1942
L. M. MUKHERJEE, D. P. BODEN,AND R. LINDAUER
Table 11: Equations Expressing Temperature (OK) Dependence of Log Qw' Based on Three Assumptions for AC, I. logQw =
ACp = B; u(1Og Qw') = 0.81
-4883.26 ~
T
- 14.6585 log T + 38.8840
logQw' =
log Qw' =
- 3694.36 ___.
ACp =
Temp, OC
AH,
A&
kcal, mol-1
oal mol-1
deg -1
AcYp = B
11. ACp = -CT; u(l0g Qw') = 1.56
111.
Table I11 : Tabulation of Thermodynamic Parameters Derived for the Apparent Ionization of Water
T
-B
- 0.00831611 + 1.1011
- CYT; u(bg Qw')
=
0.39
- 5909.13 -4-71.6761 f 0.0072792' - 27.3973 log T I'
however, that these values which are based on the assumption of complete dissociation of all the electrolytes, may be considerably altered when the effects of such association are included.
50 100 1.50 200 250 300
12.93 rt 0 . 0 2 11.47 rt 0 . 0 1 10.02 f 0 . 0 2 8.56 f 0 . 0 4 7.11 f 0.06 5.56 rt 0.07
-19.52 -23.72 -27.38 -30.63 -33.56 -36.22
ACp = - B
50 100 150 200 250 300
12.92 rt 0.01 11.36 i- 0 . 0 1 9.96 f 0.01 8.73 f 0.03 7.67 f 0.07 6 . 7 8 rt 0 . 1 3
-19.53 -24.03 -27.55 -30.30 -32.43 -34.07
f 0.07 i 0 03 rt 0 . 0 5 i 0.09 2Z 0.12 i 0.15
-29.110.36 - 2 9 . 1 1 0.36 -29.1rt0.36 -29.lct0.36 -29.13=0.36 -29.12Z0.36
- CT 2Z 0 . 0 3 i 0.04 i0.03 f 0.06 & 0.14 i 0.25
-32.9 -29.6 -26 3 -22.9 -19.6 -16.3
rt 0 . 5 f0 . 2 ct 0 . 4 f0 . 7 f1 . 1 f1.4
Behavior of Electrolytes in Propylene Carbonate. 11. Further Studies of Conductance and Viscosity Properties. Evaluation of Ion Conductancesla by L. M. Mukherjee,lb Chemistry Department, Illinois State University, Normal, Illinois 61761
David P. Boden, and Richard Lindauer Chemietry Department, Polytechnic Institute of Brooklyn, Brooklyn, New York 11901 (Received January 6 , 1970)
Conductance and viscosity characteristics of solutions of (i-Am)iN(i-Am)iB,(i-Am),NI, KI, and KC104 in propylene carbonate have been investigated at 25'. The value of A0 of (i-Am)iN(i-Am)rBand those of transference number of C104- and Ei+ as determined using concentration cells have been utilized in obtaining the conductance of Li+, K+, Et4"+, n-BupN+,and (i-Am)rN+ as well as C1-, Br-, I-, clod-, and (i-Am)kB-.
Introduction I n a previous article,2 results of conductance and viscosity measurements of certain lithium and quaternary ammoqium salts in propylene carbonate (PC) were reported. Although the conductances of the anions do not appear to differ appreciably, comparison of the limiting conductances of the perchlorates, for instance, suggests that the mobility of Li+ is noticeably lower than that of n-Ru4N+ and Et4N+. Moreover, the viscosity F coefficients of the same series of salts were found to follow the order: LiC104 > n-Bu4Nclod > EtdNC104. Thus, in all probability the relative The Journal of Phyaical Chemistry
sizes of these three cations are: Li+ > n-BurN+ > Et4N+, indicating that the lithium ions in PC are substantially solvated. It is of further interest to note in this connection that unlike the quaternary ammonium salts the agreement between the sums of crystallographic radii and the uoparameters for the lithium salts2 is generally good. (1) (a) Based on a Ph.D. thesis t o be submitted by D. P. Boden to the Graduate School of the Polytechnic Institute of Brooklyn, Brooklyn, Y . ; (b) to whom ail correspondence should be addressed. (2) L. M. Mukherjee and D. P. Boden, J . Phys. Chem., 7 3 , 3965 (1969).
w.
1943
BEHAVIOR OF ELECTROLYTES IN PROPYLENE CARBONATE On this basis, it was surmised that for the lithium salts bare ions rather than their solvated cospheres would be involved in the event of ion-ion contacts. I n the light of the above considerations, subsequent studies in PC of the conductance and viscosity characteristics of electrolytes containing very large cations seem especially interesting. In the present work the quaternary ammonium salts (i-Am)4N(i-Am)4B and (i-Am)4NI have been considered suitable for such studies. An additional advantage in using (i-Am)4N(i-Am)4Bis that in this case the cation and the anion are practically of the same size so that their mobilities can be assumed equal. The results of conductance measurements on (i-Am)qN(i-Am)qBcan be combined with those of (i-Am)rNI for obtaining the conductance of the iodide ion. With a view to relate these systems to the ones studied previouslyz two additional electrolytes, viz., K I and KC104, have also been investigated in the present work. Furthermore, as a verification of the ion conductances derived in this manner, the determination of transference number of perchlorate ion using cell I : Li(Hg), 2 mole %/LiC104(C1) LiC104(C,)/Li(Hg), 2 mole %, has also been resorted to in this investigation.
Theory The plots of the equivalent conductance us. the square root of molar concentration for (i-Arn)eN(i-Am)kB, (i-Am),NI, KI, and KC104 lie above the corresponding limiting tangents. Using this as a criterion for the absence of association,2 the data for these systems were treated according to the procedure of Fuoss and Acc a s ~ i n ausing , ~ the equation A = A" - SC'/2
+ EC log C + J C - FAOC
(1)
where A, A', C, S, E , J , and F have their usual significance. I n analyzing the viscosity data, the Jones and Dole equation was used in the form (q/qo
- l)/C'/'
=
A
+ FC1I2
(2)
Assuming that the ions of the electrolyte (i-Arn)eN(i-Am)rB are of equal size, the limiting equivalent conductance of the cation and anion in this case can be considered to be the same. Thus, if the additivity of conductance is valid, one obtains X"(CAm)rN
+
= ho(i-Am)4B- = 1/2Ao(i-Am)rN(i-Am)&
(3)
where A" (i-Am)rN(i-Am)& is the observed limiting conductance of (i-Am)&(i-Arn)kB, I n general, the constant A of the Jones and Dole equation can be related to the ion conductances and A" of an electrolyte in the following manner.
[
A = 32070(D 81.97A0 T)l'/"Ao+X"- 1 - 0.6863("+
'"-y]
(4)
Accordingly, as a consequence of eq 3, eq 4 would transform into
in the case of (i-Am)4N(i-Am)4B. A satisfactory agreement between the value of A as obtained from actual viscosity measurements and the one calculated using eq 4a would indicate the validity of our assumption that the conductances of the ions of the electrolyte (i-Am)4N(i-Am)4B are equal. The latter, in turn, would indicate the reliability of the ion conductances calculated on the basis of the conductance of either (i-Am)4N+or (i-Am)4B-. The emf, E , of cell I used for the determination of the transference number of perchlorate ion can be expressed as
E
RT
a2
F
a1
= 2tclO4-- In
-
where tCIOa- denotes the transference number of ClOaand the a's represent the mean activities of the LiC104 solutions. From our previous studies LiC104 was found to be unassociated. Therefore, eq 5 can be rewritten as
where C1 and C2 are the stoichiometric concentrations of LiC104 solutions used, and f l and f 2 are the mean activity coefficients of the two solutions. Assuming that the ionic activity coefficients are equal, the mean activity coefficients can be estimated from the extended form of the Debye-Huckel equation which assumes the form -log f*
=
0.685lp'"
1
+ 0.3629 X 108ao~/'
in PC a t 25", using a" = 2.75 A2. I n the present measurements, the ratio C2:C1 was kept between 1.5 and 2.0. The transference number of c104-calculated from each measurement using equation 6 was then plotted against the "mean" concentration defined as (C1 C2)/2, and finally extrapolated to zero mean concentration. The product of this extrapolated value of tcloa- and the Ao2~iclo4 was taken to give the value of Xo~1o4-.Conductances of all other ions were then calculated using this value of Xoc1o4-.
+
Experimental Section Chemicals. Propylene carbonate was purified according to the procedure described previously. Fisher certified reagent grade potassium iodide and potassium (3) R. M. Fuoss and F. Accascina, "Electrolytic Conductance," Interscience Publishers, New York, N. Y., 1959, pp 191-205, 207247,
Volume 74, Number 9 April SO, 1970
1944 perchlorate were used without further treatment. The purification of lithium perchlorate has been given before.2 Tetraisoamylammonium iodide was prepared by refluxing tri-iso-amylamine (5.68 g) and 1-iodo-3-methylbutane (5.93 g) in 25 ml ethyl acetate for 18 hr, cooling to - lo", filtering the crystals, and repeating the cycle for two more times with the filtrates. The combined crystals thus obtained were recrystallized from methyl acetate-n-hexane mixture to yield octagonal platelets (mp 147-149"). Tetraisoamylammonium tetraisoamylboride was prepared essentially according to the method of Coetzee and C ~ n n i n g h a m . ~A solution of isoamyllithium was obtained by the reaction of isoamyl bromide and lithium in diethyl ether while the solution of triisoamylboron in tetrahydrofuran was prepared by the reaction of diborane with 3-methylbutene-1, The two solutions were then combined under dry, oxygen-free conditions to afford a solution of lithium tetraisoamylboride. This was stored overnight and treated the following day with a solution of tetraisoamylammonium iodide in acetonitrile. The product, after the prescribed work-up, yielded the desired product, viz., tetraisoamylammonium tetraisoamylboride as short needles with mp 250-251", after two recrystallizations from methyl acetate-n-hexane mixture. Anal. Calcd for C, 80.88; H, 14.94; N, 2.36. Found: C, 80.73; H, 15.26; N, 2.69. Conductance and Viscosity Measurements. The techniques have been described previously.2 Potentiometric Measurements. A three-compartment cell similar to the one described by Durst and Hume6 was used with some modifications. Each of the two outer compartments contained a pool of lithium amalgam and the lithium perchlorate solution of appropriate concentration. The middle chamber which was separated at both sides by fritted disks was filled with the more dilute of the two IJiC104solutions. The cell was set up in a glove box which was purged with pure argon gas and maintained at a temperature of 25 f 0.1". All emf measurements were made under identical conditions, using a type K4 I, and N potentiometer. For each run an initial period of 30 min was allowed for the attainment of equilibrium. Saturated lithium amalgam (-2 mol %) prepared by shaking lithium ribbon with triple-distilled mercury has been used in all cells.
Results and Discussions The results of conductance and viscosity measurements for the systems (i-Am)dN(i-Am)qB, (i-Am)&l, KI, and KC1O4are summarized in Tables I and 11. The values of A", a", and F obtained for the differentcases are presented in Table 111. Both K I and KC104 yield A' of 30.75, which indicates that the iodide and perchlorate ion have equal mobilities in PC. The large The Journal of Physical Chemistry
L. M. MUKHERJEE, D. P. BODEN,AND R. LINDAUER
+
Figure 1. Plot of A - A' 3. SC'/z- - EC log C FAo C us. C. 0, n-Bu4NC10a; A, Et4NC10a; 0, (i-Am)4N((i-Am)aB; 0, (i-Am)rNI; A, n-BuaNBr.
difference between the limiting conductances of N(i-Am)4Band (i-Am)4NI, on the other hand, suggests that the mobility of (i-Am)4B- is considerably less than that of I-. The viscosity F coefficients of KC104, KI, and (i-Am)4NI are noteworthy in this connection. The value of F for Kc104 is about two-thirds of that obtained for LiC1042, indicating that K + is significantly smaller in size than Li+ in PC; similar comparison between K I and (i-Arn)dNI suggests that (i-Am)dN+ is slightly bigger than K+. The a0 values of the two potassium salts are reasonable and are comparable to the sums of their crystallographic radii. For the tetraisoamylammonium salts, however, the derived ao values are almost half of the values expected on the basis of the crystallographic radii of the ions. Among the quaternary ammonium salts studied previously,2 Et4NC104, n-Bu4NBr, and nBu4NC104also indicated similar relationship. One of the possible explanations for this deviation may lie in the somewhat arbitrary assumption of a total absence of ion association as implied in the treatment of the - EC data (cf. eq 1). In fact, plots of A - A' log C FAOC vs. C for these five quaternary ammonium salts do tend to diverge from linearity (Figure 1) a t concentrations greater than -0.005 M , possibly indicating a small but significant degree of association in each case. It is to be remarked in this connection, however, that the data for (i-Arn)dNI show the least departure from linearity although the relative difference between the experimental value of ao and the sum of the crystallographic radii is greatest for this salt. The low values of the a0parameters in the case of the tetraalkylammonium salts may also be due to the omission of the -J2C'/z term in the present treatment from the more comprehensive Fuoss-Onsager equation.
+
+
(4) J. F. Coetzee and G. P. Cunningham, J . Amer. Chem. Soc., 86, 3403 (1964). (5) R. A. Durst and D. N. Hume, J . Electroanal. Chem., 7, 248 (1964).
1945
BEHAVIOR OF ELECTROLYTES IN PROPYLENE CARBONATE Table I : Summary of Results of Conductance Measurements a t 25'
__--- (i-hm)rN('-Am)&------
_____ ( ~ - A ~ )____~NI
$
1o*c,M
1030,M
A
15.5083 15.3998 15.2316 14,9389 14.6428 14.4041 14.0077
0.9660 1.243 1.740 2,900 4.351 5.80 8.70
A
25.6070 25,5407 25,3397 24.9741 24.7039 24.2108 23.8172 23.1384
1,682 1.892 2,523 3.785 5.05 7.57 10.09 15.14
,--.------KI-----1030, M
A
29,5915 29.4103 29.1316 28.9100 28.4908 28.1579 27.6138 27.1847 26.4456
1.246 1.662 2.493 3.324 4.99 6.65 9.97 13.29 20.00
------KC104-----lOV, M
A
29.2757 29.1559 28.9437 28.6079 28.0080 27,3796 26.8816 26,0055
1,919 2.239 2.878 4,030 6.72 10.075 13.43 20.15
Table I1 : Summary of Results of Viscosity Measurements at 25" (i-Am)tN&----103c, IM 11, opa
----(&Am)
___-_ ?I
cpa
2.483 2.490 2.4965 2.5075 2,516
1.514 4.542 7.57 11.35 15.14
2.485 2,492 2.497 2.504 2.510
1.740 3.808 5.01 7.11 8.70 a vaolvent =
----(i-Am)dNI---103c, M
3.989 7.98 12.00 15.955 19.94
KI
KC104----
,
cpa
7,
2.492 2 501 2.510 2.520 2.530 I
1020, M
4.030 8.06 12.09 14 05 16.12 20.15 I
?I
cpa
2.491 2.500 2.508 2.513 2.518 2,528
2.480 cP.
Table I11 : Physical Constants Determined from Analysis of Conductance and Viscosity Data Electrolytea
A0
(i-Am)qN(i-Am)4B (i-Am)aNI KI KC104
16.37 26.95 30.75 30.75
a',
A
5.22 3.30 3.70 3.175
F
1.27 0.96 0.904 0.874
f 0.018 10.054 i 0.037 f 0.038
a J values: (i-Arn)dN(i-Am)aB (78); (i-Am)dNI (70); K I (85); KC104 (72.5).
No detailed consideration of this point has been undertaken in this paper. Assuming that the ions of the electrolyte (i-Am)dN(i-Am)4B are idealized spheres (of equal size) in a continuum, the hydrodynamic radius (R) of its ions can be calculated using the Einstein relation: F = (Nn/300) (R+3 X 3 ) . The radius so obtained for (i-Am)4N+(or (i-Am)4B-) from the observedovalue of the viscosity F coefficient (Table 111) is 4.69 A yielding a total centerto-center distance o,f 9.38 A for (i-Am)rN(i-Am)4B. This value 0f~9.38A is only slightly lower than the value of 10.8 ABestimated from molecular models, but it is evidently much greater than tbe conductometric estimate of the u0 parameter (5.22 A) possibly due to reasons discussed above. Substituting the value of 16.37 obtained for the limiting conductance of (i-Am)dN(i-Am)rB (Table 111) into
+
low, M
eq 4a the constant A of the Jones and Dole equation is calculated to be 0.018 in close agreement with the experimental value of 0.0174, suggesting that the inherent assumption of equality of ion conductances in this case (cf. eq 3) is apparently valid. The value of 8.185 calculated on this basis for the limiting conductance of (i-Am)rN+,has been used in the subsequent calculation of the conductances of other ions. The results of transference number measurements using cell I are given in Table IV. Table IV : Determination of Transference Number of Perchlorate Ion Using Cell I Ci, M
e,, 1w
E, V
tolor-
0: 020 0.025 0.050 0.100 0.120
0.040 0.050 0.100 0.150 0.200
0.0245 0.0245 0.0243 0.0144 0.0181
0.757 0.765 0.789 0.816 0.820
The transference number of Clod- extrapolated to zero mean concentration, is found to be 0.72. On this basis, the transference number of Li+ is calculated to be 0.28. Thus, using the value of 26.08 for the A' of LiC102 the (6) J. F. Coetzee and G. P. Cunningham, J. Amer. Chem. Soc., 87, 2529 (1965).
Volume 74, Number 0 April $0, 1970
1946
R. P. RASTOGI AND H. P. SINGH
limiting conductances of Li+ and c104-are found to be 7.30 and 18.78, respectively. I n Table V a summary of the conductances for the various ions is presented. These results are based on the conductance of (i-Am)4N+(Ao = 8.185) and those of Li+ (Ao = 7.30) and Clod- (Ao = 18.78) as determined above, and the A' values obtained for the different electrolytes. The excellent agreement between the calculated values of the mobility of iodide ion based on these two different approaches is indeed remarkable. This is considered particularly important insofar as the present evaluation of the mobilities of other ions is concerned. The fact that the mobility of lithium ion is the lowest of all cations including the tetraisoamylammonium ion supports our previous2 notion that the lithium ions are extensively solvated in PC and the effective size of a Li+ is fairly large. The slight differences in the conductances of c104-,I-, Br-, and C1- seem to indicate that the effective sizes of these anions in PC are practically the same. This behavior would signify that very little solvation, if any, is involved in these cases. The lowest mobility of the tetraisoamylboride ion is to be attributed to its much larger size. At the footnote to Table V are given the calculated values (cf. eq 4)of the constant A of the Jones and Dole
Heats of Transport of Gases.
Table V : Ion Conductances in Propylene Carbonate at 250a Salt
LiC104 LiCl
KC104 KI Et4NC104 n-Bu4NC104 n-Bu4NBr (i-Am)4N(i-Am)4B
(i-Am)sNI
AQ
At0
x-Q
26.08 27.50 30.75 30.75 32.06* 28.17 28.65 16.37 26.95
7.30 7.30 11.97 11.97 13.28 9.39 9.39 8.185 8.185
18.78 20.20 18.78 18.78 18.78 18.78 19.26 8.185 18.765
A 'values are given in the format: calcd, exptl (salt): 0.016, 0.0095 (LiC104); 0.010, 0.0075 (KC104); 0.010, 0.0065 (KI); 0.010, 0.008 (EthNC104); 0.012, 0.0075 (n-BuNC104); 0.013, 0.006 (n-Bu4NBr); 0.018, 0.0174 ( (i-Am)4N(i-Am)4B); 0.014, 0.005 ((i-Am)4Nl). I,Result of rerun (J = 92). The cell constant used in previous work (ref 2) with this salt was found in slight error; the present value of A' is considered more reliable.
equation for different systems. As is evident, the agreement between the calculated and the experimental values is generally as close as can be expected. Acknowledgment. D. P. Boden acknowledges the cooperation of ESB, Inc., Research Center, Yardley, Pa.
11. Thermoosmosis of
Binary Gaseous Mixtures without Chemical Reaction
by R. P. Rastogi and H. P. Singh Chemistry Department, Gorakhpur University, Gorakhpur (U.P.), India
(Received August 26, 1969)
Thermoosmotic pressure of mixtures of carbon dioxide and oxygen across porous unglased porcelain has been measured. Experimental data are found to be consistent with the thermodynamic theory of thermoosmosis of mixtures. The concentration dependence of heats of transport Q* for the mixtures has been estimated from the data. &* is found to vary with concentration in a linear manner showing that the transport of carbon dioxide and oxygen takes place almost independently. 1. Introduction Thermoosmosis of gases through membranes has been studied by a number of workers.*-6 ThermoOsmosis iS influenced by the nature of the membrane and pore radii. Denbigh and Raumann' found that it depended on the solubility of the permeant in the membrane. Hanley and c0workers3~~measured thermoosmosis of He, Ne, and Ar through stainless The Journal of Physical Chemistry
steel tubes under nonisothermal conditions. Thermoosmosis was found to depend on the ratio of tube (I) K. G. Denbigh and G. Raumann, P ~ o c .Roy. SOC.,A210, 618
(lQS1)* (2) R. J. Besrman, J. Phys. Chem., 61, 708 (1957). (3) H. J. M. Hanley and W. A. Steele, Trans. Faraday Soc., 61,2661
.
(1966). - -,
(4) H. J. M. Haniey, ibid., 62,2396 (1966).
