2567
Diffusion Coefficients o f Tetrabutylarnmoniurn Halides in W a t e r (1967); (b) 'T. P. Kohman, ibid., 47, 657 (1970). (4) See paragraph at end of paper regarding supplementary material. (5) K. P. Anderson, E. A. Butler, and E. M. Woolley, J. Phys. Chem.. 71, 4584 (1967). (6) D. D. Wagnian, W. H. Evans, V. B. Parker, i. Halow, S. M. Bailey, and R . H . Schumm, Nat. Bur. Stand. Tech. Note, No. 270-3 (1968); No. 270-4 (1969). (7) L. G . Silleri and A. E. Martell, "Stability Constants of Metal-Ion Complexes," The Chemical Society, London, 1964. (8) J. Kratohvil and B. Teiak, Ark. Kemi, 26, 243 (1954).
(9) K. B. Katsimirskii and V. P. Vasil'ev, "instabiiity Constants of Complex Compounds," Russian Translation, Consultants Bureau, New York, N . Y., 1960. (10) J. Kratohvil, B. Terak, and V. 8.Vouk, Ark. Kemi, 26, 191 (1954). (11) R . Alexander, E. C. F. KO, Y . C. Mac, and A. J. Parker, J. Amer. Chem. SOC.,89, 3703 (1967), in conjunction with data from ref 6. (12) C. Barraque, J. Vedel, and B. Tremillon. Buil. SOC.Chim. Fr.. 3421 (1968). (13) W. L. Marshall, J. Phys. Chem., 74, 346 (1970). (14) R . A . Matheson, J. Phys. Chem.. 73, 3635 (1969).
Diffusion Coefficients of Tetrabutylammonium Halides in Water at 25"' ,2 Hyoungman Kim,* Arnold Revzin,3 and Louis J. Gosting4 lnstitute for Enzyme Research and Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706 (Received October 27, 1972; Revised manuscript receivedJune 18, 1973) Pubiication costs assisted by the National lnstitute of Arthritis and Metaboiic Diseases
Diffusion coefficients measured with a new optical diffusiometer are reported for tetrabutylammonium halides (Bu4NX) in water a t 25". The concentration range studied extended up to 0.6 M for Bu4NC1, 0.8 M for BucNBr, and 0.06 M for the less soluble Bu4NI. The diffusion coefficients for a given concentration decreased with increasing anion size while the mobility terms, which were obtained by dividing the diffusion coefficients by a thermodynamic term, showed the reverse order. Refractive index derivatives were also determined as well as density data from which partial molal volumes were computed.
Introduction In recent years, there has been much interest in the physical chemical properties of tetraalkylammonium halides in aqueous solution. A large number of experimental results on both the equilibrium and the transport behavior of these materials has been published. These results have shown that the larger tetraalkylammonium ions significantly increase the degree of structure among neighboring water molecules. There are also cation-cation as well as cation-anion interactions in solutions of tetrabutyl- and tetraamylammonium salts, although the detailed mode of interaction is not known. The present study provides another of the fundamental transport properties, the isothermal diffusion coefficients of tetrabutyla.mmonium chloride, bromide, and iodide. It is hoped that these diffusion coefficients can be combined with activity data and with other transport properties such as the c'onductance and transport numbers, to compute the ionic transport coefficients, l i j , which have been described by :Miller.5 The ionic transport coefficients may give better insight into the nature of ionic interactions than either conductivity or diffusion data alone.6.7 As a by-product of the diffusion experiments, we have also obtained refractive index derivative and density data; from the latter we have computed the partial molal volumes of the tetrabutylammonium halides. Experimental Section Materials. Tetrabutylammonium chloride, bromide, and iodide were obtained from Eastman Organic Chemicals. Both tetrabutylammonium bromide, BusNBr, and
tetrabutylammonium iodide, B u ~ N I ,were recrystallized three or more times from once-distilled acetone. Tetrabutylammonium chloride, Bu4NC1, was first dissolved in once-distilled acetone and then was precipitated by adding purified ether. Recrystallization was performed three times. All salts were dried in the vacuum oven for a t least 1 week and then were stored in a vacuum desiccator over Pz05. For the highly hygroscopic Bu4NC1, the transfer into a weighing bottle was made in a polyethylene glove bag (Instruments for Research and Industry, Cheltenham, Pa.) filled with dry nitrogen gas. The molecular weights used are 277.925 for Bu4NC1, 322.376 for BurNBr, and 369.376 for Bu4NI. All solutions were prepared with distilled water which had been further purified with a Barnstead water purifier and then saturated with air. The density values used to calculate the air-buoyancy corrections in preparing the solutions were 1.1 for Bu4NC1 and BusNBr, 1.5 for Bu4KI, and 8.4 for the metal weights. Diffusion Experiments All diffusion measurements were performed on a new optical diffusiometer, using procedures similar to those used with previous instruments.8 A detailed description of the new device will be given e1sewhere;g here we shall describe only its main features. The heart of the instrument is a rigid steel beam, 884 cm in length, to the top of which are bolted accurately aligned stainless steel dove-tailed ways. All optical components (light source, lens, water bath windows, diffusion cell, cylinder lens, and camera) are firmly supported on the ways. Owing to its heavy weight, the water bath is not supported by the beam but instead is bolted to the floor The Journaiof PhysicalChemistry, Vol. 77, No. 21, 1973
2568
H. Kim, A. Revzin, and L. J . Gosting
and ceiling of the laboratory. Watertight seals between the windows and the bath itself are formed with flexible rubber bellows which allow minor movements of the water bath relative to the ways without inducing strains. Illumination was provided with a GE H-100.44 mercury vapor lamp fitted with a Kodak Wratten 77A filter, which emits light a t a wavelength of 5460.7 A (in air). The source slit can be made precisely horizontal or vertical as required. Our experiments were performed using a single main collimating lens of focal length about 145 cm; the optical lever arm, b, was about 309 cm. The cylinder lens is mounted in a special housing which permits it to be swung out of the light path (for Gouy experiments) or into an accurately reproducible position in the light path (for Rayleigh measurements). Diffusion cells used were the glass and fused quartz Tiselius type and had cell dimensions, a, along the optical axis of about 2.5 cm. The initial boundary between the upper and lower solutions was formed by siphoning through a single stainless steel capillary or a single platinum capillary. For both 8-corrections and the fractional part of the total number of fringes, photographs were taken on Kodak Metallographic glass plates. During free diffusion, 6 t o 12 photographs of Gouy fringes were taken on Kodak Spectroscopic IIIG glass plates. One or two Rayleigh photographs were also taken. An unusual property of Bu4NCl is that the density of its aqueous solution is less than that of pure water and decreases with increasing concentration. Therefore, the upper solution must be more concentrated than the lower solution, and the Gouy fringes lie above the undeviated slit image in contrast to the usual case. The measurements of the photographic plates were made with a photoelectric null indicatorlOJ1 mounted on a Gaertner Model M2001RS-B Toolmakers' microscope. This microscope is provided with two encoders and each axis position is displayed on a Tyco Digi-Point Readout to the nearest 0.0001 cm. The Digi-Point readout is connected to an IBM No. 29 keypunch through an interface (Instrumentation Systems Center, University of Wisconsin) and the displayed numbers on the Digi-Point Readout were directly punched onto data cards. The calculations were made with a Univac 1108 digital computer a t the University of Wisconsin Computation Center. The temperature of the water bath was measured during diffusion with a mercury-in-glass thermometer which had been calibrated against a platinum resistance thermometer. The temperature of the water bath during diffusion runs was within zk0.005" of 25" and never fluctuated by more than 0,003" during a run. The density of each solution was measured in triplicate with single-neck pycnometers of volume about 30 ml in a water bath maintained a t 25". Results and Discussion Tables I, 11, and I11 present the diffusion coefficients and other data from experiments on Bu4NC1, BurNBr, are the and Bu4N1, respectively. In these tables E and mean solute concentrations (the average for the upper and lower starting solutions) expressed in g/100 ml and mol/l., respectively, Ac is the initial concentration difference between the upper and lower solutions, J is the total number of fringes, ( A n l a c ) is the refractive index derivative, and ( D ) , is the mutual diffusion coefficient for the volumefixed frame of reference. Also given in Tables I and I1 are values for the mobility term, % , which is expressed by the
e
The Journalof PhysicalChernistry. Vol. 77. No. 2 1 , 1973
I
,
"i
04t
03
1
00
I
.
02
01
/
I
03
,
1
,
04
1
,
05
1
06
,
,
07
,
1
C8
,
09
C2 Figure 1. D X IO5 plotted against dc for tetrabutylamrnoniurn halides in water at 25" 0, B u ~ N C I ,A , Bu4NBr, 0 , Bu4NI, 0 , Bu4NBr by Pepela, Steel and Dunlop l 5
following equation.12
(D)O (D), (1) 1 C d In y / d C 1 m d In y l d m In eq 1, ( D ) ois solvent-fixed mutual diffusion coefficient, 3TI=
+
+
m is the molality, and y and y are the activity coefficients on the molar and molal scales, respectively. Values of [1 m d In y l d n ] , evaluated using the molal activity coefficients given by Lindenbaum and Boyd13 are also given in Tables I and 11. Activity data for Bu4NI are not available. Figure 1 shows the variation of ( D ) , with & for the three systems studied. The low solubility of Bu4NI restricts the concentration range over which we could study this salt. The limiting diffusion coefficients a t infinite dilution were calculated using the Nernst equation and they are found to be 0.8205 x 10-5, 0.8244 X 10-5, and 0.8217 X 10-5 for Bu4NC1, BulNBr, and Bu4N1, respectively. The limiting equivalent conductivities were taken to be14 19.31 for Bu4N+, 76.39 for C1-, 78.22 for Br-, and 76.98 for I-. The limiting diffusion coefficients for the three salts studied here are equal within about 0.5% because the limiting equivalent conductivities of the anions are very nearly the same. The filled circles in Figure 1 are the diffusion coefficients of Bu4NBr obtained by Pepela, Steel, and DunlopI5 using shearing interference optics.16 I t can be seen that results from the shearing diffusiometer and the Gouy method agree within the precision of the former. The concentration dependence of the density, d, a t 25", is given by the expressions
+
d d
= 0.99707 = 0.99707
- 5.30
+ 6.44 X
and
d
=
0.99707
+ 4.25 X 10-ic3/? 10-4c + 4.34 X
X 10-'c
10-icdL
+ 1.56 X 10%
(for Bu,NCl) (for Bu,NBr)
(forBu,NI)
where d is expressed in g/ml and c is in g/100 ml. In these expressions, 0.99707 is the rounded value of the density of pure water a t 25" while the coefficients of c and c3/2 were determined by the method of least squares. The average deviation of the measured densities from these functions is less than 0.02%. Figure 2 presents the apparent molal volumes, @ \ , and the partial molal volumes, for Bu4NC1 and BusNBr,
v.
2569
Diffusion Coefficients of Tetrabutylammonium Halides in Water
TABLE I: Experimental Results for Bu4NCI i n Water at 25" ~
E,
(AnlAc) x 103,
-Ac,
mi
c, moljl.
rn
0.7200 1.1758 2.4780 4.8122 7.721 3 13.3779 16.491 5
0.02590 0.04231 0.08916 0.17315 0.27782 0.481 35 0.59338
0.02618 0.04297 0.09182 0.18291 0.3031 6 0.56094 0.71 81 8
g/100
9/100
( W V x IO5,
(g/iO?
rnl
J
0.7731 1.2251 0.6560 0.7727 1.3875 0.5879 3.5835
59.18 93.98 50.72 60.43 109.99 47.51 293.14
~~~
i+rn ' d In y/dm
cm2/sec
ml) -
1.6670 1.6706 1.6838 1.7031 1.7263 1.7599 1.7815
311x105,1 cm2/sec
0.7353 0.7142 0.6701 0.6195 0.5725 0.5064 0.4787
0.943 0.927 0.906 0.896 0.887 0.844 0.979
0.780 0.770 0.740 0.691 0.645 0.536 0.489
0.7258a 0.7225a 0.6860 0.6566 0.5888 0.5060 0.4468 0.3981 0.3548 0.3277
0.895 0.895 0.845 0.831 0.790 0.71 1 0.687 0.690 0.682 0.664
(0.812)
TABLE II: Experimental Results for Bu4NBr in Water at 25"
0.8131 0.8131 1.6309 2.4035 4.8214 9.1336 13.5280 18.0646 22.5134 25.7892
0.02522 0.02522 0.05059 0.07455 0.14956 0.28332 0.41963 0.56035 0.69835 0.79996
0.02549 0.02549 0.05152 0.07649 0.1 5703 0.31039 0.48087 0.67400 0.88286 1.05083
0.8192 1.6262 0.7979 0.6780 0.6045 1.2655 1.2656 1.2575 0.7164 0.7023
58.36 11 5.88 57.34 48.62 43.86 93.33 94.52 94.86 54.25 53.46
1.5600 1.5604 1.5650 1.5703 1.5888 1.6149 1.6354 1.6518 1.6582 1.6667
0.812 0.790 0.745 0.712 0.650 0.577 0.520 0.494
a The two experiments at E = 0.8131 showed behavior which indicated a concentration dependence of ( 1 3 )and/or ~ dn/dc across the diffusion boundary. Thus the values given in the "D" column are not differential diffusion coefficients but are reduced height-area ratios, D A , [L.J. Gosting and H. Fujita, J. Arner. Chern. Soc., 79, 1359 (1957)l.A plot of D A vs. ( A C ) was ~ extrapolated to A c = 0 to yield the differential diffusion coefficient of 0.7269 X IO-5 cm2/sec at this concentration [P. J. Dunloo and L. J. Gostina. J . Arner. Chern. SOC., 77,5238 (1955)J. Using the differential diffusion coefficient above.
TABLE Ill: Experimental Results for Bu4NI in Water at 25" (Anlac)
0.2576 0.4062 0.6342 0.7981 0.9932 1.2394 1.5862 2.1349
0.4064 0.6092 0.6788 0.9949 0.9256 1.4799 0.7522 0.71 72
0.00698 0.01100 0.01717 0.02160 0.02689 0.03555 0.04294 0.05780
29.20 43.77 48.80 71.58 66.60 106.59 54.21 51.76
1.5643 1.5647 1.5656 1.5668 1.5670 1.5686 1.5695 1.571 7
0.761 3 0.7443 0.7250 0.71 32 0.6980 0.6820 0.6633 0.5348
calculated from the density values using the equations
-(1 1000 -I-d mM
4v = m
295-
p \ ,
h '
I>
F a'
'
290-
\
do
Bu4NCI
and 285-
I
00
1
I
01
02
,
03
,
04
I
I
05
06
,
07
,
0.8
9
C
L
dVCj
where M is the molecular weight of the solute and do is the density of pure water. The values of d&/d& were obtained from the slopes of +v us. dc curves. The apparent and partial molal volumes of Bu4NI did not change within the small concentration range studied and the average value obtained is 312.5 ml/mol. Our &, and values check very closely with corresponding results of Wen and Saitol7 for BusNBr.
Figure 2. Apparent and partial molal volumes I m l / m o l ) of Bu4NCI and Bu4NBr plotted against C: 0, 4"; 0 , V ; 0 and W , Wen and Saito.16
It is of interest to compare the concentration dependence of the diffusion coefficients of these tetrabutylammonium halides with that of more familiar 1-1 electrolytes such as the chlorides, bromides, and iodides of potassium and sodium. For the latter electrolytes the diffusion coefficients initially decrease, bottom out, and then The Journalof Physical Chemistry, Vol. 77,No. 21, 1973
2570
H. Kim, A.
Revzin, and L. J. Gosting
If tetrabutylammonium halides also form ion pairs as sug-
h
I
, dA - - -
t - L
CL’
00
Figure 3.
I
I 01
02
03
04
05 c1/2
311 X l o 5 and X ( q / q ~ X ) 0 , T Z for Bu4NCI; A , 32 f o r Bu4NBr; A ,T Z ( q / q o )for B u 4 N B r .
06
07
08
09
lo5 plotted against d??
e, m ( q / q o )for
Bu4NCI;
increase with increasing concentration.18-21 The magnitude of the initial decrease in ( D ) , is largest for the chlorides and smallest for the iodides, and a t higher concentrations (0)” values for iodides are always larger than those for bromides which, in turn, are larger than those for chlorides. Identical trends are observed for the concentration dependencies of activity coefficients. It is striking that the ordering of diffusion coefficients and of activity coefficients for tetrabutylammonium halides is opposite to that of the “simple” electrolytes as described above. The fact that the limiting equivalent conductivities of C1-, Br-, and I- have nearly identical values is attributed to ionic hydration, with the extent of hydration increasing in the order I- < Br- < C1-, thus making the sizes of the hydrated anions about the same.22 This hydration effect alone, however, should give an order of activity coefficients opposite to the experimentally found order for both potassium and sodium halides.23~2~ To explain this observation, Diamond22 proposed a type of ion pairing “through the agency of the water molecules,” with the extent of ion-pair formation in the order of NaCl > NaBr > NaI (or KC1 > KBr > KI). The ordering of the dependence of X on C for tetrabutylammonium halides which has an order opposite to that for the alkali halides has been also explained in terms of ion-pair formation; it was proposed that the extent of ionpairing, unlike to alkali halides, increases with the anion size.l3 The conductance data of tetrabutylammonium halides at low concentrations have been discussed in the same terms.14 The interpretation of diffusion data, especially a t higher concentrations, is more complicated because ( D ) , contains both mobility and thermodynamic terms. The mobility term obtained using eq 1 depends on a large number of factors, such as long range Coulombic effects, electrophoretic effects, ion-solvent interactions, viscosity, and ionpairing. It is of interest, however, to note that the n?. values for both BudNC1 and BusNBr decrease with increasing concentration while those of other 1-1 electrolyte ~ y s t r m s ~ 5 9where ~6 ion pairing is relatively well established increase with concentration. The increase in the value of 3n was attributed to the fact that when two ions form an ion pair they offer less resistance to motion.25.27
The Journal of Physical Chemistry, Vol. 77, No. 2 7 , 1973
gested by other s t u d i e ~ , l ~ 3it~is4 clear that some other effect is overcoming the effect by the ion pairing. The most obvious effect is the viscosity and this can be clearly seen in Figure 3 where the values of 3nzand nZ ( q / q o ) are plotted against P I 2 . The values of relative viscosity were calculated using the viscosity coefficients of Desnoyers and Perron28 They obtained the coefficients from their viscosity data of concentrations of u p to 0.3 M and therefore the X ( q / q o ) values in Figure 3 are also given up to that concentration. The values of n?. ( ~ / q o for ) both Bu4NC1 and Bu4NBr increase with concentration and, unlike the values of (D),, both 3n and 3n ( ~ / q ovalues ) of BulNBr for a given value of C are larger than the corresponding values of BusNC1. These observations are in agreement with the suggestion that tetrabutylammonium halides form ion pairs and that the extent of ion pairing increases with the anion size. However, those observations should not be construed as unambiguous support for the above suggestion because it is not known whether other factors such as the electrophoretic effect, ion-solvent interactions, and cation-cation i n t e r a ~ t i o n s ~ affect g - ~ ~ the mobilities of these electrolytes significantly. As mentioned earlier, a better picture of these aqueous solutions may emerge when the ionic transport coefficients are obtained. It is hoped that other data necessary for the calculation of the ionic transport coefficients will soon be forthcoming.
References and Notes This investigation was supported in part by Public Health Service Research Grant AM-05177 from the National Institute of Arthritis and Metabolic Diseases. Portions of this work were submitted by A. R. to the Graduate School of the University of Wisconsin in partial fulfillment of the requirements for the Ph.D. degree. Recipient of Wisconsin Alumni Research Foundation Fellowship (1964-1965) and National Institutes of Health Predoctoral Fellowship (1965-1969). Deceased, May 31, 1971. Recipient of PHS Research Career Award, AM-K6-16,715. D. G. Miller, J. Phys. Chern., 70, 2639 (1966). M. J. Pikal, J. Phys. Chem., 75, 663 (1971). D. G. Miller and M. J. Pikal, J. Solution Chem., 1, 111 (1972) G. Reinfelds and L. J. Gosting, J. Phys. Chem., 68, 2464 (1964) L. J. Gosting, H . Kim, M. A. Loewenstein, G. Reinfelds, and A. Revzin. Rev. Sci. lnstrum., in press. R. P. Wendt. Ph.D. thesis, University of Wisconsin, 1961 J. G. Albright, Ph.D. thesis, University of Wisconsin, 1963. Equations 33 and 35 of ref 5. S. Lindenbaum and G. E. Boyd, J. Phys. Chem., 68,911 (1964). D. F. Evans and R. I_. Kay, J. Phys. Chem., 70,366 (1966). C. N. Pepela, B. J. Steel, and P. J. Dunlop, J . Amer. Chem. SOC., 92, 6743 (1970). 0. Bryngdah1,ActaChem. Scand., 11,1017 (1957). W.-Y. Wen and S. Saito. J. Phys. Chem., 68, 2639 (1964) R. H. Stokes, J. Amer. Chem. SOC.,72, 2243 (1950) P. J. Dunlop and R. H. Stokes, J. Amer. Chem. SOC., 73, 5456 (1951). L. J. Gosting, J. Amer. Chem. SOC.,72, 4418 (1950) V. Vitagliano and P. A. Lyons, J. Amer. Chem. SOC., 78, 1549 (1956). R. M. Diamond, J. Amer. Chem. SOC.,80,4808 (1958) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,’’ 2nd ed, revised, Butterworths, London, 1965. Appendix 8.10 of ref 23. E. F. Wishaw and R. H. Stokes, J. Amer. Chern. Soc., 7 6 , 2065 (1954) J. G. Albrightand D. G. Miller, J . Phys. Chem., 76, 1853 (1972). See also page 300 of ref 23. J . E . Desnoyers and G. Perron, J, Soiution Chem., 1, 199 (1972). W.-Y. Wen and K. Nara, J . Phys. Chem., 71, 3907 (1967). R. H. Wood, etal., J. Phys. Chem., 71, 2149 (1967). A. LoSurdo and H. E. Wirth, J . Phys. Chem., 76, 1333 (1972). P. S. Ramanathan. C. V. Krishnan, and H. C. Friedmann, J . Solulion Chem., 1,237 (1972).
