1882
JAMES F. SKINNER AND RAYMOND $1. Fuoss
Conductance of Triisoamylbutylammonium and Tetraphenylboride Ions in Water at 25"'
by James F. Skinner2 and Raymond M. Fuoss Contribution No. 1763 f r o m the Sterling Chemistry Laboratory of Y a l e Uniaersity, New Haven, Connecticut (Received February 8 , 1964)
The conductances of sodium tetraphenylboride and of triisoamylbutylammonium bromide have been measured in water a t 25" over the concentration range 0.002-0.010 N . Extrapolation by the Fuoss-Onsager equation gives A, (NaBPhd) = 69.94 f 0.02 and ho (Am3BuNBr) = 98.89 f 0.03. The limiting conductances of the two large ions are nearly equal (19.69 and 20.72, respectively), and their Walden products in water are only about 10% lower than in methanol and in acetonitrile, showing that they closely approximate Stokes spheres of nearly equal volumes. Nevertheless, the former has a positive coefficient for the linear term in the conductance function while the latter has a negative one. This striking difference cannot be explained by current theory.
Recently, it was found3 that the single ion conductances in methanol of the tetraphenylboride ion and of the triisoamylbutylammonium ion were practically equal (36.50 f 0.05 and 36.74 rt 0.11, respectively). Both ions are large compared to the usual solvent molecules; the test hypothesis was made that they were so large that, even in water, they might be approximated fairly well by Stokes spheres, in contrast to small ions whose Walden products in water usually are about twice their values in other solvents. The conductances of these two salts have now been measured in water, and as expected, the single ion Walden products are nearly equal to each other (0.177 and 0.184) and also to the products in methanol and in acetonitrile (0.200). A striking difference, however, was found between the shape of the conductance curves: sodium tetraphenylboride gives the expected anabatic phoreogram, but the curve for the quaternary salt lies not only below the Onsager tangent but even below the reference curve which includes both the and the c In c long range screening terms. This contrast in behavior between two salts which at first glance appear practically identical except for interchanged sizes of anion and cation finds no explanation in terms of current theory, and clearly calls for further investigation.
Experimental Triisoamylbutylammonium bromide (TABA bromide) was prepared from the iodide, which in turn was T h e Journal of Physical Chemistry
prepared from triisoamylamine and butyl iodide. After recrystallizing the iodide several times from anhydrous ethyl acetate and petroleum ether (b.p. 60-80') (25 g. of salt to 100 ml. of hot acetate, followed by 100 ml. of petroleum ether and cooling; m.p. 119.1-119.5'), 13.5 g. was dissolved in 150 ml. of absolute ethanol, to which an excess of freshly prepared silver oxide was added. The mixture was rolled until the supernatant gave no test for iodide. Then the silver oxide and iodide were filtered off (washings added to filtrate), and the filtrate was exactly neutralized with hydrobromic acid (ea. 7 ml. of concentrated acid in 100 ml. of ethanol). The solution of bromide was first concentrated to a thick sirup, and finally evaporated to dryness a t 10 and room temperature. The product was recrystallized three times from ethyl acetate (6.5 g.!15 nil.) and dried overnight a t 70" and 1 cm.; m.p. 119.0-119,4". The salt is extremely hygroscopic; consequently, stock solutions a t about 0.02 N were prepared and standardized by potentiometric titration against analytical grade silver nitrate. All solutions were prepared by weight, of course. Volume concentrations c (moles/l. of solution) were calculated (1) This paper is based on part of a thesis submitted by J. F. Skinner to the Graduate School of Yale University in June, 1964, in partial fulfillment of the requirements for the degree of Doctor of Philosophy. (2) Sterling Research Fellow, 1963-1964. (3) M. A. Coplan and R. M. Fuoss, J . P h y s . Chem., 68, 1177 (1964).
CONDUCTANCE OF TRIISOAMYLBUTYLAMMONIUM AND TETRAPHENYLBORIDE IONSIN WATER
from weight concentrations w (moles/kg. of solution) by the equation c
== wpo(1
+ Aw)
(1)
where A has the value 0.0235. This is based on the density 0.99757 g./ml. of a solution for which w = 0.02130. Sodium tetraphenylboride as received was slightly brown. A sample (2.1 g.) was dissolved in 6 ml. of acetone at rocmi temperature; addiitioii of 70 ml. of toluene gave a, slight, opalescence. This mixture was filtered, and 130 ml. more toluene was slowly added to the filtrate. Salt separated as needles. The product was dried at room temperature and 1 mm. Five recrystallizations were made; two sufficed to give a white product. The salt decomposes a t about 280’. To calculate volume concentrations;, the constant Ai of eq. 1 is 0.125; this is based on a density of 0.99755 g./ml. for a solution with w = 0.003857. Cells and electrical and other apparatus have been described previously.4 The cells used here had constants 1.0109 + 0.01001 and 1,0462 f 0.0001; these were determined6 using potassium chloride solutions. Solvent conductances were in the range 0.87-1.13 X 10-6.
Results and Discussion The experimental results are summarized in Table I, where concentrations and equivalent concentrations are given. The quantity AA is A (calcd.) minus A (obsd.), where the calculated value is )givenby A (calcd.) = ho -
Scl”
+ E’c In c + Jc
(2)
The data were analyzed to find the values of bo and S which minimized Z ( L ~ A ) ~The . values of A, for each run are given in Table I at zero concentration; the corresponding J values are immediately below. The value at zero concentration in the AA column is the uncertainty in ho. The constants of eq. 2 are summarized in Table 11. The structures, of the two salts are superficially similar: each contains one small and one large ion. Both large ions have tetrahedral symmetry, and present hydrocarbon surfaces to the solvent. Kevertheless, as shown in Fig. 1, they show marked differences in conductance. (Some overlapping points have been omitted in the figure.) Here, the line marked “LT” is the limiting tangent A (LIT) = ho
- Sc”‘
(3)
and the solid line under it is a plot of the limiting conductance function which includes the c log c term A, = .lo - Xcl/’ E’c In c (4)
+
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Table I : Conductances in Water at 25” TABA.Br----. NaBPha
7
104~
10’
A
104~
109 AA
A
AA
89.133 18 90,110 -7 91.493 -24 92.835 -5 94,664 18 0.000 (98.90) 20 J = -59.3 f 3.1 111.040 88.849 6 87.942 90.061 8 64.042 91.437 -22 44.683 92.770 -7 22.787 94,649 15 0.000 (98.93) 20 J = -54.8 f 2.4 98.125 89.397 5 76.254 90.616 5 55.915 91.880 -9 39.213 93.085 -16 18.510 95.011 16 0,000 (98.85) 15 J = -58.4 f 2.3
64.587 49.891 33.373 18.276
64.725 6 65.233 -8 65.979 -1 66.913 3 0.000 (69.94) 10 J = 182.7 i 2.1 76.839 64.312 -5 60.657 64.837 6 46.355 65.379 3 31.370 66.085 -4 .16.463 67.067 0 0.000 (69.97) 10 J = 174.9 f 1.2 80,997 64.189 -18 60.737 64.832 13 49.481 65.248 19 32.506 65.993 -2 16,018 67.045 -11 0.000 (69.91) 20 J = 183.2 i 3.6
104.192 85.584 62.244 43.202 22.280
Table 11: Constants of Equation NaBPhr
TABA.Br
Ao J E1 E2
E‘
s
+ +
98.89 0.03 -57.5 2.6 0.2308 8.918 13.91 83.35
69.94 f 0.02 180.3 f 2 . 1 0.2308 8.918 7.22 76,70
The difference between A, and A (obsd.) is the experimental quantity from which the coefficient J of the linear term in (2) must be determined. The sodium tetraphenylboride curve is about as expected : the phoreogram is anabatic, as are the curves for most 1-1 salts in water. On the original interpretation of J ( a ) , 6one would, however, expect a larger value for J because the tetraphenylboride ion is much larger than simple ions, unless the latter are considered hydrated. ( J for sodium chloride,’ for example, is 190.) However, the curve for TABA’Br lies below the &-curve, and leads to a negative J . Clearly, someR. M. Fuoss, J . Phus. Chem., 6 5 , 999 (1961). (5) J. E. Lind, Jr., J. J. Zwolenik, and R. M. Fuoss, J . Am. Ch,em. Soc., 81, 1557 (1959). (6) R. M . Fuoss and L. Onsager, J . Phys. Chem.. 61, 668 (1957). (7) R. W. Kunze and R. h.2. Fuoss, ibid.,67, 911 (1963). (4) J. E. Lind. Jr., and
V o l u m e 68, N u m b e r 7
J u l y , 1964
1884
JAMESF. SKINNER AND RAYMOND M. Fuoss
Figure 2. Linear terms in conductance: TABA.Br, top; NaBPhd, bottom. Ordinate scale in A-units.
Figure 1. Phoreograms for TAB4,Br (ordinates right,) and for NaBPh4 (ordinates left).
thing quite different is going on in %ion encounters in the two salts; we recall that many linear terms in A iginate in pairwise interactions. A negative linear coefficient has usually been interpreted to mean ion association. Diamond8has suggested that hydrophobic ions in water would tend to associate in order to lower the free energy of the system water-salt; given only the TABA. Br result, this hypothesis rationalizes our observation. However, the tetraphenylboride anion likewise has a hydrocarbon exterior, but it gives a positive linear coefficient. There is, of course, one important difference in charge distribution between the two ions: in the tetraalkyl ion, the positive charge is localized on the central nitrogen atom, and insulated by a paraffine shell, while in the tetraphenyl anion, the negative charge is distributed over the four aryl groups, which, it might be argued, makes this ion more compatible with the surrounding polar medium. Alternatively, non-Coulomb short range forces between the bromide ion and the quaternary ion may stabilize ion pairs. I n any case, it is clear that work with a variety of related ions is needed before such cases can be understood. The difference between the two salts is shown most clearly on a A’-c plot, which is preferable to the conventional A-c‘/~ plot for examining precise conductance data. The quantity A’ is defined by the equation 01
A’ = A (obsd.)
+ Sc”* - E’c ln c
(5)
It includes the observed conductance and the theoretically predictableg long range lzonspecifcc terms in e”* and c In c as shown. The latter (divided by A,) The Journal of Physical Chemistry
are common for a given valence type in a given solvent at a given temperature. It will be noted, incidentally, that the points for a given run are equally spaced on the c-scale in Fig. 2. This is by design and not accidental. Before a theoretical value of the coefficient of the c In c term was known, it was necessary to strive for the lowest attainable concentrations in order to minimize the distance of extrapolation of the Kohlrausch c’I2 scale, and it was usual to try to space the points equally on this scale. But given E’, extrapolation can now be made for A. on the A’-c scale, and data at extreme dilutions are no longer required. The long “extrapdatjon” of Fig. I is reliable, because the limiting values are established with confidence by Fig. 2. The specific properties of a given electrolyte first appear in the difference between A ’ and the limiting conductance A’ - ho = J ( u ) c
(6)
Earlier theory6 gives J as a positive monotone increasing function of a; more recent worklo shows that ( 2 ) should be replaced by A = bo - Sc’/’
+ E’c In c + J’c
- K’cj2 (7)
where both J ’ a n d K’ depend on a. (Here j i s the activity coefficient.) I n solvents of high dielectric constant, the J’ and K’ terms cannot be separated because f 2 is too near unity in the range of concentrations (8) R. M. Diamond, J . Phys. Chem., 6 7 , 2513 (1963). (9) The coefficients S and E contain An, of course, and in this sense are specific for a given electrolyte. They are, however, independent of a , the contact distance.
(IO) R. M. Fuoss and L. Onsager, J. P h y s . Chem.. 66, 1722 (1962); 67, 621, 628 (1963); 68, 1 (1964).
CONDUCTANCE O F
TRIISOAMYLBUTYLAMMONIUM A h D TETRAPHENYLBORIDE IONS I N
where the model is valid (xu < 0.2). Consequently, (7)becomes to a good approximation in wat’er A = bo .- Sc‘”
+ E’c In c + (J’ - K’)c
(8)
and the coefficieiit of the linear term can in principle be positive or negative. I n Fig. 2 , (A’ - A,) is plotted against concentration: KaBPh4 (ordinates left) gives a straight line with positive slope, while TABA Br (ordinates right) gives one with negative slope. Any argument based on size alone must be equally valid for both salts: clearly, something else must be involved here. It might be the difference in charge distribution, or it might be another example of the frequently observed asymmetry in behavior betweein cations and anions (“cations are solvated, anions are not”), or, as already suggested, ThBA.Br ion pairs may be stabilized by non-Coulomb forces. The Walden products, however, argue against different solvation, at least as far as the free ions are concerned. (It must be kept in mind that a large part of the linear terni in ( 2 ) results from pairmise contacts.) Using A0 ( S a + ) = 50.257 and Xo (Br’) == 78.1711,we find A. (BPh4’) = 19.69 and Xo (TABA+) == 20.72 f 0.02. The corresponding Walden products in water are 0.184 and 0.177, respectively, about 10% less than the values3 in methanol (0.200 and 0.199) or in acetonitrile12 (0.199 for both by hypothesis). Whilc the value is somewhat larger for the quaternary ion, suggesting a smaller ion, the difference is nowhere nearly great enough to swing the linear coefficient in (7) from positive to negative. Also, the fact that the *
WATER
1885
product,s are so nearly equa113 in water, in methanol, and in acetonitrile argues that the ions are so large that they are beginning to be good approximations to Stokes spheres arid hence, if the Walden products are nearly alike, the hydrodynamic sizes must also be nearly the same for the two ions. Therefore, the reversal of the coefficients must have i t s origin in soinething that has not yet been considered by theory. The value of the limiting conductance of the TABA4 cation is consistent with values found by Kraus and co-workers’* for other quaternary ions. For tetraisoamylanimoniuni ion, X, = 17.13. I n general, the asymmetric ion with the same number of carbon atoms has the higher mobility; for example, Xo = 20.82 for hexadecyltrimethylammoiiiuni ion with 19 carbon atoms and ha = 20.02 for octadecyltri~nethylanimoniuin ion with 21. These values bracket our value of 20.72 for triisoamylbut,ylainmoniuii~ion with 19 carbon atoms. Summarizing, the limiting conductances of our two salts appear to be normal, but there is an unexplained difference in their behavior a t dilutions less than infinite. (11) E. B. Owen, J . Chim. Phge., 49, C27 (1952). (12) M . A. Coplan and R. &Fuoss, !I, J . Phys. Chem., 6 8 , 1181 (1964). (13) For small ions, as is well known, the Walden product in water is usually about twice that in methanol, due to the greater solventsolute interaction in the former solvent. Stokes hydrodynamics obviously does not apply. For potassium, for example, the product is 0.655 in water and 0.286 in methanol (H. S.Harned and B, B. Owen, “Physical Chemistry of Electrolytic Solutions,” 3rd Ed., Reinhold Publishing Corp., New York, N. Y., 1958, p. 231). (14) E. J. Bair and C. A. Kraus, J . Am. Chem. SOC.,73, 1129 (1951); M. J. McDowell and C. A. Kraus, ibid., 73, 2173 (1951).
Volume 68, S u m b e r 7
J u l g , 1964
