Anal. Chem. 1997, 69, 5094-5102
Influence of Electrolyte Activity on Apparent Formal Potentials Measured for Redox Probes in Water and Acetonitrile Jody Redepenning* and Eric Mechalke
Department of Chemistry, University of Nebraska, Lincoln, Nebraska 68588-0304
Properties of relatively new polymeric materials are capitalized upon to address a relatively old problem in electrochemistry, the comparison of electrode potentials measured in different solvents. In particular, electrode potentials measured in acetonitrile and in water are compared at voltammetrically relevant concentrations. Activity coefficients are measured for silver perchlorate in acetonitrile using the isopiestic technique. These results are used to interpret the influence of silver perchlorate activity on apparent formal potentials measured in acetonitrile for an electrochemically polymerized redox polymer. Similar measurements are made on the same redox polymer in water, and in both solvents the cell potentials are Nernstian for a simple ionic stoichiometry. The cell potentials measured in acetonitrile are +0.244 V of those measured in water. This difference is consistent with the difference expected from estimates of the free energy of transfer of silver perchlorate. It is also consistent with predictions based on certain extrathermodynamic assumptions concerning the free energies of transfer of the single ions. The results reported here suggest that the free energy for transferring silver perchlorate from water to acetonitrile is -21.9 ( 0.9 kJ/mol and that the potential of the Ag|a(AgClO4)CH3CN ) 1 couple is -0.227 ( 0.009 V of the Ag|a(AgClO4)H2O ) 1 couple. The influence of electrolyte activity on formal potentials measured for redox couples dissolved in acetonitrile is also investigated. Our results demonstrate that internal reference couples such as ferrocene/ferrocenium should be used with caution. Over certain concentration ranges, ion pairing may play an important role in determining formal potentials measured for dissolved reference compounds. To provide a reliable set of values to which subsequent comparisons can be made in acetonitrile, we report apparent formal potentials as a function of electrolyte activity for several popular internal reference couples.
stems from the lack of suitable reference half-cells. Three major problems plague reference half-cells in nonaqueous solvents: (1) unknown liquid junction potentials, (2) questionable extrathermodynamic assumptions concerning internal reference couples, and (3) unknown activity coefficients for the reference couple. Our efforts to overcome these obstacles have enabled us to make a series of measurements in acetonitrile that are similar to the classical measurements made on the Pt|H2|H+,Cl-|AgCl|Ag cell in water. To make such measurements it was first necessary to measure activity coefficients in acetonitrile for an electrolyte with certain desirable properties. In this case, silver perchlorate was chosen. Activity coefficients were measured using the isopiestic technique. Having activity coefficients for silver perchlorate in acetonitrile, we have been able to interpret the influence of silver perchlorate activity on the potential of the following junctionless electrochemical cell in water and in acetonitrile:
In this paper we describe our efforts to measure activity coefficients in acetonitrile, to compare the potential for the Ag|X M AgClO4 couple in water with that of the Ag|X M AgClO4 couple in acetonitrile, and to measure formal potentials for a series of redox couples as a function of AgClO4 activity in acetonitrile. These efforts were initiated due to dissatisfaction with our limited ability to interpret cell potentials in solvents other than water. Unfortunately, there is no completely unambiguous way of interpreting potentials in many nonaqueous solvents. Much of this ambiguity
(1) Butler, J. N. Reference Electrodes in Aprotic Organic Solvents. In Advances in Electrochemistry and Electrochemical Engineering; Delahay, P., Ed.; Academic Press: New York, 1970; Vol. 7; pp 77-175. (2) Covington, A. K. Reference Electrodes. In Ion-Selective Electrodes; Durst, R. A., Ed.; Special Publication 314; National Bureau of Standards: Washingtion, DC, 1969; Chapter 4, pp 107-141. (3) Hills, G. J. Reference Electrodes in Nonaqueous Solutions. In Reference Electrodes: Theory and Practice; Ives, D. J. G., Janz, G. J., Eds.; Academic Press: New York, 1961; Chapter 10, pp 433-463. (4) Lund, H. In Organic Electrochemistry: An Introduction and a Guide, 2nd ed.; Baizer, M. M., Lund, H., Eds.; M. Dekker: New York, 1983; Chapter 5, pp 187-211.
5094 Analytical Chemistry, Vol. 69, No. 24, December 15, 1997
Pt|poly-Ru(vbpy)3n+, nClO4-|X M ClO4-, X M Ag+|Ag (1) where vbpy is 4-methyl-4′-vinyl-2,2′-bipyridine and M is the molar activity. We have also examined a number of redox probes dissolved in acetonitrile. In all cases, it is clear that ionic associations between the supporting electrolyte and the redox probe can play an important role in altering values observed for the apparent formal potential. Having activity coefficients for silver perchlorate in acetonitrile, we have been able to describe these ionic associations in terms of relatively simple half reactions. We surmise that similar ionic associations may account for many of the discrepancies that are ubiquitous in the literature of nonaqueous electrochemistry. BACKGROUND Historical Context. The status of reference electrodes in nonaqueous solvents and, in particular, in acetonitrile has been reviewed by a number of authors.1-6 The most important developments concerning reference half-cells in acetonitrile are
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highlighted below. Electrodes of the second kind (e.g., Ag|AgCl) are of limited utility because of the low solubility of silver halides in CH3CN and by the propensity of these silver halides to form higher complexes with free halides in solution.7,8 The hydrogen electrode is rapidly poisoned in CH3CN.9 Hg2Cl2, calomel, disproportionates in CH3CN to form Hg0 and mercuric halides.7 The Ag|Ag+ electrode has met with the most success. Pleskov found that the couple is stable in CH3CN, but neither the liquid junction potentials nor the activity of Ag+ was known in these early studies.10 Popov and Geske were able to minimize liquid junction potentials, but the activity of Ag+ was not known.11 Although Kolthoff et al.12 and Kratochvil et al.13 were able to estimate Ag+ activities at very low concentrations using conductivity data and extended Debye-Huckel theory, these estimates are of little value at concentrations greater than ∼0.01 M. Finally, use of internal standards should be mentioned. This idea is based on Pleskov’s efforts to find a redox couple that does not interact with the solvent.10,14 If such a couple were available, its potential would be independent of the solvent in which the potential is measured. Pleskov suggested the Rb+/0 couple, but the solvation energy of Rb+ was later found to vary significantly from solvent to solvent. This led to the suggestion of Strehlow that the ferrocene/ferrocenium and cobaltocene/cobaltocenium couples should be used,15 but the potentials of these couples are also found to be influenced by solvent.16 Despite the fact that their use lacks thermodynamic rigor, it is important to acknowledge that internal reference couples do present some practical advantages. Internal reference couples provide a rapid means of comparing formal potentials measured under similar conditions. Recommendations and discussions of this subject have appeared periodically.17-20 In seeking to gain a better understanding of cell potentials measured in acetonitrile, we desired electrolyte activities in this solvent. More specifically, we desired activity coefficients for highly soluble silver salts to build upon previous successes10-13 in which the Ag/Ag+ couple was used as a reference in acetonitrile. Many if not most of the activity coefficients for electrolytes in aqueous solutions have been determined using the isopiestic technique,21,22 which involves equilibrating one solution, containing a reference electrolyte for which the activity coefficients are (5) Salomon, M. Thermodynamic Measurements. Part 2. Electrochemical Measurements. In Physical Chemistry of Organic Solvent Systems; Covington, A. K., Dickinson, T., Eds.; Plenum Press: New York, 1973; pp 137-219. (6) Mann, C. K. Electrochemical Reactions in Nonaqueous Systems; Marcel Dekker: New York, 1960. (7) Janz, G. J.; Taniguchi, H. Chem. Rev. 1953, 53, 397. (8) Coetzee, J. F. Precipitation Equilibria and Titrations in Aqueous and Nonaqueous Media. In Treatise on Analytical Chemistry, 2nd ed.; Kolthoff, I. M., Elving, P. J., Eds.; John Wiley and Sons: New York, 1983; Part 1, Chapter 28, p 349. (9) Janz, G. J.; Taniguchi, H., unpublished results sited in ref 3. (10) Pleskov, V. A. Zhur. Fiz. Khim. 1948, 22, 351. (11) Popov, A. I.; Geske, D. H. J. Am. Chem. Soc. 1957, 79, 2074-2079. (12) Kolthoff, I. M.; Thomas, F. G. J. Phys. Chem. 1965, 69, 3049-3058. (13) Kratochvil, B.; Lorah, E.; Garber, C. Anal. Chem. 1969, 41, 1793-1796. (14) Pleskov, V. A. Usp. Khim. 1947, 16, 254. (15) Strehlow, H. Z. Elektrochem. 1952, 56, 827. (16) Koepp, H. M.; Wendt, H.; Strehlow, H. Z. Elektrochem. 1960, 64, 483. (17) Ward, W. Ph.D. Thesis, Electrode Potential Measurements in Anhydrous Acetonitrile. University of Iowa, 1958. (18) Gritzner, G.; Kuta, J. Pure Appl. Chem. 1982, 54, 1527-1532. (19) Gagne, R. R.; Koval, C. A.; Lisensky, G. C. Inorg. Chem. 1980, 19, 28542855. (20) Stojanovic, R. S.; Bond, A. M. Anal. Chem. 1993, 65, 56-64. (21) Activity Coefficients in Electrolyte Solutions; Pytkowicz, R. M., Ed.; CRC Press, Inc.: Boca Raton, FL, 1979; Vol. I.
known, with another solution, containing an electrolyte for which the activity coefficients are not known. A number of technical difficulties stand in the way of acquiring meaningful data. For example, to get useful information, the temperature difference between the two electrolyte solutions should be less than 10-4 K. Fortunately, the problems associated with achieving this degree of thermal uniformity were solved in the 1930s and 1940s.23-25 By making minor modifications in earlier designs of the apparatus, we have been able to use the isopiestic technique to determine activity coefficients for several 1:1 electrolytes in acetonitrile. The primary obstacle preventing earlier use of the isopiestic technique to determine activity coefficients for electrolytes in acetonitrile was the lack of a suitable reference electrolyte. Activity coefficients for the reference electrolyte must be known over a broad concentration range. This obstacle was overcome in 1988 when Barthel et al. published a paper that included a series of carefully performed vapor pressure measurements on solutions of 1:1 electrolytes in acetonitrile.26 The authors used these vapor pressures to determine activity coefficients for several salts over concentrations ranging from ∼0.05 to 4 m. These activity coefficients, in conjunction with activity coefficients calculated at very low concentrations using the extended Debye-Huckel equation,27 have enabled us to determine activity coefficients for AgClO4 in acetonitrile over concentrations ranging from 0 to ∼1.5 m. One of the ultimate goals of the research described below was to use the activity coefficients measured in acetonitrile to provide a means of comparing cell potentials measured in acetonitrile and water. But having a self-consistent set of activity coefficients for silver perchlorate in acetonitrile and a self-consistent set of activity coefficients for silver perchlorate in water, one cannot make a direct comparison between Ag/Ag+ half-cells in these solvents. The standard states for the two activity scales are different. In one case, the standard state involves silver ions at infinite dilution in acetonitrile. In the other case, the standard state involves silver ions at infinite dilution in water. Hence, on these scales a silver electrode in contact with silver ions at unit activity in acetonitrile is not expected to be at equilibrium with a silver electrode in contact with silver ions at unity activity in water. Comparisons between EMF scales in various solvents are common, dating back to the work of Bjerrum concerning ethanol and water.28 Such comparisons are typically built upon one or more extrathermodynamic assumptions that can lead to large discrepancies in formal potentials predicted for redox couples in nonaqueous solvents.29-31 Furthermore, previous comparisons are heavily laden with jargon, little of which is generally accepted. Navigation through the (22) Activity Coefficients in Electrolyte Solutions; Pytkowicz, R. M., Ed.; CRC Press, Inc.: Boca Raton, FL, 1979; Vol. II. (23) Sinclair, D. A. J. Phys. Chem. 1933, 37, 495. (24) Robinson, R. A.; Sinclair, D. A. J. Am. Chem. Soc. 1934, 56, 1830-1835. (25) Gordon, A. R. J. Am. Chem. Soc. 1943, 65, 221-224. (26) Barthel, J.; Kunz, W. J. J. Solution Chem. 1988, 17, 399. (27) (a) Coetzee, J. F. Prog. Phys. Org. Chem. 1967, 4, 45. (b) The ionic size parameters (a) used were: aTBA+ ) 5, aAg+ ) 3.5, aClO4- ) 3, and aI- ) 3. (28) Bjerrum, N.; Larsson, E. Z. Phys. Chem. 1927, 127, 358. (29) (a) Parker, A. J.; Alexander, R. J. Am. Chem. Soc. 1968, 90, 3313. (b) Alexander, R.; Parker, A. J.; Sharp, J. H.; Waghorne, W. E. J. Am. Chem. Soc. 1972, 94, 1148-1158. (c) Cox, B. G.; Hedwig, G. R.; Parker, A. J.; Watts, D. W. Aust. J. Chem. 1974, 27, 477. (d) Parker, A. J. Electrochim. Acta 1976, 21, 671-679. (30) Popovich, O. Transfer Activity Coefficients (Medium Effects). In Treatise on Analytical Chemistry, 2nd ed.; Kolthoff, I. M., Elving, P. J., Eds.; John Wiley and Sons: New York, 1979; Part 1, Vol. 1, p 711. (31) Marcus, I. Pure Appl. Chem. 1983, 55, 977-1021.
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resulting morass is a formidable endeavor for the non-specialist, and a close inspection reveals that none of the extrathermodynamic assumptions adequately account for the influence of ionic interactions between the redox couple of interest and the supporting electrolyte. Such interactions are expected to be significant in many nonaqueous solvents. Our approach was a simple one. With complete disregard for any comparison that might ultimately be made to the aqueous scale, we first sought to construct a self-consistent EMF scale in acetonitrile. In many respects our measurements in acetonitrile are analogous to those in watersmade with complete disregard for any EMF scale in acetonitrilesinvolving the Pt|H2|H+, Cl-|AgCl|Ag cell. We sought simple electrochemical cells in acetonitrile to which others can make simple comparisons. Having access to activity scales in acetonitrile and water, we have been able to provide a readily interpretable comparison of cell potentials measured in these solvents. Interpretation of Experimental Results. To interpret data from isopiestic measurements, one uses the Gibbs-Duhem equation, which relates changes in chemical potentials of all of the components in a system at constant temperature and pressure.
∑n dµ ) 0 i
(2)
i
i
This equation can be rearranged so that unknown activity coefficients for one salt can be compared to the known activity coefficients of another salt.24
( ) ∫(
ln γu ) ln γr + ln
mr +2 mu
a1
0
)
dxar mr -1 mu xar
m1 d ln a1 ) m2 d ln a2
(4)
(3)
In the above equations γu, γr, mu, mr, au, and ar are the activity coefficients, molalities, and activities of the unknown (u) and reference (r) salts. The way in which eq 3 is used in conjunction with experimental data to determine activity coefficients is described below. The salt for which the activity coefficients is not known will be referred to as the “unknown”. The salt for which the activity coefficients are known will be referred to as the “reference”. A measurement is commenced by adding a known mass of a reference salt and a known mass of an unknown salt to separate containers. Similar amounts of solvent are added to both containers, which are then placed in a sealed vessel. Under these circumstances the vapor pressures of the electrolyte solutions in the two containers are probably not the same. Solvent will distill from one container to the other until the vapor pressures are identical. The containers are then weighed to obtain the amount of solvent present at equilibrium. In short, if the number of moles of each salt and the number of kilograms of solvent present at equilibrium are known, then the molal concentrations of both solutions are known. Using the following procedure, one can obtain activity coefficients for the unknown salt from the concentrations of the salt solutions at equilibrium. After completing a series of equilibrations over a range of concentrations, the equilibrium concentrations are plotted (mr/mu vs mr, or mu vs mr) and a polynomial fit is made to obtain values of mu/mr at convenient values of mr for which the activity coefficients are tabulated (e.g., 0.1, 0.2, 0.3 m, etc.). Thus, the first and second terms on the right-hand side of 5096
eq 3 can be obtained. The integral in eq 3 is evaluated using an adaptation of the graphical procedure described by Lewis and Randall.32 The quantity (mr/mu - 1)/ar1/2 is plotted vs ar1/2, and a polynomial fit of this plot is integrated (from 0 to the appropriate ar) to give the value of the integral. At low electrolyte concentrations, the use of isopiestic data to determine activity coefficients becomes problematic. The influence of dissolved electrolytes on the vapor pressure of the solvent becomes minimal at low electrolyte concentrations. The resulting large relative uncertainties in the equilibrium electrolyte concentrations produce large uncertainties in (mr/mu - 1)/ar1/2. Not only do these uncertainties influence the integrity of activity coefficients calculated at low concentrations using eq 3, but because we integrate from ar ) 0, the uncertainties at low concentrations also influence the values determined at higher concentrations. Equilibrium molalities at low concentrations are desirable but are experimentally inaccessible using the isopiestic technique. This problem can be circumvented using the extended Debye-Huckel equation27 to calculate activity coefficients at low concentrations. These activity coefficients can then be used as follows to calculate equilibrium molalities at concentrations that are inaccessible using the isopiestic technique. Molalities, m1 and m2, for solutions of two different electrolytes at equilibrium can be calculated if the activity coefficients, γ1 and γ2, are known for each electrolyte as a function of molality. The Gibbs-Duhem equation provides the means for determining the equilibrium molalities. For present purposes we choose to express the Gibbs-Duhem equation (eq 2) as shown in eq 4.
Analytical Chemistry, Vol. 69, No. 24, December 15, 1997
It will ultimately be necessary to integrate from ai ) 0 to nonzero values for the activity; hence, it is desirable to modify eq 4 to avoid problems associated with ln ai at infinite dilution. Using the following identity
d ln x )
2dxx xx
dxa1 )
∫
(5)
we rewrite eq 4 as
∫
a1
0
2m1
xa1
a1
0
2m2
xa2
dxa2
(6)
Equation 6 can be evaluated graphically to obtain equilibrium molalities of the two electrolytes. First, let us consider the lefthand side of eq 6. Knowing γ1 for each m1, one can calculate a1 and plot 2m1/(a1)1/2 vs (a1)1/2. A polynomial fit to this plot can be integrated to provide a value, V(m1), for the integral on the left-hand side of eq 6 at a selected value of m1. Knowing γ2 for each m2, one can calculate a2 and plot 2m2/(a2)1/2 vs (a2)1/2. A polynomial fit to this plot can be integrated to provide values for the integral on the right-hand side of eq 6 as a function of m2. At equilibrium, V(m1) ) V(m2). So, having V(m1) at m1, one can quickly determine m2 from a plot of V(m2) vs m2. The equilibrium (32) Lewis, G. N.; Randall, M. Thermodynamics and the Free Energy of Chemical Substances; McGraw-Hill: New York, 1923; pp 268-272.
molalities calculated in this manner for dilute solutions can be combined with isopiestic data obtained for more concentrated solutions. EXPERIMENTAL SECTION Materials. Acetonitrile (Burdick & Jackson, distilled in glass,
