by R. L. Kay; see ref 8. See ref 4. T. H. Mead, 0. L. Hughes, and H. Hartley, J. Chem. Soc., 1207 (1933), and M. Barak and H. Hartley, 2.Physik. Chem., J. Am. Chem. SOC.,76, 5902 (1954). A165, 273 (1933). H. Sadek and R. M. FUOSS, R. L. Kay, S. C . Blum, and H. I. Schiff, J . Phys. Chem., 67, 1223 (1963). " Ion conductances obtained from the salt conductances reported in ref 3 and the assumption that both ions of triisoamylbutylammonium tetraphenylboride have equal conductances of 58.13 as reported by M. A. Coplan and R. M. FUOSS, J. Phys. Chem., 68, 1181 (1964).

'

'

'

Volume 70,Number 7 July 1966


2328

Figure 1. The limiting Walden product for the alkali-halide and tetraalkylammonium ions as a function of crystallographic size, temperature, and solvent. Theoretical predictions are shown by the dotted curves.

reference electrolyte are available.I2 Where necessary, all conductances were recalculated to bring them into conformity with the Fuoss-Onsager equation (1) or (2). The data for D20 and the nonaqueous solvents refer to 25". The Walden products are plotted in Figure 1 as a function of the reciprocal estimated crystallographic ionic radii.I3 It is obvious from the data for the alkali and halide ions in Figure 1 that Stokes' law14 given in terms of the Walden product by

Xo?/lZI = F2/6?rNr. The Journal of Physical Chemistry

(3)

does not nearly describe the hydrodynamic behavior of the ions in any solvent, a fact that has been recognized for some time. One likely correction to Stokes' (12) Owing to its unique transport mechanism, data for the H + ion are not included. Although transference data are available for liquid ammonia solutions a t -37O (J. L. Dye, It. Sankuer, and G. E. Smith, J . Am. Chem. Soc., 82,4797 (1960)).ionic conductances are not known with a precision comparable to the data included in Table I V and, consequently, have not been included. Rough calculations indicate that the Walden product is about 0.50 for the halide ions and about 0.40 or less for the alkali ions, values considerably less than those for aqueous solution. (13) See ref. 5,pp 125,461. (14) See ref 11, p 284.

MOBILITYOF SYMMETRICAL IONS IN AQUEOUS SOLUTION

law has been proposed by Fuoss15 and quantitatively evaluated by Zwanzig.l6 This calculation takes into account the retardation due to the relaxation of solvent dipoles around the moving ion. It has been pointed out by Frank” that the correction satisfactorily predicts the maximum in the hoq curve but is too low in magnitude by a factor of almost 3, as can be seen in Figure 1. He has also shown that any reasonable modification of the equations involved is not nearly sufficient to account for the large discrepancy. A similar low result is obtained for methanol solution as is shown in Figure 1. At this point, most discussions of the Walden product have taken one of the following two approaches. If the Xoq product results in a Stokes radius, as calculated from eq l, greater than or equal to the crystallographic ionic radius, the ion in question is considered to be solvated or unsolvated, respectively. On the other hand, Stokes radii less than the crystallographic radii (X,q above the Stokes’ law line in Figure 1) cannot be attributed to solvation effects, and an appeal is made to the unrealistic model on whick Stokes’ law is based. A suitable calibration curve is then devised to correct for this deficiency.13J* Our results for the tetraalkylammonium ions, which are discussed in detail below, show that the assumptions on which these calibration curves are based are invalid. Furthermore, it is impossible to obtain absolute values for the hydrodynamic ionic radii by merely appealing to solvation as a means of overcoming the inherent limitation of the model on which Stokes’ law is based. Our approach here is to consider only ratios of Walden products in an effort to reduce errors due to inadequacies of the model and limitations of the concepts involved1gand thereby make our conclusions more meaningful. In Figure 1, one aspect stands out very clearly: the Walden products for the alkali and halide ions in aqueous solution are substantially higher and show considerably more variation with crystallographic size than the corresponding values for nonaqueous solutions, all of which group closely together.z0 This apparent excess of mobility in aqueous solution could be attributed to far greater solvation in the nonaqueous solvents, and such an explanation would be sufficient if it were not for the temperature dependence of the Walden product. Unfortunately, although precise conductance data are available for methanol solution at 25 and transference measurements have been reported only for 25” (see Table IV), and a split into ionic conductances is not possible a t 10”. However, as can be Seen in Table V, the change in the A0q product from 10 to 25” for various salts is from 4 to 30 times greater in water than it is in methanol, but, for both sol-

2329

vents, the change is in such a direction as to require greater solvation a t higher temperatures, a prospect that is most unlikely. The Zwanzig equation predicts that the Walden product should increase 0.5% for a change in temperature from 10 to 25”, whereas the opposite behavior is observed for the alkali halides in aqueous solution. Table V : Temperature Dependence of t h e Walden Product in HzO and CHsOH -(Aor))iao/(Ao?)zsa---

Ha0

CHsOH

Et4NBr PrrNBr Bu4NBr

1.042 1.037 1.034 1.034

1,009 1.007 1.006 1.001

Me4NI Bu~NI

1.044 1.035

1.011 1.002

Me4NBr

It is generally accepted nowz1that the larger alkali and halide ions possess an excess mobility in aqueous solution owing to their ability to break hydrogen bonds in their immediate vicinity and thereby reduce the local viscosity. An increase in temperature reduces the amount of hydrogen bonding in water and thereby reduces the effectiveness of these ions as structure breakers. The subject of water structure and its effect on ionic properties has been discussed most recently by Frankzz and reviewed by K a v a n a ~ but , ~ ~Gurneyz4was the first to collect most of the evidence and clarify the con~

(15) R. M. Fuoss, Proc. Natl. Acad. Sci. Li. S., 45, 807 (1959). (16) R. Zwanzig, J . Chem. Phys., 38, 1603 (1963). (17) H. S. Frank, “Chemical Physics of Ionic Solution,” B. E. Conway and R. G. Barradas, Ed., Electrochemistry Society, John Wiley and Sons, Inc., New York, N. Y., 1966. (18) E. R. Nightingale, Jr., J . Phys. Chem., 63, 1381 (1959). (19) D. G. Miller, ibid., 64, 1598 (1960). (20) It could be argued that the excess mobility of many ions in aqueous solution is due to the very high dielectric constant possessed by water. However, the same ions in other solvents of high dielectric constant do not show this large excess mobility. For example, the Walden products for formamide solutions a t 25O, e = 109.5, range from 0.28 to 0.45 for the alkali ions and 0.57 to 0.55 for the halide ions. In Figure 1, it can be seen that these values are still lower than those for aqueous solutions. Transference data are from J. M. Notley and M. Spiro, J . Phys. Chem., 70, 1502 (1966). (21) R. H. Stokes and R. Mills, “Viscosity of Electrolytes and Related Properties,” Pergamon Press Inc., New York, N. Y., 1965, p 54. (22) H.‘S. Frank, Federation Proc., 24, S1 (1965). (23) J. L. Kavanau, “Water and Solvent-Water Interactions,” Holden-Day, Inc., San Francisco, Calif., 1964. (24) R. w. Gurney, “Ionic processesin Solution,” &fcGraw-Hil, Book CO., Inc., New York, N. Y., 1953.

Volume YO, Number 7

July 1966

2330

cepts involved as far as transport properties are concerned. Here, we will use the Frank and Wen2bmodel for ions in aqueous solution since it is sufficient in detail to explain the abnormal transport properties of the alkali, the halide, and the quaternary ammonium ions, as well as their temperature and pressure dependence. It has been used already to explain the difference in the Walden product obtained for HzO and DzO solutions.2 In this model, the competitive influences of neighboring solvent dipoles and ionic charge on any given water molecule result in three separate regions around an ion. If the ionic charge predominates by a considerable amount, electrostriction occurs in which water molecules are immobilized to a considerable extent around the ion to form a solvation sheath. At much larger distances, where the effects of the ionic charge are insignificant, a given water molecule will be oriented solely by its neighboring water molecules, and consequently this region will have the properties of pure water. I n the intermediate region, the ionic charge will not be strong enough to orient the water molecules completely, but it will interfere with the formation of the normal three-dimensional structures present in water. This region will be one with less solvent structure than bulk water, and this structure-breaking effect will become greater the smaller the charge-to-surface ratio of the ions. The region of immobilized water resulting from the structure-making effects of electrostriction will increase with increasing charge-to-surface ratio of the ions. Another effect has been postulated for the quaternary ammonium ions that possess large hydrophobic side chains. A water molecule at the surface of these large ions is influenced very little by either the ionic charge or the inert hydrocarbon chain on its one side. Consequently, the water molecules on this hydrophobic surface can be oriented to a greater extent by their nearest neighbors and can, in effect, be oriented into cages about the hydrocarbon side chains that are similar in structure, possibly, to the polyhedral clathrate hydrates of these ions.26 These clathrate like structures can be considered a type of hydration, since they increase the size of the moving entity as is also the case with electrostrictive hydration. Ions experiencing this effect should have lower mobilities in aqueous solution than in nonaqueous solution since only water appears able to form any appreciable amount of three-dimensional structure. On the basis of this model, at least part of the excess conductance of the alkali and halide ions in aqueous solution as shown in Figure 1 can be readily explained. With the possible exception of Lif, Na+, and F-, these ions are structure breakers in that they break down the hydrogen bonding in the water in their viThe Journal of Physical Chemistry


cinity and thereby decrease the local viscosity and increase the mobility of the ions. Perhaps the best experimental evidence comes from a comparison of the limiting diffusion coefficients of argon2' and Kf and C1- ions in aqueous solution. As has been pointed out by Muller and Stokes,28although these are isoelectronic, the K+ and C1- ions are 34 and 39% faster, respectively, than the argon atom (see Figure 1). This difference can be attributed to the structurebreaking influence of the ions and possibility to the structure-making influence of the inert argon atoma29 The diffusion coefficient of argon at 25" converts to a Walden product of approximately 0.49 and possibly indicates the maximum amount of the excess mobility in aqueous solution (34-39%) that can be attributed to the structure-breaking effect of the ions. As has been pointed out above, the decrease in Walden product with increased temperature for structure-breaking ions is due to the fact that there is less structure to break at higher temperatures. The fact, however, that the Walden products for these structure-breaking ions are still well above 0.49 a t looo5indicates that this structural effect persists at even more elevated temperatures. 30 The smaller ions with large charge to surface ratios, such as the Li+, F-, and even Na+ ions, are less effective as structure breakers, and their conductance is controlled almost entirely by electrostrictive hydration that varies relatively little with increased temperature. The Walden products for multivalent ions are not shown in Figure 1, but, for the monatomic cations, they are all less than 0.3 in aqueous solution and are almost independent of ionic size and temperature, indicating that, because of their high charge density, their conductance is controlled almost exclusively by the amount of electrostrictive hydration. It is interesting to apply these ideas to the effect of (25) H. S. Frank and W. Y. Wen, Discussions Faraday SOC.,24, 133 (1957). (26) P. T. Beurskens and G. A. Jeffrey, J . Chem. Phys., 40, 906 (1964). (27) R. E. Smith, E. T. Friess, and M. F. Moralis, J . Phys. Chem., 59, 382 (1955). (28) G. T. A. Mllller and R. H. Stokes, Trans. Faraday SOC.,53, 642 (1957). (29) H. S. Frank and M. W. Evans, J . Chem. Phys., 13, 507 (1945); A.Ben-Naim, ibid., 42, 1512 (1965). (30) For example, BurNBr in aqueous solution has been shown to have an excess partial molar heat capacity at 25O of almost 120 cal/deg mole due presumably to clathratelike structures of water enforced about its hydrocarbon side chains. This exces8 heat capacity is still detectable a t temperatures as high as 130° (T. Ackermann, private communication, 1965). In this respect, it is interesting to note that Aoq for &SO4 decreases with increasing temperature between 100 and 400' a t pressures high enough to keep the density of water equal to 1.0 (A. S. Quist, E. U. Franck, H. R. Jolley, and W. L. Marshall, J . Phy8. Chem., 67, 2453 (1963)).


l*lot

Pic'I

I

I

0

I

I

1

I

lo3P(kg/cm*)

1

I

2

I

1

3

Figure 2. T h e relative change of the Walden product with pressure in 0.01 N aqueous and methanol solutions a t 25'.

increased pressure on the Walden product in aqueous solution. One effect of increased pressure is to break down the bulky three-dimensional water structure and thereby produce a less structured solvent. This is verified by the fact that water is the only known liquid with a negative pressure coefficient of viscosity.31~92 As the pressure increases, all ions should become less effective structure breakers owing to this decreased amount of structure, and, consequently, the ions should lose some of their excess mobility. A possible second effect dealing with electrostrictively hydrated ions can also be predicted. Electrostriction results in a decrease in volume, as is shown by the increase in the dissociation constant of weak electrolytes as the pressure i n ~ r e a s e s . ~Thus, ~ , ~ ~ small ions should become more hydrated as the pressure increases and therefore should have a lower conductance. Both of these effects are evident in Figure 2 where the ratio of the Walden product at 30" and pressure P to that at atmospheric pressure and the same temperature are plotted as a function of press~re.~sThe Walden product for a 0.012 N solution of NaNOa in methanol increases very rapidly with increased pressure, whereas for all the salts in aqueous solution3* the relative change in the Walden product as the pressure increases is considerably lower. Furthermore, the change with pressure is the lowest for the salts containing the best structure-breaking ions, such as the iodide and cesium ions. It can be seen that the Walden product actually decreases with increased pressure for KI and NaI. These observations are consistent with the idea that pressure breaks down the clusters of water structure and reduces the excess

2331

conductance of structure-breaking ions. The main inconsistency with this argument is the fact that the sodium salts are all lower than the corresponding potassium salts, although potassium ion is a known better structure breaker. This could be a manifestation of the second effect; namely, increased hydration due to the high pressure could affect the sodium ion If it were not for the more than the potassium extensive hydration of the F- and Li+ ions, NaF and LiCl would show a much greater increase in A7 with pressure. Further evidence that the interpretation of the pressure data given here is basically correct can be found in the effect of temperature on the pressure dependence of the Walden product. No effect, within the experimental error, is found in the pressure dependence of the Walden product for methanol solutions35on changing the temperature from 30 to 75". In Figure 3, the results for aqueous solutions36 are plotted where R7ao/Rmois given by

At 75" and P = 1 atm, there is less structure in water than at 30" and P = 1 atm. Consequently, there (31) P. W. Bridgman, "The Physics of High Pressure," G. Bell and Son, Ltd., London, 1949, Chapter XII. (32) K. E. Bett and J. B. Cappi, Nature, 207, 620 (1965); J. B. Cappi, Ph.D. Thesis, University of London, 1964. We are indebted to Dr. Bett for a copy of these data prior to their publication. (33) 9. D. Hamann, P. J. Pearce, and W. Strauss, J. Phys. Chem., 68, 375 (1964). (34) F. H. Fisher and D. F. Davis, ibid., 69, 2595 (1965). (35) The conductance data for methanol solutions are those of S. B. Brummer and G . J. Hills, Trans. Faraday SOC.,57, 1823 (1961). The scatter in the points is due mainly to the lack of precision in the viscosity data.31 The conductance data for the various salts in aqueous solution a t 30 and 75O were taken from W. A. Zisman, Phys. Rev., 39, 151 (1932), which, in the case of KCl, were found to be in fair agreement with the more recent data of F. Hensel and E. U. Franck, 2. Naturforsch., 19, 127 (1964). The viscosity data of Bett and Cappisl for water a t 30 and 75O were used. These data are in poor agreement with those of Bridgman but appear to be preferable since they are more consistent with the viscosity data a t lower temperatures and agree better with those of W. Weber, 2. Angew. Phys., 15, 342 (1963), a t lower pressures. (36) The concentration here is 0.01 M . The relative Walden product has been found to be insensitive to concentration changes in the range 0-0.02 M.34 (37) R. A. Horne, Nature, 200, 418 (1963), has taken the opposite point of view that pressure "breaks up the structure of ionic hydration'' so that LiCl lies higher than the other salts in Figure 2 since it undergoes the greatest decrease in the amount of hydration as the pressure increases. This interpretation, however, is not in agreement with the known fact that electrostrictive hydration results in a decrease in volume and therefore should be the preferred state as the pressure increases, as is noted above from the change of dissociation constants of salts with pressure. Also, his conclusion that all solvent structure has been destroyed a t pressures above 2000 to 3000 kg/cmZ is not well founded. It should be noted that Zisman's data have already been corrected for the solvent compressibility, and consequently the dotted line in Figure 2 of Horne's paper should not contain this factor.



2332

I

1.04F

I

I

H20, 45*C o n20, 250c ti&, iooc 0

020 Q

CHsOH

0 C2H50H V CHsCN

CH~NOZ

O0.3 .

I

0

f

I

1

I

1

2

I

I

3

~

MeZ(Et0l

1

103P(kg/cm2)

Figure 3. The Walden product a t 75" relative to 30" as a function of pressure for aqueous solutions of the alkali halides.

24--BJ,N+ I

should be less decrease of the Walden product at 75" upon increase in the pressure than at 30" for structurebreaking ions, and that is the result obtained from the data shown in Figure 3. The use of this double ratio is extending the data to the limit of their precision, but the results clearly illustrate that, in contrast to the other ions, the structure-making Li+ ion shows little change with temperature. Tetraalkylammonium Ions. The limiting Walden products for these ions are plotted in Figure 1 for comparison with the alkali and halide ions but are presented in more detail in Figure 4 as a function of the estimated crystallographic radii.13 It can be seen that, with the exception of Me4N+and Et4N+ in hydroxylic solvents, the Walden products for these large ions in nonaqueous solvents are almost identical and fall on the solid line. In aqueous solution, however, the MepN+ion lies well above this line, suggesting it to be a structure breaker in aqueous solution as was found to be the case from a comparison of mobility data for HzO and D20 solutions.2 At the other end of the scale, the Walden products for the Am4N+,Bu4N+,and Pr4N+ ions are well below this nonaqueous line, suggesting that in aqueous solution these ions are larger than in nonaqueous solvents. This is in keeping with the idea that clathrate-like structures form about the hydrocarbon portions of these ions as the length of the side chain increases. Such enforcement of water structure about the hydrophobic side chains of these ions would tend to increase the local viscosity as well as increase the size of the moving entity and thereby decrease the mobility. The effect of temperature on the Walden product for these large cations is seen more readily in Figure 5, where the data of Lange3*at 0" are included with our own at 10, 2.5 and 45". Only the Et4N+ ion shows no temperature dependence, owing presumably to a canThe Journal of Physical Chemistry

0.18

0.20

0.22

I 0.24

I/b

1

1

I

0.26

0.28

0.30

(

12

Figure 4. The limiting Walden product for various quaternary ammonium ions as a function of estimated crystallographic radii, temperature, and solvent.

cellation of the effects of structure breaking and structure making as judged by this criterion. The temperature dependence of viscosity B coefficients6 indicates this ion to be a slight structure maker whereas its mobility in D20 relative to Hz02 indicates a slight structure-breaking tendency. These seemingly conflicting results illustrate that the Et4N+ ion is a borderline case and that the different transport properties reflect slightly different aspects of ion-solvent interaction. The Me4N+ion has a negative temperature coefficient, typical of structure-breaking ions, as was found with the larger alkali and halide ions. As the temperature increases, there is less structure available to be broken, and the Me4N+ ion is less effective in reducing the local viscosity. The Pr4N+and Bu4N+ions both have positive temperature coefficients as would be expected of ions forming clathratelike structures around their hydrocarbon side chains. As the temperature increases, these cages of water melt and produce a smaller and therefore faster-moving entity. Thus, the temperature dependence, the H20-Dz0 comparison,2 and the above comparison of Walden products in aqueous and nonaqueous solutions are consistent with the Frank-Wen25 model for aqueous ionic solutions. It is also consistent with viscosity B coefficients and their temperature dependencea6 Further evidence for the existence of water structure enforcement about the hydrocarbon chains of the large tetraalkylammonium ions can be seen in Figure 4. The unsymmetrical Me3(hexyl)N+39 and &'le3(38) J. Lange, 2. Physik. Chem., A168, 147 (1934).


1

1

1

1

I

0.4

1 0.

xorl

0.

1

0

I 10

I

20

1

30

I 40

I

50

TOC

Figure 5. The change of the limiting Walden product for the tetraalkylammonium ions with temperature.

PrN+ * ions follow the same pattern outlined above for the symmetrical tetraalkylammonium ions, but if a hydroxyl group is substituted for a terminal methyl group, the mobility of the resulting ion is somewhat greater than its alkyl analog. Thus, the Me3(EtOH)N+ 4 0 ~ ~ and 1 the Mez(EtOH)zN+41 ions have greater mobilities than the MeSrN+ and the Et*N+ ions, respectively. Although the mobility difference is small, it is considerably greater than the possible error in the measurements. Contrary to the opinion of Spivey and Sne11140we believe that the introduction of a dipole moment into the side chains of these ions interferes with the formation of cages of structured water about the side chains and therefore produces a smaller moving entity than is the case with the alkyl analog. This is in keeping with the concept that it is the inert nature of the hydrocarbon chain that permits neighboring water molecules to orient themselves into a caged structure. Preliminary experiment@ with the (EtOH)4N+ion indicate that it has a considerably higher mobility than its alkyl analog, the Pr4N+ ion. Similar conclusions were reached from partial molal volume and activity coefficient measurements on this ion at relatively high concentrations in aqueous solution.43

2333

It should be noted that, although the Xoq product for the i-Am3BuN+ ion in methanol lies on the nonaqueous line, the corresponding value for aqueous solution is not nearly so low as the symmetrical R4N+ ions. This would indicate that enforcement of water structure about four isoamyl groups placed tetrahedrally about a charged nitrogen atom may be less favorable than around four n-amyl groups. Temperature data would be of considerable help in answering this question. The temperature dependence of the Walden product for the R4N+ions casts considerable doubt on the significance of hydration numbers calculated from Stokes' law as modified by Robinson and Stokes.13 These hydration numbers are based on the assumptions that all of the quaternary ammonium ions are unhydrated, that only the n-Am4N+ ion fits Stokes' law in that its Stokes' radius and estimated crystallographic radius are identical, and that the smaller quaternary ammonium ions deviate from Stokes' law behavior because they are not of sufficient size so that the solvent can be considered a continuum.44 On this basis, they developed a correction factor for this size deficiency and applied it to the Stokes radii of the other ions to obtain the hydrated radii and thereby hydration numbers. However, the temperature dependence of the Walden product for the larger R*N+ ions indicates definitely that these ions are hydrated, a fact that completely invalidates the assumption on which these calibration curves and hydration numbers are based. Nonelectrolytes and Dipolar Ions. Diffusion data for a number of nonelectrolytes and amino acids have been r e p ~ r t e dfor~ aqueous ~ ~ ~ ~ solutions at 1 and 25" and for methanol solutions at 25". We can use these data as a further test of the applicability of the concepts discussed above by again considering ratios of Walden products. Stokes' law, as applied to diffusion coefficients,states in eq 5 that (39) M.J. McDoweU and C. A. Kraus, J . Am. Chem. SOC.,73,2170 (1551). (40) H.0. Spivey and F. N. Snell, J . Phys. Chem., 68, 2126 (1964). (41) J. Varimbi and R. M. Fuoss, ibid., 64, 1335 (1960). A value of Xo(Mea(EtOH)N+) = 38.16 was obtained by weighting these data and those of Spivey and Snell'o by the standard deviation of the measurements. (42) D. F. Evans, G . P. Cunningham, and R. L. Kay, to be published. (43) W. Y.Wen and 9. Saito, J . Phyhys. Chem., 69, 3569 (1965). (44) E.R. Nightingale'8 made the added assumption that the MerN ion was hydrated, and thereby he was able to develop a correction factor to be added to the Stokes' radius that converged to a finite value as the Stokes' radius approached zero. Otherwise, his hydration numbers are based on the same assumptions as Stokes and Robinson's. (45) L. G.Longsworth, J . Am. Chem. Soc., 75, 5705 (1953). (46) L. G.Longsworth, J . Phys. Chem., 67, 689 (1963). +


ROBERTL. KAY AND D. FENNELL EVANS

2334

DoqlT = k/6?rrS

(5)

that is, it is the quantity Doq,/T that should be independent of solvent and of temperature. The ratios of the Walden product for a number of nonelectrolytes in water and methanol, as given in Table VI, indicate that they diffuse too fast in water or too slowly in methanol; that is, they are either good structure breakers in aqueous solution or they are affected to greater extent by solvation in methanol than in water. Without temperature dependence of diffusion, it is difficult to distinguish between these two effects, and no such data are available for the substances listed in Table VI. However, as can be seen in the series, formamide, acetamide, and propionamide, the diffusion coefficient decreases in aqueous solution relative to methanol solution as the hydrocarbon portion of the molecules increases in length, a direction to be expected if the hydrocarbon chains were enforcing water structure. The absence of a charge in these polar nonelectrolytes could permit even a methyl group to add considerably to water structure enforcement in contrast to what is found for the charged Me4N+ion. Likewise, urea and its mono- and dimethyl derivatives behave in a manner similar to the amides as methyl groups are added. Urea, itself, has a Walden product 42% greater in water than in methanol. This could be a good indication of structure-breaking properties for urea in aqueous s~lution.~'

Table VI:

(UO,)H~O/(&~I)CH~OH a t 25"

Formamide Acetamide Propionamitle

1.27 1.18 1.08

Urea Methylurea 1,3-Dimethylurea

1.42 1.20 1.06

Ethylene glycol Glycerol Erythritol Dextrose Sucrose

1.15 1.18 1.14 1.18 1.16

Water

1.71"

a The recent; data of Wang (see ref 48) would increase this ratio to 1.93.

Wanga has recently shown that the Walden product for the self-diffusion of water in water is independent of temperature. The almost 50% decrease in the Walden product for water in methanol indicates that the moving entity in methanol is definitely a solvated species. The ratios given in Table VI for compounds with multiple hydroxyl groups are greater than unity indicating either structure breaking in water or greater solvation effects in methanol. The latter conclusion is preferable since it is in agreement with the temperaThe Journal of I'hy8icaE Chemistry

ture dependence of the Walden products for aqueous solution45given in Table VII. The ratio of the Walden product at 25" compared to that at 1" for the mono-, di-, and trisaccharides is greater than unity, typical of structure-making compounds. Since we have shown that exposed hydroxyl groups appear to inhibit the formation of clathrate structures in aqueous solution, we conclude that the sugars are solvated in both water and methanol but more so in methanol. Solvation is temperature dependent in the case of the sugars but not for the Li+ ion because in sugars the solvation involves dipole-dipole interaction in contrast to the stronger charge-dipole interaction of ions with solvent. Table VII: Temperature Dependence of the Walden Product in Aqueous Solution (Dr)/T)zsO (DslT)iO

Glucose Sucrose Raffinose

1.019 1.025 1.026

Glycine Diglycine Triglycine

0.974 0.992 0.995

a-Aminopropionic acid (alanine) 8-Aminopropionic acid (13-alanine) p-Hydroxy-a-aminopropionic acid (serine)

1,001 0.984 0.997

a-Aminobutyric acid a-Aminoisovaleric acid (valine) a-Aminocaproic acid (norleucine) a-Aminoisocaproic acid (leucine)

1.012 1.029 1.035 1.034

Glycylleucine Leucylglycine

1,032

1.029

The negative temperature coefficient of the "Walden product" for glycine (Table VII) indicates it is a fair structure breaker in aqueous solution, but as the charge separation increases in di- and triglycine, this property diminishes. As the hydrocarbon portion increases in length in the higher homologs of glycine, the structuremaking features become more pronounced as seen by the increasing ratio in the series glycine, alanine, cyaminobutyric acid, valine acid, and leucine. Dis(47) This conclusion is in agreement with the temperature dependence of viscosity B coefficients for urea in aqueous solution calculated from the data of H. M. Chadwell and B. Asnes, J . Am. Chem. Soc., 5 2 , 3507 (1930). Their data show that B increases from a p proximately 0.025 to 0.045 between 5 and 25O. A positive aB/hT has been shown8 to be typical of structurebreaking solutes in aqueous solution. See M. Abu-Hamdiyyah, J . Phus. Chem., 69, 2720 (1965), for an alternate point of view. (48) J. H. Wang, ibid., 69, 4412 (1965).


placement of a charged amino group or a polar hydroxyl group into the hydrocarbon portion of the amino acid reduces t,he structure-making properties of the hydrocarbon portion as seen by the lower ratio for serine and @-alanine compared to that for alanine. These observations are verified by the entropies of dilution of Robinson for some of these compounds.49 The two dipeptides at the bottom of Table VI1 reflect the structure-making properties of leucine. We feel that the analysis of ionic mobilities based on the model of structure-breaking and structuremaking properties of ions in aqueous solution is preferable to that based solely on electrostrictive hydration and arbitrary corrections to Stokes' law. The material we have discussed here adds considerably to the validity of this approach. No system has been found whose transport properties in aqueous solution are in conflict with this model. Furthermore, similar conclusions have been reached from a wide variety of measurements including nmr,5O dielectric dispersion,61 viscosity,6heats of dilution,52and ~ o l u b i l i t y . ~ ~ It should be noted at this point that much of the success of this analysis of ionic mobilities has resulted from three rat,her unique properties of conductance data. First, they can be obtained rapidly with high precision. Second, owing to the existence of good theories for the measurable range, the data can be unambiguously extrapolated to infinite dilution where ion-solvent interactions are a maximum and ion-ion interactions disappear. Third, salt conductances can be split unambiguously at every temperature into ionic values. Also, the investigation of salts with common ions permits an internal check to be made on the accuracy of t h e measurements. (2) Concentmtion Dependence. The ion-size parameters given in Table I1 follow the same pattern that was

2335

found for these salts in aqueous solutions1 a t 10 and 25". They are much lower than the value 3.7 found for the same ions in nonaqueous ~ o l v e n t sare , ~ about the same for the bromides, but decrease with increasing cation size for the iodides. As was the case at the lower temperatures, a better fit of the data was obtained for Pr4NI and Bu4NI if they were assumed to be slightly associated salts and eq 2 was used for their analyses. The actual values of K A quoted here could be considerably in error owing to the problem of separating the last two terms of eq 2 when K A is small, but they do agree with those obtained a t 10 and 25" and for DzO solutions within experimental error. This result could be interpreted as indicating that the ionic association involved is insensitive to solvent structural changes. However, this could be another example of the "compensation law"54in which changes in enthalpy and entropy compensate one another,62 resulting in little change in the free energy and therefore in the association constant. It is obvious that conductance data alone are not sufficient to answer this question.

Acknowledgment. This work was supported by Contract No. 14-01-0001-359 with the Office of Saline Water, U. S. Department of the Interior. (49) A. L. Robinson, J . Chem. Phys., 14, 588 (1946). (50) H.G.Hertz and M. D. Ziedler, Ber. Bunsenges. Physik. Chem., 67, 774 (1963); 68, 821 (1964). (51) G. H. Haggis, J. B. Hasted, and T. J. Buchanan, J . C h m . Phys., 20, 1452 (1952). (52) Y.C.Wu and H. L. Friedman, J . Phys. Chem., 70, 166 (1966); S. Lindenbaum, ibid., 70, 814 (1966). (53) J. E. Desnoyers, G. E. Pelletier, and C. Jolicoeur, Can. J . Chem., 43, 3232 (1965). (54) D. J. G. Ives and P. D. Marsden, J . Chem. SOC.,649 (1965).


The Effect of Solvent Structure on the Mobility of Symmetrical Ions in

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