158
D. FENNELL EVANS AKD PHILIP GARDAM
Transport Processes in Hydrogen-Bonding Solvents.
11. Conductance of
Tetraalkylammoniurn Salts in 1-Butanol and 1-Pentanol at 25 O
by D. Fennel1 Evans1 and Philip Gardam Department of Chemistry, Case Western Reserve University, Cleveland Ohio 44106
(Received JuZy 24, 1968)
Conductance measurements are reported for Me4NC1, BudNC1, XIerNBr, Et&&, PrrNBr, BuiNBr, E t X I , Phh-1, Bu~NI, i-Am3BuNI,HeptaNI, and Bu4NC104in 1-butanol and BurNBr,Bu4NI,i-.lmsBuN, and Kept (SI in 1-pentauol at 25'. The data were analyzed by the Fuoss-Onsager equation. The extent of ionic associatioil was found to increase with increasing size of the anion and is discussed in terms of a multiple-step association process. The variation of ionic mobilities in methanol, ethanol, l-propanol, and l-butanol is compared to that predicted by the Zwaiizig equation niid found to agree only in a qualitative maimer. Introduction This is the second in a series of papers discussing the transport properties of electrolytes in hydrogen-bonded solvents. I n the first paperJ2the conductances of the tetraalkylammonium salts in ethanol and propanol at 25' were reported. Contrary to the predictions of electrostatic theory, ionic association of these salts was found to increase with increasing anion size. I n an effort to obtain further information about this homologous series of solvents, we have extended the measurements to the higher alcohols l-butanol and 1pentanol. Experimental Section The tetraalkylammonium salts were purified by recrystallization. The solvents used in the recrystallization and the temperature at which the salts were dried have been given e l ~ e w h e r e . ~ - ~ Conductivity grade l-butanol arid l-pentanol were prepared by drying Fisher reagent grade alcohol over calcium oxide for several days and then distilling from a fresh batch of calcium oxide. The distillations were carried out in a 1.3-m Stedman column under nitrogen, and only the middle fraction was retained. The densities of butanol and pentanol a t 25" were found to be 0.80576 and 0.81096, respectively. These values are in agreement with those given in the literature, 0.80572 for butanol5 and OS110 for pentanolS6 The viscosities of butmol and pentanol, 0.02589 and 0.03476 P, respectively, were determined in two Cannon Ubbelohde viscometers. The dielectric constants were measured in the allglass platinum cells described by Kay and Vidulich.6 The value of ~~5 17.45 found for butanol is in agreement with that given by Dannhauser and B ~ i h e €25 , ~ 17.51. The value of €25 15.04 was determined for pentanol. The electrical equipment, conductance cells, and techniques were similar to those reported previously.2-4'8 Briefly, the measurements were carried out The Journal of Phusical Chemistry
in Kraus-type conductance cells and increments of salt were added to the cell in small Pyrex cups with the aid of the Hax-es-Kay cup-dropping device,g except for suns I1 for Ale4NC1 and Bu4XCl. Because of the extreme hygroscopic nature of these salts and the difficulties in weighing (with sufficient accuracy) the small amounts required, the results obtained with the cup-dropping device mere checked using a JZininx weight buret with Teflon stopcock. The cell was initially filled with solvent to a level above that of the tubes which connect the electrode compartments to the erlennieyer flask. &4 concentrated stock solution was added to the conductance cell from the weight buret in small increments. The manipulations were held t>oa minimum and were accomplished rapidly to minimize contamination by atmospheric moisture.1° Results The measured equivalent conductances and the corresponding electrolyte concentrations in moles per liter are shown in Table I for l-butanol and Table I1 for 1-pentsnol. Also given is A , the density increment used to calculate the volume concentration. These increments were obtained by density measurements on the most concentrated solutions used in the conductance (1) To whom all correspondence should be directed. (2) D. F. Evans and P. Gardam, J . Phys. Chem., 72, 3281 (1988). (3) D. F. Evans, C. Zawoyslii, and R. L. Kay, ibid., 69, 3878 (1965). (4) R. L. Kay, C. Zawoyski, and D. F. Evans, ibid., 69, 4208 (1965). (5) J. Timmermans, "Physico-chemical Constants of Pure Organic Compounds," Elsevier Publishing Co., New Yorli, N. Y . , 1950. (6) G. A. Vidulich and R. L. Kay, Rev. Sci. Instrum., 37, 1662 (1968). We wish t o thank Professor Kay for the use of the facilities of his laboratory and for his help in carrying out the measurements. (7) W. Dannhauser and L. W. Bahe, J . Chem. Phys., 40, 3058
(1664). (8) C. G. Swain and D. F. Evans, J . Amer. Chem. Soc., 8 8 , 383 (1968). (9) J. L. Hawes and R. L. Kay, J . Phys. Chem., 69, 2420 (1665).
(10) T. L. Broadwater, Ph.D. Thesis, Case Western Reserve University, 1968,
159
TRANSPORT PROCESSES IN HYDROGEN-BONDING SOLVENTS Table I : Equivalent Conductances in Butanol at 25” 104c
A
104c
A
Et4NBr = 0.07 4.285 13.082 7.894 11.411 12.026 10.245 17.386 9.250 22.006 8.639 27.057 8.124 32.571 7.676 39.141 7.255
PrdNI A = 0.10 4.756 12.677 9.885 10.736 14.855 9.643 20.229 8.843 26.193 8.197 32.341 7.692 38.834 7.265 45.989 6.897
BLI~NC~O~ = 0.08 3.435 12.623 7.852 10 193 13.369 8.689 18.951 7.766 25.225 7.054 32.493 6.466 40.089 6.009 48.697 5.607
PrdNBr = 0.08 3.724 12.867 7.784 11.163 12.266 10.037 16.958 9.237 22.196 8.588 27.560 8.081 33.276 7.654 40.103 7.245
Bu~NI = 0.10 3.548 12.620 7.286 10.859 11.103 9.797 15.940 8.878 20.684 8.238 26.126 7.684 31.521 7.256 37.135 6.896
BurNBr A = 0.07 2.712 12.814 6.375 11.080 10,153 10.007 14.385 9.190 18.741 8.578 23.731 8.042 29.225 7.582 35.041 7.195
i-ArnaBuNI A = 0.12 3.281 12.398 7.240 10.455 11.496 9.277 16.684 8.357 21.943 7.705 27.475 7.193 33.583 6.752 40.325 6.369
A
Bu.iXCl = 0.05 Run I 2.400 12.870 7.136 10.913 12.106 9.803 17.075 9.061 22.530 8.463 27.472 8.039 33.165 7.650 39.864 7.276 Run I1 1.215 13.828 3.408 12.398 6.343 11.235 11.128 10.055 15.614 9.313 20.931 8.678 26.216 8.194 30.077 7.903
A
measurements and were assumed to follow the relationship d = do A&, where represents the moles of salt per kilogram of solution. The data were analyzed with the Fuoss-Onsager equation in the formgrll
+
A = A,
- S(cr)’/* - E c y In
(CY)
A
14.480 12.070 10.793 9.861 9.081 8.412 7.933 7.517
1.170 3.231 5.196 7.276 9.657 12.455 15.054 17.843
A
10412
EthNI = 0.11 3.616 14.132 7.757 11.957 12.232 10.600 17.105 9.660 22.124 8.969 27.843 8.361 33.942 7.868 40.026 7.471
A = 0.07
Run I1 2 030 12.873 5.044 10.535 8.484 9.140 12.262 8.188 18.841 7.148 24.157 6.586 31.723 6.008 34.988 5.812
A
HeptrNI A = 0.10 2.656 11.875 6.244 10.041 9.887 8.959 13.539 8.230 17.276 7.677 20.968 7.249 25.152 6.858 29.780 6.508 34.931 6.187
XehNBr
MedNC1 = 0.03 Run I 2.981 11.953 8.062 9.262 15.160 7.071 22.561 6.721 30.347 6.085 38.750 5.597 48.113 5.194
A
10412
+
( J - B h o ) c ~- K ~ f ’ ~ y (1) h The value of B, which corrects for the effect of the added electrolyte on the viscosity of the solvent, was set equal to zero. The value of B does not affect the limiting conductance or the association constant. I n all nonaqueous solvents where the B correction has been determined, the value of d was increased by the con-
A
A
A
stant amount of 0.2 A for all of the tetraalkylammonium halides. Shown in Table I11 are the parameters obtained from the Fuoss-Onsager equation by a least-squares computer program.1z Included are the standard deviations in each parameter and the standard deviation, a h , of the individual points. Some indication of the precision of the measurement can be obtained from the iodide - bromide difference of 1.07 st 0.04 for the EtdX+, PrdN+, and Bu4N+ salts. The corresponding bromide - chloride difference for the (11) R. M. Fuoss and F. Accascina, “Electrolyte Conductance,” Interscience Publishers, New York, N. Y ., 1959. (12) R. L. Kay, J. Amer. Chem. Soc., 82, 2099 (1960). Volume 78, Number 1 January 1969
160
D. FENNELL EVANS AND PHILIP GARDAM calculated from the corresponding values in methanol using the Walden product. When the calculated values were compared with those obtained from trnnsference numbers, they agreed to within 1%. The limiting ionic conductances for ions in butanol given in Table IV were estimated by a similar procedure using the limiting ionic conductance for i-Am3BuNf and He4N+ ions in ethanol and the ethanol-butanol viscosity ratio. An iodide value of 9.32 0.01 was obtained from Ao(i-AmrBuN1) - Xo(i-Am3BuN+) and Ao(Hept4NI) Xo(I-Iept4N+).
Table 11: Equivalent Conductances in Pentanol a t 25' 10%
A
lOlC
A
BucNBr A = 0.07 3.350 7.188 7.615 5.780 12.397 4.998 18.228 4.416 23.823 4. u45 29.347 3.774 35.108 3.556 41.224 3 375
Hept4NI A = 0.11 2.326 7.077 5.748 5.588 9.154 4.848 12.827 4.354 16.574 3.995 20.857 3.689 25.186 3.455 30.032 3.249
Bu~NI = 0.09
i-AmsBuNI A = 0.10 2.426 7.556 5.141 6.231 8.943 5.268 13.514 4.615 18.118 4.181 22.746 3.865 27.683 3.611 34.707 3.339
I
A 3.266 6.698 10.934 15,220 20.647 26.042 31.838 39.861
7.329 6.008 5.173 4.643 4.188 3.870 3.613 3.345
*
-
Table IV : Estimated Limiting Ionic Conductances in Butanol MeaN + EtdN Pr'N Bu~N i-Am3BuN f
f
f
f
Ao
d
KA
6.9 f 0 . 2 7.09 rt 0.07 5.2 f 0 . 1 5.5 i 0 . 0 8 6.3 f 0 . 5 6.3 A 0 . l 5.4 f O . l 5 . 4 i.o.1 6.4 f 0 . 3 5.5 r t o . l 5.5 f O . 1 5.9 i.0.l 5.5 f O . 1 5.7 AO.1
2270i30 2 2 0 0 i 10 620ilO 640i 5 2110i.30 1330 ct 10 92Ort10 860 i 5 1410i30 1160i.15 118OzklO 1360i.15 1260 ct 10 2200rf20
0.02 0.005 0.02 0.007 0.02 0.01 0.007 0.005 0.02 0.01 0.01 0.01 0.007 0.01
2520 i.30 3220&40 3290f30 3220i.40
0.008 0.01 0.01 0.09
uA
Butanol Me4NC1 Bu4NCl Me4NBr Et4NBr PrrNBr Bu4NBr EtaNI Pr4NI BL~~NI i-Am3BuNI Hept4NI Bu~N C104
17.61i.0.07 17.49 A 0.01 15.41A0.03 15.55 i.O.01 17.88i0.04 18.70i.0.04 17.01 i 0.02 16.07 i.0.01 19.72i.0.08 18.12i0.05 17.16A0.03 16.99i0.03 15.57 f 0 . 0 2 19.06zk0.05
Pentanol BudNBr Bu~NI i-AmBuNI Hept4NI
1 1 . 3 1 i 0.03 32.00rt0.05 11.62i.0.03 10.76A0.03
6.82 i.O.09 6.5 z k O . 1 6.8 i O . 1 6.6 f 0 . 2
MerN+ and Bu4N+ salts is 0.51 =t 0.06. The conductance of Bu4NIin butanol a t 0,25, and 50" has been determined by Venkatasetty and Brown.la The agreement of their result at 25" with that given here is within the precision of their measurements. The lack of transference numbers prevents the data given in Table I11 from being unambiguously split into limiting ionic conductances. In a previous paper,Z it was shown that the limiting ionic conductances for the large tetraalliylammonium ions in ethanol could be The Journal of Physical Chemistry
Bept4N C1Br-
f
I-
6.25 7.76 8.23 9.32 11.22
Discussion
Table I11 : Conductance Parameters in Butanol and Pentanol a t 25', Calculated from Eq 1 Salt
9.67 10.40 8.80 7.84 7.67
Limiting Ionic Conductances. Shown in Figure 3. is a plot of X O vs. ~ l/rz, the reciprocal of the estimated crystallographic radius of an ion, for ions in the four alcohols, methan01,~ethanolJ2propano1,z and butanol. The A07 product in the alcohols shows considerable variation for the smaller ions. This is the type of behavior to be expected from solvation, since the mobility of the ions should decrease as the size of the solvent molecules increases. However, a decrease in mobility with decreasing dielectric constant, eo, and increasing relaxation time, 7,is also in accord with the predictions of the Boyd-Zwanzig equation14 A07 =
F2/N(6nr
+ B/r3)
(2)
where B is a function of solvent properties only and is given by B = ( 2 e 2 / 3 ) ( ~ / 7 ) [ (-~ ~e)/eO2]. This theory takes into account the retardation due to the relaxation of solvent dipoles around a moving ion and is in essence a correction to Stokes law. Equation 2 is based on continuum theory and is a t present the most complete solution to the problem of ionic mobilities based on this model. I n a recent discussion of this theoryJ16 it was demonstrated that it will not account for (1) the temperature dependence of ionic mobilities in aqueous solution, where structural effects are present, (2) the variation in mobilities in nonaqueous solvents such as methanol, ethanol, and acetonitrile, which appear to be determined by specific ion-solvent interactions, and (3) the change in ion mobility in HzOEtOH or HzO-dioxane mixtures, where solvent struc(13) H.V. Venkatasetty and G. H. Brown, J . Phys. Chem., 6 7 , 954 (1963). (14) R. Zwanzig, J . C'hem. Phys., 38, 1603 (1963). (15) R. L. Kay, G. P. Cunningham, and D. F. Evans in "Flydrogen Bonded Solvent Systems," A. Covington and P. Jones, Ed., Taylor and Francis, Ltd., London, 1968,in press.
161
TRANSPORT PROCESSES IN HYDROGEN-BONDING SOLVENTS 18.8;
15.5/Xa7
+ (15.3 x 10*2/i3) K ~ / ~-) E(m )/E021 ~ ~
0.3
-
-
tOH
-
A01
0.2
-
2 0.1
:'\Stokes
.;--\
2 / I
Zwanrig E q u a t i o n
\ \\
\\\/
'\
1'
/ f
LOW
\
,-.;,
'-. - - - - .-
'
\
'\-
I
I
I
~
% -
I
,-MeOH I BuOH,
suggested by Atkinson and Mori.'s This can be expressed more succinctly as L* = 18SF (15.3 X 1012/i3)R* and a plot of I,* us. R* should be linear. A value of i can be obtained from both the intercept and slope. Shown in Figure 2 is a plot of L* us. R* for cations and anions in the four alcohols, and the points for a given ion are scattered about a straight line. The extent to which this scatter reflects the failure of eq 2, or to what extent it reflects the uncertainty in r and consequently in R*, cannot be determined at this time. This scatter indicates an uncertainty of about 20% in r . However, any line drawn within the scatter of the points will still give values of ;from the slope which differ from those determined from the intercept by a factor of 3 to 10. For example, two lines drawn through the points for the bromides, with the maximum and minimum slope possible, gave +(slope) = 6.55 and ;(intercept) = 2.01, and ;(slope) = 8.15 and ;(intercept) = 2.34, respectively. Therefore even in this
+
eOH
I
-
70-
I
ct-
e
Br-
A
1
I
I 1
I
I-
ture and preferential solvation are important. A L* 60 more favorable examination, in terms of the predictions of this continuum theory, would be the variation of 50 ionic mobilities in the homologous alcohols. Since the 40 functional group of the solvent is common to all, the - _ _ _ ~ system mould be expected to provide optimum condii-Am3BuNt V Me,N+ 0 Pr4Nc A tions to test the theory. Et4Nt 0 Bu4Nt 0 Hept4Nt 0 The variation of Xoq with ionic size for methanol and 100 " " butanol, as calculated from eq 2, is shown in Figure 1. 90 The values of r , the relaxation time of the solvent, and the dielectric constant at infinite frequency were taken 80 from the compilation of Buclcley and Maryott.l6 L* . A/ V 70 1 The static dielectric constant, EO, and viscosity, q, are the values given in this paper and the preceding 60 one^.^,^ The predicted value of X O is ~ too small by 50 almost a factor of 3. Frank has shown that there is no value of 1" which, when substituted into eq 2, will re40 produce the magnitude of the measured Xoq in aquet t MeOH EtOH PrOH B u O d ous solution," and the same argument applies here. = (B/~T)"~, The equation predicts a maximum a t I 3 5 7 9 R' x which correspo@s to a value of 1". = 5.7 A in methanol and i = 6.85 A in butanol. The experimental curves Figure 2. A plot of L* us. R* for ions in the alcohols MeOH, do exhibit a maximum which moves to larger values of i EtOH, PrOH, and BuOH. as the series MeOH, EtOH, PrOH, and BuOH is ascended. However, the experimentally determined (16) F. Buclcley and A. A. Maryott, National Bureau of Standards maxima are at approximately 2.9 for MeOH and 4.2 8 Circular No. 589, U. S. Government Printing Office, Washington, fur BuOH. D. C., 1958. (17) 12. 8. Frank, "Chemical Physics of Ionic Solutions," B. E. ConAn alternate form in which eq 2 can be used when way and It. G. Barradas, Ed., John Wiley and Sons, Inc., New York, comparing results in a number of solvents is in the N. Y., 1966, p 61. linear form (18) G. Atkinson and Y . Mori, J. Phys. Chem., 71, 3523 (1967). 0
e
h
h
-
;,,,
Volume 73, Number 1 January 1969
1G2
D. FENNELL EVANS AND PHILIP GARDAM
3.5
tone (MEK),22except for the fact that the bromides are more associated than the iodides in these solvents. Thus it would appear that salts in the alcohols follow the simple exponential law predicted by electrostatics, as is the case with the ketones, and that only the magnitude of K A needs to be explained.
t1
3.0
2.51
y I
2.0
1
I
log KA
Table V -ROH--
LK
(slope)
cept)
(slope)
3.2 3.3 3.3 3.6 3.6 3.6 2.8 2.8 2.8 2.8 2.8 4.2
3.3 2.4 4.2 4.1 3.6 3.6 5.1 5.1 5.1 6.1 5.1 7.2
&I
