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Conductance of alkali metal perchlorates in propylene carbonate at 25°C
dC~L
ELSEVIER
O~
Journal of Electroanalytical Chemistry 403 (1996) 245-249
Short communication
Conductance of alkali metal perchlorates in propylene carbonate at 25°C Alessandro D'Aprano a,*, Mark Salomon b, Margherita Iammarino
a
a Department of Chemistry, La Sapienza University, P. le A.Moro, 5 00185 Rome, Italy b US Army ARL, Chemical/Biological Sciences Division, Fort Monmouth, NJ 07703, USA Received 24 May 1995; in revised form 8 August 1995
Keywords: Stokes hydrodynamic radii; Conductance; Alkali metal perchlorates; Propylene carbonate
1. Introduction In view of its high relative dielectric constant (about 64.9) and wide liquid range ( - 49°C to 242°C), the aprotic solvent propylene carbonate (PC) has become the principal solvent or co-solvent for use in rechargeable lithium batteries. However, problems such as the slow but continuous corrosion (reduction) of PC at lithium anodes and the relatively low conductance of solutions, principally because of the relatively high viscosity of PC (rl = 2.5 mPa s) still exist. To address these and related problems, the present authors have investigated the use of macrocyclic ligands to coordinate Li ÷ which, at least in PC solutions, often results in an increase in both solution conductivity and lithium ion transference number depending upon the nature of the macrocyclic ligand and the solvent [1,2]. In extending our studies to the determination of complex formation constants derived from conductivity data, the specificity for formation of complexes of the alkali metal cations with the "double-crown calixarene" calix[4]arenebis-crown-6 has been determined in the solvents methanol (MeOH), acetonitrile (AN) and PC [3]. In determining the conductivity parameters for these complex ternary systems (i.e. salt + ligand + solvent), the conductivity parameters for the binary systems (salt + solvent) are required. Where possible, the conductivity data for these binary systems have been taken directly from the literature, but where the literature data are not completely consistent we have reinvestigated those binary systems which appear conflicting
* The results presented in this paper will be included in the thesis to be presented by Margherita lammarino as required for partial fulfilment of requirements for the degree of Dottore di Ricerca in Scienze Chimiche. * Corresponding author. 0022-0728/96/$15.00 © 1996 Elsevier Science S.A. All rights reserved SSD1 0 0 2 2 - 0 7 2 8 ( 9 5 ) 0 4 3 10-1
[3]. A literature search revealed that, while the molar conductivities A 0 reported by different authors for the alkali perchlorates in MeOH [4-8] and AN [9-11] generally agree within 0.05%, the values in PC [12-17] are not consistent and in some cases differ by more than 4.5%. While there is general agreement that values of the ion pair formation constants in PC are small, significant differences exist based, in part, upon the conductivity equation used in the analyses. In view of the extensive use of PC in the development of lithium batteries and in order to have a self-consistent set of conductivity data in PC for reference for general solvation studies of electrolytes in this solvent, we have reinvestigated the conductivity behavior of the alkali metal perchlorates and explored several models based on the Fuoss equations for analyses of these data.
2. Experimental 2.1. Chemicals
Propylene carbonate (Fluka, "puriss" grade), with a water content less than 0.002% as determined by Karl Fischer titration, was used without further purification. The relevant physical properties of this solvent, measured using the techniques described below, are in agreement with literature values within the limits of experimental error (Table 1). Reagent grade perchlorates were recrystallized three times from water + methanol mixtures (1:1 by volume) and dried by heating under vacuum at 150°C. The dried salts were stored in a dessicator over phosphorus pentoxide.
246
A. D'Aprano et al./Journal of Electroanalytical Chemistry 403 (1996) 245-249
Table 1 Physical properties of PC at 25°C
Table 2 Conductance of alkali perchlorate in PC at 25°C
d o g cm - 3
17 mPa s
e
107 K0 S cm - l
Ref.
104c/mol dm -3 A / S cm 2 mol- i 104c/mol d m - 3 A / S cm 2 mol- i
1.2001 1.1998 1.1989 1.1987 1.1993 1.1996 1.1999 -1.1998
2.511 2.513 2.508 2.553 2.513 2.512 2.519 2.480 2.53
64.4 64.9 65.4 65.1 64.9 64.95 65.4 64.4 64.97
1.I 0.9 0.3 2.0 0.3 --0.2 --
This work [12] [ 13] [ 19] [14] [18] [15,20] [ 16] [21]
LiCIO 4 14.111 22.469 41.947 68.514 93.997 117.39 154.43
25.614 25.320 24.788 24.373 24.026 23.690 23.280
KCIO4 16.260 23.963 39.098 60.169 83.887 109.75 132.72 161.33
28.720 28.476 28.068 27.573 27.115 26.708 26.397 26.071
CsClO4 12.693 26.003 40.686 60.247 79.985 101.89 119.57 138.67 156.62
30.210 29.728 29.292 28.824 28.438 28.039 27.756 27.470 27.232
2.2. Apparatus and procedure Densities were measured with a digital density meter (PAAR, DMA 6 0 / 6 0 2 ) thermostated at 25.000 + 0.002°C with a Heto PT-CBII temperature controller. The instrument was calibrated using water and acetone [22]. Dielectric constants were measured at 1 MHz using a Boonton Corporation bridge (model 75D) and a stainless steel cell [23]. Complete descriptions of the apparatus, general techniques and cell calibration are described elsewhere [24]. Viscosities were measured in an automated Schott viscometer (model AVS 440) at 25 + 0.02°C. Conductance runs were carried out using a weight-titration method [1], and measurements were determined with an accuracy of + 0.05% using a Wayne Kerr model 6425 precision component analyzer. The electrical resistances of solutions, measured at 1, 2, 5 and 10 kHz, were extrapolated to infinite frequency for the usual correction. A Fuoss-Chiu type conductance cell [25] of volume about 100 ml was used. The cell constant K c = 1.24894+ 0.00002 cm-J was determined with KCi aqueous solutions according to the method described by Lind et al. [26]. The temperature of the cell was maintained at 25 +_ 0.002°C in an oil thermostat volume of 120 1.
3. Results and calculations Molar conductivities A/S cm 2 mol-~ were calculated from the electrolytic specific conductances K after correcting for the pure solvent conductance K0 using the relation A = 1000 ( K - K 0 ) / C M x , where CMX is the total salt molar concentration. A summary of the conductance results is given in Table 2. Data analysis was carried out with the Fuoss 1980 (F80) [27-30] and the Fuoss-Hsia (FH) conductance equations [31] using the expansion developed by Femandez-Prini and Justice [32] without (FI-IJP) and with (FHJPC) the inclusion of the Chen effect [33]. Details of these equations and of the computer programs used to find the best values of A 0, the molar conductivity at infinite dilution K a, the ion
NaClO4 13.801 24.301 39.076 55.751 70.216 87.117 108.645 128.74 147.96
26.985 26.650 26.253 25.908 25.640 25.387 25.082 24.827 24.629
RbCIO4 13.448 26.862 39.858 60.515 80.196 99.860 120.29 139.26 158.88
29.624 29.101 28.763 28.283 27.894 27.550 27.232 26.950 26.713
pair association constant and the association distance R are given in Refs. [34] and [35]. The results of these analyses are given in Table 3.
Table 3 Conductance parameters for alkali perchlorates in PC at 25°C Electrolyte
Equation
A 0 / S cm 2 mol- i
Ka / d m 3 mol- t
R/,~
100 (tr/Ao)
LiCIO4
F80 FHJP FHJPC
26.73+0.03 26.734-0.03 26.72 4- 0.03
5.14-0.1 0 1.0 + 0.3
1 4 + _ 2 0.02 5.89 0.03 6.24 0.03
NaCIO4
F80 FHJP FHJPC
28.16+0.02 28.17+0.01 28.17+0.01
4.65:0.4 0.6-t-0.2 1.74-0.2
10+2 5.66 5.68
0.01 0.01 0.01
KCIO4
F80 FHJP FHJPC
30.074-0.04 30.08 4- 0.02 30.08+0.02
5.3 +0.7 1.5 4- 03 2.64-0.3
11 4-3 5.53 5.59
0.02 0.02 0.02
RbC104
F80 FHJP FHJPC
30.834-0.02 30.864-0.01 30.854-0.01
6.1 4-0.2 1.64-0.1 2.74-0.1
134- 1 6.06 6.08
0.01 0.01 0.01
CsCIO4
F80 FHJP FHJPC
31.41 +0.02 31.434-0.01 31.42 _+0.01
6.5 4-0.2 1.55:0.2 2.5 4- 0.2
144- 1 6.52 6.68
0.01 0.01 0.01
A. D'Aprano et al./ Journal of Electroanalytical Chemistry 403 (1996) 245-249 Table 4 I n f i n i t e d i l u t i o n m o l a r c o n d u c t i v i t i e s for the alkali m e t a l p e r c h l o r a t e s in
PC at 25°C Salt
A 0/S
cm 2 mol- l
This
Ref.
Ref.
Ref.
Ref.
Refs.
work
[12]
[13]
[141
[15]
[16,17]
LiCIO 4
26.73
27.35
--
27.33
26.75
26.08
NaCIO 4
28.17
--
28.23
27.89
--
--
KCIO 4
31).08
--
30.31
29.64
--
30.75
RbCIO 4
30.85
--
--
30.34
--
--
CsC104
31.42
--
--
31.10
--
--
4. Discussion
Inspection of Table 3 shows that, while the limiting equivalent conductances calculated for each electrolyte do not depend upon the conductivity equation used to analyze the primary. (c, A) data, specific differences are found for Ka and R which are related to the models upon which the F80 and the FH equations are based. In fact, depending on the model, the physical meanings of these quantities are quite different. In the F80 equation K~ and R are respectively the association constant for solvent-separated ion pairs and the closest approach distance between the Gurney co-spheres surrounding the counter-ions, whereas in both the FHJP and FHJPC equations K a is the association constant for contact ion pairs and R, as formulated originally by Justice [36], can be equated to the shortest distance between counter-ions which normally does not exceed the Bjerrum distance q (see Refs. [15,18,21,37] for details). Thus, while extrapolations to infinite dilution generally yield almost identical A 0 values in both methods, the differences in the formulation of the distance parameter will yield slightly different values for R and hence K~. Where comparisons are available, the present results for these parameters are in general agreement with literature values. For example for LiCIO 4 in PC and using the FHJP equation, Barthel et al. [15] and Ue [12] report values of K~ of 0.9 dm 3 mol-~ and 2.8 dm 3 molrespectively, which agree with our values given in Table 3. Our results for NaC10 4 and KC10 4 (Table 3) are also in moderate to very good agreement with those of Hanna and Al-Sudani [13] who report K~ values of around 1.0 dm 3
247
mol-1 and 6.0 dm 3 mol-1 respectively for NaC104 and KC104. On the other hand, Mukherjee and coworkers [16,17] employed the Fuoss-Onsager equation which includes the viscosity factor F (they cite Ref. [38]), and Jansen and Yeager [14] used a similar equation but included the C3/2 term and also cite Ref. [38]: Mukherjee and coworkers report no ion association, whereas Jansen and Yeager report negative or zero values for K a for LiC104, NaC104 and KCIO4. While the K~ values calculated from F80 are generally higher than those obtained using the FHJP method (see Table 3), both approaches now yield a consistent set of K a values for the alkali metal perchlorates in PC. Analysis of Table 4 reveals that our A 0 values for LiCIO 4 and NaCIO 4 are in good agreement with the values reported by Barthel et al. [15] and by Hanna and Al-Sudani [13] for these electrolytes, whereas the other literature data are scattered within - 0 . 6 8 and +0.65 S cm 2 mol -~ compared with the present values. These discrepancies can be attributed partially to the small differences in the physical properties of the solvent used (see Table 1), the purity and dryness of the salts, and differences in the method of calculation as discussed above. The transference number of K ÷ in KCIO 4 solution in PC has been determined accurately by Zana et al. [39]. Combining their result (t+(KCIO 4) = 0.3846) with our A 0 values, the limiting ionic conductances h~ of the alkali metal cations in PC have been calculated and the results are summarized in Table 5. Literature h~- values, which include the "best estimates" given in Ref. [39], are included in Table 5. A perusal of Table 5 reveals that only for Li ÷ and K + do our values agree with those reported in Ref. [39], and significant differences (up to 3.7%) can be observed for the other alkali cations. Such discrepancies can be explained by considering the procedure used by Zana et al. [39] to obtain their best estimate of the ionic conductances. Despite the accuracy of their potassium transference number measurements, the unreliability of the conductance data of alkali perchlorates in PC available at that time forced the authors to combine their transference number (t~_(Et4NCIO 4) = 0.4170) measured in Et4NCIO 4 solution with Jansen and Yeager's [14] value for A0(Et4NCIO 4) to obtain the ionic conductance of the
Table 5 I n f i n i t e dilution s i n g l e - i o n m o l a r c o n d u c t i v i t i e s in P C at 2 5 ° C Ion
Ao/S
cm 2 mol- t
This work
R e f s . [12,40]
R e f s . [13]
R e f . [15]
R e f s . [16,17]
8.22
8.81 a
8.89
8.24 b
Na +
9.66
9.04
9.72
9.45
--
--
K÷
11.57
10.68
11.80
11.17
--
11.97
11.52
Rb +
12.34
11.38
--
11.90
--
--
11.91
Cs*
12.91
12.17
--
12.66
--
--
CIO 4
18.51
18.93 a
__
18.44
D a t a f r o m R e f . [12], r e m a i n i n g d a t a in this c o l u m n f r o m R e f . [40].
b B a s e d on A ° f r o m R e f . [15] a n d A ° ( C 1 0 2 ) f r o m p r e s e n t a n a l y s e s .
7.28
R e f . [39]
Li ÷
a
__
R e f . [14]
8.32 9.46
12.67 18.43
248
A. D'Aprano et al./ Journal of Electroanalytical Chemistry 403 (1996) 245-249
Table 6 Stokes radii for alkali metal cations in PC at 25°C a
Ion
Rc/A.
Li + Na + K+ Rb + CS +
Rs/A
0.60 0.95 1.33 1.48 1.69
This work
Ref. [12]
Ref. [13]
Ref. [14]
Ref. [15]
Refs. [16,17]
3.98 3.39 2.83 2.65 2.52
3.71 -----
-3.36 2.77 ---
3.70 3.49 2.94 2.76 2.59
3.96 -----
4.32 -2.67 ---
derive the value for h0(Li+). In view of these considerations, we conclude that the agreement between the best estimates of individual ionic conductances for K ÷ and Li + from Zana et al. [39] and our values obtained directly from t °+(KC104) and A0(KC104) data is indicative of the reliability of the present results and analyses. Data from Table 5 have been used to calculate the Stokes hydrodynamic radii using the equation [41] R s = F2/67-rrlNho +
a R¢ is the Pauling radius.
perchlorate ion (A0(CIO~-)= 18.43 S cm 2 mol-1). Based on this value, the single-ion conductances for the remaining ions, except for Li +, were derived using the conductance data of Jansen and Yeager. When such a procedure is applied to K + ion there is a discrepancy of the order of 2% between the experimental transference number (t+ (KCIO 4) = 0.3846) and that calculated as t % [ A o ( K + ) / A o ( K C I 0 4 ) = 0.3768. Thus, assuming the reliability of their transference number measurements, the authors preferred to report, as their best estimate, a value for A0(K+) calculated from
The results are summarized in Table 6 together with the Pauling radii R c. Fig. 1 shows a plot of R s versus R e. An inspection of the figure reveals that, in agreement with the solvation effect, our data lie on a smooth curve that regularly decreases passing from lithium to cesium. Differences between our data and those calculated from the literature conductance data are also shown in the figure.
Acknowledgment
Financial support by M.U.R.S.T. (Ministero dell'Universith e della Ricerca Scientifica e Tecnologica) under grant "Ricerca Ateneo" is gratefully acknowledged.
A0(K + ) = A0(C10 ~-) / [ t°+ (KCIO4)/t °_ (KC104) ] =11.52 S cm 2 mo1-1 which is independent of the KC10 4 conductance. As far as the Li + ion is concerned, Zana et al. [39] rejected Jansen and Yeager's [14] value for A°(LiC104) and instead used the precise conductance results of Barthel et al. [15] to 4.50
'
'
'
'
l
'
r
'
'
l
'
'
~
'
l
. . . .
I
'
'
'
'
1
'
'
'
'
O
R/B, 3.50
3.00
2.50 0.55
0.75
0.95
1.15 R¢ / $
1.35
1.55
1.75
Fig. 1. Stokes hydrodynamic radii of alkali ions in propylene carbonate at 25°C versus Panling radii: [] this work; O Ref. [12]; O Ref. [13]; zx Ref.
[14]; • Ref. [151; • Refs. [16,17].
References [1] A. D'Aprano, M. Salomon and V. Mauro, J. Solution Chem., 24 (1995) 685. [2] A.F. Danil de Namor, M.A. Liosa Tanco, J.C.Y. Ng and M. Salomon, Pure Appl. Chem., in press. [3] A. D'Aprano, J. Vicens, Z. Asfari, M. Salomon and M. Iammarino, to be published. [4] A. D'Aprano, J. Phys. Chem., 76 (1972) 2920. [5] F. Accascina and G. Craia, Sci. Tec., 3 (1959) I1. [6] J.E. Pine and P.J. Sherrington, Trans. Faraday Soc., 57 (1961) 1795. [7] F. Accascina and G. Craia, Sci. Tec., 3 (1959) 203. [8] F. Conti and G. Pistoia, J. Phys. Chem., 72 (1968) 2245. [9] F. Accascina and S. Schiavo, Ric. Sci., 7 (1966) 556. [10] R.L. Kay, B.J. Hales and G.P. Cunningham, J. Phys. Chem., 71 (1967) 3925. [11] C.H. Springer, J.F. Cotzee and R.L. Kay, J. Phys. Chem., 73 (1969) 471. [12] M. Ue, J. Electrochem. Soc., 141 (1994) 3336. [13] E.M. Hanna and K. AI-Sudani, J. Solution Chem., 16 (1987) 155. [14] M.L. Jansen and H.L. Yeager, J. Phys. Chem., 77 (1973) 3089, 78 (1974) 1380. [15] J. Barthel, R. Wachter and H.-J. Gores, Faraday Discuss. Chem. Soc., 64 (1978) 285. [16] L.M. Mukherjee and D.P. Boden, J. Phys. Chem., 73 (1969) 3965. [17] L.M. Mukherjee, D.P. Boden and R. Lindauer, J. Phys. Chem., 74 (1970) 1942. [18] J. Barthel, H.-J. Gores, G. Schmeer and R. Wachter, Top. Curr. Chem., I l l (1982) 33. [19] R.M. Fuoss and E. Hirsch, J. Am. Chem. Soc., 82 (1960) 1013. [20] J. Barthel, H.J. Gores, P. Carlier, F. Feuerlein and M. Utz, Ber. Bunsenges. Phys. Chem., 87 (1983) 436. [21] J. Barthel, R. Wachter and H.-J. Gores in B.E. Conway and J. O'M. Bockris (Eds.), Modem Aspects of Electrochemistry, Vol. 13, Plenum Press, New York, 1979.
A. D'Aprano et al./Journal of Electroanalytical Chemistry 403 (1996) 245-249 [22] Handbook of Chemistry and Physics, CRC Press, Boca Raton, FL, 1985. [23] J.E. Lind Jr. and R.M. Fuoss, J. Phys. Chem., 65 (1961) 999. [24] A. D'Aprano, I.D. Donato and E. Caponetti, J. Solution Chem., 8 (1979) 135. [25] Y.-C. Chiu and R.M. Fuoss, J. Phys. Chem., 72 (1968) 4123. [26] J.E. Lind, J.J. Zwolenick and R.M. Fuoss, J. Am. Chem. Soc., 81 (1959) 1557. [27] R.M. Fuoss, Proc. Natl. Acad. Sci. USA, 77 (1980) 34. [28] R.M. Fuoss, J. Phys. Chem., 79 (1975) 525. [29] R.M. Fuoss, J. Phys. Chem., 82 (1978) 2427. [30] R.M. Fuoss, J. Solution Chem., 15 (1986) 231. [31] R.M. Fuoss and K.-L. Hsia, Proc. Natl. Acad. Sci. USA 57 (1967) 1550. [32] R. Fem~indez-Prini and J.-C. Justice, Pure Appl. Chem., 56 (1984) 541. [33] M.S. Chen, Ph.D. Thesis, Yale University, 1969.
249
[34] A. D'Aprano, F. Accascina and R.M. Fuoss, J. Solution Chem., 19 (1990) 65. [35] M. Salomon and E.J. Plichta, Electrochim. Acta, 28 (1983) 1681. [36] J.-C. Justice, J. Phys. Chem., 65 (1968) 353, Electrochim. Acta, 16 (1971) 701. [37] J.-C. Justice in B.E. Conway, J.O'M. Bockris and E. Yeager (Eds.), Comprehensive Treatise of Electrochemistry, Vol. 5, Plenum Press, New York, 1983, Ch. 3. [38] R.M. Fuoss and F. Accascina, Electrolytic Conductance, Interscience, New York, 1959. [39] R. Zana, J.E. Desnoyers, G. Perron, R. Kay and K. Lee, J. Phys. Chem., 86 (1982) 3996. [40] I.P. Safonova, B.K. Patsatsiya and A.M. Kolker, Russ. J. Phys. Chem. (Engl. Transl.), 68 (1994) 232. [41] R.A. Robinson and R.H. Stokes in Electrolyte Solutions (2nd revised ed.), Butterworths, London, 1965, p. 44.
ELSEVIER
O~
Journal of Electroanalytical Chemistry 403 (1996) 245-249
Short communication
Conductance of alkali metal perchlorates in propylene carbonate at 25°C Alessandro D'Aprano a,*, Mark Salomon b, Margherita Iammarino
a
a Department of Chemistry, La Sapienza University, P. le A.Moro, 5 00185 Rome, Italy b US Army ARL, Chemical/Biological Sciences Division, Fort Monmouth, NJ 07703, USA Received 24 May 1995; in revised form 8 August 1995
Keywords: Stokes hydrodynamic radii; Conductance; Alkali metal perchlorates; Propylene carbonate
1. Introduction In view of its high relative dielectric constant (about 64.9) and wide liquid range ( - 49°C to 242°C), the aprotic solvent propylene carbonate (PC) has become the principal solvent or co-solvent for use in rechargeable lithium batteries. However, problems such as the slow but continuous corrosion (reduction) of PC at lithium anodes and the relatively low conductance of solutions, principally because of the relatively high viscosity of PC (rl = 2.5 mPa s) still exist. To address these and related problems, the present authors have investigated the use of macrocyclic ligands to coordinate Li ÷ which, at least in PC solutions, often results in an increase in both solution conductivity and lithium ion transference number depending upon the nature of the macrocyclic ligand and the solvent [1,2]. In extending our studies to the determination of complex formation constants derived from conductivity data, the specificity for formation of complexes of the alkali metal cations with the "double-crown calixarene" calix[4]arenebis-crown-6 has been determined in the solvents methanol (MeOH), acetonitrile (AN) and PC [3]. In determining the conductivity parameters for these complex ternary systems (i.e. salt + ligand + solvent), the conductivity parameters for the binary systems (salt + solvent) are required. Where possible, the conductivity data for these binary systems have been taken directly from the literature, but where the literature data are not completely consistent we have reinvestigated those binary systems which appear conflicting
* The results presented in this paper will be included in the thesis to be presented by Margherita lammarino as required for partial fulfilment of requirements for the degree of Dottore di Ricerca in Scienze Chimiche. * Corresponding author. 0022-0728/96/$15.00 © 1996 Elsevier Science S.A. All rights reserved SSD1 0 0 2 2 - 0 7 2 8 ( 9 5 ) 0 4 3 10-1
[3]. A literature search revealed that, while the molar conductivities A 0 reported by different authors for the alkali perchlorates in MeOH [4-8] and AN [9-11] generally agree within 0.05%, the values in PC [12-17] are not consistent and in some cases differ by more than 4.5%. While there is general agreement that values of the ion pair formation constants in PC are small, significant differences exist based, in part, upon the conductivity equation used in the analyses. In view of the extensive use of PC in the development of lithium batteries and in order to have a self-consistent set of conductivity data in PC for reference for general solvation studies of electrolytes in this solvent, we have reinvestigated the conductivity behavior of the alkali metal perchlorates and explored several models based on the Fuoss equations for analyses of these data.
2. Experimental 2.1. Chemicals
Propylene carbonate (Fluka, "puriss" grade), with a water content less than 0.002% as determined by Karl Fischer titration, was used without further purification. The relevant physical properties of this solvent, measured using the techniques described below, are in agreement with literature values within the limits of experimental error (Table 1). Reagent grade perchlorates were recrystallized three times from water + methanol mixtures (1:1 by volume) and dried by heating under vacuum at 150°C. The dried salts were stored in a dessicator over phosphorus pentoxide.
246
A. D'Aprano et al./Journal of Electroanalytical Chemistry 403 (1996) 245-249
Table 1 Physical properties of PC at 25°C
Table 2 Conductance of alkali perchlorate in PC at 25°C
d o g cm - 3
17 mPa s
e
107 K0 S cm - l
Ref.
104c/mol dm -3 A / S cm 2 mol- i 104c/mol d m - 3 A / S cm 2 mol- i
1.2001 1.1998 1.1989 1.1987 1.1993 1.1996 1.1999 -1.1998
2.511 2.513 2.508 2.553 2.513 2.512 2.519 2.480 2.53
64.4 64.9 65.4 65.1 64.9 64.95 65.4 64.4 64.97
1.I 0.9 0.3 2.0 0.3 --0.2 --
This work [12] [ 13] [ 19] [14] [18] [15,20] [ 16] [21]
LiCIO 4 14.111 22.469 41.947 68.514 93.997 117.39 154.43
25.614 25.320 24.788 24.373 24.026 23.690 23.280
KCIO4 16.260 23.963 39.098 60.169 83.887 109.75 132.72 161.33
28.720 28.476 28.068 27.573 27.115 26.708 26.397 26.071
CsClO4 12.693 26.003 40.686 60.247 79.985 101.89 119.57 138.67 156.62
30.210 29.728 29.292 28.824 28.438 28.039 27.756 27.470 27.232
2.2. Apparatus and procedure Densities were measured with a digital density meter (PAAR, DMA 6 0 / 6 0 2 ) thermostated at 25.000 + 0.002°C with a Heto PT-CBII temperature controller. The instrument was calibrated using water and acetone [22]. Dielectric constants were measured at 1 MHz using a Boonton Corporation bridge (model 75D) and a stainless steel cell [23]. Complete descriptions of the apparatus, general techniques and cell calibration are described elsewhere [24]. Viscosities were measured in an automated Schott viscometer (model AVS 440) at 25 + 0.02°C. Conductance runs were carried out using a weight-titration method [1], and measurements were determined with an accuracy of + 0.05% using a Wayne Kerr model 6425 precision component analyzer. The electrical resistances of solutions, measured at 1, 2, 5 and 10 kHz, were extrapolated to infinite frequency for the usual correction. A Fuoss-Chiu type conductance cell [25] of volume about 100 ml was used. The cell constant K c = 1.24894+ 0.00002 cm-J was determined with KCi aqueous solutions according to the method described by Lind et al. [26]. The temperature of the cell was maintained at 25 +_ 0.002°C in an oil thermostat volume of 120 1.
3. Results and calculations Molar conductivities A/S cm 2 mol-~ were calculated from the electrolytic specific conductances K after correcting for the pure solvent conductance K0 using the relation A = 1000 ( K - K 0 ) / C M x , where CMX is the total salt molar concentration. A summary of the conductance results is given in Table 2. Data analysis was carried out with the Fuoss 1980 (F80) [27-30] and the Fuoss-Hsia (FH) conductance equations [31] using the expansion developed by Femandez-Prini and Justice [32] without (FI-IJP) and with (FHJPC) the inclusion of the Chen effect [33]. Details of these equations and of the computer programs used to find the best values of A 0, the molar conductivity at infinite dilution K a, the ion
NaClO4 13.801 24.301 39.076 55.751 70.216 87.117 108.645 128.74 147.96
26.985 26.650 26.253 25.908 25.640 25.387 25.082 24.827 24.629
RbCIO4 13.448 26.862 39.858 60.515 80.196 99.860 120.29 139.26 158.88
29.624 29.101 28.763 28.283 27.894 27.550 27.232 26.950 26.713
pair association constant and the association distance R are given in Refs. [34] and [35]. The results of these analyses are given in Table 3.
Table 3 Conductance parameters for alkali perchlorates in PC at 25°C Electrolyte
Equation
A 0 / S cm 2 mol- i
Ka / d m 3 mol- t
R/,~
100 (tr/Ao)
LiCIO4
F80 FHJP FHJPC
26.73+0.03 26.734-0.03 26.72 4- 0.03
5.14-0.1 0 1.0 + 0.3
1 4 + _ 2 0.02 5.89 0.03 6.24 0.03
NaCIO4
F80 FHJP FHJPC
28.16+0.02 28.17+0.01 28.17+0.01
4.65:0.4 0.6-t-0.2 1.74-0.2
10+2 5.66 5.68
0.01 0.01 0.01
KCIO4
F80 FHJP FHJPC
30.074-0.04 30.08 4- 0.02 30.08+0.02
5.3 +0.7 1.5 4- 03 2.64-0.3
11 4-3 5.53 5.59
0.02 0.02 0.02
RbC104
F80 FHJP FHJPC
30.834-0.02 30.864-0.01 30.854-0.01
6.1 4-0.2 1.64-0.1 2.74-0.1
134- 1 6.06 6.08
0.01 0.01 0.01
CsCIO4
F80 FHJP FHJPC
31.41 +0.02 31.434-0.01 31.42 _+0.01
6.5 4-0.2 1.55:0.2 2.5 4- 0.2
144- 1 6.52 6.68
0.01 0.01 0.01
A. D'Aprano et al./ Journal of Electroanalytical Chemistry 403 (1996) 245-249 Table 4 I n f i n i t e d i l u t i o n m o l a r c o n d u c t i v i t i e s for the alkali m e t a l p e r c h l o r a t e s in
PC at 25°C Salt
A 0/S
cm 2 mol- l
This
Ref.
Ref.
Ref.
Ref.
Refs.
work
[12]
[13]
[141
[15]
[16,17]
LiCIO 4
26.73
27.35
--
27.33
26.75
26.08
NaCIO 4
28.17
--
28.23
27.89
--
--
KCIO 4
31).08
--
30.31
29.64
--
30.75
RbCIO 4
30.85
--
--
30.34
--
--
CsC104
31.42
--
--
31.10
--
--
4. Discussion
Inspection of Table 3 shows that, while the limiting equivalent conductances calculated for each electrolyte do not depend upon the conductivity equation used to analyze the primary. (c, A) data, specific differences are found for Ka and R which are related to the models upon which the F80 and the FH equations are based. In fact, depending on the model, the physical meanings of these quantities are quite different. In the F80 equation K~ and R are respectively the association constant for solvent-separated ion pairs and the closest approach distance between the Gurney co-spheres surrounding the counter-ions, whereas in both the FHJP and FHJPC equations K a is the association constant for contact ion pairs and R, as formulated originally by Justice [36], can be equated to the shortest distance between counter-ions which normally does not exceed the Bjerrum distance q (see Refs. [15,18,21,37] for details). Thus, while extrapolations to infinite dilution generally yield almost identical A 0 values in both methods, the differences in the formulation of the distance parameter will yield slightly different values for R and hence K~. Where comparisons are available, the present results for these parameters are in general agreement with literature values. For example for LiCIO 4 in PC and using the FHJP equation, Barthel et al. [15] and Ue [12] report values of K~ of 0.9 dm 3 mol-~ and 2.8 dm 3 molrespectively, which agree with our values given in Table 3. Our results for NaC10 4 and KC10 4 (Table 3) are also in moderate to very good agreement with those of Hanna and Al-Sudani [13] who report K~ values of around 1.0 dm 3
247
mol-1 and 6.0 dm 3 mol-1 respectively for NaC104 and KC104. On the other hand, Mukherjee and coworkers [16,17] employed the Fuoss-Onsager equation which includes the viscosity factor F (they cite Ref. [38]), and Jansen and Yeager [14] used a similar equation but included the C3/2 term and also cite Ref. [38]: Mukherjee and coworkers report no ion association, whereas Jansen and Yeager report negative or zero values for K a for LiC104, NaC104 and KCIO4. While the K~ values calculated from F80 are generally higher than those obtained using the FHJP method (see Table 3), both approaches now yield a consistent set of K a values for the alkali metal perchlorates in PC. Analysis of Table 4 reveals that our A 0 values for LiCIO 4 and NaCIO 4 are in good agreement with the values reported by Barthel et al. [15] and by Hanna and Al-Sudani [13] for these electrolytes, whereas the other literature data are scattered within - 0 . 6 8 and +0.65 S cm 2 mol -~ compared with the present values. These discrepancies can be attributed partially to the small differences in the physical properties of the solvent used (see Table 1), the purity and dryness of the salts, and differences in the method of calculation as discussed above. The transference number of K ÷ in KCIO 4 solution in PC has been determined accurately by Zana et al. [39]. Combining their result (t+(KCIO 4) = 0.3846) with our A 0 values, the limiting ionic conductances h~ of the alkali metal cations in PC have been calculated and the results are summarized in Table 5. Literature h~- values, which include the "best estimates" given in Ref. [39], are included in Table 5. A perusal of Table 5 reveals that only for Li ÷ and K + do our values agree with those reported in Ref. [39], and significant differences (up to 3.7%) can be observed for the other alkali cations. Such discrepancies can be explained by considering the procedure used by Zana et al. [39] to obtain their best estimate of the ionic conductances. Despite the accuracy of their potassium transference number measurements, the unreliability of the conductance data of alkali perchlorates in PC available at that time forced the authors to combine their transference number (t~_(Et4NCIO 4) = 0.4170) measured in Et4NCIO 4 solution with Jansen and Yeager's [14] value for A0(Et4NCIO 4) to obtain the ionic conductance of the
Table 5 I n f i n i t e dilution s i n g l e - i o n m o l a r c o n d u c t i v i t i e s in P C at 2 5 ° C Ion
Ao/S
cm 2 mol- t
This work
R e f s . [12,40]
R e f s . [13]
R e f . [15]
R e f s . [16,17]
8.22
8.81 a
8.89
8.24 b
Na +
9.66
9.04
9.72
9.45
--
--
K÷
11.57
10.68
11.80
11.17
--
11.97
11.52
Rb +
12.34
11.38
--
11.90
--
--
11.91
Cs*
12.91
12.17
--
12.66
--
--
CIO 4
18.51
18.93 a
__
18.44
D a t a f r o m R e f . [12], r e m a i n i n g d a t a in this c o l u m n f r o m R e f . [40].
b B a s e d on A ° f r o m R e f . [15] a n d A ° ( C 1 0 2 ) f r o m p r e s e n t a n a l y s e s .
7.28
R e f . [39]
Li ÷
a
__
R e f . [14]
8.32 9.46
12.67 18.43
248
A. D'Aprano et al./ Journal of Electroanalytical Chemistry 403 (1996) 245-249
Table 6 Stokes radii for alkali metal cations in PC at 25°C a
Ion
Rc/A.
Li + Na + K+ Rb + CS +
Rs/A
0.60 0.95 1.33 1.48 1.69
This work
Ref. [12]
Ref. [13]
Ref. [14]
Ref. [15]
Refs. [16,17]
3.98 3.39 2.83 2.65 2.52
3.71 -----
-3.36 2.77 ---
3.70 3.49 2.94 2.76 2.59
3.96 -----
4.32 -2.67 ---
derive the value for h0(Li+). In view of these considerations, we conclude that the agreement between the best estimates of individual ionic conductances for K ÷ and Li + from Zana et al. [39] and our values obtained directly from t °+(KC104) and A0(KC104) data is indicative of the reliability of the present results and analyses. Data from Table 5 have been used to calculate the Stokes hydrodynamic radii using the equation [41] R s = F2/67-rrlNho +
a R¢ is the Pauling radius.
perchlorate ion (A0(CIO~-)= 18.43 S cm 2 mol-1). Based on this value, the single-ion conductances for the remaining ions, except for Li +, were derived using the conductance data of Jansen and Yeager. When such a procedure is applied to K + ion there is a discrepancy of the order of 2% between the experimental transference number (t+ (KCIO 4) = 0.3846) and that calculated as t % [ A o ( K + ) / A o ( K C I 0 4 ) = 0.3768. Thus, assuming the reliability of their transference number measurements, the authors preferred to report, as their best estimate, a value for A0(K+) calculated from
The results are summarized in Table 6 together with the Pauling radii R c. Fig. 1 shows a plot of R s versus R e. An inspection of the figure reveals that, in agreement with the solvation effect, our data lie on a smooth curve that regularly decreases passing from lithium to cesium. Differences between our data and those calculated from the literature conductance data are also shown in the figure.
Acknowledgment
Financial support by M.U.R.S.T. (Ministero dell'Universith e della Ricerca Scientifica e Tecnologica) under grant "Ricerca Ateneo" is gratefully acknowledged.
A0(K + ) = A0(C10 ~-) / [ t°+ (KCIO4)/t °_ (KC104) ] =11.52 S cm 2 mo1-1 which is independent of the KC10 4 conductance. As far as the Li + ion is concerned, Zana et al. [39] rejected Jansen and Yeager's [14] value for A°(LiC104) and instead used the precise conductance results of Barthel et al. [15] to 4.50
'
'
'
'
l
'
r
'
'
l
'
'
~
'
l
. . . .
I
'
'
'
'
1
'
'
'
'
O
R/B, 3.50
3.00
2.50 0.55
0.75
0.95
1.15 R¢ / $
1.35
1.55
1.75
Fig. 1. Stokes hydrodynamic radii of alkali ions in propylene carbonate at 25°C versus Panling radii: [] this work; O Ref. [12]; O Ref. [13]; zx Ref.
[14]; • Ref. [151; • Refs. [16,17].
References [1] A. D'Aprano, M. Salomon and V. Mauro, J. Solution Chem., 24 (1995) 685. [2] A.F. Danil de Namor, M.A. Liosa Tanco, J.C.Y. Ng and M. Salomon, Pure Appl. Chem., in press. [3] A. D'Aprano, J. Vicens, Z. Asfari, M. Salomon and M. Iammarino, to be published. [4] A. D'Aprano, J. Phys. Chem., 76 (1972) 2920. [5] F. Accascina and G. Craia, Sci. Tec., 3 (1959) I1. [6] J.E. Pine and P.J. Sherrington, Trans. Faraday Soc., 57 (1961) 1795. [7] F. Accascina and G. Craia, Sci. Tec., 3 (1959) 203. [8] F. Conti and G. Pistoia, J. Phys. Chem., 72 (1968) 2245. [9] F. Accascina and S. Schiavo, Ric. Sci., 7 (1966) 556. [10] R.L. Kay, B.J. Hales and G.P. Cunningham, J. Phys. Chem., 71 (1967) 3925. [11] C.H. Springer, J.F. Cotzee and R.L. Kay, J. Phys. Chem., 73 (1969) 471. [12] M. Ue, J. Electrochem. Soc., 141 (1994) 3336. [13] E.M. Hanna and K. AI-Sudani, J. Solution Chem., 16 (1987) 155. [14] M.L. Jansen and H.L. Yeager, J. Phys. Chem., 77 (1973) 3089, 78 (1974) 1380. [15] J. Barthel, R. Wachter and H.-J. Gores, Faraday Discuss. Chem. Soc., 64 (1978) 285. [16] L.M. Mukherjee and D.P. Boden, J. Phys. Chem., 73 (1969) 3965. [17] L.M. Mukherjee, D.P. Boden and R. Lindauer, J. Phys. Chem., 74 (1970) 1942. [18] J. Barthel, H.-J. Gores, G. Schmeer and R. Wachter, Top. Curr. Chem., I l l (1982) 33. [19] R.M. Fuoss and E. Hirsch, J. Am. Chem. Soc., 82 (1960) 1013. [20] J. Barthel, H.J. Gores, P. Carlier, F. Feuerlein and M. Utz, Ber. Bunsenges. Phys. Chem., 87 (1983) 436. [21] J. Barthel, R. Wachter and H.-J. Gores in B.E. Conway and J. O'M. Bockris (Eds.), Modem Aspects of Electrochemistry, Vol. 13, Plenum Press, New York, 1979.
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[34] A. D'Aprano, F. Accascina and R.M. Fuoss, J. Solution Chem., 19 (1990) 65. [35] M. Salomon and E.J. Plichta, Electrochim. Acta, 28 (1983) 1681. [36] J.-C. Justice, J. Phys. Chem., 65 (1968) 353, Electrochim. Acta, 16 (1971) 701. [37] J.-C. Justice in B.E. Conway, J.O'M. Bockris and E. Yeager (Eds.), Comprehensive Treatise of Electrochemistry, Vol. 5, Plenum Press, New York, 1983, Ch. 3. [38] R.M. Fuoss and F. Accascina, Electrolytic Conductance, Interscience, New York, 1959. [39] R. Zana, J.E. Desnoyers, G. Perron, R. Kay and K. Lee, J. Phys. Chem., 86 (1982) 3996. [40] I.P. Safonova, B.K. Patsatsiya and A.M. Kolker, Russ. J. Phys. Chem. (Engl. Transl.), 68 (1994) 232. [41] R.A. Robinson and R.H. Stokes in Electrolyte Solutions (2nd revised ed.), Butterworths, London, 1965, p. 44.