'l'1l.E J O U R N A L
OE'
PHYSICAL CHEMISTRY Regislered in U . 6'. Patent Ofice @ Copyright, 1968, bg the American Chenzical ij'ocielg
VOLUME 73, NUMBER 3 MARCH 1969
Transference Number Measurements in Acetonitrile as Solvent by Charles H. Springer,' J. F. Coetzee: Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania
15R13
and R. L. Kay Mellon Institute, Carnegie-Mellon University, Pittsburgh, Pennsylvania
15813
(Received September $ 3 , 1 9 6 8 )
The transference number of tetramethylammonium ion in tetramethylammonium perchlorate has been determined in anhydrous acetonitrile as solvent using a rising boundary sheared cell with tetraphenylarsonium perchlorate as indicator and with electrical monitoring of the boundary. A scale of single-ion conductivities based on the limiting value of this transference number (0.4768 =t 0.0002) differs by 0.35 conductivity unit from a scale based on the assumption that tetraisoamylamrnonium and tetraisoamylboride ions have equal mobilities.
Introduction Reliable values of single-ion conductivities are useful for a variety of purposes, among them the investigation of ion-solvent interactions. The split of electrolyte conductivities into the ionic components ideally requires transference numbers, the accurate measurement of which presents serious experimental problems in many nonaqueous solvents. Transference numbers of high accuracy have been determined in few anhydrous solvents, with r~itrornethane~ as the only example of the important class of dipolar aprotic solvents. For several other solvents, including acetonitrile,4 provisional scales of single-ion conductivities have been based on the assumption that the constituent ions of certain reference electrolytes, such as tetraisoamylammonium tetraisoamylboride, have equal mobilities. However, the unambiguous evaluation of the validity of such scales still requires the direct measurement of transference numbers. We now report the results of such measurements in acetonitrile, which indicate that the error in the tentative scale based on the conductivity of tetraisoamylammonium tetraisoamylboride amounts to 0.35 conductivity unit.
Experimental Section Transference number measurements were carried out using a moving boundary method with electrical
monitoring of the boundary, as developed by Kay, Vidulich, and Fratiel10.~ A complete description of the apparatus can be found in ref 5 and can be compared to a similar method described by Lorimer, Graham, and GordonSB A rising boundary sheared cell with a cadmium anode 2nd a silver-silver chloride cathode was employed to measure the transference number of the tetramethylammonium ion constituent in tetramethylammonium perchlorate. A stopcock TKLS used to form the boundary. Tetraphenylarsonium perchlorate served as indicator. Measurements had to be restricted to tetran~ethylammoniumion since no other system could be found among 17 tried1 that gave reproducible results. The cell was calibrated at 25' using aqueous solutions of potassium chloride for which the transference numbers are k110wn.~ After each run the cell was cleaned (1) From the P1i.D. thesis of this author, University of Pittsburgh, 1968. (2) Please address all correspondence t o this author. (3) R. L. Kay, R. C . Blum, and H. I. Schiff, J . Phys. Chem., 67, 1223 (1963). (4) J. F. Coetzee and G. P. Cunningham, J. A m T . Chem. Soc., 87, 2529 (1965). (5) R. L. Kay, G. A . Vidulich, and A. Fratiello, J . Chem. Inslr., in press. (6) J . W. Lorimer. J. R. Graham, and 4.R . Gordon, J . Amer. Chem. Soc., 79, 2347 (1957). (7) L. G. Longsworth, M d . , 54, 2741 (1932).
47 1
c. H. SPRINGER,
472
with acid dichromate solution and rinsed thoroughly with distilled and then conductivity water. Finally, the cell was filled with conductivity water and allowed to stand t o leach out any dichromate that might still be present. Before a run was made, the cell was dried by passing dry filtered air through it. Before runs were made with acetonitrile, the cell was filled with dry solvent and allowed t o stand overnight. All measurements were carried out in a constanttemperature oil bath maintained a t 25 f 0.002' by means of a mercury-in-glass thermoregulator. The absolute temperature was determined with a calibrated resistance thermometer and a Mueller bridge. All solutions were prepared by weight, vacuum corrected, and concentrations were converted to a volume basis by means of solution densities determined from the following relationship: d = do A f i where do is the density of the pure solvent and f i is the concentration expressed in moles of solute per kilogram of solution. The parameter A was determined from the results of a number of density measurements. Conductivity water was prepared by passing distilled water first through a commercial ion exchanger and then through a 1.2-m column of mixed-bed ion exchange resin. Conductivity water was collected from the column only after a thorough rinsing of the resin. In ohm-' this way water with a conductivity of 1-2 X em-1 was obtained. Technical grade (Matheson) acetonitrile was purified by the procedure described befores with the addition of a final fractional distillation under nitrogen from calcium hydride through a 1.22-m vacuum-jacketed Stedman column. The solvent was stored under nitrogen and had the following properties: density, 0.77663 g m1-I; viscosity, 3.409 mp ;9 dielectric constant, 35,95;g conductivity, 1-2 X lo-* ohm-' em-'; water content, less than 1 mM as determined by Karl Fischer titration. Tetraniethylanimoniuni perchlorate was precipitated by adding slowly an aqueous solution of tetramethylammonium chloride to an aqueous solution of sodium perchlorate. The salt was recrystallized four times from hot water and dried for 24 hr in vacuo a t 70'. Tetraphenylarsonium perchlorate was precipitated by mixing equivalent amounts of aqueous solutions of tetraphenylarsonium chloride and sodium perchlorate and was recrystallized from hot acetonitrile. Because of the low yield of this process, tetraphenylarsonium chloride first was recrystallized by adding anhydrous ether to its solution in acetonitrile. In order to remove hydrogen chloride, which mas an impurity in some samples, and which forms a stable adduct with tetraphenylarsonium chloride, basic alumina (Brockman Activity 1,80-200 mesh) was added to a solution of the salt in acetonitrile. After shaking overnight, the mixture was filtered and the salt regained by adding anhydrous ether.
+
The Journal of Physical Chemiatry
J. F. COETZEE,AND R. L. KAY
Results The transference number of the tetramethylammonium ion constituent of tetramethylammonium perchlorate was measured over the concentration range to 1.23 X M . The transference num6.25 X bers were independent of current and of following solution (indicator) concentration, provided the latter was above the limiting Kohlrausch value given by the relationship: TL/CL = TF/CF, where T is the transference number, C is the concentration in moles per liter, and the subscripts refer to the leading and following solution, respectively. No volume correction was applied because the details of the electrode reaction are not known sufficiently well. This omission probably is unimportant since the volume correction should be negligible at all but the highest concentrations. As has been the case in other transference number studies, both in aqueous7 and in nonaqueous solutions,'O~ll internal consistency of the data required application of a solvent correction larger than the conductivity of the pure solvent, possibly because of contamination during handling or electrolysis of traces of water. The proper correction was taken to be that (single) value which produced optimum constancy of the limiting value of the transference number calculated as described below from the individual transference numbers measured over the entire concentration range. A solvent correction of 1.6 X 10-70hm-1 em-l was applied, which amounted t o a maximum correction of 0.15%. Table I contains the corrected data averaged for each concentration; at least three runs were made a t each concentration, The third column contains the average deviation. Since the transference number is not a linear function of concentration, extrapolation t o infinite dilution does not always give an unambiguous result. Following a suggestion of Longsworth,' a limiting value of the transference number was calculated from the measured value a t each concentration using the equation12
To+ I= T+
+ (0.5 - Tf) A0
where A, is the electrophoretic contribution t o the conductivity. In the limiting Onsager equation, the electrophoretic term is given by
whereas consideration of the finite size of the ions leads ( 8 ) J. F. Coeteee, G. P. Cunningham, D. K. RIcGuire, and G. R. Padmanabhan, Anal. Cham., 34, 1139 (1902). (9) G. P. Cunningham, G . A . Vidulich, and R . L. Kay, J. Chem. Eng. Data, 12, 338 (1967). (10) A. Fratiello, Ph.D. Thesis, Brown University. 10G2. (11) G. A. Vidulich. Ph.D. Thesis, Brown University, 1988. (12) R . L. Kay and J. L . Dye, Pror. N o t . A c a d . Sci. U . S., 49, 5 (1963).
TRANSFERENCE NUMBERMEA~UREMENTS IN ACETONITRILEAB SOLVENT
473
Table 11: Conductivity of MerNClOA and Ph,AsC10, in Acetonitrile ------>‘fE4~C10~--I.
I
t
I
KO
lob c
3
A
1-70 X 10-8 A
0.071
8.7445 17.0497 25.2430 33.6414 43.6337 52 0947 61.3173 I
Figure 1. A plot of To+ as given by eq 1 as a function of concentration for NIe4KC104in acetonitrile: 0 electrophoretic effect from limiting law, eq 2; 0 electrophoretic effect from extended Fuoss-Onsager eq 3 with (e = 8.
8.0006 16 7803 25 8105 33.3053 41.5158 49 2200 56.2015 I
I
+
A, = @C1’2/(1 ~ d )
(3)
I
The values of A,, 6, K, and d used were 198.2, 233.5, 0.4858Cl/2, and 8, respectively, Tlralues of To+ were calculated using both expressions for the electrophoretic effect, and were plotted as a function of concentration as shown in Figure 1. Both expressions lead to the same limiting value of 0.4768. Addition of small amounts of water (less than 0.01 41) had no measurable effect on the transference number. We estimate that the above value is accurate to 1 part in 2000. In order to construct a scale of single ion mobilities, conductance measurements were made with tetramethylammonium and tetraphenylarsonium perchlorates. The measured equivalent conductivities in ohme1 cm-2 mol-I at various molar concentrations are given in Table I1 along with the conductivity KO of the pure solvent and the value of A used to calculate concentration. The data were analyzed in terms of the Fuoss-Onsager theory,l* according to which the following expression applies to nonassociated electrolytes A =
A0
- ASC’~~ + EC log C + (J - F&)C
(4)
A
104c
185.47 180,22 176.31 173.00 169.68 167.23 164.87
= 1.63 X lo-’-
---KO
to the expression
------PhrAsClOr------7
104c
KO
=
5 4094 10 9002 16 5933 22.3367 28.0988 34 0167 40 1667
I
=
0.181
151.32 148.16 145.82 143.95 142.33 140.89 139 56
I
I
I
I
I
---KO
186.07 18OS40 176.13 173.20 170.44 168 16 166.23
1.45 X 10-8A
I
= 1.47 x 10-8-
5.2285 10,4746 15.9201 21.3818 26.9427 32,7438 38.5493
151.51 148 45 146.15 144.31 142.72 141 26 139.98 I
I
In eq 5 , K A is the association constant and all other symbols have their usual meaning.l3 The least-squares computer programs used for the analyses have been described elsewhere.14-Ie Although the equations include the viscosity correction FAo none was applied because it is not clear what value to use for F. In any case, the viscosity correction affects neither A. nor K A and only results in small changes in J and the ion size parameter d which is contained in J . The parameters obtained from an analysis of the conductance data using both eq 4 2nd 5 are given in Table 111. The standard deviations for each parameter have been included along with the standard deviation UA for the individual conductivity values. Only the
Table 111: Conductance Parametera for Me4KC104 and PhaAsClO4 in Acetonitrile
whereas for associated electrolytes it becomes A =
A0
- S(Cy)”*
+ ECy log Cy
Salt
+ ( J - FAo)Cy - KACYA~’( 5 )
AP
Q
K A
VA
RiIeJVClO+
197.58 i0.12 198.16 1 0 . 0 0 7 197.64 f 0.11 198.1410.02
2.11 i0.04 3.13 i0.03 7.0 10 . 2 2.11 f 0,04 3.1 1 0 . 1 6 . 5 & 0 . 6
0.10 0.01 0.09 0.05
Ph4AsC104
169.52 f 0.06 159.58 & 0 . 0 5
4.51 i0.05 4.55 & 0.05
0.05 0.04
Table I: Summary of Corrected Transference Data Averaged for Each Concentration 104c
T + (cor)
Av
dev
6.2833 12.488 24.950 49.268 79.845 124.80
0.4762 0.4759 0.4756 0.4753 0.4749 0.4738
0.0003 0.0003 0 * 0001 0.0002 010002 0.0001
(13) R . RI. Fuoss and F. Accasrina, “Electrolytir Conductance,” Interscience Publishers, Inc., XRWYork, K.Y.,1959. (14) R. L.Kay, J . Amer. Chem. Soc., 8 2 , 2099 (1960). (15) J. L. Rawes and R. L. Kay, J . Phys. Chem., 69, 2420 (1965). ( 1 6 ) G. P. Cunningham, Ph.D. Thesis, University of Pittsburgh, 1964.
Volume 75, Number 9 March 1960
C, M, +SPRINGER, J, F, COETZEE,AND R, L, KAY
474
Table IV: Limiting Equivalent Conductivities of Selected Salts in Acetonitrile at 25' Salt Me4NBr Et4NBr Pr4NBr Bu4NBr (i-Am) aBuNBr (&Am)4NBr PhdAsBr Me4NI PrrNI (EtOH) 4NI BuNI Ph&I MeaR'ClOc CSClOl RbClOa a
Ao
Ref
195.2 185.5 171.0 162 * 1 158.5 157.4 156.6 196.7 172.9 166.0 164.0 158.1 198.2 191.0 189.5
17 18 17 17 18 18 18 17 17 19 17 18 a 20 20
Salt
LiClOd Kc104 NaC104 BurNClOi (i-Am) aNC104 PhaAsCIOc CsBPhr RbBPhr KBPh4 NaBPhc (Et0H)aNBPha BurNBPha (i-Am) (NBPh, MeaNPi BurNPi (i-Amj)NB(i-Am)4
Ao
Ref
173.0 187.5 180.4 165.1 160.6 159 5 145.4 143.8 141.8 135.4 122.3 119.7 115.0 171.8 139,4 114.5
20,21 20 20 4 4 a
I
20 20 20 20 19 4 4
17 17 4
This investigation.
parameters obtained from eq 4 are given for tetraphenylelectron unit) arsonium perchlorate, since eq 5 gave small negative H association constants indicating that no significant \--24 -169 association occurs. H-C-CkN From our data for tetramethylammonium per/// +87 chlorate (Ao = 198.2 and To+= 0,4768) it follows that K Xa(Me4N+)= 94.5and X0(C1O4-) = 103.7. +82 A selected list of Aa values for a variety of s a l t ~ * J ~ - ~ ~ is given in Table IV, All data were analyzed in ternis of eq 4 and 5 , From these numbers the list of best Table V: Limiting Equivalent Conductivities of Single Ions values of single-ion conductivities given in Table V was in Acetonitrile at 25' in Order of Decreasing constructed, based on the above values for tetraniethylEstimated Reliability nmnioniuin m d perchlorate ions. The uncertainty in a given Xo value generally increases with increasing nuinCation XO+ Anion X0ber of A. values required for its derivation. In Table T7 94.6 Clot103.7 Rlealu'" entries are in order of decreasing estimated reliability. ~~
Discussion Applicabilitu of the Refwenee Electrolyte Tetruisoam& am?noniu?nTel~aisoamulboride. It is particularly interesting to compare the conductivities of the ions of the above reference electrolyte. Coetzee and Cunningham4 have based n scale of single ion conductivities on the nssuinption that (i-Ani) 4N+and (i-Ani) qB- have equal mobilities, because these ions have virtually the same size, and furthermore, solvation effects should be small since the ions are large and symmetrical and not very polarizable, and the single charge is reasonably well shielded. However, the results of the present investigation indicate that the mobility of the cation is 1.2% smaller than that of the anion. We have commented beforez2on differences in the interaction of acetonitrile with cations and anions. Recently, Pople and Gordon23 have carried out an approximate molecular orbital calculation of the charge distribution in the acetonitrile molecule, with the following results (expressed in loF3 The Journal of Physical Chemistry
BUN+ ((-Am) 4N+ PhrAsi'
cs+
Rb+ K+ Na+ (EtOR)aN+ Et4Nt Pr4NS Lit (&Am) aBuN+
(17) D . F. Evans, C. 6 9 , 3878 (1965).
61.4 56.9
Br-
65.8 87.3
Ph4B((-Am) 23Pi-
85.6
I-
100m7 102.4 58.3 57.6 77.7
83.6 76.9 64.0 84.8 70,3 69.3 67.8
Zawoyski, and R. L. Kay, J. P h y s . Chem.,
(18) R . L. Kay, unpublished data. (19) G. P. Cunningham, D. F. Evans, and R . L . Kay, J. Phys. Chem., 7 0 , 3998 (1966). (20) R . L. Kay, B. J. Hales, and G . P. Cunningham, I b i d . , 71, 3925 (1967). (21) F. Accascina, Rec. S c i . Rend., 7, 656 (1966). (22) J. B'. Coetzee and J. J. Campion, J. Amer. Chem. SOC.,89, 2517 (1967). (23) J. A .
Pople and hI. Gordon, i b i d . ,
8 9 , 4253 (1967).
ILE TRANSFERENCE NUMBER MEASUREMENTS IN ACETONITR
Although this charge distribution accounts only approximately for the measured dipole moment of acetonitrile, it nevertheless is clear that since considerable delocalization of positive charge occurs, the ion-dipole interaction of an anion with acetonitrile will be more diffuse and less energetic than that of a cation of equal size, numerical charge, and polarizability. However, rough calculations indicate that even for a cation, when it is as large as (i-Am)4N+,the interaction with acetonitrile probably is too small to compete with solventsolvent i n t e r a ~ t i o n s . ~ Consequently, ~~*~ it probably would not be realistic t o invoke differences in solvation in order to rationalize the difference in mobilities of these ions, However, it is likely that the two ions are unequally “wetted” by acetonitrile. It was pointed out by Lambz6 that the coefficient G7r in the Stokes equation results from the assumption that the medium wets the moving particle. If the particle is not wetted but slips through the medium, the coefficient becomes 47r. One could speculate that the greater mobility of the anion results from a superior ability to slip through acetonitrile. It seems evident that no known reference electrolyte can be expected to provide highly accurate splits of conductivities in a variety of dissimilar solvents. Applicability of the Conductance Theory. The measurement of conductivities and of the corresponding transference numbers as a function of concentration provides a means of evaluating the theory of conductance. The Fuoss-Onsager theory attributes the decrease in mobility with increasing concentration to the electrophoretic and the relaxation effects. In evaluating these effects a hard sphere, solvent continuum model has been used. An essential feature of this model is that for symmetrical electrolytes the relaxation and electrophoretic terms are the same for both ions. Kay and Dye12have shown that as a consequence the transference number should be independent of the relaxation
Figure
2. The electrophoretic effect calculated from eq 6: limiting law; pC1/2/(1 ~d);
0,data;
..
*
-]
pc”2 - C(P4lclc.
---]
+
AS
.?b I
SOLVEKT
475
p
‘, c
- - _ Calc.,
.::I.
F-0, &
E
3
P I
I
Figure 3. The points are a plot of the experimentally determined extended terms in the relaxation effect as given by eq 8. The dotted curve is a plot of eq 9 for 6 = 3.
effect and should be given by t’he expression
where the subscript e refers to the electrophoretic effect and other symbols have their usual meaning. For the special case of a symmetrical electrolyte, since Aeh = $A,, eq 6 can be rearranged into eq 1, An experimental value for the electrophoretic effect, therefore, can be obtained from a combination of conductivity and transference data. In Figure 2 experimental values of the electrophoretic effect for tetramethylammonium perchlorate in acetonitrile are conipared with values predicted by the FuossOnsager theory. It is evident that while the limiting equation (2) overestimates the electrophoretic effect, eq 3 with Zi = 8 %i gives good agreement with the experimental values. Thus, the transference data are consistent with a reasonable value for the ion size parameter. This should be contrasted with the value of 3 A obtained from the conductance data. This unreasonably low value may be caused by the eliniination of the viscosity correction FAo in eq 4 or by the fact that in the final conductance equation the electrophoretic effect has been written in an expanded form of which only two terms have been used. In order t o be consistent in the elimination of ternis of order or greater, eq 3 was expanded and used in the form
(24) Only ion-dipole and dipole-dipole interactions were considered. since these make the largest contribution t o the total interaction energy. For these large ions, quadrupole, induced dipole, dispersion and other interactions, as treated in Buckingham’s theory,25 could be ignored, because of their high order dependence on distance. (25) A. D. Buckingham. Discussions Faraday SOC..24, 151 (1957). (26) H . Lamb, “Hydrodynamics,” Dover Publishing Co.. New York, N. Y., 1945, p 602.
Volume 73, Number 3 March 2969
C, H, SPRINGER, J. F, COETZEE,AND R, L, KAY
476
If the electrolyte is associated, eq 9 becomes AAr = E C y log Cy
Figure 4. A plot of the ratio of cation to anion Conductance given by eq 12 for MerNCIOc in noetonitrile,
ag
The effect of this reduction can be seen in Figure 2. For d = 8, the electrophoretic effect calculated from eq 7 is too small at high concentrations but the lower value of d = 3 gives values of Ae that are higher than the experimentally determined values. Also, any reasonable estimate of F would result in an increase in ii of 0.3 a t most. Consequently, it seems that the low d value must be attributed to the approximations used in the evaluation of the relaxation effect. A procedure has been described12whereby the measured contribution to the conductance from the relaxation effect ran be compared with the theoretically predicted contribution. By introducing the quantity Ah,
E
A - (A,
-
Ae) (1 -
uC’”)
(8)
the terms for the experiinental electrophoretic effect and the limiting relaxation effect are removed from the measured conductances, leaving only the extended terms for the relaxation effect, as well as the association term when applicable. In the Fuoss-Onsager theory, AAr for an unassocinted electrolyte is given by A& =
EC log C
+ J’C
where J‘ = J
The Journal o j Phusical Chemistrv
- ( a @+
g)
(9)
+ J’Cy - KACyhf2
(11)
Experimental and theoretical values of AA, are shown in Figure 3 from which it can be seen that a value of d even lower than 3 is required to fit the experimental relaxation effect if the experimentally determined electrophoretic effect is used. The association constant is too small for its effect to be gauged. Thus, it seems that the failure of the conductance data to give reasonable values of ti may be caused by approximations in the evaluation of the relaxation effect in the conductance equation. An evaluation of the electrophoretic effect can also be obtained directly from single-ion conductivity data since it can be shown that the ratio X-/X+ is given by X-/X+
= X(,
- X,)/(Xo+
- A,+)
(12)
and therefore is independent of the relaxation effect, as is the case for the transference number. The hard sphere, solvent continuum model assumes that Xe- = A,* = 0.5he. If this assumption is correct, a plot of the ratio calculated from eq 12 vs. C1lzshould have the same slope as a similar plot of the experimental ratio. Values of Ae were calculated from eq 3, and experimental values of A& were obtained from transference numbers and corresponding equivalent conductivities for finite concentration. The results are illustrated by Figure 4. It seems that for tetraethylammonium perchlorate in acetonitrile the assumption that the electrophoretic effect is the same for both ions is valid.
Acknowledgments, We gratefully acknowledge financial support by the following agencies: National Aeronautics and Space Administration (for a Predoctoral Traineeship t o C. H. S.), National Science Foundation (Grant No. GP-6478 X to J. F. C.) , and the Office of Saline Water, U. S. Department of the Interior (Contract No. 14-01-0001-1729 to R. L. K.).
