17568
J. Phys. Chem. 1996, 100, 17568-17572
Electrical Conductances of Tetraphenylphosphonium and Tetraphenylboride Salts in C1 to C4 Alcohols Yixing Zhao and Gordon R. Freeman* Chemistry Department, UniVersity of Alberta, Edmonton, Alberta, Canada T6G 2G2 ReceiVed: May 22, 1996; In Final Form: August 6, 1996X
The electrical conductances of three large-ion salts, tetraphenylphosphonium chloride (TPPC), tetraphenylphosphonium bromide (TPPB), and sodium tetraphenylboride (STPB), have been measured in water and each of the C1 to C4 alcohols at different temperatures. The molar conductivities of the large ions TPP+ and TPB- vary inversely with the solvent viscosity η and with the carbon number N of the solvent molecules: (N + 1)1/2ηλ0 ) constant. The value of this constant is slightly dependent on the chain structure of the alcohol: for TPP+, 28.6 (10-7 Pa‚s‚S‚m2/mol) in 1-alkanols, 30.0 in 2-alkanols, 30.4 in isobutanol, 26.9 in tert-butyl alcohol; for TPB- the respective values are 30.0, 31.5, 31.9, and 27.9. In water the values of (N + 1)1/2ηλ0 of TPP+ (18.4) and TPB- (17.7) are the lowest, while the values for the small ions (44.6, Na+; 69.8, Br-; 67.9, Cl-) are the highest among all the solvents. In alcohols and water, the activation energies for molar conductivities (EΛ0) of the three salts are nearly the same as those of Eη of the solvents, with one exception. In tert-butyl alcohol the values of EΛ0 (21 kJ/mol, TPPB; 22, TPPC; 19, STPB) are similar to those of the corresponding salts in other butanols and much lower than Eη of tert-butyl alcohol (31 kJ/mol). The activation energy of diffusion of the large tetraphenyl ions through the butanols, the molecular sizes of which are much smaller than the tetraphenyl ions, is relatively insensitive to the molecular structure of the butanols.
Introduction (es-)
in solvents, In the study of diffusion of solvated electrons the mobilities of ions are needed as reference data.1,2 In our study of the reactivities of es- with ions in water/alcohol mixed solvents,3-5 the conductances of ionic solutes were also measured to approximate the mutual diffusion coefficients of the reactants (es- + ion) in a solvent. Both reactivity of esand the mobilities of es- 6 and ions7-12 in solvents are affected by the solvent structure. In preparation for the measurement of diffusion coefficients of es- in butanols, we have measured the electrical conductances of tetraphenylphosphonium chloride (TPPC), tetraphenylphosphonium bromide (TPPB), and sodium tetraphenylboride (STPB) in water and the C1 to C4 alcohols at different temperatures. The mobilities of the small ions in water and the smaller alcohols are known, so we have determined the mobilities of the large tetraphenyl cation and anion in these solvents. The ionic mobilities were then deduced from the measured salt conductances in the larger alcohols. The only available data are the conductances of tetraphenylphosphonium ion in water at 298 K,13 tetraphenylboride ion in water at 298 K14 and methanol at 298 K,15 and tetraphenylphosphonium ion in 2-propanol at 283-303 K.16 For a salt made up of two large ions such as tetra-n-butylammonium, triphenylborofluoride, and tetraphenylboride (TPB), an approximation that λ0+ ) λ0- ) Λ0(salt)/2 has been made on the basis of the experimental results.14-15,17-19 In the present paper we also tested this approximation. Experimental Section Materials. The alcohols used were methanol (Aldrich, ACS spectrophotometric grade, 99.9% or ACS reagent, g99.8%), ethanol (Sigma-Aldrich, reagent, HPLC grade), 1-propanol * Tel: 403 492 3468. FAX: 403 492 8231. E-mail:
[email protected] X Abstract published in AdVance ACS Abstracts, October 1, 1996.
S0022-3654(96)01484-0 CCC: $12.00
(Aldrich, 99+%, spectrophotometric grade, or BDH laboratory reagent, g98%), 2-propanol (Aldrich, ACS spectrophotometric grade, 99.5+%), 1-butanol (Aldrich, spectrophotometric grade, 99.5+%), 2-butanol (Aldrich, anhydrous, 99+%), isobutanol (Aldrich, ACS spectrophotometric grade, 99+%, or BDH laboratory reagent, g95%), and tert-butyl alcohol (Fluka, >99.7%, or BDH, analytical reagent, g99%). Each alcohol with added sodium borohydride (2g/L) was fractionally distilled under argon through an 80 × 2.3 cm column packed with glass beads (6 mm). The middle 50% of the distillate was collected and stored in a flask under argon positive pressure. The water content, measured by Karl-Fisher titration, was 0.05 mol %. Nanopure water (from Barnstead, NANOpureII) was used for the measurements in water. Tetraphenylphosphonium chloride (TPPC) (Aldrich, 98%), tetraphenylphosphonium bromide (TPPB) (Aldrich, 97%), and sodium tetraphenylboride (STPB) (Aldrich, ACS reagent, 99.5+%) were used as received. They were kept in a vacuum desiccator with calcium chloride. At the end of the project the conductances were measured again in water and found to be the same as at the beginning, within (0.1%. Techniques and Sample Preparation. The technique of the conductance measurement is similar to that in ref 20. Pyrex conductivity cells with platinized platinum electrodes (YSI3403) were obtained from Yellow Springs Instrument Co., Inc. A secondary standard solution (YSI3161, specific conductance of 1000 ( 5 mS/cm) available from Yellow Springs Instrument Co., Inc. was used to calibrate the cells. Graduated cylinders, 25 cm3 (16 cm long, 1.4 cm i.d.), were used to contain the electrolyte solutions. To obtain a tight seal between the cylinder and the measurement cell, the cell was fitted into a one-hole no. 2 rubber stopper. Two layers of Parafilm (American Can Co.) were wrapped around the stopper-container junction to provide a tight seal, which was especially important at high temperatures. The temperature range of the measurements was ∼277 to ∼343 K. © 1996 American Chemical Society
Tetraphenylphosphonium and Tetraphenylboride Salts
J. Phys. Chem., Vol. 100, No. 44, 1996 17569
A 10 L glass Dewar filled with water was used as a thermostatic bath, controlled to (0.01 K by a temperatureregulating system.21 The temperature was measured with a platinum resistance digital thermometer (Fluke, Model 2189A) to (0.01 K. Electrical conductance measurements were done at 1 kHz with an impedance bridge (Model 1608-A, General Radio Co.). For conductances > 0.6 µS, conductance mode Gp was used. For the conductances between 0.1 and 0.6 µS, capacitance mode Cp was used. When conductances were < 0.1 µS, the bridge was set at capacitance mode Cs. The specific conductance (κobs: S/m) was calculated from the following equation:
κobs ) CL
(1)
where L is the measured conductance (Siemen) and C is the cell constant (m-1). The value of the molar conductance (Λ0) was obtained from a plot of specific conductances against five different solute concentrations and the pure solvent. The activation energies of the conductances (EΛ0) were obtained from Arrhenius plots of Λ0. Results and Discussion Molar Conductivities of Salts. Sodium tetraphenylboride (STPB) dissolved easily in water and the alcohols, although dissolution in butanols was slower. Tetraphenylphosphonium chloride (TPPC) and tetraphenylphosphonium bromide (TPPB) dissolved easily in water and methanol to propanols. The dissolution of TPPC and TPPB in 1-, 2-, and isobutanols was slow, and the solution was stirred by magnetic stirrer for about 1 h to ensure completion. The dissolution of TPPC and TPPB in tert-butyl alcohol was completed overnight with stirring. The difference in dissolution rates between STPB and TPPC or TPPB is probably because Nas+ is more strongly solvated than are Cl- and Br-.22,23 To avoid curved lines in the plots of specific conductances against solute concentrations, caused by ionic atmosphere effect24 or ion association,25 low concentrations were used: water, 0.075-0.375 mol/m3 (TPPB), 0.05-0.25 mol/m3 (TPPC and STPB); methanol, 0.1-0.5 mol/m3 (STPB), 0.05-0.25 mol/ m3 (TPPB and TPPC); ethanol, 0.1-0.5 mol/m3; 1-propanol and 2-propanol, 0.15-0.75 mol/m3; 1-butanol, 0.03-0.15 mol/ m3; 2-butanol, 0.03-0.15 mol/m3 (TPPC and STPB), 0.060.30 mol/m3 (TPPB); isobutanol and tert-butyl alcohol, 0.020.10 mol/m3. The lines in the plots of specific conductances against the salt concentrations are straight except at 343 K (the highest temperature measured), where the lines for STPB in water, TPPC in ethanol and tert-butyl alcohol, and TPPB in tert-butyl alcohol are slightly bent downward toward the highconcentration end. In this case, the initial slope was taken for the conductivity and it is labeled by * in Figures 1-3 (Table 1 lists the symbols used). The results indicate that ionic atmosphere effect and ion association7 are negligible in Figures 1-3. The conductance of each salt was measured at least twice. The reproducibility was (0.1% in water, (1% in methanol, then increasing with alcohol viscosity at 298 K to (4% in tertbutyl alcohol. Agreement with the few previously available data was excellent (Table 2). Figures 1-3 are Arrhenius plots of the molar conductivities of each solute in water and C1 to C4 alcohols. The molar conductivities of the three solutes at 298 K are listed in Table 2. In C1 to C4 alcohols the molar conductivity of each solute decreases with increase of viscosity η and decrease of relative permittivity . In a given alcohol the molar conductivities of the three solutes are similar, but TPPB > TPPC > STPB. This
Figure 1. Arrhenius plots of molar conductivities of sodium tetraphenylboride (STPB) in water and C1 to C4 alcohols. Refer to Table 1 for symbols.
Figure 2. Arrhenius plots of molar conductivities of tetraphenylphosphonium bromide (TPPB) in water and C1 to C4 alcohols. Refer to Table 1 for symbols.
order is inversely related to the strength of solvation of the smaller ions; that is, Br- < Cl- < Na+ in a solvent.22,23 Therefore, the differences in molar conductivities are mainly due to the smaller ions, because the more strongly the ion is solvated, the larger the actual size of the species that diffuses, and therefore, the lower the mobility. The relatively small changes in conductivities on going from water to methanol, despite the much smaller viscosity of the latter (Table 2), are due to the larger effective radii of the ions when they are solvated by methanol than when solvated by the smaller water molecules.
17570 J. Phys. Chem., Vol. 100, No. 44, 1996
Zhao and Freeman
Figure 3. Arrhenius plots of molar conductivities of tetraphenylphosphonium chloride (TPPC) in water and C1 to C4 alcohols. Refer to Table 1 for symbols.
TABLE 1: Symbols for Figures 1-3 solvent × O b 0 9
water MeOH EtOH 1-PrOH 2-PrOH
solvent 1-BuOH 2-BuOH i-BuOH t-BuOH
4 2 ] [
TABLE 2: Molar Conductivities of Salts and Solvent Parameters at 298 K Λ0 (10-4 S‚m2/mol) solvent water MeOH EtOH 1-PrOH 2-PrOH 1-BuOH 2-BuOH i-BuOH t-BuOH
η (mPa‚s)a 0.89 0.557 1.10 1.96 2.08 2.60 3.05 3.40 4.45
a 78.5 32.6 24.3 20.1 18.4 17.4 16.7 17.6 12.4
TPPBb c
99 (98.8 ) 91 41.0 19.7 17.8 13.7 11.5 11.1 8.0
TPPCb d
97 (96.7 ) 88 39.0 18.5 17.2 13.2 11.1 10.7 7.7
STPBb 70 (69.9e) 82 (82.3f) 35.0 17.1 16.5 12.5 10.5 10.0 6.9
a Table 4 in ref 26. b TPPB, tetraphenylphosphonium bromide; TPPC, tetraphenylphosphonium chloride; STPB, sodium tetraphenylboride. c References 13 and 29. d Reference 13. e Reference 14. f References 19 and 29.
Estimate of Ionic Conductivities. Since the ionic conductivities of Na+, Cl-, and Br- in water, methanol, and ethanol at 298 K are known, the ionic conductivities of tetraphenylboride (TPB-) and tetraphenylphosphonium (TPP+) in these solvents can be calculated. The values are listed in Table 3. The measured ionic conductivity (10-4 S‚m2/mol) in water is 20.7 for TPP+ and 19.9 for TPB-, and they are close to the literature values of 20.4 (TPP+)13 and 19.7 (TPB-).14 The values of the ionic conductivities of the large ions TPP+ and TPB- are nearly the same. The value for TPB- in methanol is 36.3 × 10-4 S‚m2/mol, which is consistent with Fuoss’s measurement (36.5).19 However, in methanol and ethanol, unlike in water, the values for TPP+ are slightly lower than those for TPB-. In 1-propanol, values of the ionic molar conductivities of Na+, Cl , and Br- are not available. However, the molar conductivi-
ties of the alkali halides KI, KBr, NaI, and NaBr at 298 K allow us to estimate the values of the ionic molar conductivities (Table 4). The Λ0 value (19 × 10-4 S‚m2/mol) for NaBr from ref 27 appears not to be correct. From KI (Λ0 ) 26 × 10-4 S‚m2/ mol)12,28 to KBr (Λ0 ) 24 × 10-4 S‚m2/mol)12,28 in 1-propanol, the molar conductivity decreases 2 units when I- is replaced by Br-. The same decrease should occur on going from NaI to NaBr. We take Λ0 ) 24 × 10-4 S‚m2/mol for NaI12,27,28 to be correct, in which case Λ0 ) 22 × 10-4 S‚m2/mol for NaBr. Table 4 gives the values of ionic molar conductivities of K+, Na+, I-, and Br-,29 and the λ0-/λ0+ ratios for the four ions in methanol and ethanol at 298 K. The average λ0-/λ0+ ratios are I-/K+, 1.3; Br-/K+, 1.1; I-/Na+, 1.5; and Br-/Na+, 1.3. We assume that in 1-propanol at 298 K approximately the same ratios apply to the ions. By splitting the molar conductivity values of the alkali halides in the same λ0-/λ0+ ratios, the ionic molar conductivities of the ions were estimated by selfconsistency (Table 4). Thus, in 1-propanol at 298 K the ionic molar conductivities of Na+ and Br- are λ0(Na+) ) 9.5 × 10-4 S‚m2/mol; λ0(Br-) ) 12.5 × 10-4 S‚m2/mol (Tables 3 and 4). In methanol and ethanol the average ratio of λ0(Br-)/λ0(Cl-) is about 1.06 and λ0(Cl-)/λ0(Na+) is about 1.2 (Table 3); using the same ratios in 1-propanol, the ionic molar conductivity of Cl- is taken as 11.8 × 10-4 S‚m2/mol (Table 3). The λ0(TPB-) and λ0(TPP+) in 1-propanol can be calculated (Table 3). The two values are similar. From 2-propanol to tert-butyl alcohol, no relevant conductance data are available. The following method was used to estimate λ0(TPB-) and λ0(TPP+) in these alcohols. From methanol to 1-propanol at 298 K, the average ratios of λ0(Br-)/ λ0(Cl-) and λ0(TPB-)/λ0(TPP+) are 1.06 and 1.05, respectively. From 2-propanol to tert-butyl alcohol at 298 K the same ratios and the measured molar conductivities for TPPC, TPPB, and STPB are used for the estimation of λ0(TPB-) and λ0(TPB+). The values are listed in Table 3. In C1 to C4 alcohols at 298 K, molar conductivities of all the ions decreases on going from methanol to tert-butyl alcohol. However, the average λ0-/λ0+ ratios are unchanged; that is, TPB-/TPP+ ) 1.05 (Table 3). On going from methanol to tertbutyl alcohol, the large ions TPB- and TPP+ have lower mobilities than the smaller ions do; λ0(TPB-) and λ0(TPP+) are similar, but λ0(TPB-) > λ0(TPP+). Therefore, the approximation14-15,17-19 for large ions (λ0+ ) λ0-) may be changed into λ0+ ≈ λ0-. Correlations of Λ0 with Solvent Properties. Similar to Chen and Freeman’s results7 for LiNO3 in C1 to C10 n-alcohols, the values of ηΛ0 of the present three salts are not constant in C1 to C4 alcohols. For example, for TPPB (Table 2) the values of ηΛ0 (10-4 mPa‚s‚S‚m2/mol) range from 51 in methanol to 38 in isobutanol. Thus Λ0 decreases faster than the η-1 that one might expect from Walden’s rule.24 For LiNO3 in C1 to C10 n-alcohols the value of (N + 1)1/2ηΛ0 is nearly constant,7 where N is the number of carbon atoms in the alcohol molecule and the 1 corresponds to the oxygen atom. This indicates that the size of the solvating molecules and random folding of the carbon and oxygen chain with (N + 1) links decrease the mobility of salts in alcohols by a factor of (N + 1)-1/2.7 The factor accounts for the increase of ion size by solvation with larger molecules. Figure 4 shows plots of (N + 1)1/2ηΛ0 for the present three salts and (N + 1)1/2ηλ0 for the five ions against 1/η of water and C1 to C4 alcohols at 298 K. For the three salts and the three inorganic ions in the alcohols the value of (N + 1)1/2ηΛ0 tends to increase with decreasing fluidity, with some scatter (the
Tetraphenylphosphonium and Tetraphenylboride Salts
J. Phys. Chem., Vol. 100, No. 44, 1996 17571
TABLE 3: Calculation and Estimate of Ionic Molar Conductivities in Water and Alcohols at 298 K λ0 (10-4 S‚m2/mol)
ratio
Na+
Cl-
Br-
TPP+a
TPP+b
TPB-
TPB-/TPP+
Br-/Cl-
Cl-/Na+
Br-/Na+
waterc
50.1
76.3
78.4
1.52
1.6
52.3
55.5
1.02
1.06
1.14
1.2
EtOHc 1-PrOHd
18.7 9.5 (9.5) 8.9 7.4 5.9 5.8 4.1
24.3 11.8 (11.7) 10.0 8.3 6.7 6.7 5.0
25.8 12.5 (12.4) 10.6 8.8 7.1 7.1 5.3
14.7 7.5 (7.3) 7.2 4.9 4.4 4.0 2.7
15.2 7.2 (7.3) 7.2 4.9 4.4 4.0 2.7
19.9 (19.7)g 36.3 (36.5)h 16.3 7.7 (7.7) 7.6 5.1 4.6 4.2 2.8
1.03
45.8
20.6 (20.4)f 35.5
0.96
MeOHc
20.7 (20.4)f 35.7
1.09 1.04 (1.05) 1.06 1.04 1.05 1.05 1.04
1.06 1.06 (1.06) 1.06 1.06 1.06 1.06 1.06
1.30 1.2 (1.2) 1.1 1.1 1.1 1.2 1.2
1.4 1.3 (1.3) 1.2 1.2 1.2 1.2 1.3
solvent
2-PrOHe 1-BuOHe 2-BuOHe i-BuOHe t-BuOHe
a Calculated from the experimental conductivity values for TPPC (Table 2). b Calculated from the experimental conductivity values for TPPB (Table 2). c Values for TPP+ and TPB- were calculated by subtracting the literature values27 of the molar conductivities of Na+, Cl-, Br- from the salt conductivities. d Values for TPP+ and TPB- were calculated from the estimated molar conductivities of Na+, Cl-, Br- from the reported values12,27,28 of related salts. See text for details. Refer to e for the values in parentheses. e Values for TPP+ and TPB- were calculated based on molar conductivities of TPPC, TPPB, and STPB (Table 2), and assumed ratios: TPB-/TPP+ ) 1.05, and Br-/Cl- ) 1.07. Refer to the text for details. f Reference 13. g Reference 14. h Reference 19.
TABLE 4: Ionic Molar Conductivities of K+, Na+, I-, and Br- in Methanol,a Ethanol,a and 1-Propanolb at 298 K λ0 (10-4 S‚m2/mol) MeOH EtOH
e
λ0-/λ0+ ratio
K+
Na+
I-
Br-
I-/K+
av
Br-/K+
av
I-/Na+
av
Br-/Na+
av
53.7 22.0
45.8 18.7
62.7 28.7
55.5 25.8
1.2 1.3
1.3
1.0 1.2
1.1
1.4 1.5
1.5
1.2 1.4
1.3
1-PrOH
Λ0 (10-4 S‚m2/mol)
λ0+ (10-4 S‚m2/mol)
λ0- (10-4 S‚m2/mol)
ratio
KI KBr NaI NaBr
26c 24d 24c,d 22e (19)d
11.5 11.5 9.5 9.5
14.5 12.5 14.5 12.5
I-/K+ ) 1.3 Br-/K+ ) 1.1 I-/Na+ ) 1.5 Br-/Na+ ) 1.3
a Reference 29. b Estimated values from molar conductivities of some alkali halides in 1-propanol.12,27,28 c References 12, 28. d Reference 27. Estimated value, refer to the text for details.
Figure 4. Correlations of (N + 1)1/2ηΛ0 with fluidity (1/η) of solvents at 298 K: (O) TPPB; (9) TPPC; (4) STPB; (]) TPB-; ([) TPP+; (+) Na+; and (•) Br-.
values for Cl- lie just below those for Br- and were omitted to simplify Figure 4). The values of (N + 1)1/2ηλ0 for each large ion at 298 K are constant in a given class of alcohols. The values for TPP+ ion are (10-7 Pa‚s‚S‚m2/mol) 28.6 in 1-alkanols from methanol to
1-butanol; 30.0 in 2-alkanols; 30.4 in isobutanol; and 26.9 in tert-butyl alcohol (Figure 4). The respective values for TPBare 30.0, 31.5, 31.9, and 27.9. The value tends to increase slightly with chain branching, except in the rigid-molecular tertbutyl alcohol, where the value of (N + 1)1/2 underestimates the effective radius of the solvated ion. In water the values of (N + 1)1/2ηΛ0 for the two large cation salts (TPPB and TPPC) are the highest among all the solvents, while the value for the large anion salt (STPB) is the lowest. On the basis of Stokes-Einstein equation,24 a diffusion coefficient is inversely proportional to the effective hydrodynamic radius of the particle. TPP+ and TPB- are much larger ions than Na+, Br-, and Cl- ions are; therefore, the values of (N + 1)1/2ηλ0 for both TPP+(18.4) and TPB-(17.7) are the lowest, while the values for the small ions (44.6, Na+; 69.8, Br-; 67.9, Cl-) are the highest among all the solvents. The values for the anion TPB- are slightly larger than those for the cation TPP+ in alcohols; however, in water the value of TPP+ is slightly higher than TPB-. Activation Energy EΛ0 and Eη. Table 5 lists the values of activation energies (EΛ0) for the three salts along with the activation energy of viscosity (Eη) in water and C1 to C4 alcohols. The values of EΛ0 of the three salts in a given solvent are almost the same. On going from methanol to isobutanol EΛ0 increases with increase of viscosity; EΛ0 is close to Eη in all solvents except tert-butyl alcohol. In tert-butyl alcohol the values of EΛ0 (kJ/mol) are 21 for TPPB, 22 for TPPC, and 19 for STPB. They are similar to EΛ0 for the corresponding salts in the other butanols and are much lower than Eη (31 kJ/mol) in tert-butyl alcohol. Eη is related to the movement of the solvent molecules past each other in their own liquid. The more
17572 J. Phys. Chem., Vol. 100, No. 44, 1996
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TABLE 5: Activation Energy of Molar Conductivities of Salts and Viscosities of Solvents activation energy (kJ/mol) solvent
η(mPa‚s)
a
water MeOH EtOH 1-PrOH 2-PrOH 1-BuOH 2-BuOH i-BuOH t-BuOH
0.89 0.557 1.10 1.96 2.08 2.60 3.05 3.40 4.45
78.5 32.6 24.3 20.1 18.4 17.4 16.7 17.6 12.4
a
a
TPPB
TPPC
STPB
Eηb
15 9.7 13 17 20 20 24 23 21
15 9.6 13 17 20 20 23 23 22
16 9.6 13 17 20 20 23 22 19
17 11 14 18 22 19 26 24 31
Reference 26, 298 K. b References 8 and 30.
spherelike and rigid molecules of tert-butyl alcohol have greater difficulty diffusing through their liquid than do the more chainlike and flexible molecules of 1-butanol diffusing through theirs. The diffusion of rigid spheres through each other requires that a larger and better defined volume be opened up or rearranged during a diffusive step (volume of activation) than does the diffusion of flexible chains. In this process the larger volume of activation requires a larger activation energy. Evidently the tetraphenyl ions are so much larger than the solvent butanol molecules that the solvent acts more or less as a continuum, and the solvent molecular structure has less of an effect. It would be worthwhile to measure EΛ0 for small-ion salts in the four isomeric butanols, to determine whether there is a stronger correlation with Eη. Acknowledgment. We thank the Natural Sciences and Engineering Research Council of Canada for financial assistance and Mr. Ronald Gardner for maintaining the electronic equipment. References and Notes (1) Schmidt, K. H.; Han, P.; Bartels, D. M. J. Phys. Chem. 1992, 96, 199.
(2) Del Buono, G. S.; Rossky, P. J.; Murphrey, T. H. J. Phys. Chem. 1992, 96, 7761. (3) Peiris, S. A.; Freeman, G. R. Can. J. Chem. 1991, 69, 157. (4) Chen, R.; Avotinsh, Y.; Freeman, G. R. Can. J. Chem. 1994, 72, 1083. (5) Zhao, Y.; Freeman, G. R. Can. J. Chem. 1995, 73, 392. (6) Freeman, G. R. In Kinetics of Nonhomogeneous Processes; Freeman, G. R., Ed.; John Wiley & Sons Inc.: New York, 1987; Chapter 2. (7) Chen, R.; Freeman, G. R. J. Phys. Chem. 1995, 99, 4970. (8) Zhao, Y.; Freeman, G. R. Can. J. Chem. 1995, 73, 2131. (9) Kacperska, A.; Taniewska-Osinska, S.; Bald, A.; Szejgis, A. J. Chem. Soc., Faraday Trans. 1 1989, 85, 4147. (10) Perie, M.; Perie, J. J. Solution Chem. 1989, 18, 45. (11) Janz, G. J.; Danyluk, S. S. Chem. ReV. 1960, 60, 209. (12) Janz, G. J.; Tait, M. J. Can, J. Chem. 1967, 45, 1101. (13) Perie, M.; Perie, J.; Chemla, M. J. Solution Chem. 1988, 17, 203. (14) Skinner, J. F.; Fuoss, R. M. J. Phys. Chem. 1964, 68, 1882. (15) Kunze, R. W.; Fuoss, R. M. J. Phys. Chem. 1963, 67, 385. (16) Papadopoulos, N.; Ritzoulis, G. Collect. Czech. Chem. Commun. 1989, 54, 1475. (17) Fowler, D. L.; Kraus, C. A. J. Am. Chem. Soc. 1940, 62, 2237. (18) Fuoss, R. M.; Hirsch, E. J. Am. Chem. Soc. 1960, 82, 1013. (19) Coplan, M. A.; Fuoss, R. M. J. Phys. Chem. 1964, 68, 1177. (20) Chen, R.; Freeman, G. R. Can. J. Chem. 1993, 71, 1303. (21) Senanayake, P. C.; Gee, Norman; Freeman, G. R. Can. J. Chem. 1987, 65, 2441. (22) Burger, K. SolVation, Ionic and Complex Formation Reactions in Non-Aqueous SolVents; Elsevier: New York, 1983; pp 34, 36, 38. (23) Gordon, J. E. The Organic Chemistry of Electrolyte Solutions; John Wiley & Sons: New York, 1975; p 216. (24) Atkins, P. W. Physical Chemistry, 4th ed.; W. H. Freeman and Company: New York, 1990; pp 251, 752, 765-766. (25) Bockris, J. O’M.; Reddy, A. K. N. Modern Electrochemistry; Plenum Press: New York, 1975; Vol. 1, p 450. (26) Zhao, Y.; Freeman, G. R. Can. J. Chem. 1995, 73, 284. (27) Hovorka, F.; Simms, J. C. J. Am. Chem. Soc. 1937, 59, 92. (28) Gover, T. A.; Sears, P. G. J. Phys. Chem. 1956, 60, 330. (29) Dobos, D. Electrochemical Data; Scientific Publishing: New York, 1975; pp 87-89. (30) Lai, C. C.; Freeman, G. R. J. Phys. Chem. 1990, 94, 302.
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