S.BLUMAND H. I. SCHIFF
1220
Vol. 67
TRANSFERENCE KUISIBERS ASD IONIC CONDUCTANCES OF SOME QUATERNARY ARIMONIUR/I CHLORIDE AXD BROMIDE IONS IS NITROMETHANE A T 25' B Y S. BLUMilXD H. I. SCHIFF Depaitment of Chemistry, McGill University, .Montreal, Canada Received November 9, 1968 The transference numbers of Me4N +, EthN +, Pr4N+, Bu4N +, C1-, and Br- ions in nitromethane have been determined over the concentration range 0.0002 to 0.01 N . A combination of existing experimental techniques has been used which makes the moving boundary method applicable to most electrolytes. Limiting ionic conductances, calculated from these results and the equivalent conductances of the preceding paper, show these electrolytes t o be fairly strong, with increasing strength in the order Me4NX < Et4NX < PriNX < Bu4NX. The chlorides are more associated than the corresponding bromide, although bromide appears to be the smaller ion. Comparisons of the Walden product and the ratios of ionic conductances for these ions in a number of solvents are discusoed in terms of solvation effectfi. $queous NaCl and LiCl solutions were used as indicators for the Introduction falling boundary cell and K I 0 3 solutions for the rising boundary Development of new theories of electrolytes must be cell. These cell constants were obtained with an accuracy of accompanied by accurate data on individual ion bebetter than one part in 3000 and were found to be independent of havior in a variety of solvents. Although accurate current, concentration of leading solution, or small deviations of indicator concentration from those required by the Kohlrausch equivalent conductance measurements have been ratip. Ratios of leading solution to indicator solution conductreported for a number of non-aqueous solutions, experiances determined from the recorder traces differed from those calmental difficulties have, with few exceptions, restricted culated from known conductance data for these solutions by measurements of transference numbers to aqueous about 5%. This is an improvement over the 10% deviations 1 can probably be attributed to reported by Lorimer, et ~ 2 . ~which solutions. an improvement in the rectifier circuit. The experimental ratios The experimental difficulties stem mainly from the were found to be the same for all pairs of microelectrodes within need t o extend the measurements to highly dilute soluexperimental error. tions in solvents of low dielectric constant. The normal As mentioned in the preceding paper,4 nitromethane solutions optical methods for following a moving boundary canof halides were found to dissolve silver halides. For this reason the type "A" liquid junction chambers of Elias and Schiff3were not be used because of the vanishingly small differences used in the cathode compartment of each cell. The cathodes conin refractive indices between leading and indicator sisted of 0.5 cm. X 1 cm. X 0.007 em. strips of platinum which solutions. Recently, however, Lorimer, Graham, and were silver-plated and dipped in fused silver halides. A suffiGordon1 have developed a conductometric method for ciently thick silver halide coating was obtained in this way to prevent stripping and ensuing gas evolution during electrolysis. following such boundaries, which has been applied to Tests showed that no contamination of the nitromethane solusolutions of alkali halides in ethanol.2 This method has tions resulted from the use of the probe chambers. The anodes been used in the present work along with the liquidconsisted of bars of cadmium which showed no attack by the junction technique described by Elias and S ~ h i f f . ~ nitromethane solutions. This modification makes the conductometric method Purification of the solvents and the quaternary ammonium halides has been described in the preceding paper,4 as have applicable to any electrolyte. been the methods for preparing and handling the solutions. The present paper reports measurements of the transThe quaternary ammonium picrates were prepared and purified ference numbers of tetramethyl-, tetraethyl-, tetraby the method of Hirsch and Fuoss7 and, before use, were dried propyl-, and tetrabutylammoniuni chlorides and brounder vacuum for 24 hours a t 56'. Partial molal volumes of the picrate solutions were required for the volume corrections of the niides in nitromethane at 25'. The data have also been transference data. The densities of these solutions could be repcombined with the conductance data of the preceding resented over the concentration range of interest by the equation paper4to obtain limiting ionic conductances. d = 1.13124 + bm, where b is 0.0133 for Pr4T\'Pic and 0.0103
Experimental The transference cells were similar to those described by Kay and Gordon.6 A falling boundary cell equipped with their type VI11 shearing stopcock was used to obtain cation transference numbers of Me4N- and EtrN-halide solutions, with the corresponding Bu4N-halide solutions serving as indicators. A rising boundary cell equipped with a type 111shearing Atopcock was used to obtain anion transference numbers of PrdNand Bu4N-halide solutions, with the corresponding quaternary ammonium picrates serving as indicators. Measurements were restricted to these ions, since no other indicators could be found which had sufficiently high solubilities and large enough differences in ionic mobilities. The volumes between microelectrodes were calibrated from the known transference numbers of aqueous KCl solutions.6 (1) J. W.Lorimer, J. R. Graham, and A. R. Gordon, J . Am. Chem. Soc., 79, 2347 (1957). (2) J. R. Graham and A . R. Gordon, ibid., 79, 2350 (1957). (3) L. Elias and H. I . Schiff, J . Phya. Chem., 60, 595 (1956). (4) A . K. R. Unni, L. Elias, and H. I. Schiff, ibid., 67, 1216 (1963). (5) R. L. Kay and A. R. Gordon, J . Chem. Phys., 21, 131 (1953). (6) R. W. Allgood, D. J. Le Roy, and A. R. Gordon, ibid., 8 , 418 (1940).
for Bu4NPic. For the falling boundary cell, the cathode side was closed and the volume correction was
AV
=
TA+~A f XV A ~
VAgX
where T.i+is the transference number of BudN* and X is C1 or Br, and VAX is the partial molal volume of the solute. For the rising boundary cell, the anode side was closed and the volume correction was
where Tpia- is the transference number of picrate ion and A is either Pr4N- or Bu4N. The cell was immersed in a constant temperature bath regulated at 25.000 & 0.005'. To minimize current leakage, the tubes surrounding the electrodes were filled with silica gel and the laboratory was air-conditioned. The a x . detection circuit was essentially identical with that described by Graham and Gordon2 except for the rectifier section preceding the strip-chart recorder. An R.C.A. Type 2N-109 (7) E. Hiraoh and R. M. Fuoss, J . Am. Chem. Soc., 82, 1018 (1960).
Julie, 1963
T R A N S F E R E N C E K U M B E R S OF
(QUATERNARY AMMONIUM CHLORIDE
CEL.L
... ....
* .
..L
BROMIDE IONS
1221
‘I
t
‘I-+-
AND
F.
‘Q:
5651’ 6 /’--C, --O.OY
PW&R
su
Y 41
::
0.2-14M II I I ,431I 0 20 60 80 100 40 1 0 4 ~ -
--
-1 -1
I
Fig. 1.-Constant
Fig. 3.-Longsworth
I
current circuit.
I
function us. concentration: 0, EtdNC1; 0 , Et4NBr. I
I
I
I
I
I
‘r
‘ I
0 ,611 .
4
6
$
k20
I
40
60 1 0 -+~ ~
80
100
0
Fig. 4.-Longsworth
Fig. 2.--Longsworth function us. concentration: 0, MeaNCl; e, MeaNBr. transistor was chosen because it provided a high degenerative bias on the incoming signal and produced very linear reclification. Low currents were passed through the cell to prevent resistance heating from causing boundary instability; for dilute solutions in particular the energy generated in the boundary tube should be less than 0.1 watt.* The “feed-back” circuit shown in Fig. 1 provided currents from 5 to 500 microamperes which remained constant within 0.3Yo for a change in cell resistance of a factor of 2 and over a period of several hours. The current was determined from the voltage drop, measured potentiometrically, across a standard resistance in series with the cell. Current readings were taken every 200 seconds and averaged over the time required for the boundary t o pass 2 sets of microelectrodes. The maximum possible error in the current measurements was 0.01%. Time was measured with the combination of a pendulum clock (frequently checked against station WWV), an electric counter, and a chronograph pen on the recorder.
Results and Discussion The transference number of each ioii was measured for more than 20 different concentrations over the range 2 X to 1 X N . At each concentration a t least two experiments were performed with different boundary currents. For experiments with the falling boundary cell, volume corrections were negative and amounted to 7 or 8 units in the last decimal place for the most concentrated solutioiis and became insignificant hr. The volume corrections for the below 1 X rising boundary cell were positive and about one-half as large as those for the falling boundary cell. Solvent corrections were necessary only for concentratioiis be(81 A. R. Gordon, private communication.
20
I
40
-,60
1 0 ~ ~
80
L
IO
function us. concentration: 0, PrdNCl; 0 , Pr4NBr. I
I
I
,645-
0
20
40
104~+
60
80
10
Fig. 5.--Longsworth function us. concentration: 0, Bu4KC1; e, BudNBr.
low 1 X lO-3N and iiever amounted to more than 2 or 3 units in the last decimal place. Figures 2-5 shorn that plots of the L o n g s ~ o r t h ~ function To’ us. C are linear in this coiicentration range and therefore permit accurate extrapolations to limiting values of the transference numbers. Such plots essentially represent deviations from theoretical behavior aiid can be used to show that the precision of the data is 0.04% at coiicentrations above 1 X N and about 0.06% at lower concentrations. Transference numbers a t rounded concentrations obtained from large scale plots of this type are shown in Table I. (9) L. G. Longsworth, .I. An. Chem. Soc., 64, 2741 (1932).
S . BLUMASD H. I. SCHIFF
1222
TABLE I TRANSFERENCE NUMBERS AT ROUND CONCENTRATIONS Mec 104.
NC1
Me4NBr
Et4NC1
EtaNBr
Pr4NC1
PraNBr
BunNC1
BuaNBr
C Tt Tt Tt Tt TTTT100 0.4645 0.4631 0.4252 0.4240 0.6237 0.6298 0.6651 0.6661 50 .4652 ,4639 ,4271 .4261 ,6352 .6261 .6601 ,6614 20 .4659 ,4648 ,4287 ,4280 ,6218 ,6227 ,6555 .6569 10 .4663 ,4653 ,4290 ,4297 ,6201 .6209 .6531 .6547 6 .4667 .4656 .4304 .4297 ,6188 .6197 .6515 ,6529 2 .4669 .4658 ,4310 ,4303 .6177 ,6187 .I3499 .6514 0 .4674 .4663 ,4320 .4314 .6157 .6165 .6474 .6487
The slopes of the T us. V% plots are negative and approach their limiting values from above when the transference number is less than 0.5 and vice-versa when the transference number is greater than 0.5. This behavior is similar to that reported by Longsworthlo for strong aqueous solutions. The Longsworth function can be modified for incompletely dissociated electrolytes to the form
Vol. 67
ionic conductances in nitrobenzene mere derived from the values quoted by Witschonke and Kraus12 for Bu~?;+. These authors found the value of Ao for tetrabutylammonium triphenylhorofluoride to be 23.8 ohm-l cm.2 and assumed that, since the two ions mere very large, they had identical ionic conductances. The ionic conductances in the other solvents were calculated from reported limiting equivalent conductances and transference numbers of the anions. It should be pointed out that some of the equivalent, conductancc values are from earlier literature and somewhat unreliable. TABLEI11 IONCONDUCTANCE-VISCOSITY PRODUCES IN VARIOUS SOLVEXTS Ion 1000 q D Xu
RIeaN +
Xoa 1OOXo?/D Xo
EtaN
Xoq
Pr4N
lOOXoq/D Xo holt
where hef = A' - (ARO
+B ) C C
lOOXoq/D Xo
The degree of dissociation a was calculated by the Fuoss-Shedlovsky and suggested the order of clectrolytic strength to be Bud?;+ > Pr4N+ > Et4X+ > Me4N+ and Br- > C1-. Straight lines could be drawn through plots of this modified Longsworth function us. aC which were identical with the straight lines shown in Fig. 2-5. However, the experimental points fell closer to the lines when incomplete dissociation was assumed. Severtheless, the high degree of dissociation calculated by the Fuoss-Sliedlovsky method and the linearity of the Longsworth function do not support considering these to be weak electrolytes. Limiting Ionic Conductances.-Table I1 presents limiting values of transference numbers and ionic conductances. The numbers in brackets were calculated from the havalues of the preceding paper and the experimental Tovalues, assuming TO+ TO- = 1. Agreement of the limiting ionic conductances for a given ion, calculated from different salts, is within experimental error. The assumption that the sum of the limiting transference numbers is unity is justified by the agreement of the calculated Xo values with those determined experimentally for the same ion.
+
Salt
MedNC1 MeaXBr EtdNC1 EtrNBr Pr4NC1 Pr4NBr BurPu'Cl BueXBr
TABLE I1 ANCES LIMITING IONIC CONDUCT xt 0 Tt 0 T- 0 A0 (0.5326) 54.97 117.62 0.4674 54.94 ( .5337) 117.83 .4663 47.68 ( .5680) 110.37 .4320 (.5686) 47.71 110.60 .4314 .6157 (39.15) 101.88 ( .3843) (39.16) .6165 102.10 ( ,3835) .6474 (34.14) 96.83 (.3526) (.3513) ,6487 (34.09) 97.04
A-
0
(62.65) (62.89) (62.69) (62.89) 62.73 62.94 62.69 62.95
Limiting ionic conductances provide a more satisfactory test of Walden's rule than do equivalent conductances. Values of the Walden product, Xov, are compared in Table 111 for five solvents. The (10) L. G. Longsworth. J . A m , Chem. Sac., 67, 1185 (1935). (11) R . M. Fuoss and T. Shedlovsky, ibid., 71, 149G (1949).
BuaN +
Xoq
lOOXos/D ho
CI -
Xoq
lOOXov/D Xo
Br-
Xoq
100hov/D
CHsNOz 6.27 36.67 54.96 0.345 0.941 47.70 0.299 0.815 39.15 0.245 0.662 34.12 0.214 0.584 62.70 0.393 1.072 62.94 0.395 1.077
COHINOS 18.3 34.8 17.3 0.317 0.911 16.4 0.300 0.862 13.5 0.247 0.709 11.9 0.218 0.626
22.2 0,406 1.167 21.6 0.395 1.135
CHaOH
CgHsOH
4.45 32.6 69.1 0.376 1.153 54.0 0.294 0.902 43.9 0.252 0.773 39.218 0.214 0.656 52.3818 0.285 0,905
10.8 24.3 30.814 0.333 1.370 27.3'6 0.295 1.214
56.5518
23.5118
0.308 0.978
0.254
H20 8.95 78.5 44.9217 0.402 0.512
...
32.6617 0.292 0.372 23.4517 0.210 0.267
.,
19.1317
.. . ... .
,.,
... 21.8518 0.236 0.971
1.045
0.171 0.218 76.3618 0.683 0.870 78.2419 0.700 0.892
Reasonable agreement of the Waldeii product is obtained for the cations but not for the anions. This is not surprising since one of the tacit assumptions in Walden's use of Stoke's law is that the ions retain their radii as the solvent is changed, and one mould expect a greater degree of solvation for the smaller anions than for the larger cations. The Walden product is, however, approximately constant for the anions in the 2 nitro-solvents which have almost the same dielectric constants. The product is not constant for the 2 alcohols which have different dielect'ric constants nor for methanol and nitromethane which have similar dielectric constants but are cheniically different. Account is taken of the dielectric constant in the , by Van Rysselberghe and function X o ~ / Dsuggested FristromZ0and shown for these solvents in Table 111. This function improves the agreement between solvents for the anions but not for the cations. The close agreement for all the ions in the 2 nitrosolvents may, perhaps, be taken as evidence in support of the assumption made by Witschonke and Kraus. The relative solvation effects can be seen more clearly when limiting ionic conductance ratios are considered. Viscosity effects will tend to cancel and, if Stoke's (12) C. R. Witsohonke and C. A. Kraus, ibid., 69, 2472 (1947). (13) J. P. Butler, H. I. Schiff, and A . R. Gordon, J . Chem. Phys., 19, 752 (1951). (14) T. H. Mead, 0. H. Hughes, and H. Hartley. J. Chem. Sac., 1207 (1933). ( 1 5 ) H. Ulich and E. J. Birr, Z. angew. Chern., 41, 443 (1928). (16) R. J. Graham, G. S. Kell, and A. R . Gordon, J . Am. Chem. Soc., 79 2352 (1957). (17) H. fir. Daggett, E. J. Bair, and C. A. Kraus, ibid., 73, 789 (1951). (18) H. E. Gunning and A. R. Gordon, J. Chem. P h y s . , 10, 126 (1942). (19) H. E. Gunning and A. R. Gordon, ibid., 11, 18 (1943). (20) P. Van Rysselberghe and R. M. Fristrom, J. Am. Chern. Soc., 67, 680 (1945).
June, 1963
CONDUCTAKCE OF QUATERNARY AMMOXIUM
law is assumed to apply to ions, the change in the ratio from one solvent to another should give information about the effectiveradii of the ions under consideration.2 Table IV shows a number of these ratios. For the hydroxyl solvents the cation/anion ratios increase with decreasing dielectric constant and are much higher in the alcohols than in the nitro-solvents, This suggests a higher degree of solvation of anions in the alcohols and/or of cations in the nitro-solvents in agreement with the expected behavior of these solvents. Appreciable anion solvation in the alcohols has been suggested.z The ratios in nitromethane are somewhat larger than might have been expected from thje aprotoic nature of thiss olvent. Althoughr ather unreliable, calculations of solvation numbersz1 indicate a small degree of solvation for the MeJ+ ion in nitromethane and little, if any, for the larger ions. The anion/anion ratios show chloride to be the slower ion in all the solvents but nitrobenzene. Chloride would therefore appear to be the larger ion as a result of solvation and would be expected to be less associated. This is, however, contrary to the evidence obtained (21) R. A. Robinson and R. H. Stokes, "Electrolytic Solutions," 2nd Edition, Butterworth, 1959.
1223
BROMIDES
CHLORIDES AKD
TABLEIV LIMITING IONIC CONDUCTANCE RATIOSIN VARIOUSSOLVENTS h,O
- Ratio
h0&fs4N+/hoCI~0Me4N+/~0BrhoEtaN+/hoClhoEt4N+/hoBrxoPr4N+/bIhoPr4N+/hoBr-
hoBu&"XoCIXOB~~N+/~OB~.
h°Cl-/hoBrho&fs&/hoEtaNt hoM,4N+/hopr4N+ ho&fa4Nt/hoB,4N+
CHaNOz CeHsNOi
CHsOH
CpHsOH
HnO
0.877 .873 .I761 .I758 ,624 .B22 ,544 .542 .996 1.150 1 .404 1.611
1.319 1.222 1.031 0.955
1 ,409
0.588 ,574 ,427 ,417 ,307 ,300 ,251 ,245 .978 1,365 1.916 2.347
0.779 .801 .739 .759
1.311 1.249 1.161
...
...
*.. ...
.536 .551 1.028 1.055
0.765 0.709 0.926 1.280
0.930 1.128
1.454
1.723
., ,
,,,
.
...
... ,,,
...
,..
from the dependence on concentration of the transference numbers and equivalent conductances. This point has been discussed in the preceding papera4 Cation/cation ratios decrease with increasing molecular weight and indicate the same order of ionic size. This can be taken as evidence against a large degree of solvation of the Me4N+ ion. Acknowledgment.-The authors are indebted to the National Research Council of Canada for a Grant-inAid and for the award of several fellowships to S. B.
THE ELECTROPHORETIC AND RELAXATION CONTRIBUTION TO THE CONDUCTANCE OF SEVERAL QUATERNARY A3IR.TO.XIUM CHLORIDES AND BROMIDES I N NITROMETHANE EIY ROBERTL. KAY, Metcalf Research Laboratory, Brown University, Providence 12,R. I .
S. C. BLUM,AND H. I. SCHIFF Department of Chemistry, McCill University, Montreal, Quebec Received November 9, 1962 The conductance of tetramethyl-, tetraethyl-, tetrapropyl-, and tetrabutylamnionium chlorides and bromides in nitromethane is analyzed by the Fuoss-Onsager conductance theory. Only the methyl salts are associated to any extent. The d values range from 3.3 to 4.1 and are considerably lower than expected for the rather large ions involved. The values of the limiting ionic conductances obtained from A0 and the limiting transference numbers are in fair agreement except for the tetramethyl salts. The electrophoretic contribution to the conductance has been calculated from the concentration dependence of the transference numbers and shown to agree with that predicted by the Fuoss-Onsager theory in most cases. Using the measured electrophoretic effect and the measured conductances, the relaxatiop contribution was determined and compared t o that obtained from the Fuoss-Onsager equation using the same d as was used to fit the conductance data alone. The slightly higher values of d required are accounted for by a C8/2term eliminated from the electrophoretic effect in the conductance equation. The nieasured electrophoretic effect is the game for all the salts with possibly two exceptions whereas the extended terms in the relaxation effect are shown to be negative and to increase in magnitude with decreasing size of the cation. It would appear that the rather low d values for these salts cannot be explained by a solution viscosity correction.
Introduction I n the two preceding papers, conductances* and transference numbers2 for Me4S-, Et411\-, Pr4S-, and Bu4X- chlorides and bromides in nitromethane a t 25' have been reported. These yield the first precise ion conductances in dilute solution for ions of considerable size variation and therefore permit a more thorough test of existiiig electrolyte theories than has been possible in the past. It is the purpose of this paper to report the results of an analysis of' the data by the (1) A. K. R. Unni, L. Elias, and H. I. Schiff, J . Phya. Chem., 67, 1216
(1863).
(2) S. Blum and H. I. Schiff, ibid., 67, 1220 (1963).
Fuoss-Onsager t l - ~ e o r y ~and . ~ the Kay-Dye experimental method of cvaluating the electrophoretic and relaxation contribution to conductance.5 A considerable number of investigations have been made as to the validity of the Fuoss-Onsager coiiductance equation.6 It has been found to reproduce the measured conductances of the alkali halides in aqueous and methanol solutions but an assumption of association is required for solvents of lower dielectric constant.' (3) L. Onsager and R. M. Fuoss, ibid., 36, 2689 (1932). (4) R. 111. Fuoss and L. Onsager, zbzd., 61, 668 (1957); 62, 1339 (1958). ( 5 ) R. L. Kay and J. L. Dye, Proe. Natl. Acad. Sei., 49, 5 (1963). (6) E. C. Evers and R. L. Kay, Ann. Rev. Phys. Chem., 11, 21 (1960). (7) R. L. Kay, J . Am. ('hem. Soc., 82, 2099 (1960).
