PHYSICAL A N D INORGANIC CHEMISTRY [CONTRIBUTION NO. 1622 FROM THE STERLING CHEMISTRY LABORATORY OF YALE UNIVERSITY, NEW HAVEN, CONNECTICUT 1
Electrolyte-Solvent Interaction. IX. Tetra-alkylammonium Tetraphenylborides in Acetonitrile-Carbon Tetrachloride Mixtures at 25 O BY DONALD S. BERNS' AND RAYMOND M. Fuoss RECEIVED MAY19, 1960 The conductances of tetramethyl-, tetraethyl-, tetra-n-progyl- and tetra-n-butyl-ammonium tetraphenylhorides have been measured a t 25' in acetonitrile-carbon tetrachloride mixtures covering the range 10 < D < 36 in dielectric constant. Limiting conductances and association constants follow the sequence expected from the structure of the salts. The apparent Stokes radius is linear in reciprocal dielectric constant; extrapolated values for the hydrodynamic radii of the above cations are 2.37,2.75,3.31 and 3.84. The center-to-center distance for anion and cation a t contact in an ioqpair, derived from the linear dependence of the logarithm of association constant on reciprocal dielectric constant, is 0.75A. (about 10%) larger than the sum of the hydrodynamic radii.
Reduction of conductance data to molecular parameters characteristic of solute and solvent requires among other things a knowledge of single ion conductances. It has been shown2 recently that these can be obtained for non-aqueous systems from measurements of the conductance of tetrabutylammonium tetraphenylboride in a given solvent system by assuming that Xo(BurN+) = Xo(BPh4-) = A0/2. The interpolation for limiting conductances in solvent mixtures by means of Walden's Rule Aoq = const. is unreliable, however, since experiment shows that this product varies systematically with composition. Study of Walden products for a number of systems showed4that the dielectric constant D of the solvent is the controlling independent variable and that single ion conductances are in fair agreement with the semiempirical equation
2.75; Pr4N+, 3.31; Bu4N+, 3.84) are in the sequence expected from structure and agree well with values derived by electrostatic theory from the association constants.5
Experimental
Materials.-Tetra-n-butylammonium tetraphenylboride Bu4NBPh4 was prepared as beforeo; m.p., 233-235' (the "223'" in ref. 6 is a misprint); density, 1.023 at 25'. Tetra-n-propylammonium tetraphenylboride Pr4NBPh4was prepared from Pr4NI and NaBPh4. After several recrystallizations from 2:1 acetone-water, the melting point was 205-207°, unchanged after one more recrystallization ; denTetraethylammonium tetraphenylsity, 1.049 at 25'. boride EtdNBPhr was prepared from EtrNBr and NaBPhr and recrystallized from 4:1acetone-water. A crystal change appears a t 260-265'; m.p., 350'; density, 1.069 a t 2 5 ' . Tetramethylammonium tetraphenylboride was prepared from Me4NBr and NaBPh4 and recrystallized from 2:l acetone-water (200 cc./g.); m.p. > 350'; density, 1.084a t 25'. Acetonitrile (Matheson) was kept over potassium XOT = (Fe/1800~)/(Rmf s / D ) (1) hydroxide pellets (100g./500 g. solvent) for 24 hr. and then over anhydrous sodium carbonate for several days. I t was where q is solvent viscosity, the coefficient is 0.8194 finally distilled from Drierite after several hours refluxing; X lo+, R, is the hydrodynamic radius of after discarding a small forerun, the conductance remained constant a t about 5 x 10-8 mho or less; b.p. 81.5' a t 760 the ion and s is a constant presumably characterismm. Carbon tetrachloride was stored over barium oxide tic of the ion-solvent interaction. The suggestion and distilled from activated alumina; b.p. 76.8' a t 760 mm. was made that s has its origin in a process which oc- Solvent Liixtures were prepared by weight. Densities, viscurs in a mixed solvent having a polar component, cosities and dielectric constants? (1 megacycle, General due to the orientation and relaxation of dipoles in Radio 716 CS1 Bridge) were measured for each mixture used; these data are summarized in Table I which also gives code the solvent as the ion moves through it. for identification of the various mixtures. As a The purpo~:.of this paper is to present a system- numbers control on the purity of the salts, check conductance runs atic study of eq. 1,using as test compounds the series after several repeated recrystallizations were made in aceof salts tetra-methyl, ethyl, n-propyl and n-butyl tonitrile for each salt; in no case were discrepancies greater ammonium tetraphenylborides in the solvent sys- than 0.02% (the estimated precision) observed. Salts were weighed on the microbalance (50-100 mg.) and tem acetonitrile-carbon tetrachloride. This series added t o solvent in the cell after the solvent conductance was gives a sequence of cations of increasing size; fur- determined. All solutions were made up by weight; volume thermore, all of them, as well as the anion, have concentrations c (eq./l.) were calculated from the known volumes considerably larger than the volumes of the weights of materials and the densities of the solutions. T h e were obtained by measuring densities of solutions in constituent molecules of the solvent. The data latter ac the range of 2-5 X I O w s N and assuming that p = po were found to conform to eq. 1. Furthermore, the where pa is solvent density, and (Y is a constant for a given hydrodynamic radii found (MerN+, 2.37; Et4N+, salt and solvent mixture. If w g. of solute of molecular
+
(1) California Research Corporation Postdoctoral Fellow, Ysle University 1959-1960. (2) R. M. Fuoss and E. Hirsch, THISJOURNAL, 89, 1013 (1960). (3) H.Sadek and R . M Fuoss, ibid., 79, 301, 5803 (corr.) (1950); 78, 5897 (1954); 78, 5902 (1954); 18, 5905 (1954); 81,4507 (1959). (4) R. M.Fuoss, Proc. Null. Acad. Sci. U. S.,46, 807 (19.59).
(5) E. Hirsch and R . M. Fuoss, THISJOURNAL, 89, 1018 (1960) (6) F. Accascina, S. Petrucci and R. M. Fuoss, ibid., 81, 1301 (1959). (7) The dielectric constants of systems 3, 4 and 5 of ref. 6 should be revised as follows: 27.20 for 40.23% CClr, 22.00 for 55.25% and 14.40 for 74.89%.
5585
5586
‘ I I
2 3 H
I
G+D 2
u 1H
. 8 2 1
1
r-dxy e o
I
n
“0
j
_1
I
v
0
./
DONALD S. BERM AND
1
1
Vol. 82
RAY,?.IOND 11.2. FUOSS
comparison with the standard). Measurements were all made at 25 f 0.002”, using a Shedlovsky10 bridge with a calibrated Leeds and Northrop decade box in the known arm. The data are summarized in Tables 11-V.
TABLE I1 CONDUCTANCE OF Me4NPhdB IN CHsCN-CClr MIXTURES AT 25 10‘ c -No.
-1
6.2569 4.9123 3.6592 2.4743 1.4209 -No.
A
143.64 144.59 145.62 146.81 148.09 141.51 142.59 143.85 145.34 147.30
104~ A -----NO. 13-
A
3-
102.19 103.60 105.19 106.93 108.94 7-
-No.
-1
10.3079 8.1980 6.0939 4.1286 2.0826
104 c
-NO. 8.1123 6.3266 4.6010 3.0707 1.7434
?No.
84.87 86.53 88.30 90.53 92.56
6.8124 5.2678 3.9102 2.5107 1.5317
8.6685 6.9386 5.3309 3.7196 2.1601 6.0170 4.7641 3.7972 2.6804 1.5299
60.12 62.10 64.38 67.34 71.28 17-
46.57 48.77 50.90 54.10 58.90
TABLE I11 CONDUCTANCE OF Et4NPh4BIN CH3CN-CC14MIXTURES AT 25’ 104~ --NO.
14.0136 8.6159 6.4489 4.3738 2.2095 -NO. 8.8750 7.0887 5.3756 3.7857
A
-1
130.63 133.11 134.36 135.78 137.72 -2
117.63 118.74 119.87 121.16
104 c -NO.
104~
A
-NO. 10.1896 89.13 9.2780 7.8836 90.67 7.2174 5.8284 92.31 5.3598 3.9937 94.12 3.5925 2.4114 96.09 2.0332 -NO. -9 -NO. 11.7671 76.04 9.1371 8.9259 77.94 6.8476 5.1009 81.38 5.3366 4.1412 82.53 3.6277 2.4433 85.02 2.0337 -4
11-
A
64.76 66.73 68.94 71.65 75.07 15-
53.47 55.92 58.12 61.03 65.12
TABLE IV CONDUCTANCE OF Pr4NPhcBIN CHaCN-CClc MIXTURESAT 25’ A
104 c
-NO.
10.9717 8.2757 5.8928 3.9043 2.1320 -NO.
-1
A
10’ c
-NO.
6 -
14-
A
118.04 10.2439 78.07 8.6932 53.17 119.20 8.0037 79.41 6.8989 54.80 120.63 3.9367 82.86 5.0312 56.91 122.01 2.2243 84.83 3.3700 59.41 123.59 1.9087 62.48 -1
9.4486 7.2967 5.5479 3.7657 2.0964
104 c --No.
--No.
1
h
-NO.
18-
118.83 11.0478 66.07 6.4290 40.47 119.91 8.6411 67.60 5.0539 42.29 120.94 6.4687 69.27 3.7091 44.62 122.20 4.2563 71.45 2.5619 47.34 123.72 2.4508 73.87 1.5423 50.80
Discussion The data of Tables 11-V were analyzed by the IBM-650 computer, using Kay’s program” (with slight modification) for the equation12 A = do
- Sc1/ry1/2 + Ecy log c y + Jcy + J&y)’/* FAc
- K A C Y (2) ~ ~
(10) T. Shedlovsky, ibid., 61, 1793 (1930); H. Bisenberg and R. M Fuoss,i b i d . , 76, 2914 (1953). (11) R. L. Kay, ibjd., 81, 2099 (1960). We are indebted to Professor Kay for use of the program before its publication and for many helpfd discussions. (12) R. M. Fuoss and F. Accascina, “Electrolytic Conductance,” Interscience Publishers, Inc., New York, N . Y., 1959. Sjrmbols used in this paper-’aredefined in Chapters 15 and 17.
Nov. 5 , 1960
TETRA-ALKYLAMMONIUM
TETRAPHENYLBORIDE-SOLVENT INTERACTIONS
TABLE V CONDUCTANCE OF Bu4NPh4B IN CHsCN-CC14 MIXTURES AT 25' 104 c -No.
1-
16.0902 9.1684 6.1596 8.1150 2.7i64 -NO.
A
107.59 110.30 111.89 113.95 114.25 1-
12.1003 9.5708 6.7915 4.6413 2.3533
108.99 110.05 111 48 112.80 114.59
104~ A --No. 5-
104~ A -No. 12-
7.0327 5.4431 4.0635 2.6842 1.5191
9.7081 7.6241 5.7048 3.8144 2.1505
73.37 74.52 75.78 77.33 79.16
-NO.
8-
-NO.
8.2582 6.5722 4.9163 3.3977 1.8704
66.26 67.42 68.77 70.28 72.34
5.6492 4.4807 3.3693 2.4125 1.3090
( I t will be noted that the
J 2
56.17 57.61 59.17 61.13 63.37 16-
47.63 49.12 50.86 52.77 55.83
term, with
J z = (2L/r/24)(~/cL/~)~(1.07i6b2 - 2b
-
1)ho
-
dKauz/c (3)
is retained in (2), although i t has been neglected in a number of recent publications from this Laboratory. This term is indeed small, but its retention has been foundla to reduce a spurious systematic change of ion size with solvent composition.) The derived constants, A0 and KA,for the systems studied are summarized in Table VI, together with the values of UJ,the ion size derived from J . In the case of the solvents of high dielectric constant, association was slight, so the limiting form of (2) corresponding to K A = 0 , y = 1 was used in these cases in order t o obtain preliminary values of Ao. Also, for these systems, where (2) gave a K A value of dubious precision while the limiting form for no association gave too small an U-value (viaJ), a different procedure14 was adopted. Using preliminary values for A, obtained from (2) or its limiting form, A g can be computed, where A f SC'/* Ec log c FAc - Jc - J~c'/* (4) AK provided a value of a (which evaluates J and Jz) is known. Then a plot of A g , which is also given by AK = A. - KAcPA (5) for cases where association is slight, against cf"A evaluates AOand K A . I n (4),we set u = a A , where aa is the sum of the radii obtained by applying (1) to the preliminary values of Ao. The final plots of R = 0.8194 X lO-*/X~.rl against reciprocal dielectric constant are shown in Fig. 2 where the various circles represent the observed points and the solid lines are drawn with the constants obtained from a least square treatment of a R D - D plot. (This method of evaluating the constants puts more weight on the data a t high dielectric constant, where the precision of extrapolation for A L is higher.) I n Table VI is shown a comparison of observedI5 values of 110 with the values obtained by taking appropriate sums from
-
Xo(Bt4N+) =
& ( E t N + ) = 0.8194 X 10*/,(2.748
&(Me"+)
= 0.8194
x
10-/%(2.366
f 4.20/0)
+ 6.87/0)
5587 (9) (10)
The value of R , for the Me4N+ion (2.37 8.) agrees fairly well with a molecular model, but the increments AR, = 0.38, 0.56, 0.53 between successive members of the series are less than that corresponding to one methylene group. The flexibility of the alkyl chains in the R4Nf ions would, of course, lead to an equivalent hydrodynamic sphere whose radius is less than the length of an extended chain. Data for the Bu4N+ion are now available4 in five solvent systems; the corresponding values of R+, are 3.84 in MeCN-CCL, 3.55 in PhN02-CC14, 3.35 in MeOH-CC14, 3.53 in EtOH-CCla and 4.46 in dioxane-water. Except for the last system, R+, appears to be substantially independent of the solvent. Further work on a wider variety of systems is needed, of course, but it now seems justifiable to hope that R , will turn out to be a constant characteristic of a given ion in aprotonic solvents, from which many solution properties then can be predicted theoretically with good precision.
+
Xo(BPhr-)
+ 5.07/0) (3.313 + 4.80/0)
= 0.8194 X 1 0 " / ~ (3.842
Xo(Pr,N+) = 0.8194 X lo-*/?
(6) (7) (8)
(13) John E. Lind, Jr., Dissartatlon, Yale University, 1960. (14) R. M. Fuoss and F. Accascina, Proc. N o f l . Acad. Sci. U.S., 46, 1383 (1959). ( 1 5 ) T h e Petrucci points* for BucNBPha in Fig. 2 (solid circles) are plotted using the corrected dielectric constants.1
Fig. 2.-Dependence
of apparent Stokes radii on dielectric constant.
Equations 7-10 evidently permit the calculation of the limiting conductances of the four salts in any mixture of MeCN and CCL with D 3 10 and represent the best available means of extrapolating into the region of still lower dielectric constants where direct determination from A - c data is impossible. The average variation over the 21 systems of Table VI for [A0 (calcd.) - A0 (obsd.)] is 0.46%; if the three cases (marked with an asterisk) in which the variation exceeds statistical expectation are excluded, the variation over the remaining 18 systems is 0.3 yo. (It should be mentioned that the precision of the A - G data in a given solvent is of the order of 0.0270; the above variation of 0.3oj, represents the over-all consistency of all the data for a given salt in the different solvent mixtures.) The coefficient J , which is essentially a measure of the curvature of the phoreograms, in principle permits evaluation of the center-to-center distance a j of anion and cation a t contact. As a quantity obtained from a second derivative, kwever, its precision is of course much less than that of a from A,. The values of aJ are summarized in Table VI. The uncertainty in the numerical values is reflected
5588
DONALDS. REKNS .ANI)R.~YYIOND I f . Frross
I
0
50
I 100-0
I
’
10~1~ ---do 3
50
of
Fig. 3.-Dependence
UJ
on dielectric constant.
in the following facts: (1) the values change only slightly from ?\le4NBPh4to Bu4NBPh4; (2) they are smaller than the corresponding aA values and also smaller than the values estimated from models; and (3) they vary systematically with solvent, as shown in Fig. 3 where U J is plotted against D+ for the four salts. The last item appears to be especially significant; it suggests that there are still some small unknown linear terms in the A-c funcTABLE VI DERIVEDCOXSTANTS NO.
D
Ka
aJ
An(ob5d.)
An (calcd .)
152.27 114.85 99.31 83.60 74.39
152.58 114.16 99.67 82.72 75.20*
MerNBPhl 1 3
7 13 1;
36.01 22.32 17.45 13.06 10.68
5.1 7.1 6.1 6.6 7.6
VOl. 82
3 20 62 328 1110
0
3
6
IOO/D
Fig. 4.-Test of equation 11; dependence of association constant on ion size and dielectric constant, same code as Fig. 1.
In acetonitrile, with a dielectric constant of 36, ion association is almost negligible due to the large size of the ions. Consequently the computer finds i t difficult to separate the Jcy and K4f2Ac? terms, both of which are to first approximation linear in c. In the mixtures of lower dielectric constants, where f2A becomes significantly different from A,, reliable values of both J and K A can be obtained by equation 2. As mentioned above, we simplified the analysis of the data by using U A to compute J and JZ and extrapolated by means of equation 5 in order to obtain the final values of A0 and KA. Theoretically l6 K A = (4~Nu~/3000)e*
EtcSBPhr
(11)
(where b = eZ/uDkT) for systems in which ionsolvent interaction is small; for the RdNBPh4 salts 1 under consideration here (11) evidently is an ade9 quate approximation, as shown in Fig. 4 where log 11 ( K A / u is ~ )plotted against 1/D. The four straight 1.i lines as drawn originate a t log (4aN/3000), showing t h a t the Gilkerson17 term exp ( - E , / k T ) is Pr4TBPh4 unity within the experimental error. From the 1 36.01 5.8 1 128.36 128.59 slopes of the lines, we evaluate aK values as follows: 90.17 6 5.5 31 91.29 19.46 Me4NBPh4, 6.96; Et4NBPh4, 7.30; Pr4NBPh4, 10 5.5 70 81.55 16.13 81.56 7.95; Bu4NBPH4, 8.36. These are in the expected 14 6.0 235 71.62 12.31 71.46 sequence and like the ah values (Me4NBPhd, 6.21 ; 18 9.80 64.02* 7.0 880 63.10 Et4NBPh4, 6.59; Pr4NBPh4, 7.15; BudNBPhr, Bur NBPhc 7.68) give center-to-center distances somewhat 119.31 1 119.48 5.8 6 36.01 smaller than dimensions from models. The dif85.54 6.4 21 85.03 5 19,s; ference between aK and aA is practically constant 78.57 17 18 78.37 6.0 45 Y (average, 0.75) ; agreement within 10% of values 70.06 12 13.92 133 70.04 6.4 obtained from two completely independent sources 16 365 64.18 63.93 11.16 7.1 (A, + a.4, hydrostatic; K A + u K , electrostatic) tion which are now being absorbed in J . A studvI3 supports the hypothesis that the a values are addiof the conductance equation shows that terms linear tive molecular parameters characteristic of the ions in c which are still missing from the theoretical and not merely numbers obtained by curve-fitting. equation probably would vary as D V 3 or D F 4 . As already mentioned, the U J values are less reliable Hence our present opinion is that no attempt should than a.4 ora^, but comparison of the latter with Fig. be made to “explain” the trend of a J by an ad hoc 3 shows that even the U J values are a t least reasonhypothesis such as solvation. I t is a t least gratify- able in magnitude. For quantitative arguments, ipg that the values of a j turn out to be within an however, the values of a from A0 and/or K Anaturally A.-unit or so of the expected values. More weight are preferable, because they are defined to a much must be given to ion sizes determined from A0 by better precision. (1) or from the association constant (as will be pre(16) R . M. Fuoss, THISJOURNAL, 80, 5059 (1958). sented below). (17) W. R. Gilkerson, J. Chem. Phys., 211, 1199 (1956). 1 7
36.01 30.62 20.60 17.05 14.21 12.14
5.2 4.9 5 .4 5.8 6.9 5.9
4 8 21 60 184 408
142.77 128.08 102.95 93.18 84.91 i6.72
142.60 128.49 102.64 92.36 84.41 77.99*
