J. Phys. Chem. 1982, 86, 3996-4003
3996
production of oxygenates and reduced metal.' Our results for CO adsorption indicate that if reaction to produce C02 is a chief mode of reduction of the oxide, then concomitant dissociation of CO, on metallic patches on the surface can serve to reoxidize the surface. Therefore, C02 formed during the synthesis reaction, or added with the reactants as in the case for the methanol s y n t h e ~ i smay , ~ perform a valuable function in keeping at least a portion of the catalyst surface oxidized and active for the synthesis of oxygenated products. Conclusions We have examined the adsorption and interaction of CO, C02, and D2 with an Rhz02.5Hz0sample that had been dosed at 450 "C. Our major findings are as follows: 1. Approximately 40% of adsorbed D2 reacts to form D 2 0 which desorbs over a broad temperature range cen-
tered at 270 "C. The D, that desorbs does so at a temperature (115 OC) that is too high to be due to adsorption on metallic patches on the surface. 2. Approximately 75% of adsorbed CO reacts to form C02which desorbs between 190 and 245 OC depending on coverage. 3. Both CO and Dz desorb without significant reaction on an oxide sample that had been reduced to the metal in agreement with literature findings. 4. Adswbed C 0 2 desorbs intact at 170 OC regardless of coverage on the oxide while it dissociates on the metal and only CO desorbs as a result.
Acknowledgment. This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Sciences Division of the US. Department of Energy under Contract W-7405-ENG-48.
Ionic Volumes of Electrolytes in Propylene Carbonate from Densities, Ultrasonic Vibration Potentials, and Transference Numbers at 25 OC Raoui Zana,+ Jacques E. Desnoyers,$ Gerald Perron,$ Robert L. Kay,'§ and Kuoshin Lee§ CNRS. Centre de Recherches sur les Macromolecules, 67083 Strasbourg-Cedex, France; Facult6 des Sciences, Unlversit6 de Sherbrooke, Sherbrooke, Quebec, Canah JIK 2R 1; and Department of Chemistry, CarnegkcMellon Universm, Pittsburgh, Pennsylvania 15213 (Recelved: March 12, 1982; In Final Form: May 27, 1982)
Measurements of densities, ultrasonic vibration potentials (uvp's), and transference numbers of electrolytes in propylene carbonate (PC)at 25 "C were combined to give standard partial molar volumes V(ion) of individual ions in PC. Cations and anions of the the same size have approximately the same V(ion), which is in contrast with the ionic values that would be obtained from an extrapolation of the iio(R,NI) to zero cation molecular mass, which yields much more negative values for anions than cations. The electrostriction in PC is close to that in water, ethylene glycol, ethanol, and dimethyl sulfoxide and about the same for cations and anions.
Introduction Propylene carbonate (PC) is an extremely valuable solvent for e1ectrolytes.l It has a relatively high dielectric constant (64.9), has good solvent properties for most electrolytes, and, being aprotic, can sustain metals as reactive as alkali metals. As such it is used in recently developed batteries involving lithium metal.2 It is often suggested as a reference solvent for solvation studies of electrolyte^.^ A survey of the literature shows that, with the exception of enthalpies of solution,4 the solution properties of electrolytes in PC are poorly known. For instance, the limiting equivalent conductances A,, of ions in P P 7differ in some cases by more than 15%, whereas a precision of better than 0.1% is usually obtained on these quantities. Also, few reliable partial molar volumes are found in the literature.B-10 Finally, essentially no precise data on partial molar heat capacities and compressibilities are available. Our current interest in the properties of ions in nonaqueous solvents, together with the peculiar structure of the PC molecule
CNRS.
* Universite de Sherbrooke. 8 Carnegie-Mellon
University. 0022-3654/82/2086-3996$01.25/0
and the paucity of reliable volumetric and transport data on ionic solutions in PC, led us to undertake a thorough investigation of ionic volumes in a joint study involving three laboratories. The transference numbers of K+ in KClO, solutions and of Et,N+ in Et4NC104solutions were accurately determined at Carnegie-Mellon University. These data provided a basis from which the A,, of ions in PC could be obtained from the reported equivalent conductances of electrolytes. The partial molar volumes of a number of electrolytes in PC were determined at the (1) W. H. Lee, 'Chemistry of Non-Aqueous Solvents", Vol. 4, J. T. Lagoski, Ed., Academic Press, New York, 1976,Chapter 6. (2)T. Sakai and K. Teratsukaea, Jpn. Kokai Tokkyo Koho 78,101, 628 (1979);Ray-0-Vac Corp. Jpn. Ltd.,ibid., 81,08,386 (1981),Chem. Abstr., 94,216584g,(1981);Daini Seikosha Co.Ltd. Jpn. ibid., 81,01,468 (1981),Chem. Abstr. 94,216682e,(1981). (3)H.L. Friedman and C. V. Kriahnan in 'Water: A Comprehensive Treatise", Vol. 3,F. Franks, Ed., Plenum Press, New York, 1973,p 1. (4)C. V. Krishnan and H. L. Friedman in "Solute-Solvent Interactions", Vol. 2,J. F. Coetzee and C. D. Ritchie, Eds., Marcel Dekker, New York, 1976,Chapter 9. (5)L. M. Mukherjee,D. P. Boden, and R. Linduer J. Phys. Chem., 74, 1942 (1970). (6)M. Jansen and H. L. Yeager, J. Phys. Chem., 77,3089(1973);78, 1830 (1974). (7)N. Matsura, K. Unemoto, and Y. Takeda, Bull. Chem. SOC.Jpn., 48,2253 (1975). (8)M.Dack, K. J. Bird, and A. J. Parker, Aust. J . Chem., 28, 955 (1975). (9)R. Gopal, D. K. Agarwal, and R. Kumar, Z. Phys. Chem. (Frankfurt am Main), 84, 141 (1973). (IO) K. Sing, D. K. Agarwal, and R. Kumar, J. Indian Chem. SOC.,52, 304 (1975).
0 1982 American Chemical Society
Ionic Volumes of Electrolytes
University of Sherbrooke. Finally, the ultrasonic vibration potentials of electrolyte solutions in PC, determined in Strasbourg, were combined with the above data to obtain partial molar volumes of single ions in PC."J2 Data on partial molar heat capacities and isentropic compressibilities will be reported at a later date.13
Experimental Section The PC used for density and ultrasonic vibration potential (uvp) measurements was purchased from Aldrich Chemical Co. (99% pure). It was used as received in the uvp measurements since preliminary experiments showed that, within the experimental error, the same uvp was obtained for a given solution for PC used without purification or after distillation under vacuum. The PC used for the density measurements was first distilled under vacuum and stored over 3-A molecular sieves. The PC used for transference measurements was also distilled under vacuum. The water content of the purified product was found to be about 0.1 g L-' by Karl Fischer titration and by 6OO-MHz 'H NMR spectroscopy. Gas-chromatographic analysis indicated that the probable impurities (1,2-propylene glycol, allyl alcohol, and propylene oxide) were present to less than 10 ppm. All electrolytes are essentially the same as those used in a previous study in a~etonitrile,'~ except for Me4NC104, Pr4NC1,and LiC104in density measurements, and RbC104 and CsC104 in uvp measurements. Me4NC104was obtained from the neutralization of Me4NOH by HC104, evaporation to dryness with 2-propanol, and recrystallization in ethyl acetate. Pr4NC1 (Eastman Kodak) was recrystallized from a mixture of 2-propanol and ether and was dried under vacuum over P205. LiC104 (Alfa Inorganic) was recrystallized from acetonitrile and dried under vacuum, over P20b RbC104 and CsC104were prepared by neutralization of RbOH and CsOH (Fluka) by a slight excess of perchloric acid in solution, recrystallized from water, and dried under vacuum in the presence of Pz06. The KC104 used for transference measurements was recrystallized twice from conductivity water, dried under vacuum, and stored in a desiccator over PzOb The Et4NC104 and Bu4NC104 were polarography grade (Eastman Kodak) and were used as received. All solutions for density measurements were prepared by weight. Corrections for vacuum were not made since the error introduced by this omission is inside the experimental error on the volume scale. The cation transference numbers were measured at 25 f 0.01 "C by means of the moving-boundary method, employing a new design of the RF boundary detector15J6and a sheared-type cell in which the following solution was Bu4NC1O4 A cadmium anode and a Ag/Ag20 cathode gave satisfactory results for all systems studied. Further details concerning the instrumentation can be found in ref 15. The densities were measured by using the same instruments as in a previous study.14J7 The water content of the PC and of the solutions was determined by the Karl Fischer technique (Aquo-test I1 from Photovolt). All (11)P. Debye, J. Chem. Phys., 1, 13 (1933). (12)R. Zana and E. Yeager, J. Phys. Chem., 71, 521,4241 (1967). (13)G. Perron, G. Trudeau, and J. E. Demoyere, in preparation. (14)R. Zana, G. Perron, and J. E. Desnoyers, J. Solution Chem., 8, 729 (1979). (15)K. Lee, Ph.D. Thesis, Carnegie-Mellon University, Pittsburgh, PA, 1981. (16)K. Lee and R. L. Kay, Aust. J. Chem., 33, 1895 (1980). (17)P. Picker, E. nemblay, and C. Jolicoeur, J. Solution Chem., 3, 377 (1974). (18)H.Hailand, J. Solution Chem., 5,773 (1976).
The Journal of Physical Chemistry, Voi. 86, No. 20, 1982
3997
TABLE I: Corrected Transference Numbers for Et,NClO, and KC10, in PC at 25 "C l0ZCl
0.5000 1.0000 2.0000 3.0000
solvent t+(obsd)" correction Et,NCIO, 0.4126, (2.3) +0.0002, 0.4119, (1.6) +0.0001, 0.4102, (1.8) +O.OOOO, +O.OOOO, 0.4092, (1.2)
0.4128, 0.4120, 0.4102, 0.4092,
0.4998 1.0000 1.8800 3.0023
KClO, +0.0003 0.3785 (1.1) 0.3772 (1.7) +0.0001 0.3753 (1.0) 0.3737 (1.7)
0.3788 0.3773 0.3753 0.3737
(mol L-l)
t+
a Average deviations (in the fourth decimal point) are in parentheses.
measurements were performed in winter, when the relative humidity of the laboratory was low; consequently, no special precautions had to be taken in handling the samples. The density of PC at 25 "C was found to be 1.19965 g ~ m - ' on ~ , a sample containing 0.0165 g L-' of water. This result is in very good agreement with the value 1.19966 g reported by H~i1and.l~ The densities of PC containing increasing amounts of water were measured, and a calibration curve was prepared which allowed a correction of all densities to pure PC. Throughout the measurements the temperature was kept at 25 "C. It was controlled to fO.OO1 K with a Sodev thermostat and its absolute value determined with a Hewlett-Packard quartz thermometer to within 0.01 K. The uvp values were measured at 207 kHz with the same apparatus as used in previous studies.14J9 The temperature was kept at about 24 OC. This small difference between the temperatures at which the uvp and the transport numbers and partial molar volumes were determined has been shownz0to result in an error on the calculated ionic partial molar volumes well below the overall error (f2 cm3 mol-'). The addition of small amounts of water, comparable with those taken up by the solution in a typical experimental run,was found to result in a negligible change of the measured uvp. Addition of larger amounts of water (0.2 M) resulted in a measurable decrease of the uvp. Care was therefore taken to minimize the time required for measurements and to avoid contact with the ambient atmosphere during the runs.
Results Transference Numbers. Table I contains the averaged values of the cation transference number t+(obsd) for Et4NC104 and KC104 for triplicate runs at each of the listed salt concentrations. The average deviations (in the fourth decimal place) in parentheses indicate a reproducibility of better than 0.05%. The dc current varied from 60 PA for the most dilute to 0.7 mA for the most concentrated solution. At each concentration the current was varied by 30% or more to ensure that the boundary velocity was not affected by Joule heating. Owing to the negative change of the density of Bu4NC104solutions with concentration, it was necessary to use falling boundaries in which the initial concentration of BQNC1O4 was greater than that required by the Kohlrausch ratio, which was approximately 0.8.21 The observed transference numbers listed in Table I for the solvent conductance by using have been (19)F.Kawaizumi and R. Zana, J. Phys. Chem., 78,627,1099(1974). (20)E.Yeager and R. Zana, J. Phys. Chem., 76,1087 (1972). (21)A. R. Gordon and R. L. Kay, J. Chem. Phys., 21, 131 (1953).
The Journal of phvsicai Chemistry, Vol. 86, No. 20, 1982
3998
Zana et al.
1'
40
t (C,mole
1-1)"'
iC,mole
I
I
1-0"'
I
I
I
K C 104 - PC- 25°C .38
I
C(mole 1-1) I
0 01
C( mole 1-1 1 0 02
0.01
1
0.03
I
0.02
0.03
Figure 1. Transference numbers of electrolytes in propylene carbonate at 25 (d) t+O' of KC10,.
a specific conductivity of PC of lW7 S cm-' and the solution conductance of Jansen and Yeager.6 The final values of t+ in Table I have not been corrected for the volume changes, in the closed (cathode) side of the cell,that result from electrolysis and the transport process. At this writing the density data for CdC104 required for a calculation of the correction23are not available. However, the volume correction is directly proportional to the salt concentration and should not affect the extrapolated transference number t+O, to a first approximation, particularly when eq 2 (see below) is used. This work is concerned primarily with the determination of t+O. Some concern was given to the significant water content of the PC (about 0.1 g L-' or 6 X M H20, which is comparable to the salt concentrations used). As a check, the water content of the PC used in runs at 0.02 and 0.03 M Et4NC104was doubled. The measurements yielded identical transference numbers, within experimental error. In Figure 1,a and b, are plots of t+ vs. c1l2 for Et4NC104 and KC104. The straight lines are the slopes calculated from the Onsager limiting theoryH
t+ = t+O - [(0.5 - t+o)/A&?~'/2
(1)
In eq 1,4is the limiting molar conductance of the leading electrolyte and /3 = 82.5/[q(e2')1/2],where t = 64.9226and (22) L. G. Longsworth, J. Am. Chem. SOC.,54, 2741 (1932). (23) J. R. Gwyther and M. Spiro, J. Chem. Soc., Faraday Trans. 1,72, 1410 (1976). (24) R. k Robinson and R. H. Stokes, "Electrolyte Solutions",2nd ed., Butterworths, London, 1959, Chapter 7.
OC:
(a) t + of Et,NCIO,;
(b) t + of KCIO,; (c) t+O' of Et,NCIO,;
7 = 0.0248 P.6 As can be seen in Figure 1, a and b, the transference numbers for both Et4NC104and KC104 approach the limiting slopes from above, typical behavior for completely dissociated, symmetrical electrolytes with transference numbers less than 0.5.2s,27Also, it has been found22that for such electrolytes the deviation from eq 1 in the form Aot+ O . ~ @ C ~ / ~ t+O' E = t+O + AC (2) A. + P C ' / ~
+
are linear in C so that the intercepts of plots of t+O' vs. C (Figure 1,c and d) give the limiting transference numbers. In this way we obtained t+O(Et4NC104)= 0.4170 t+O(KC104)= 0.3846
Two determinations of transference numbers have been reported for PC solutions. Those of Gopal and Jhaa were carried out by the Hittorf method for KI in PC at 25 "C. A plot of their data as a function of c1l2 and their extrapolated value clearly indicate that they obtained their limiting transference number of 0.396 by an extrapolation of a straight line through their data rather than by using the limiting Onsager slope. In contrast to the generally observed positive deviations from the limiting slope as is (25) R. Paynes and I. E. Theodron, J . Phys. Chem., 76, 2892 (1972). (26) M. Spiro in 'Physical Methods of Organic Chemistry", Vol. 1, Part 11-A,A. Weieeberger, Ed.,Wiley, New York, 1971. (27) R. L. Kay in 'Electrochemistry", E. Yeager and A. J. Salkind, Eds., Wiley, New York, 1973, Chapter 11. (28) R. Gopal and J. S. Jha, Indian J. Chem. Sect. A , 15, 80 (1977).
Ionlc Volumes of Electrolytes
The Journal of Physical Chemistry, Vol. 86, No. 20, 7982
TABLE 11: Best Estimate of Limiting Conductances in PC at 25 "C
TABLE 111: Comparison of Reference Electrolytes at 25 "C A, */A
A0
ion Li+ N a+
K+ Rb+ CS' Me,N+ Et," Pr,N+ Bu,N+ (i-Am)," Br1SCN-
c10, Ph,B(i-Am),B-
best estimate
ref 6O
ref 5"
8.32' 9.46 11.52 11.91 12.67 14.17 13.1gd 10.47 9.00d 8.19d 18.90 18.33d 21.77 18.43d 8.1Oe
8.89 9.44 11.17 11.89 12.65 14.16 13.17 10.46 8.98
7.28
8.15d
8.17
8.17 18.91 18.35 22.12 18.45
3999
11.99
solvent
(i-Am),N(i-Am),B 0.988
CH,CN CH,CONH, CH,NO, Me,SO PC
0-
(i-Am),BuN(Ph),B 0.991 1.043
1.000
1.078 1.005
> 1.011
13.30 9.41 8.19 19.24 18.76 18.76
T
41
t
8.19
Jansen and Yeager. Mukerjee, Boden, and Linduer. ' Calculated from conductance data for LiClO, from ref 30. Calculated from t+O (Et,NClO,) and conductance data from ref 6. e Calculated from conductance data for Bu,NPh,B from ref 29. a
shown here for Et4NC104and KC104,increasing negative deviations are observed in the Gopal and Jha data for KI. Conductance data6 indicate that KI is not significantly associated in PC. The abnormal concentration dependence of their data could be a reflection of errors introduced by using an Ag wire cathode and by errors inherent to the Hittorf method. The reversibility of the Ag/AgI electrode has not been demonstrated in PC, and AgI is known to be slightly soluble in PC. By combining our transference numbers with known conductance data6 (see below), we calculated t+O(KI) = 0.3858 or about 2.6% lower than the value found by Gopal and Jha. Mukherjee et al.5 have reported anion transference numbers for LiC104 in PC at 25 "C from the emf method using the extended Debye-Huckel equation to calculate the activity coefficient ratios over a concentration range = 0.02-0.12 M. They quote a limiting value t!(LiC104) 0.72. In order to check their result they measured the conductance of the reference electrolyte (i-Am),N(i-Am),B and assumed that the conductances of its two ions were equal. Combining these two results with their conductance data for other electrolytes, they obtained &,(ClOc)= 18.78 from the transference measurements and &(LiC104), and 18.76 from the split of the reference electrolyte conductance-excellent agreement, but fortuitous since the transference data were quoted to only about 1%. Using their list of ionic conductances, we have calculated t+O(Et4NC104)= 0.4148 and t+O(KC104)= 0.3890, which are 0.5% lower and 1.4% higher, respectively, than the precise transference numbers that we report. Jansen and Yeagere were unable to obtain transference numbers in PC by the familiar autogenic moving-boundary method because of solvent decomposition. Instead they also resorted to the same reference electrolyte, (i-Am)4N(i-AmJB, as Mukherjee et al.5 and obtained the same ho to within 0.15%. Jansen and Yeager also report the conductances of several electrolytes, and their ionic conductances are compared with those of Mukherjee et al. in Table 11. There are serious differences, as high as 23%, for several ions. Using Jansen and Yeager's ionic con(29)R.M.Fuoss,J. B. Berkowitz, E. Hirsch, and s. Petrucci, Proc. Natl. Acad. Sci. U.S.A., 27,44 (1968). (30)J. Barthel, R. Wachter, and M. Gores, Faraday Discus. Chem. SOC.,64,285 (1978).
0
02
04 ( m o l kg'' )
0.6
Flgure 2. Apparent molar volumes of some electrolytes in propylene carbonate at 25 O C .
ductances, we calculate t+O(Et4NC104)= 0.4165 and t+O(KC104)= 0.3772. The datum for Et4NC104is within about 0.1% of our value but that for KC104 is about 2% lower. In order to determine ionic volumes, it is necessary to extract from these data an accurate set of ionic conductances. Although this is not possible, we can establish a consistent set of data from our best estimate of the ionic conductances. These are also given in Table I1 and were calculated as follows. We calculated &,(ClOc)18.43from our transference data and Jansen and Yeager's value for AO(Et4NC104).This is in excellent agreement with the value obtained from the conductances of the reference electrolyte and a series of salts with common ions.6 This leads to most of the data in Table I1 listed under "best estimate" using, in each case, the Jansen and Yeager conductance data. The one serious discrepancy using this procedure is with the K+ ion. Although the conductance data from ref 6 for KC104 and KI lead to the same value of &(K+) = 11.19 using &,(I-)= 18.33and X(C104-) = 18.43, it is in poor agreement with the transference data reported here, Le., t+OAo(KC104)= 11.39 or almost 2% higher. If the conductance data for KC104of Jansen and Yeager are correct, Xo(K+)is equal to the entry from ref 6 in Table 11. On the other hand, if the transference data are correct, &(K+) can be calculated from Xo(K+) = &,(C104-)[t+o(KC104)/t-o(KC104)] (3) which is independent of the potassium salt conductance data and gives &,(K+)= 11.52. We have preferred to use the latter result. We have also selected the conductance data of Barthel et al.30for the Li+ ion because of the extreme care taken in handling this difficult salt. Values of &,+/&,for reference electrolytes at 25 "C are listed in Table 111. Apparent Molar Volumes. The apparent molar volumes q5v of the various electrolytes were calculated from differences in densities and are listed in Table IV. The limiting standard partial molar volumes V20was obtained from a plot of q5v against the square root of the molality.
4000
The Journal of Physical Chemistry, Vol. 86, No. 20, 1982
Zana et ai.
TABLE IV: Densities (in g ~ m - and ~ ) Apparent Molar Volumes (in cm3 m o l - ' ) of Electrolytes in Propylene Carbonate at 25 "C LiBr
m/(mol kg') 103(d- d o ) 0.007 21 0.587 0.017 52 1.414 0.025 73 2.084 0.049 66 3.983 0.067 70 5.400 0.089 1 2 7.087 0.114 38 9.038 0.139 1 5 10.951
LiC10,
0.008 22 0.022 68 0.028 53 0.049 53 0.067 44 0.088 63
0.609 1.684 2.107 3.653 4.951 6.479
37.17 37.05 37.30 37.32 37.52 37.69
NaI
0.019 46 0.040 30 0.070 34 0.135 80 0.161 75 0.189 97
2.586 5.383 9.327 17.926 21.293 24.958
32.53 31.90 32.55 32.73 32.89 32.97
NaClO,
0.010 93 0.020 10 0.029 8 0 0.048 98 0.067 74 0.088 73 0.157 73 0.210 42 0.326 44
0.940 1.740 2.581 4.238 5.84 1 7.635 13.441 17.844 27.302
42.28 41.85 41.79 41.80 41.94 42.00 42.38 42.51 42.97
0.009 29 0.021 55 0.027 5 8 0.050 8 3 0.062 84 0.083 07 0.102 86 0.119 25
1.318 3.046 3.893 7.148 8.836 11.639 14.370 16.641
39.14 39.39 39.50 39.75 39.70 39.96 40.15 40.18
0.007 8 8 0.018 92 0.029 56 0.049 47 0.071 8 8 0.091 0 3 0.108 77
0.037 0.088 0.137 0.223 0.310 0.386 0.45
188.18 188.22 188.24 188.32 188.43 188.47
0.028 04 0.035 20 0.049 25 0.051 04 0.071 80
1.429 1.784 2.489 2.573 3.602
178.73 178.88 178.87 178.95 178.97
0.018 54 0.034 84 0.059 60 0.078 32 0.098 70 0.120 79 0.020 1 3 0.04041 0.063 50 0.084 40 0.102 54 0.120 6 1 0.142 87
- 1.155 -2.162 - 3.687 -4.822 - 6.048 -7.377
-0.817 - 1.287 - 1.711 - 2.07 6 - 2.436 - 2.881
228.41 228.44 228.60 228.60 228.64 228.74 235.94 236.16 236.29 236.38 236.43 236.47 236.54
0.018 03 0.030 8 9 0.058 73 0.079 46 0.098 89 0.121 72 0.140 10
-0.917 - 1.562 - 2.960 -3.970 - 4.907 -6.005 -6.860
304.31 304.26 304.50 304.46 304.46 304.54 304.49
KI
Et,NClO,
Et,NI
Pr,NCl
Pr,NBr
Bu,NBr
- 0.403
m/(mol kg-') KCIO,
0.006 44 0.007 24 0.020 59 0.029 4 1
103(d - d o ) 0.617 0.687 1.946 2.780
48.94 49.57 49.73 49.71
RbI
0.008 88 0.019 25 0.037 7 1 0.056 17
1.703 3.679 7.190 10.680
43.67 44.09 44.28 44.51
CSI
0.1161 0.021 05 0.029 9 1 0.040 02
2.775 5.020 7.122 9.518
50.40 50.66 50.81 50.91
Me,NClO,
0.009 1 2 0.019 93 0.032 54 0.049 76 0.072 74 0.092 14 0.112 38
2.299 4.975 8.060 12.374 17.704 22.224 26.858
127.17 127.31 127.41 127.30 127.61 127.71 127.82
Et,NCl
0.009 63 0.020 9 1 0.029 60 0.048 8 9 0.066 1 5 0.087 8 2 0.126 06
- 0.305 - 0.658 - 0.925 -1.518 - 2.046 -2.172 - 3.878
160.15 160.08 159.96 159.92 159.90 159.96 160.02
Et,NBr
0.019 14 0.051 26 0.064 27 0.083 35 0.102 35 0.114 37 0.142 1 5 0.158 46
0.240 0.636 0.793 1.014 1.233 1.364 1.672 1.852
166.43 166.48 166.51 166.60 166.65 166.71 166.78 166.81
i-Pen,NBr
0.019 1 6 0.039 42 0.061 84 0.079 36 0.101 3 1 0.139 76 0.216 3 1
- 1.569 - 3.202 -4.981 - 6.348 -8.025 -10.935 -16.346
372.91 372.95 373.02 373.06 373.04 373.28 373.10
NaPh,Br
0.018 70 0.039 99 0.059 28 0.079 1 8
0.098 0.201 0.294 0.386
281.62 281.73 281.76 281.79
Ph,AsCl
0.038 1 7 0.057 46 0.079 34
2.219 3.339 4.576
308.14 307.88 307.87
Ph,PBr
0.013 07 0.026 59 0.040 96
0.706 1.438 2.207
311.84 311.59 311.52
Ph,CH
0.018 82 0.037 9 1 0.056 58 0.009 33 0.012 66 0.023 35 0.044 83 0.072 26 0.108 50 0.202 21 0.300 20 0.390 80 0.688 36 0.988 70 1.814 9 0 3.000 50 3.725 60 4.420 00
@V
15.82 16.28 16.08 16.61 16.90 17.04 17.36 17.55
H2O
-0.687 -1.375 -2.040 - 0.043 -0.059 -0.117 - 0.221 -0.363 - 0.546 -1.003 -1.517 - 1.955 -3.334 -4.681 -8.021 -12.308 -14.715 - 16.643
@V
229.19 229.14 229.13 18.26 18.26 18.49 18.44 18.51 18.53 18.49 18.56 18.53 18.43 18.38 18.21 18.05 17.98 17.88
The Journal of Physical Chemistry, Vol. 86, No. 20, 1982 4001
Ionic Volumes of Electrolytes
TABLE IV (Continued) m/(mol kg-l) n-Pen,NBr
0.02007 0.06062 0.08217
103(d- d o ) - 1.660 -3.232 -6.634
TABLE V: Standard Partial Molar Volumes o f Electrolytes in PC at 25 'CQ solute Av solute VZ VZ
@V
ml(mo1 kg-')
373.50 373.66 373.67
0.095 17 0.11297 0.15476
AV
LiBr LiClO, N a1 NaClO, KI KC10, RbI CSI Me,NClO, Ph,AsCl NaPh,B Ph,PBr a
15.32 5.94 Et,NCl 159.85 0.38 36.77 2.93 Et,NBr 166.15 1.60 31.86 2.61 Et,NI 178.43 2.11 41.28 2.77 Et,NClO, 188.01 1.53 38.78 4.14 Pr,NCl 228.18 1.56 48.77 6.00 Pr,NBr 235.64 2.45 43.21 5.57 Bu,NBr 304.17 1.00 49.82 5.57 n-Pen,NBr 373.49 0.60 126.93 2.60 i-Pen,NBr 372.85 0.58 229.15 Ph3CH 307.96 18.52 -0.11 281.47 1.16 H,O 311.65 Parameters of eq 4 for @ vin cm3 mol-l and m in mol
kg- l .
Typical plots are shown in Figure 2, and parameters of eq 4
4v= V j + Avm'f2
(4)
are given in Table V. In general, the solubilities of the electrolyte are high enough to allow reasonable extrapolations from six to seven data points in the concentration region 0.01 to 0.15 mol kg-'. With Ph4AsCl and Ph4PBr only a few points could be obtained at low molalities and V? was taken as the average value. Some difficulties were also encountered with LiC104,NaI, and Pr4NC1where the viscosity of the solutions increased significantly with concentration. Association does not seem to be a major problem with these electrolytes since most plots of 4v are quite linear in m1f2. However, the higher slopes observed with some systems (e.g., LiBr, KC104)might suggest some association. Few literature data can be used for comparison with the present values. Dack et al.8 have measured 4v of NaI, KI, NaBPh4, Ph4AsC1,and Ph3CH at two concentrations only. These data generally agree with ours inside their claimed uncertainty of approximately 2 cm3 mol-'. The data by Gopal et al.9 and by Sing et al.1° were all at high temperatures. A better idea of the precision of the present V 2 can be obtained from the additivity principle. The differences between NaC104 and NaI, KC104, and KI, and Et4NC104 and Et4NI are respectively 9.40,9.99, and 9.58 cm3mol-'. Those between Et4NBr and Et4NC1and between Pr4NBr and Pr4NC1are respectively 6.3 and 7.4 cm3 mol-'. Some
103(d- d o ) -7.639 - 9.003 -12.172
@V
373.66 373.69 373.69
of these electrolytes were actually hard to study in view of their limited solubility (e.g., KC104) or hygroscopic character (e.g., R4NC1). Therefore, we are confident that the present V j values are accurate to better than 1 cm3 mol-' in most cases. The value of AVcannot be calculated since d In t / d P is not known. However, it has been shown18that this term can be approximated by the isothermal compressibility &, Using isentropic compressibilities, specific heats, and coefficients of thermal expansion from our laboratory or from the literature,' we obtained ,tlTas in previous studies.18 ~f~ The predicted value for Av is then 2.8 cm3 m ~ l - kg1I2, which is of the correct order of magnitude (see Table V). Utrasonic Vibration Potentials. Uvp measurements were performed at concentrations ranging from 1 X to 3 X M whenever the alkali metal iodides and perchlorates were sufficiently soluble. The values of the /~ between two points of the solution uvp c $ ~measured onehalf wavelength apart are listed in Table VI. The sign of the uvp was assigned as previously. These values show the usual behavior: very small, if any, dependence on concentration, and a regular increase of 4xf2with the cation molecular weight. This behavior is to be expected from the theory of uvp, and it has consistently been observed in our previous studies of electrolyte solutions in organic ~olvents.'~J~ Ionic Partial Molal Volumes in PC. The partial molar volumes of cations (V+O)and anions (V?) were calculated from the equations
V+O = t-OV+O (l/do)(t+'M+ - t-OM-) - 1O5&pO(O.2O75aUdo) (5) =
V j - v+o
(6) where u, the velocity of ultrasonic waves in the solvent, measured in this work, has been found to be 1.455 X lo5 cm s-', do is the density of the solvent (1.19966 g ~ m -see ~, above); t+O and t! = 1 - t+O are the transport numbers of the cation and anion at infinite dilution, M+ and M- are the molecular masses of the dry ions in g mol-', 41f2is expressed in microvolts, and a is the rms velocity amplitude in cm s-l of the solvent molecules in the ultrasonic field. At the frequency of 207 kHz at which the measurements were performed eq 3 is valid for solutions of 1-1 electrolytes in PC at concentrations C > 2 X M. This explains why the values of 4x12for the various salts in Table VI at C < 2 X M are slightly smaller than those M. The values of used in the calcuat C > 2 X V-0
TABLE VI: Values o f @A/* for 1-1 Electrolytes in PC at 207 kHz and 24 "C salt
c/(mol L-I)
LiI NaI
2 x 10-3
5 x 10-3
10-1
-120
-130 -109
-133.5 -110.5
-133.5 -111
- 88
-88.5 - 43
- 85 - 41
KI RbI CSI LiClO, NaClO, KClO, RbClO, CSC10, Values of heating at 220
10-3
-3 - 69 - 48 - 28 13 58
'8
-41.5 -2 - 69 -47.5 - 29.5 12.5 56.5
-2 -70.5 - 49 -31
adopted in the calculations of ionic partial molal volumes. overnight.
2X
lo-'
- 116 - 89 - 44
-70.5 - 50.5
3 X lo-' selected valueQ - 115
-70.5 - 52
- 133.5 - 112 -88.5
-42 -2 -70.5 -48.5 - 29.5 12.5 57
The sample of LiC10, has been dried by
4002
Zana et al.
The Journal of Physical Chemistty, Vol. 86,No. 20, 1982
TABLE VII: Partial ion
-
VO (ion) ion
-
Molar
Volumes (in cm3mol-') of Ions in PC at 25 "C
c1-
Br-
1-
c10, -
Li+
19.7a
26.3
38.3
47.gb
-11.lC
Et,N+
Pr,N+
Bu,N+
Me,N+
n-Pen,N+
N a+
K+
Rb+
-6.4'
0.5'
4.9'
11.5'
Ph,B-
Ph,P+
Ph,As+
i-Pen,"
CS'
V o(ion) 79.0 140.1 208.9 277.9 347.2 346.6 288.3 287.9 285.4 From p ( B r l - p (C1-)=-6.7 cm3 mol-'; p (I-) - p (C1-) = 18.6 cm3 mol-'; and (ClOJ (C1-) = 28.1 cm3 mol-'. From V o(ClO,-) - V" (I') = 9.6 om3 mol". From the V,O values for iodides, with VO (I-) = 38.3 cm3 mol-'.
vo
lation of the ionic partial molar volumes are those listed under the last column of Table VI and which usually correspond to concentrations close to 5 X M, i.e., where 4xj2should be constant, and where ionic association should still be negligible for the investigated salts. The values of t+O and t-O used in the calculations were those obtained from the Xo values in Table I1 (column "best estimate"), whereas the values of V20were those of Table V, or obtained by means of the additivity rule, when the solubility of the salt was too small for meaningful density mol kg-'). Thus, the measurements (solubility < following values were used: P(Li1) = 27.2 cm3 mol-'
I
a, ( x - )
I
vo
I
I
I
1
I
I
l
\>.+\*- ,y
P(RbC10,) = 52.8 cm3 mol-'
'*,
P(CsC104) = 59.4 cm3 mol-' The rms velocity amplitude a in PC solutions was not known and could not be directly measured with the available facilities. The same procedure as in previous studies was therefore used to determine a and the ionic partial molar volumes. u is then considered as a parameter, and for each anion X (I- or C104-) involved in a salt CiX, P(X)cix was calculated for values of u between 8 and 14 cm s-l, Le., above and below the probable effective value of a during the experiments. For the five salts involving the anion X, the values 5
( W X ) ) = CP(X)CiX/5 1
a v w = [ ( ( P ( X ) )- P(X)cix)/nl"2 were calculated as a function of a. The effective value of a was taken as that where the standard deviation av(X) goes through a minimum. Figure 3 shows that the av(X) for I- and C10, go through pronounced minima at a = 8.7 and 8.9 cm s-l, respectively, corresponding to P(I-) = 38.3 cm3mol-' and P(C10;) = 46.7 cm3mol-'. The difference V(C104-)- P(I-) = 8.4 cm3mol-' is in agreement with the average value 9.6 cm3, calculated from the V; data of Table V, within the experimental error of the uvp method ( f 2 cm3 mol-') and of the V20data (f0.5 cm3mol-'). The values of the partial molar volumes of all ions have been calculated from the V20data of Table V, using the value obtained by the uvp method for the iodide ion. The result for this ion was favored over that for C10, because iodide salts were generally much more soluble than perchlorate salts and thus the problem associated with the dissolution of water during the experiments was largely avoided. The values of P(ion) are listed in Table VII. The overall experimental error on these values is estimated to be f 2 cm3 mol-'. Discussion
Comparison of P ( i o n ) with Other Ionic Scales. The methods used to split Vo(ion)into its ionic components have been recently revie~ed.~'Here we shall consider the (31) B. E. Conway, J . Solution Chem., 7, 721 (1978).
I
6
1
I
8
IO
a (cm
I
12
s-l)
Figure 3. Variation of standard deviation of Po(I)and Po(CIO,-) for various MI and MCIO, electrolytes in propylene carbonate at 25 'C.
same four methods, based on various nonthermodynamic assumptions as in the study of ions in acet~nitrile.'~ (1) Mukerjee's method32yields a smooth curve on which fall all alkali metal and halide ions when using the value P ( I - ) = 36.8 cm3mol-'. This value agrees with that obtained from the uvp method within the experimental accuracy. The fact that Mukerjee's method holds in PC suggests that anions and cations of equal size exert the same electrostriction on the surrounding solvent molecules. This expectation will be confirmed below. (2) Millero's TATB method,33 which assumes that Po(Ph,As+)/P(Ph,B-) = 1.03371,yields P(I-) = 35.3 cm3 mol-', i.e., a value slightly outside the error range of the uvp value but still in reasonable agreement with this value. Note that the TATB method also yielded a value too small for the anion (Br-) partial molar volume in a~etonitri1e.l~ This suggests that the value of the ratio of the van der Waals volumes of Ph4As+and Ph4B- adopted by Millero may be slightly too large. (3) The extrapolation method34applied to the results of Table IV yields p ( I - ) = 17 or 22 cm3mol-' depending on whether the extrapolation includes or does not include the datum point corresponding to Me4N+. This scale would lead to the improbable situation where there would be a positive electrostriction for cations and a large negative one for anions. In any case, as for all nonaqueous solvents investigated thus far, and where VZodata were available for tetraalkylammonium salts, the V(anions) obtained by the extrapolation method are always much smaller than those from the uvp-density method. In fact, it has been clearly pointed out by the proponents of the method35why the extrapolation method is valid in water (32) P. Mukerjee, J . Phys. Chem., 65, 740 (1961). (33) F Millero. J. Phvs. Chem.. 75. 280 (1971). (34) B. E. Conway, R:E. V e n d ; and J. E: Desnoyers, Trans. Faraday SOC.,62, 2738 (1966).
Ionlc Volumes of Electrolytes
'6nx
The Journal of Physical Chemlstty, Vol. 86, No. 20, 1982 4003
