Polarography in Sulfolane and Reference of Potentials in Sulfolane and Other Nonaqueous Solvents to the Water Scale J. F. Coetzee,’ J. M. Simon, and R. J. Bertozzi Department of Chemistry, University of Pittsburgh, Pittsburgh, Pa. 15213
A procedure for the purification of sulfolane was developed, and tests were applied for certain classes of impurities. A study of the polarographic properties of the alkali metal ions showed that the current at short drop life is anomalously low, but normal at longer times. This phenomenon is attributed to a depletion effect resulting from the high viscosity of sulfolane. Potentials in sulfolane are referred to the water scale by a procedure based on the representation of the relative polarographic half-wave potentials of the alkali metals in sulfolane and in water by a modification of the Born equation. It is estimated that the standard reduction potential of rubidium ion in SUIfolane is 0.11 V more positive than in water and 0.06 V more negative than in acetonitrile, both values including a correction for the difference in solvent molality. These results are compared with those for several other nitriles and acetone. It appears that the magnitude of the liquid junction potential between the aqueous saturated calomel electrode and 0.1 M solutions of tetraethylammonium perchlorate in sulfolane, the nitriles or acetone does not exceed a few hundredths of a volt. Qualitative observations are made for several other solvents. Some of the uncertainties in this and other procedures that have been used for the comparison of potentials in different solvents are discussed.
INRECENT YEARS the study of nonaqueous solutions has progressed rapidly, with particular emphasis on the dipolar aprotic class of solvents. The most thoroughly studied member of this class is acetonitrile ( I , 2), but other members, such as dimethylsulfoxide and N,N-dimethylformamide, also have received considerable attention (3). Dipolar aprotic solvents have very weak hydrogen bond donor properties but nevertheless have high dipole moments, and dielectric constants that typically fall in the intermediate range of 20 to 45. Certain members also have relatively weak hydrogen bond acceptor properties. The relative overall inertness of solvents of this type provides an opportunity to carry out reactions that are masked either by the solvent itself in more reactive solvents, such as water, or by solute association reactions in solvents of lower dielectric constant. An example of such a relatively inert dipolar aprotic solvent is acetonitrile. Another, and in some respects even more promising, example is tetrahydrothiophen 1,1 -dioxide (tetramethylenesulfone, sulfolane), which comparatively recently has become available in commercial quantities, Some of its physical properties have been reported as follows: bp 285 “C, mp near 28 “C (4, and (at 30 “C) density 1.2623 g. ml-l, viscosity 0.1029 poise, and 1
Please address all correspondence to this author.
(1) J. F. Coetzee, in “Progress in Physical Organic Chemistry,” Cohen, Streitwieser, and Taft, Eds., Interscience, Vol. 4, p 45 (1967). (2) I. M. Kolthoff and M. K. Chantooni, Jr., J . Amer. Chem. SOC., 91, 25 (1969); also extensive earlier bibliography. (3) C. D. Ritchie, in “Solute-Solvent Interactions,” J. F. Coetzee and C. D. Ritchie, Eds., Marcel Dekker, p 219, 1969. (4) R. W. Alder and M. C. Whiting, J. Chem. SOC.,1964, 4707 766
e
ANALYTICAL CHEMISTRY
dielectric constant 43.3 (5). The relatively high viscosity constitutes the main drawback of this solvent. We have been carrying out a systematic investigation of the properties of a variety of electrolytic solutes in sulfolane as solvent, with the emphasis on acid-base and other reactions that are particularly sensitive to the nature of the solvent employed. In order to compare the results (which will be reported elsewhere) with those obtained in water and other solvents, it is necessary to estimate the free energies of transfer of individual ions from one solvent to another. This problem, which alternatively may be stated in terms of the estimation of single ion activities and single electrode potentials, liquid junction potentials, and medium or solvent activity coefficients, requires extrathermodynamic assumptions and constitutes a major dilemma in chemistry. We have discussed elsewhere (6) some of the uncertainties associated with such estimations, and have advocated a procedure based on the representation of the relative polarographic half-wave potentials of pairs of the alkali metals in water and in acetonitrile by a modification of the Born equation. This and other procedures recently were summarized by Parker and Alexander (7). In this communication we use the same procedure to compare potentials in sulfolane with those in water, in acetonitrile, and in several other solvents. In addition, a description is given of our purification procedure for commercial sulfolane, as well as of certain peculiarities encountered in polarographic measurements in this solvent. EXPERMENTAL
Purification of Sulfolane and Tests for Impurities. The main impurity in commercial sulfolane (Shell or Phillips) is 3-sulfolene, which may be present in amounts up to 2% by weight (8). In certain applications of sulfolane, this impurity could be objectionable. Furthermore, it decomposes thermally at temperatures well below the boiling point of sulfolane into butadiene and sulfur dioxide, the latter being a particularly objectionable impurity. Consequently, we have devoted special attention to the removal of sulfolene. Commercial sulfolane was heated in 1-liter batches with 10-15 grams of solid sodium hydroxide at 170-80 “C for 24 hours while bubbling a slow stream of Airco Prepurified nitrogen through the solvent by means of a gas dispersion tube. After this treatment, the thermal decomposition of sulfolene should be complete (9) and volatile impurities should have been eliminated. Sulfolane itself exhibits good thermal stability at temperatures up to 200 “C (9). The product at this stage had a dark reddish brown color and a conductivity of 4 to 6 X ohm-’ cm-’. It was decolorized by stirring (5) R. Fernandez-Prini and J. E. Prue, Trans. Faraday SOC.,62, 1257 (1966). (6) J. F. Coetzee and J. J. Campion, J. Amer. Chem. SOC., 89, 2513, 2517 (1967). (7) A. J. Parker and R. Alexander, ibid., 90, 3313 (1968). (8) G. A. Olah and N. A. Overchuck, Can. J. Chem., 43, 3179 (1965). (9) Shell Chemical Co., Technical Bulletins IC: 63-13 R (Sulfolane) and PD-146 (3-Sulfolene).
with 10-15 grams of Fisher Norit-A Decolorizing CarbonNeutral at 80-90 "C for 6 hours, followed by suction filtration through a medium porosity glass filter. The product was then passed through a 4-foot column packed with a mixed bed of acid and base macroreticular ion exchange resins (Rohm and Haas Amberlyst-15 and Amberlyst A-21). Conventional ion exchange resins have been shown to function inadequately in many nonaqueous solvents because of physical breakdown of the resin and unfavorable exchange kinetics; macroreticular resins appear to be superior in these respects (10, 11). The column was heated to 70-80 "C to increase the exchange rate and also the flow rate, since the viscosity of sulfolane is high. The effluent was clear and had a low conductivity of 2 X 10-9 ohm-' cm-l. It was then vacuum distilled from calcium hydride in a Buchi rotary vacuum evaporator at a pressure of 0.01-0.02 torr and an oil bath temperature of 90-100 "C. Water maintained at 30 "C was circulated around the condenser to prevent freezing of the distillate. The 8 0 z center cut was collected and transferred under nitrogen to a storage bottle. The final product had a conductivity of 2 X 10-9 ohm-' cm-I, a dielectric constant of 43.3 and a density of 1.2625 g ml-I. Its water content was 1 X 10-aM, as determined by Karl Fischer titration using a Precision Scientific Co. Auto Aquatrator. In contrast to a previous report (8), Karl Fischer titrations in our purified solvent gave reproducible and reliable results. Acidic and basic impurities were determined by potentiometric titration of sulfolane diluted with an equal volume of methanol, which had been purified by ion exchange, using methanolic solutions of sodium methoxide and perchloric acid as titrants and a glass electrode as indicator (12). Using microburets, impurities could be determined in concentrations as low as l X 1 0 P eqv. l-'. The starting material of commercial sulfolane contained 4 X eqv. 1-1 acidic and 2 x 10-4 eqv. 1-1 basic impurities, while the corresponding concentrations in the purified solvent were 5 X and less than 1 X eqv. l-l, respectively. Gas chromatographic analysis revealed no impurities in the purified solvent. The polarographic range of the purified sulfolane is wide. With 0.1M tetraethylammonium perchlorate as supporting electrolyte, anodic discharge occurs at +0.04 volt and cathodic discharge at -3.50 volt us. an Ag/(O.lM AgC104 in sulfolane) reference electrode (hereafter designated as AgRE). The corresponding values us. an aqueous saturated calomel electrode (SCE) as reference are 0.70 volt more positive. Over most of this polarographic range, the residual current of our purified sulfolane was very low (allowing for the high viscosity). For example, at -2.7 volt us. AgRE, the residual current (with 1712'3t1/6= 1.0) was only 0.2 PA, which is of the order expected for the capacitor current alone at this potential. The shape of the current-potential trace also indicated that the faradaic component of the residual current was negligible. No trace was found of sulfur dioxide, which gives a (first) cathodic wave at - 1.4 volt us. AgRE. It should be stressed that the purification procedure outlined above was developed with four main objectives: (a) to remove the principal impurity, sulfolene; (b) to reduce acidic and basic impurities to the lowest level attainable, which is essential for our acid-base studies now in progress; (c) to allow purification of large batches of solvent on a continuous basis; and (d) to eliminate the need for more than one vacuum distillation. The vacuum distillation requires (10) R. Kunin, E. Meitzner, and N. Bortnick, J. Amer. Chem. SOC., 84, 306 ( 1 962). (11) Rohm and Haas Co., "Technical Notes on Amberlyst 15 and Amberlyst A 21," Philadelphia, Pa., 1968. (12) C. D. Ritchie and P. D.-Heffley, J. Amer. Chem. Sac., 87, 5402 (1965). (13) J. F. Coetzee, Pure Appl. Chem., 13, 427 (1966).
frequent attention from the operator, and constitutes the bottleneck in the procedure. The gas stripping and ion exchange steps require a considerable length of time, but little attention from the operator. Nevertheless, further study may lead to simplification of the procedure. Since it is improbable that a feasible all-purpose purification procedure can be found for a relatively inert solvent that will guarantee the absence of interfering impurities in all conceivable experiments, purification procedures should be tailored to the intended use of the solvent, as was done in the case of acetonitrile (13). The different procedures recommended for that solvent leave different relative amounts of the three main classes of impurities-namely, water and other acidic and basic components, unsaturated nitriles, and aromatic compounds. Each of these classes of impurities interferes in certain experiments, but not in others. During the course of this work, other purification procedures for sulfolane have been published. It is possible that one of these may be more suitable for a particular use of the solvent than the one described here. FernandezPrini and Prue ( 5 ) obtained sulfolane with a conductivity of 2-5 X 10-9 ohm-' cm-1 and a water content of less than 5 x 10-3M by carrying out two vacuum distillations, one from solid sodium hydroxide. Headridge, Pletcher, and Callingham (14) vacuum distilled successively from sodium hydroxide, sulfuric acid plus hydrogen peroxide, and calcium hydride. Desbarres, Pichet, and Benoit (15) pretreated the solvent with sulfuric acid plus hydrogen peroxide, extracted it with methylene chloride, and after further pretreatment vacuum distilled; the product contained 8 X 10-2M water, but solutions of salts were further dried with Molecular Sieves or calcium sulfate. A detailed comparison of the overall effectiveness of the various procedures is not possible at this stage. In particular, acidic and basic impurity levels have not been reported before. However, discharge potentials reported by Headridge et al. for 40 "C are in satisfactory agreement with our values for 30 "C. On the other hand, there is only partial agreement with the data of Benoit et al. for 25 "C. Their potentials (referred to our reference electrode) at a current of 2 pA for 0.1M tetraethylammonium perchlorate are the following, with our values given in parentheses: dropping mercury electrode, +0.06 and - 3.3 volt (+0.13 and -3.55); rotated platinum electrode, +1.7 and -2.9 volt ($2.3 and -2.9). Other Chemicals. The origin of chemicals is indicated as follows: K, K and K Laboratories, Inc.; S, G. Frederick Smith Chemical Co.; F, Fisher Purified; E, Eastman White Label. Lithium perchlorate (K), potassium perchlorate (S), rubidium perchlorate (K), cesium perchlorate (K), and silver perchlorate (S) were dried at 100 OC in uacuo. Sodium perchlorate (F) was recrystallized from water and also dried at 100 "C in uacuo. Tetraethylammonium perchlorate was prepared as described elsewhere (16) from tetraethylammonium bromide (E) and sodium perchlorate (F). Apparatus and Experimental Procedure. A 3-electrode polarograph was used, consisting of a Heath Model EVA-19-2 Polarographic Module, a Heath Operational Amplifier System Model EVW-l9B, a Heath Operational Amplifier Chopper Stabilizer Model EVA-19-4, and a Heath Dropping Mercury Electrode Apparatus Model EVA-19-6 or a platinum microelectrode having an area of 8.8 mm2 rotated at 600 rpm with a Sargent synchronous motor. The electrolysis vessel was a Sargent S-29391 polarographic cell, which has a capacity of ca. 20 ml. The second working electrode was a mercury pool. The reference electrode (AgRE) consisted (14) J. B. Headridge, D. Pletcher, and M. Callingham, J. Chem. SOC.,1967, 684. (15) J. Desbarres, P. Pichet, and R. L. Benoit, Electrochim. Acta, 13, 1899 (1968). (16) J. F. Coetzee and J. L. Hedrick, J. Phys. Chem., 67,221 (1963).
VOL. 41, NO. 6, MAY 1969
767
Table I. Test for Diffusion Control of Polarographic Reduction of Sodium Ion in Sulfolane as Solvent (3.18 X 1 0 - a M NaCIOa in 0.1M EtaNClOa at 30 "C) h(cm). r,secb Slopec id, pAb jdh-lll 1.688 0.285 35 9.0 55.5 0.283 58.0 1.894 45 7.0 2.081 0.281 55 6.0 59.7 2.280 0.283 65 5.0 59.7 61.5 2.572 0.279 85 3.8 Not corrected for back pressure; correction probably is small. * Measured at -2.75 V us. AgRE. c Slope (in mV) of E us. log [(id - i)/i] plot; theoretical value = 60 mV at 30 "C. In all cases, the half-wave potential is -2.56 V us. AgRE. 0
Table 11. Polarographic Properties of Alkali Metal Ions in Sulfolane as Solvent -Ei/zr V
Salta Idb Slope, mV us. AgRE 64 2.67 LiC104 0.78 60 2.56 NaC104 0.72 0.79 58 2.66 KC104 62 2.67 RbC104 0.80 0.82 56c 2.66c CSClO4 a Conditions: concn near 2 X 10-aM in 0.1M EtaNC104 as supporting electrolyte; h = 75 cm; temp. = 30 "C. b Diffusion current constant: I d = id/C m213f 1 ' 6 , corresponding to current at maximum drop size. Slight maximum present, not sufficiently pronounced to affect half-wave potential seriously.
of a Sargent S-30515-C silver electrode dipping into 0.5 ml of 0.1M silver perchlorate in sulfolane contained in a 8-mm i.d. glass tube fitted with an asbestos fiber sealed into the tip. The resistance of this type of electrode was near 0.5 megohm. Even though leakage of silver perchlorate through the fiber tip appeared to be negligible, an extra safeguard was provided by inserting the AgRE into an intermediate salt bridge consisting of a IO-mm i.d. glass tube fitted with an Ace Glass porosity D glass frit and containing 2 ml of supporting electrolyte solution. The salt bridge tube was dipped into the electrolysis solution as close as possible to the dropping mercury electrode, in order to minimize the uncompensated part of the iR-drop. The electrolysis solution was deaerated with Airco Prepurified nitrogen which was 99.997 by weight pure and contained 0.001 oxygen and 0.0012x water. It was unnecessary to presaturate the nitrogen with sulfolane, as the vapor pressure of sulfolane at 30 "C is only ca. 0.1 torr. All measurements were carried out at 30.0 f 0.5 "C. Because of the high viscosity of sulfolane, diffusion coefficients are low. Consequently, somewhat higher than usual concentrations of electroactive species were used (generally 2-3 x 10-3M). In all cases the supporting electrolyte was 0.1M tetraethylammonium perchlorate. All currents were corrected for residual current. Diffusion currents of the alkali metal ions were measured at -2.85 volt us. AgRE, with m = 0.75 mg sec-* and t = 4.0 sec. All potentials reported in this communication are reduction potentials. The rising sections of polarographic waves were remeasured manually, and potentials were checked with an external potentiometer.
x
RESULTS AND DISCUSSION
Polarographic Properties of Alkali Metal Ions in Sulfolane. All polarograms obtained with the dropping mercury electrode in sulfolane exhibit an important peculiarity. For example, for the alkali metals, plots of E us. log[& - i ) / i ] are linear 768
ANALYTICAL CHEMISTRY
with slopes near the theoretical value of 60 mV for a reversible one-electron reaction, provided current values corresponding to maximum drop size are used. However, if mean current values are used, the plots exhibit much greater scatter and the best straight lines have slopes considerably greater than 60 mV, typically near 70 mV. The current-potential trace for the rising part of the wave also deviates from that normally encountered, in that as the diffusion plateau is approached, the current at minimum drop size increases proportionately much less than the maximum current does, giving a pronounced flare to the current-potential envelope. Consequently the polarogram is more drawn-out for mean than for maximum current values. We attribute this phenomenon to the high viscosity of sulfolane, which may prevent sufficiently rapid establishment of the bulk concentration of electroactive species in the region of solution where the new drop is beginning to grow and where the previous drop has depleted the electroactive species. As the drop continues to grow, this effect should diminish, as observed. Furthermore, the influence of depletion at short life times of the drop should increase as the diffusion plateau is approached, again as observed. If this interpretation is correct, the same phenomenon should be encountered in other high viscosity media, such as ethylene glycol and glycerol. All diffusion current constants and slopes of waves reported in this paper were derived from maximum current values. Polarograms were obtained for sodium at various heights of mercury. The results are summarized in Table I. It is clear that the reduction of sodium ion at the dropping mercury electrode in sulfolane is diffusion controlled. In Table 11, polarographic data obtained for the alkali metals are summarized. Certain of our results can be compared to some extent with those reported in two papers that have appeared after this work essentially had been completed. Headridge et al. (14) reported half-wave potentials for sodium, potassium, and rubidium at 40 "C measured against a silver-silver chloride reference electrode immersed in sulfolane saturated with tetraethylammonium chloride and silver chloride. Exact comparisons are impossible because of the temperature difference and because their waves deviated somewhat more from reversibility than ours did, but the two sets of half-wave potentials are reasonably consistent in that they differ by a nearly constant value of 1.12, 1.11, and 1.14 V for sodium, potassium, and rubidium, respectively. Benoit et al. (15) measured the half-wave potentials of lithium, sodium, and potassium at 25 "C against an Ag/(O.OlM AgC104 in sulfolane) reference electrode, reported to have a potential of f0.640 V us. SCE--i.e., 0.060 V more negative than that of ours at 30 OC. Again, the waves deviated more from reversibility than ours did. Furthermore, the two sets of half-wave potentials are in poor agreement. A rough comparison based on referring the half-wave potentials to our electrode, gives values that are 0.14, 0.13, and 0.11 V more negative than ours for lithium, sodium, and potassium, respectively. It may be worthwhile to determine whether these discrepancies are caused by the fact that the one set of data applies to a temperature below the normal freezing point of sulfolane. The diffusion current constants listed in Table I1 can be compared to those observed in aqueous solution. After allowing for the difference in viscosity by multiplying the constants for sulfolane by (0.103/0.0080)1'2or 3.6, and after converting currents at maximum drop size to effective average currents by multiplying by 6/7, values similar to those for aqueous solutions at 30 "C are obtained. This fact indicates
that the diffusing species in the two solvents have roughly the same effective size. However, the observation that the value for lithium ion is larger than that for sodium, which agrees with the conductivity data of Della Monica et al. (17), is unusual. It may mean that because of steric crowding a smaller number of sulfolane molecules migrates with the small lithium ion than with sodium ion. Incidentally, the fact that the conductivities of the halide ions are abnormally high and increase from iodide to chloride (17) indicates that these ions are extremely weakly solvated by sulfolane. We are determining the solvent activity coefficients of these ions. Reference of Potentials in Sulfolane to the Water Scale. A variety of approaches have been followed to refer potentials measured in one solvent to another solvent (usually water) as standard state (6, 7, 18). In many cases, the results are not in very good agreement and it is difficult to assess the relative reliability of different approaches. It is important to realize that the problem essentially reduces to the evaluation of the generally small difference (the free energy of transfer of a reference ion) between two large numbers (the free energies of solvation of the ion in the two solvents). This problem is superimposed on the basic one already referred to, namely, the uncertainties associated with concepts such as the free energy of individual ions necessitate the introduction of extrathermodynamic assumptions. Certain approaches suffer from a basic weakness, in that they involve estimations of the two large numbers referred to, an analytically unfavorable situation. This is true of ab initio statistical mechanical calculations of solvation enthalpies based on Buckingham’s theory, which have a more satisfying theoretical basis than is the case for the semi-empirical procedures (19). However, at present the reliability of such calculations is seriously impaired by gross uncertainties associated with factors such as the type of coordination in the primary solvation shell, the precise magnitude of the quadrupole moment of the solvent molecules, and the precise values of interaction distances to be used in the equations, some of which have a high order dependence on distance. A method which evaluates the free energy of transfer directly therefore is to be preferred at this stage, particularly if this can be done for a reference ion alone without invoking the counter-ion of a salt, other ions or corresponding uncharged species (7). We have described such a method elsewhere (6) and repeat here only the essential details. The basic assumption is that the interaction of the alkali metal ions with sulfolane and with water is predominantly electrostatic in nature, and that the solvation energy differences of pairs of these ions in sulfolane can be related to corresponding differences in water by appropriate sets of modified Born equations :
In Equation 1 , A G*:” is the electrostatic component of the free energy of solvation of a mole of electrolyte, N is Avogadro’s number, e the electronic charge, D the bulk dielectric constant of the solvent, z+ and z- the charge numbers, and r+ and r- the crystallographic radii of the cation and anion, (17) M. Della Monica, U. Lamanna, and L. Senatore, J . Phys. Chem., 72, 2124 (1968). (18) H. Strehlow, in “Chemistry of Nonaqueous Solvents,” J. J. Lagowski, Ed., Academic Press, Inc., New York, Vol. 1, p 129 (1966). (19) L. Weeda, “Ionic Enthalpies of Solvation,” thesis, Vrije Universiteit, Amsterdam, 1967.
respectively, and r,‘ and r-’ are empirical correction temp which have values of 0.72 f 0.03 8, and 0.45 f 0.11 A, respectively, for the alkali halides in water (20). The physical significance of these correction terms is quite involved, in that they allow empirically for a host of shortrange effects, such as dielectric saturation and Van der Waals forces, including the fact that cations and anions have quadrupole interaction energies of opposite sign. Of course, there is an inherent danger in the use of Equation 1 , because it contains two independently adjustable parameters. Furthermore, the values of r-’ for the individual halide ions in water vary much more than the r+’ values for the alkali metals do. As pointed out before (6), we believe that solvation energies of individual ions calculated from the experimental values for salts by using Equation 1 (18) are too inexact for the reliable evaluation of ionic free energies of transfer from water to acetonitrile, and in fact may lead to the wrong sign for the free energy of transfer of the alkali metal ions. Fortunately, where values are available for some property of the cations alone, such as their standard potentials or polarographic half-wave potentials, it is possible to eliminate the anions from consideration, and to use Equation 1 in the reduced form
When AG,” is expressed in kcal mole-’ and r, and r,’ in
+)
A,
the coefficient Ne’ ( 1 is 164 for water (D = 78.5) and 2 162 for sulfolane (D = 43). The probable reliability of the calculations is increased further by two additional restrictions: only free energy differences for pairs of cations are calculated for each solvent, and then the differences of these differences in the two solvents are evaluated. This double comparison procedure should reduce further many of the uncertainties normally associated with the Born equation. A basically similar procedure has been applied by Strehlow to the watermethanol pair (18). In Table 111, the half-wave potential of each alkali metal is referred to that of rubidium, first for sulfolane and then for water as solvent, and finally the two sets of numbers are compared in column 5. Qualitatively, the fact that the AAEIl2values of ions smaller than rubidium are positive, while that of the larger cesium ion is negative, indicates strongly that all alkali metal ions are solvated more weakly by sulfolane than by water. For example, in both solvents the free energy of solvation of lithium ion must be “greater” (more negative) than that of the larger cesium ion, but the AAEljz values show that the difference is largest in water, by an amount corresponding to 0.23 volt or 0.23 X 96,500/4.18 or 5.3 kcal mole-’. We now invoke the modified Born equation. For the difference in solvation energy of cesium and lithium ions in water, Equation 2 predicts A G 0 c s - ~ i= -164
1
(1.69
+ 0.72 - 0.68 + 0.72 49.1 kcal mole-’
Hence, in sulfolane this difference amounts to 49.1 - 5.3 = 43.8 kcal mole-’. Substitution into Equation 2 for sulfolane gives 43.8 = -162
1
1.69
+ r+’
0.68
+ r+’
(20) R. M. Noyes, J . Amer. Chem. SOC.,84,513 (1962). VOL. 41, NO. 6, MAY 1969
769
Table m. Reference of Standard Potentials of Alkali Metals in Sulfolane (SL)and Acetonitrile (AN) to the Water (W) Scale Ion (AEI/z)sL~ (AEi/z)wc AAEiizd AAEl/20alod.e A E O ~ L : W / , ~ AE'AN.W~>* Li+ 0.68 0.00 -0.20 0.20 0.20 0.31 0.40 (0.35) (0.42) Na+ 0.98 0.11 0.01 0.10 0.10 0.21 0.29 (0.23) (0.29) K+ 1.33 0.01 -0.01 0.02 0.03 0.14 0.20 (0.15) (0.21) Rb+ 1.48 0.00 0.00 0.00 0.00 0.11 0.17 (0.13) (0.18) cs+ 1.69 0.01 0.04 -0.03 -0.02 0.09 0.15 (0.11) (0.16) a Crystallographic radius (A); ref. 21. * Volts us. (El/z)BLof Rb+, at 30 'C; comparisons based on Rb (rather than Cs) scale for reasons indicated in refs. 18 and 22, and because Cs wave has slight maximum in several solvents. c Volts us. (EIl2)wof Rb+, at 25 "C. AAEm = ( A E ~ / z ) sL (AEi/z)w.
Calculated from Equation 2 with r+l values of 0.81 and 0.72 A for SL and W, respectively; see text. A E s L . ~ ' = EEL' - Ewe, both on the water scale and corrected by -0.05 V for the difference in solvent molality. 0 Values in parentheses obtained by empirical graphical procedure (see text); preceding values are preferred. h AEAN-W''= EAN' - Ew', both on the water scale and corrected by -0.02 V for the differencein solvent molality; recalculated from the data in ref. 6, using present radii for Li+ and Na+. e
Table IV. Estimation of Solvent Shifts of Rubidium Standard Potential and of Liquid Junction Potential us. the Aqueous Saturated Calomel Electrode Acetonitrile Propionitrile Isobutyronitrile Benzonitrile Acetone / 0.21 9 0.26 0.23 AAE1/z(Li)O 0.12 0.10 0.10 0.13 0.06 AAE1IZ(Na)n / 0.03 / 0.03 0.01 AAEidK)" AAEi/z(Rb)n Db r+ I C AENAS-W YRBY ELJ'
0.00
0.00
0.00
0.00
0.00
36.0 26.1 20.2 25.2 20.7 0.82 0.80 0.79 0.83 0.74 0.18 0.20 0.11 0.17 0.16 +0.02 -0.07 -0.05 -0.05 -0.04 Data for 25 "C, from ref. 22. b Dielectric constant of solvent. c Radius correction term in Equation 2 (A). d Solvent shift of rubidium standard potential (V), corrected for solvent molality. e Average value of liquid junction potential (V), calculated from available A E X A ~ values . ~ " for all ions; to be added algebraicallyto potentials measured with cu. 0.1M EtaNCIOa as supporting electrolyte us. aqueous SCE. Value for sulfolane is -0.04V. Note that correction for solvent molality is included; if it were possible to measure ELJ directly, the experimental value would not contain this correction. f Not measured. g Wave not reversible.
from which a value for r,' for sulfolane of 0.81 A is calculated. Similarly, the best value of r,' for all the data is 0.81 A. Values of A A E l i z calculated from Equation 2 with r,' = 0.72 and 0.81 A for water and sulfolane, respectively, are entered in column 6 of Table 111. Agreement with the experimental values is satisfactory. Finally, the same calculations indicate that the half-wave (or standard) potentials of lithium, sodium, potassium, rubidium, and cesium are more positive in sulfolane than in water by 0.36, 0.26, 0.19, 0.16, and 0.14 volt, respectively. It still remains to allow for the difference in solvent molality in the two solvents (6), requiring a correction of -0.05 V. The corrected AE" values are entered in the last column of Table 111. In reference 6 (acetonitrile) we have used Pauling radii. There is some reason to believe that the Goldschmidt-Ahrens radii used here are preferable. The Pauling values for sodium (0.95) and especially lithium (0.60) differ from those used here. However, in the double comparison method employed, very nearly the same value of r,' is obtained with the two sets of radii. The best values of r,' for acetonitrile are 0.82 and 0.81 A for the Goldschmidt-Ahrens and Pauling scales, respectively. The formation constants of the ion pairs produced by perchlorate ion with the different alkali metal ions in sulfolane 770
ANALYTICAL CHEMISTRY
are small and similar [6.5 to 9.4 1. mole-'] (9,and thecorrection for this effect (22) is negligible. The same is true for acetonitrile (23). It is to be noted that the potentials of the particular reference electrodes actually used in the two solvents are not relevant in the calculation of AE" values. An important point must be emphasized. Our qualitative conclusion that the alkali metal ions are solvated more weakly by sulfolane than by water does not depend on the validity of the modified Born equation. However, it does involve the assumption that the nonelectrostatic ("neutral") component of the free energy difference of a given pair of these ions is similar in the two solvents. The correction for this nonelectrostatic effect is zero if the "zero-energy assumption" (6, 20) is accepted. If the "inert gas assumption" (20) is preferred, a correction can be computed from the relative solubilities of pairs of the corresponding inert gases in the two (21) L. H . Ahrens, Geochim. Cosmochim. Acta, 2, 155 (1952). (22) J. F. Coetzee, D. K. McGuire, and J. L. Hedrick, J. Phys. Chem., 67, 1814 (1963). (23) R. L. Kay, B. J. Hales, and G. P. Cunningham, ibid., 70, 3925 (1967).
solvents. Such solubility data are not available for sulfolane, but they are for water and acetonitrile ( 2 4 ) and the correction is small. We also have used an alternative empirical procedure to estimate these solvent shifts of standard potentials. For both sulfolane and acetonitrile, a plot of AAE112(referred to cesium, rather than rubidium) us. the function
($- $) where i represents the ions from lithium through rubidium, is linear through the origin within experimeatal error (~k0.02 volt), with slopes of 0.27 and 0.30 volt A-I, respectively. The products of these slopes and the reciprocal radii of the ions give the AE" values (corrected for solvent niolality) entered in parentheses in the last two columns of Table 111. This procedure is related to that used by Izmailov and others (18) to split solvation energies of electrolytes into the ionic components for individual solvents. As with the modified Born method, its restriction here to pairs of solvents may increase its reliability. Nevertheless, it is not clear a priori how much reliance can be placed on this purely empirical procedure. By combining the AE" values in the order listed in Table I11 with the corresponding half-wave potentials measured in water against the SCE (22) and in sulfolane against the AgRE (Table 11), individual positive values of 0.65, 0.65, 0.66, 0.67, and 0.66 volt are calculated for the potential of the AgRE (SL, 30 "C)referred to that of the SCE (W, 25 "C). The average value of +0.66 V happens to agree closely with the value of $0.700 V measured directly at 30 "C, using a salt bridge consisting of 0.1M tetraethylammonium perchlorate in sulfolane. This indicates that the liquid junction potential involved in the direct measurement is small (-0.04 V). By introducing a rough activity coefficient c:rrection based on the Debye-Huckel equation (6) with n = 4 A, the standard potential of silver ion in sulfolane is found to be near +0.74 V us. SCE, or 0.19 V more positive than in water. Parker and Alexander's estimates of solvent activity coefficients (7) correspond to a value 0.07 V more negative than in water. The agreement is very poor, even for estimates as hazardous as these. However, for the AE" value of -0.07 V to be valid, it is a necessary condition that all alkali metal ions except lithium must be more strongly solvated in sulfolane than in water, which differs qualitatively from our conclusion. Similarly, their estimate for silver ion in acetonitrile amounts to a conclusion for rubidium and cesium ions which differs qualitatively from ours. However, it should be realized that we are comparing solvation energies in solvents containing supporting electrolytes, although we doubt that this perturbation is very significant. Applicability of Modified Born Procedure to Other Solvents. The method described here requires the availability of reliable values for the half-wave or preferably the standard potentials of the alkali metals. Obviously, the values for sodium and especially lithium are particularly important for the success of this procedure. Serious difficulties are encountered in measuring standard potentials in solvents that have some degree of Bronsted acidity, because of reaction with the alkali metal amalgam (18). Unfortunately, in several solvents the polarographic waves of the alkali metals, particularly lithium, are not sufficiently reversible to allow quantitative evaluations. Several solvents for which quantitative or semiquantitative (24) Fan-tih Chiang, Ph.D. thesis, University of Minnesota, 1967, pp 107, 203.
conclusions can be drawn are listed in Table IV. The values for acetonitrile are included for comparison. Our previous value of -0.03 V for the liquid junction potential at the acetonitrile-water interface was based on the standard potential value reported by Pleskov for rubidium in acetonitrile and on the Pauling scale of ionic radii. When the evaluation is based instead on our half-wave potentials for all the alkali metals and on the Goldschmidt-Ahrens radii, using the AE" values in Table 111, individual values of +0.02, +0.02, +0.02, +0.02, and +0.03 volt are calculated for the liquid junction potential. Our initial comparisons of half-wave potentials in the above solvents ( 2 2 ) were based on Pleskov's uncorrected rubidium scale, and now must be re-evaluated. However, after introduction of the refinements discussed in this communication, general comparisons remain qualitatively the same. As far as specific comparisons based on small potential differences are concerned, a minor dependence of the half-wave potentials of the alkaline earth metals, copper(1) and silver(1) on the dielectric constants of non-aromatic nitriles was noted. This trend was ascribed to differences in the stability of the metal perchlorate ion pairs; it now appears that this effect is unimportant. Finally, phenylacetonitrile should be eliminated from consideration, because the polarographic wave of rubidium obtained in this solvent deviates too much from reversibility (22, Table 11). It seems to be a fortuitous consequence of the choice of supporting electrolyte that most of the liquid junction potentials listed in Table IV are relatively small. A change in supporting electrolyte may cause a significant shift in the half-wave potential measured against the SCE, particularly in solvents of lower dielectric constant (22, Table I). For example, with 0.1M tetrabutylammonium iodide as supporting electrolyte in benzonitrile, the value of ELJincreases from -0.05 V to -0.15 V. We have attributed such variations before ( 2 2 ) to structure making effects. On the basis of more recent evidence (6), it now seems more reasonable to invoke changes in medium activity coefficients of the supporting electrolyte ions. Qualitative conclusions can be drawn about a few other solvents. The polarographic waves of the alkali metals in liquid ammonia at -36 "C deviate somewhat from reversibility (25). Nevertheless, the AAEl/2 values of -0.23, -0.12, and -0.05 volt for lithium, sodium, and potassium, respectively, indicate that these ions are solvated more strongly by ammonia at - 36 "C than by water at 25 "C (as expected), to a degree roughly equal to that by which they are solvated more weakly by acetonitrile than by water. In dimethylsulfoxide and N,N-dimethylformamide the wave for lithium is irreversible, but those of sodium and potassium are reversible (26). The AAEI/2 value of sodium (referred here to potassium) is 0.00 volt in both solvent. It would be rash to draw definite conclusions from a single AAEl,2 value, but it nevertheless seems unlikely that the free energies of transfer of sodium, potassium, rubidium, and cesium ions from water to dimethylsulfoxide or N,N-dimethylformamide can be very large. In the case of lithium ion, the possibility of specific interactions with certain solvents, which are not recognized by the Born equation, should be kept in mind. In conclusion, it must be emphasized that at present it is impossible to prove unambiguously the validity of any (25) H. A. Laitinen and C. J. Nyman, J. Amer. Chem. SOC.,70, 2241 (1948). (26) D. L. McMasters, R. B. Dunlap, J. R. Kuernpel, L. W. Kreider, and T. R. Shearer, ANAL.CHEM., 39,103 (1967).
VOL. 41, NO. 6, MAY 1969
771
procedure proposed for the comparison of potentials in different solvents. However, if a given procedure is to have any possible general validity, it must generate self-consistent and reasonable predictions. This is a necessary, but not sufficient, condition for its validity. Probable uncertainties in different procedures can be identified, as was done in this communication and elsewhere (6, la), although it is difficult to gauge the magnitude of the uncertainties. In certain cases the applicability of a given procedure to a given pair of solvents can be questioned because it generates predictions that are qualitatively in conflict with strong experimental evidence. Two examples of such evidence will be given. First, as discussed above, there are strong polarographic indications that the alkali metal ions are solvated more strongly by water than by either sulfolane or acetonitrile. The same conclusion applies to the remaining solvents listed in Table IV. Likewise, nuclear magnetic resonance and infrared studies indicate that in acetonitrile-water mixtures lithium ion is preferentially solvated by water over virtually the whole range of solvent composition (27). Any procedure which predicts the opposite, is open to criticism for comparisons of potentials in these solvents with those in water. However, it
17, 1969. We thank the National Science Foundation for financial aid under grant number GP-6478X.
(27) Unpublished results, this laboratory, 1968.
(28) H. Schneider and H. Strehlow,2.Physik. Chem., 49,44 (1966).
may be more appropriate for other pairs of solvents; we believe this to be the case for the procedure based on the ferrocene potential (6). Second, Hittorf transference measurements for silver nitrate in acetonitrile-water mixtures show directly that silver ion is preferentially solvated by acetonitrile, and nitrate ion by water (28). Again, any procedure which fails to predict both of these experimental facts is not appropriate for comparisons between acetonitrile and water. It is clear that at present the reliance which can be placed on any given approach available for the comparison of potentials in different solvents depends on the extent to which its predictions can be tested by independent experimental evidence. ACKNOWLEDGMENT
We thank C. E. Wilson of this department for his valuable advice and experimental help during the polarographic measurements.
RECEIVED for review December 10, 1968. Accepted February
A Solid-State Control led-PotentiaI DC Polarograph with Cyclic Scanning and Calibrated First- and Second- Derivative Scales H. C. Jones, W. L. Belew, R. W. Stelzner, T. R. Mueller, and D. J. Fisher Analytical Chemistry Dioision, Oak Ridge National Laboratory, Oak Ridge, Tenn. 37830 This instrument is a versatile, reliable polarograph incorporating desirable design features of previous ORNL DC polarographs and having additional functional features and operating conveniences. Precision scan rates (less than 0.1% relative standard deviation) from 0.1 to 10 volts/minute in a 1, 2, 3, 5 sequence are provided. Current ranges from 0.02 *A to 10 mA in a 1,2,5 sequence are available. Efficient filtering of the current signal from the polarographic cell makes possible the use of active first- and secondderivative networks giving accurate derivative waves on precisely calibrated scales. The gain of each derivative network is changed automatically as the scan rate is changed to make the recorded derivative peak heights essentially independent of scan rate, thus eliminating the need for a range search. When the ORNL Polarographic Drop Time Controller is used with this polarograph at a drop time of 0.5 second and a scan rate of 1 volt/minute, polarograms can be recorded in approximately 30 seconds with a relative standard deviation of 0.2% at a concentration of 10-%l. MANYSOPHISTICATED polarographic techniques, such as pulse polarography, square-wave polarography, Tast polarography, and two-cell differential polarography, have been introduced. Excellent DC polarographic results can be obtained by use of advanced instrumentation and attention to experimental details. This approach challenges the above techniques in simplicity of instrumentation and application. Derivative D C polarography carried out by taking the time-derivative of the average cell current has been found to be an extremely 772
ANALYTICAL CHEMISTRY
useful technique. The sensitivity, precision, and resolution attainable by this method are comparable to those attained by most other polarographic techniques. One disadvantage of derivative D C polarography had been the slow scan rate necessary to attain good resolution of overlapping polarographic waves. Shorter drop times with low average mercury flow rates make it possible to obtain better resolution at fast scan rates. Rapid scan rates provide increased sensitivity and allow shorter analysis time. The instrument described here is a versatile polarograph having capabilities of previous ORNL DC polarographs (1-3), but with improved performance, functional and operational features not included in previous instruments, and low maintenance requirements and reliability resulting from the use of solid-state operational amplifiers. The potentiostat is capable of delivering 20 mA at 10 volts to the polarographic cell. Accurate current ranges having full scale values of 0.02 pA to 10 mA are provided. An electronic scan generator is used to vary the cell potential linearly at scan rates ranging
(1) M. T. Kelley, H. C. Jones, and D. J. Fisher, ANAL.CHEM., 31, 1475 (1959). (2) M. T. Kelley, D. J. Fisher, and H. C. Jones, [bid., 32, 1262 (1960). (3) D. J. Fisher, W. L. Belew, and M. T. Kelley, “Polarography 1964,” Vol. 1, G. J. Hills, Ed., Macrnillan, London, 1966, pp 89-134.
