March 20, 1930
CONDUCTANCE OF TETRABUTYLAMMONICM TETRAPHENYLBORIDE 1301
ened significantly by the polar solvent especially when hydrogen bonding can occur, thus two lines close together often appear as one. Weak lines are difficult to observe in water because of the wellknown trouble in getting water free from colloidal matter and motes. patterns for H2S04JH2P04- and The silicate ion showed a marked resemblance t h a t has already been pointed out.21 As one goes from H2S04-toH2P04- and on to H2Si04=, there is a de-
[CONTRIBUTIOS FROM L'ISTITUTO
DI
crease in sharpness of the spectral lines, however. Since the observed silicate spectrum is consistent with t h a t expected for the H?SiO4= form, the weight of evidence strongly favors this as the structure. Acknowledgment.-The authors are grateful to the Office of Ordnance Research of the U. S. Army for support. PROVIDESCE, R. I.
CHIMICA FISICADELL' VNIVERSITA DEGLI
STUD1 DI
KOMA]
The Conductance of Tetrabutylammonium Tetraphenylboride in Acetonitrile-Carbon Tetrachloride Mixtures at 25" BY FILIPPO ACCASCINA, SERGIO
PETRUCCI AND
RAYMOND A I .
F'C'OSS'
RECEIVEDOCTOBER 7, 1958 The conductance of Bu&.BPh, was measured in acetonitrile (D = 36.0) and in six mixtures of M e C S with CC14 with dielectric constants of 33.2, 28.8,24.9, 15.35, 7.20 and 4.80. Association to ion pairs is slight (K.4 = 14.3) in MeCK but steadily increases as the dielectric constant decreases; a t D = 4.80, K.4 = 3.0 X lo6. Triple ion clustering also occurs in the two mixtures of lowest dielectric constants. The system illustrates the transition from almost negligible association in hIeCS, where the phoreogram lies above the Onsager tangent, to the case of marked association where cA2 is approximately constant. Both ions are very large compared t o the solvent molecules; nevertheless, the Walden product decreases with increasing CCl, content of the solvent. This variation shows that Stokes law must be corrected for the electrostatic interaction between the ions and the dipoles of the polar constituent of the solvent.
Introduction Recent theoretical work2 has shown that the conductance of ionophores can be described on the basis of a model in which the ions are represented as charged spheres in a continuum. I n solvents of high dielectric constant, the conductance changes with concentration primarily because the long range electrostatic forces between the ions reduce the mobility as the concentration increases; with decreasing dielectric constant, the conductance decreases still more rapidly, because part of the solute is then present as non-conducting ion pairs. Tetrabutylammonium tetraphenylb~ride~ is an electrolyte in which both ions are very large compared to ordinary solvent molecules and have centrally located charges. This salt, therefore, conforms quite well to the theoretical model. The purpose of this paper is to present conductance data on Bu4N.BPh4 in acetonitrile (D= 36.0) and in a series of mixtures of this solvent with carbon tetrachloride, which cover the dielectric constant range down to 4.80 (93% CC14). A continuous transition is observed, from almost negligible association (KA = 14.3) in acetonitrile to marked association (KA = 2.96 X 106) a t D = 4.80. This system thus supplements work on the system tetraethylammonium picratemethanol-water4 which covered the range of moderate to completely negligible association. While the continuum model serves to describe the electrostatic effects, however, it is found to be inadequate for the hydrodynamic properties. Despite the fact t h a t the ions of Bu4N.BPh4 are both much (1) On sabbatical leave from Yale University, second semester 3957-1958. Grateful acknowledgment is made for a Fulbright G r a n t . (2) R. M . Fuoss, THISJ O U R N A L , 8 0 , 3163 (1958). ( 3 ) R. M . Fuoss, J. B. Berkowitz, E. Hirsch a n d S. Petrucci, Puoc. S a l . A c a d . Sci., 4 4 , 27 (1958). ( 4 ) F. Accascina, A. D'Aprano and R. RI. Fuoss, THISJOURNAI., 8 1 , 1038 (1959).
larger than the molecules of either acetonitrile or carbon tetrachloride, the Walden F roduct A O is~ not constant but decreases with increasing carbon tetrachloride in the mixed solvent. A relaxation field between ions and solvent dipoles could account for the inconstancy of A o ~ . Experimental Materials.-Tetrabutylammonium
bromide (Eastman, special order, unpurified raw product from tri-n-butylamine and n-butyl bromide) was dissolved in benzene a t 80" (5 cc./ g. ) and precipitated by adding hot n-hexane (15 cc./g.) and allowing t o cool. The hygroscopic precipitate was dried over phosphorus pentoxide in an evacuated desiccator for 24 hr. and then kept a t 40" and mm. for a week. This procedure was repeated twice; m.p. 116-117" (or on some batches, a metastable form' melting a t 101-102° was obtained). Tetrabutylammonium tetraphenylboridea was prepared by metathesis from purified tetrabutylammonium bromide and sodium tetraphenylboride.6 T h e latter was dissolved in conductance water ( 2 % solution); after filtration to remove a small amount of insoluble impurities, an equivalent amount of tetrabutylammonium bromide in 2y0 aqueous solution was slowly added. The bulky white precipitate was washed 5 times by decantation. a f t e r drying, the product was recrystallized 4 times from 1:3 water-acetone (200 cc./g. salt) and finally dried for several days a t 40" and lo-,, mm.; m.p. 223-225". Acetonitrile was treated as recommended by IVawzonek and Runner'; b.p., 81.5' a t 760 mm. For conductance work, the purified solvent was distilled from P?Oj, using a conductance cell between the condenser and the receiver to monitor the product; distillate with conductance 5 9 x mho was collected. Due t o its hygroscopicity, acetonitrile was always transferred from one container to another by dry nitrogen pressure after the final distillation. ( 5 ) H. h l . Daggett, E. I . Bair and C. A. Kraus, ibid., 73, 7U9 (1951). ( 6 ) G. Wittig a n d P. Raff. A n n . , 573, 105 (1951); bibliography 1949-1955, A. J. B a r n a r d , J r . , Ciien?. A n a l . , 44, 104 (1935). (7) S. Wawzonek a n d hl. E. R u n n e r , T i a m . Elecli.ochein. Soc., 99, 457 (1962); see also P. U'alden and E. I. Birr, Z . p h y s i k . Chem., 1 4 4 8 , 269 (1929): A. I. Popov a n d N. E. Skelly, THISJ O U R N A L , 77, 3722 (1955).
FILIPPO XCCASCINA, SERCIO PETRUCCI AXD KAYMOXD -1.1.Fuoss
1302
Carbon tetrachloride was washed with hot concentrated sodium hydroxide solution to eliminate carbon bisulfide, then washed with water and dried over PaOj. The conductance of the final distillate was far below the limit of detectability . Apparatus and Method.-Two conductance cells were used. The first4 had a constant of 0.1550 cm.-', as determined by measurements on potassium chloride (5 times recrystallized from conductance water),8 using Shedlovsky's data.9 The second cell (lightly platinized electrodes) had a constant of 0.07356, as determined by comparison with the first, using solutions of Burh'BPhj in acetonitrile. As a control, the conductance of tetramethylammonium picrate in nietllanol vias determined: t h e results were in satisfactory agreement with those of Evers.lo Most of the measurements were made using a Jones bridge (Leeds and X'orthrup); some were made a t the Sterling Chemistry Laboratory of Yale University, using a Shedlovsky bridge. All d a t a were extrapolated t o infinite frequency in order to eliminate polarization errors. The cells mere immersed in a thermostat at 25.00 j=0.005", which was monitored by a platinum resistance thermometer and Mueller bridge. Solvent mixtures were prepared by weight, and volume concentrations were calculated from the densities. All solvent transfers were made with precautions to avoid contamination by atmospheric moisture. The solvent densities do are given in Table I; then final electrolyte concentrations were calculated by use of the equation d = do 0.225~0 where co is the concentration calculated using do as first approximation. (JVithin t h e experimental error, t h e coefficient 0.225 mas the same for solutions in acetonitrile, isobutyronitrile and in a 50-50 mixture of acetonitrile and carbon tetrachloride.) Corrections (maximum, about 0.017,) were made for the amount of solvent in the vapor phase; for the mixtures, we assumed ideal behavior in computing this correction. At least 20 mg., and usually 50 mg., of salt mas weighed in a weighed glass cup on the microbalance; then cup and contents were placed in the cell containing solvent (or solution); a magnetic stirrer was used to ensure uniformity of composition of the solution.
+
PROPERTIES
wt. so CClr
0.00 17.G3 28.20 44.06 44 94
57.70 67.31 71.91 80.37 80.97 100.00
OF
1'01.
s1
The fifth column of Table I1 gives the value of KU corre sponding the highest stoichiometric concentration a t which conductance was measured in a given solvent. Here, K is the Debye-Hiickel parameter, and d was set equal to 9.0. The solvent conductance K~ is given in the s i x t h column. The conductance data are summarized in Table 111, where A is equivalent conductance and c is concentration (equivnlents of salt per liter of solution).
Discussion The seven systems investigated cover the range 36.0 3 D 3 4.SO;in acetonitrile, only about 0.3c/;, of the solute is present as ion pairs a t c = 2 X while a t the same concentration in the mixture with D = &SO, only about 4% of the solute is present as free ions, the other 96yo being associated to pairs and triples. These systems thus serve to illustrate the transition from almost negligible association to marked clustering of ions under the influence of mutual electrostatic forces, as the dielectric constant is decreased. Katurally, different methods must be used to analyze the data, according to the magnitude of the association constant K A . I n acetonitrile and in,solvent 2, the conductance curve lies above the Onsager tangent; in solvent 3 ( D = 2S.S), the points are practically on the tangent; then with decreasing dielectric constant, the curves become progressively steeper in our working range of concentrations and all lie below the limiting tangent. A preliminary analysis of systems 1-3 is shown in Fig. 1 where A',, is plotted against concentration; the variable A',,, defined by the equation A ' , = A(1
+ FC) +
Sc'//2+,1,i2
+ E c y log c y
(I)
represents the observed conductance A, corrected for the static viscosity and the theoretically preTABLE I dictable square root and logarithmic terms in moACETOSITRILE-CARBOSTETRACHLORIDE bility.13 For systems l and 2, the fraction of solute associated to pairs is so small that y in (1) can be MIXTURES replaced by unity; for systems 3-5, we used the apd 100 'I D proximation 0.7771
0.3438
....
....
0.9063 1. 0015 .... 1.0998 1.1841
,3822
....
,5376 ,5942
35 99 33.06 3U. 68
,4191 ,1187 4595 ,4995
1.3176 ....
....
1,5851
,9017
27.91 19.80
... 11.54 2.25
Solvent properties are summarized in Table I. T h e densities were determined, using an Ostwald-Sprengel pycnometer, which is especially convenient for work with mixtures of components of different volatilities, because it can be filled rapidly. Viscosities were measured, using both Ostwald and Ubbelohde viscometers. Dielectric constants were measured, using a General Radio Schering bridge and the cell described by Sadek and Fuoss.11 For calibration, we used D = 34.82 for nitrobenzene and D = 32.63 for methanol.'* The physical constants of the solvents used in the conductance experiments were interpolated graphirally from the data of Table I ; these values are summarized i n Table 11, which also gives code numbers for later use. ( 8 ) C. A. Kr aus a n d \V. B. Dexter, THISJ O U R N A L ,4 4 , 2408 (1922). (9) T. Shedlovsky, A. S. Brown a n d D. A. MacInnes, Tunns. Elec/ r o c h e m . S a c . , 66, 16.5 (1934). (10) E. C . Evers, THISJou~Nar,,73, 1739 (1951). (11) H. Sadek and R . M. Fuoss, i b i d . , 7 6 , 5897 (1954). 112) A. A . X a r y u t t a n d E , R. S m i t h , S . B . S . Circular. 614, l(10.51).
7 = A,'[&
- S(CA/Ao)'/2]
(2)
I t will be seen that the plots are linear, with a slope which increases as dielectric constant decreases ; the intercepts a t c = 0 evaluate the limiting conductance 11,. lissociation is so slight in systems 1-1 that the J J - X method? cannot be used to evaluate the association constants, because the plots are practically horizontal. 4 different method was therefore used, based on an extrapolation of the association constants which are obtained for systems 5-7. System 5 ( D = 15.35) shows marked association. I n this case, the term KAcyf2A is very much larger than ( J c y E c y log cy) and the approximate equation
+
h = )(.4"
- Sc'.12-1'/'z)
(3)
adequately represents the conductance curve; extrapolation by the method of Fuoss and KrausI4 or of S h e d l ~ v s k y ' ~may ~ ' ~ be used. The Shedlovsky plot is shown in Fig. 2 ; from slope and intercept, we (13) T h e symbols in Eq. 1, as well as those used later in this paper, have t h e meanings given in rrf. 2 . (14) R. 31,Fuoss a n d C. A. Kraus. T H I S J O U R N A L , 55, 470 (193:3): R. &I. Fuoss, Chent. Rez's., 1 7 , 27 (1933). (15) T. Shedloxsky, J . Prnizkliit Insl., 336, 739 (1938). (10) R. hl. Fuoss a n d T. Shedlovsky, T H I S J O U R N A L , 71, l-liJ(i
(1949).
lfarch 20, 1939
CONDUCT.4NCE O F
TETRABUTYLAMMONUBI TETRXPHENYLBORIDE 1303
TABLE I1 PROPERTIES OF SOLVENTS FOR CONDUCTANCE EXPERIMENTS ra at
S O
% CC14
D
1007
c (max.)
1 2 3 4
0 00 16.90 40.23 55.25 74,89 90,26 94.97
35.99 33.20 28.20 24.90 15.35 7.20 4.80
0.344 .362 .406
0.18 .14
.448
.14 .14 I39 .32
7
6
I
.09
,550 ,711 ,796
TABLE I11 CONDCCTAXCE OF Bu4IYeBPha IN MeCn-CC14 MIXTURES AT 25 O 104,
106,
A
A
so. 1 2.478 2.494 3.062 3.447 4.278 4.843 6.783 7.508 8.911 10.139 13.530 16.787
No. 4
114.5 114.5 113.95 113.6 112.95 112.5 111.3 110.85 110.15 109.6 108.15 107.0
0.938 2.138 3 . 708 5.338 6.562
106,5 105.8 103.4 102.25
4.030 6.105 12.626 14.287 16.085
No. 3 0,4535 0.923 2.338 3.489
96.5 95.65 93.75 92.7
0.498 1.501 2.719 4.717 6,909
KO
AQ
KA
AO?
119.60 112.24 98.80 88.30 70. 26 (54.35) (48.55)
14.3 17.8 20.0 36.0 146 4 . 0 9 x 104 2 . 9 6 X loe
0.411 ,406 .401 ,395 ,386 ( ,386) ( ,386)
clustering. We therefore used the Fuoss and Kraus equation" h c ' / l g = hoK~-'/p
+ (Xo/kKA'/:)(l
- A/
Ao)C
(5)
to analyze the data for systems 6 and 7. In eq. 5 , XO is the limiting conductance of the triple ion double cluster (AzB+) (ABz-), k is the constant for the triple ion equilibrium and g is a function which approximates the effects of long range electrostatic forces. Figure 3 shows the data for systems 6 and
T\-0. 5
0.2905 1.0165 2.2025 4.000 2.045 3.615 4.542
No. 2 3.040 3.883 7.453 9.628
84.95 83.25 81.65 80.3 79.4
10'
24.0 16.0 8.0 12.0 1.7 0.6 0.2
67.15 64.8 62.7 60.25 62.85 60.6 59.55
iYo. 6 19.32 16.54 13.25 12.80 12.33 so. 7
4.61 3.05 2.33 1.95 1.74
1
00
15
c .lo'
Fig. 1.-Determination
of hofor systems 1-4.
obtain K A = 165 and AO = 69.66. By the y - x method, we find K A = 120 and A0 = 69.6; the points scatter rather badly, and this value of K A is preliminary. A better value will be obtained in the second approximation by means of equation 11. This system shows the effect of neglecting the higher terms in the conductance equation; the use of the approximation 3 gives too high an association constant. In systems 6 and 7, association to pairs is so pronounced that (3) practically reduces to the limiting form cA' = A o 2 / K ~
(4)
when combined with the mass action equation, because y becomes negligible compared to unity. This means that an extrapolation by the modifiedl4-I6 Ostwald dilution law can only evaluate the quotient Ao'/KA; the plot is so steep t h a t the intercept l/Ao becomes indistinguishable from zero. Also, in this low range of dielectric constant, it becomes necessary to include the effects of higher
(C A ~ * S ) X ~ O ~ Fig. 2.-Shedlovsky
plot for system 5.
(17) R. M. Fuoss and C . A. Kraus, THIS JOURNAL, 66, 2387 (1933).
1304
FILIPPO X C C . ~ S C ISERCIO ~A, PETRUCCI A N D RAIXOND 51. Fnoss
Vol. SI
I
61
-
/”
I
6, 90 26% ici,
l/DXlO‘
ion plot for systems 6-7.
Fig 3 -Triple
of association constant on dielectric constant.
Fig. 4.-Dependence
7 , plotted according to eq. 5. By using Walden’s rule and the value 907 = 0.386 (based on the final value of A, for system 5 ) , we find from the intercepts a t c = 0 the values RA = 4.09 X l o 4 and 2.96 X l o 6 for systems 6 and i , respectively. X s s ~ m i n g ~ ~ that XO = & / 3 , these values of K Aand the slopes of the lines of Fig. 3 give K = i . 2 X and 1.0 X for the triple ion constants of the two systems. In Fig. 4, the logarithms of the pairwise association constants are plotted against reciprocal dielec117 tric constant; the three points for systems 5-6-i can be approximated by a straight line as shown. -4ssuming’’: that Kq
=
Kaq eb
(6)
b
e2/aDkT
(7)
I 25
5
75
where =
the slope gives c2 = 8.5 for BuJV.BPh4. This value is, as expected, larger t h a t the preliminary values reported3 for this salt in several solvents where, for lack of information on the dependence of association on dielectric constant, the approximation K A = 0 had to be made. IYith the information obtained from systems 5-7) it becomes possible to analyze the data for the solvents of higher dielectric constant. IVe define a new variable A K by the equations =
.i’,
-
Jr
10
125
15
--
I
h
110
014023% CC! I 98
1
2
3
4
5
6
1
2
3
4
5
5
(8)
(9)
= i o - KlCj.21,
which are readily obtained from the general conductance equation by rearrangement. Here y has been approximated by unity, and the value3 F = 2.0 was used to calculate -1, = A(1 F c ) . Now J is an explicit function of a ; we used d = 5.0, 7.0 and 9.0 to calculate ](a) and then - 1 by ~ means of (8). ,kcording to (9),- 1 should ~ be a linear function of cf2A,; as shown in Fig. 5 , the data give straight lines when so plotted. The terms Jc and K A Q A , in the conductance equation oppose each other; therefore a larger CL corresponds to a larger K A . The problem is t o solve equations 8 and 9 for J and KA. No solution is possible without additional information, of course, because these equations actually are parts of the equation
+
hi, = .io
I
a.0
+ JC - K.q CJ’’A,
(10)
(18) J. 1’. Denison a n d J. B. Ramsey, THIS J O U R N A L , 77, 2013 (195,i); R.hl. Fuoss, ibid., 80, 5O.X (19.?8).
I 0
I Ca.A,,f’
Fig. 5 -Equations
7
x 10’
8 and 9 for applied t o systems 1-4.
which, for high dielectric constants and low concentrations, is approximately A’, = A n
+(J -
KAIiOjC
(11)
In other words, the data serve only to evaluate the difference ( J - KA&). But the information in Fig. 4 provides a method of resolving the difference into its two components. The slopes of the lines of Fig. 5 give &(a) as a function of the trial values of 6 used in computing ](a). If we assume that a is independent of solvent composition, then the cor-
March 20, 1959
OPTICAL DENSITYWITHIN ROTATING ULTR-4CENTRIFUGE CELLS
1305
rect value of a is the one which will give a set of log K A - D-' points for systems 1 4 which will lie on the extrapolation of the line through the points for systems 5-7. The four points a t the left in Fig. 5 are those obtained using 6 = 9.0 in (8). Within the validity of the various approximations made, this is in satisfactory agreement with the value if. = 8.5 found from the slope of Fig. 4. The points obtained in (8) lie below any reausing J (5.0) and J ('7.0) sonable extrapolation of the line approximating the points for systems 5-7. Now J ( a ) represents the change in mobility due to the higher terms in the conductance equation, while KA(a) of course describes the ion-pair equilibrium. The agreement between the values of a from J and from K A shows t h a t charge-charge interaction suffices to describe the behavior of BudN.BPh4 in the solvent system CH3CN-CC14. From the viscosity coefficient F , the value of the hydrodynamic radius was found3 to be 5.4 h.,assuming the two ions to be of equal size. Center-to-center distance a t contact, based on viscosity data, then would be 10.8. This is in fair agreement with the electrostatic parameter, 6 = 9, considering the completely different physical processes underlying the two results. Molecular models show that the nearest one can possibly bring the borqn and nitrogen atoms of BulIV.BPh, is about 7 A. ; this must represent the lowest possible bound for 8. The two ions are, of course, not spheres; the boron-nitrogen distance averaged over random orientations of the two ions a t contact must certainly be larger than this minimum figure, as we found above from the conductance (and viscosity) data. Finally, we consider the Walden products shown
[CONTRIBUTIOS X'o. 2383
FROM THE
GATESASD CRELLIXLABORATORIES OF CHEMISTRY, CALIFORXIA INSTITUTE OF TECHNOLOGY]
A Rotor Aperture for the Determination of Optical Density within Rotating Ultracentrifuge Cells BY E. ROBKIN,M. MESELSON AND J. VINOGRAD RECEIVED SEPTEMBER 18, 1958 T h e design and applications of an exponential aperture for analytical ultracentrifuge rotors are described, Images of the rotating aperture and ultracentrifuge cell are recorded side by side on absorption photographs. Photometry of these photographs provides the necessary data for accurate evaluation of optical density within the rotating cell,
The photographic determination of optical density within a cell during the operation of the analytical ultracentrifuge is of importance in many experiments.' It is convenient in such work to employ the film within the linear range of its characteristic response to exposure and to measure its optical density with a photometer possessing linear response to film optical density. These two conditions are expressed by the relation /3 log exposure = Pen Deflection
+
fi
(1)
where ,R and "f1, are constants characteristic of the film specimen and the photometer. (1) T. Svedberg and K. 0. Pederson, "The Ultracentrifuge," The Clarendon Press, Oxford, 1940, pp. 240-253.
Because film characteristics vary with emulsion and conditions of exposure and development, a verification of film linearity must be made whenever accurate work is to be done. A convenient method for calibrating the response of the film and photometer has been developed through the construction of a special aperture in the rotor. Light passing through this rotating aperture produces a graded blackening on the film alongside the image of the centrifuge cell (Fig. 1). The shape of the aperture is chosen so that the photometric record of the graded blackening will be a straight line whenever the conditions expressed by equation 1 ate satisfied. The appropriate aperture shape is given by e ( r ) = exp(Klr
+ K2)
(2)
