Conversion of Polarographic and Other Potentials from One Reference Electrode to Another Keiichi Tsuji’ and Philip J. Elving2 The University of Michigan, Ann Arbor, Mich. MEASURED potential data from electrochemical measurements-e.g., half-wave potentials obtained in the polarography of aqueous systems-are commonly recorded against the saturated calomel electrode (SCE). Although these values inevitably include the liquid-junction potentials between saturated KCl and sample solutions, which can be fairly largee.g., if the sample solution is strongly acidic-they are nevertheless useful, at least for the comparison of data from different laboratories. Actual polarographic measurements, for example, are not always carried out using SCE as the reference electrode. Thus, a mercurous sulfate electrode (MSE) is sometimes used as the external reference electrode because of its supposed merit of less polarization on current passage ( I ) or to avoid contamination of the sample solution by chloride ion. In such cases, the measured potential values have to be converted to the SCE basis by correcting for the potential difference between the two reference electrodes. There seems to be no standard procedure for the measurement of this potential difference if the normal electrode half-reaction data are not used; the most common one would presumably involve measuring the emf of a galvanic cell comprising the two electrodes in direct contact with each other-e.g., a galvanic cell consisting of SCE and MSE connected to each other by a saturated KC1 bridge. Because published polarographic potential data thus obtained are most useful if they can be duplicated, within experimental error, when the polarography of the identical solution is carried out using SCE as the external reference electrode, it should be pointed out that the experimental procedure outlined for the conversion of potential data can at times introduce errors into the converted values, which exceed the range of normal experimental error. [The accuracy of measurement of polarographic half-wave potentials is discussed by Meites (2).] In a polarographic system using reference electrode A , in which the iR drop across the cell is negligibly small or fully compensated, the measured potential difference between the indicating electrode such as a DME and the reference electrode, E, is given, by analogy to the potentiometric system, by
where Eind, is the potential of the indicating electrode, E A the potential of reference electrode A , and EjAvS,the liquid-junction potential between reference electrode and sample solution. If electrode A is connected to the sample solution by a bridge, whose electrolyte composition is not the same as that of the solution in the electrode, the fixed liquid-junction po1 Present address, The Institute of Physical and Chemical Research, Yamatomachi, Saitama, Japan. 2 To whom correspondence should be addressed.
(1) P. Zuman, “Organic Polarographic Analysis,” Pergamon Press, New York, N. Y., 1964, pp 34-5. (2) L. Meites, “Polarographic Techniques,” 2nd ed., Interscience Publishers, New York, N. Y., 1965.
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ANALYTICAL CHEMISTRY
tential between electrode solution and bridge is, for the sake of convenience, considered to be included in the potential E A , and EjAtSis understood to represent the liquid-junction potential between the bridge and sample solution. Consider another polarographic system with the same sample solution and reference electrode B. The measured potential difference between indicating electrode and electrode B will be E’
=
E’ind.
- (EB + EjBv”)
(2)
where the symbols have similar meanings as in Equation 1. When the states at the indicating electrodes in regard to the reactions involved are identical-Le., Eind. = E’ind.-the difference between E and E’, E,, is
E,
= (EA
- Ea) + (EjAvS- EjBvs)
(3)
E, is the potential difference to be corrected for if the converted value is to represent the potential which would be obtained using another reference electrode. On the other hand, the emf of a galvanic cell consisting of the two electrodes in direct contact is (EA
- EB) + Ed”.” = E,*
(4)
If E,* is used, instead of E,, for the conversion of the potential data, an error, AE,, will be introduced in the result-Le.,
AE, = E,
- E,*
= E,A.S
- EjBv”
- EjA,B
(5)
-which usually is not zero, except when any two or all of the three solutions--i.e., the two electrode solutions (or the bridge solutions, when the electrodes have liquid bridges connecting them to the sample solution) and the sample solution-are identical. The failure to warn against the kind of error represented by AEc is probably due to the assumption that the individual liquid-junction potentials in Equation 5 are themselves small with their differences being hardly larger than normal polarographic experimental error. The experiments, subsequently described, show that this is not always true. Actually, Bates ( 3 ) has emphasized that such residual liquid-junction potential errors can be appreciable. In order to obtain E,, it is usually impracticable to evaluate the individual liquid-junction potentials EJAgSand EjBt5. Fortunately, E, is directly measurable because it is equal to the emf of the galvanic cell consisting of the two electrodes, which are connected to each other oia the sample solution. The experiments which follow show that conversion of potential data, using the values of E, thus obtained, always gives satisfactory results. EXPERIMENTAL.
The polarograph used was based on a potentiostat utilizing solid-state operational amplifiers. The potential of the ~~
(3) R. G. Bates, “Determination of pH,” Wiley, New York, N. Y., 1964.
Table 1. Conversion of Polarographic Half-Wave Potentials Measured with One Reference Electrode to Values Against Another Reference Electrode EI/Zus. SCE, mV Sample soh Reference electrode A SCEC calcd using AEc,mV Expt. composition Nature Biz,mV (observed) Ec*,mV E,, mV Ef E, Found Calcdb 1 0.401mM TIzSO4; MSE (1F NazS04; -849 -459 414.3 390.3 -435 -459 -24.0 -10.8 0.02F LiCl 0.01F &Sod) 2 0.401mMTIZSO4; MSE (1FNa2S04; -863 -458 413.3 405.5 -450 -458 -7.8 3.6 0.02F LiCl 0.01FH2SO4)e 3 0.401mM TIzSOa; MSE (1F NazS04; -861 -463 414.2 397.6 -447 -463 -16.6 -4.2 0.01F HzS04) 0.2F LiCl 4 0.401mMTIzS04; MSE(1FNaZSO4; -868 -462 413.5 406.0 -455 -462 -7.5 3.3 0.2F LiCl 0.01F HzSOa)C -13.8 -664 -643 20.6 -643 0.0 20.6 -664 SCEc 5 0.208mM CdCIz; 1F HCI 32.3 -8.7 -642 407.7 440.0 -675 -643 MSE(1FKzS04) -1083 6 0.208mMCdClz; 1F HCI -642 409.1 442.5 -642 33.4 -8.71 -675 MSE(lFKgS04)b -1084 7d 0.208mMCdCl2; 1F HCI 0 Reference electrode B. Calculated on basis of Henderson’s equation (3). c With 1F KNOa agar bridge. d Two-electrode configuration (cf. text) with the polarographic current passed through the bridge. e With 1F &So4 agar bridge. f Calculated on the basis of the junction without the agar bridge. DME was controlled by a 10-turn helical potentiometer, which permitted 2-mV minimum adjustment. Current, measured by a recorder with a pen speed of 0.6 sec/full scale, was manually plotted against potential to give the normal polarographic curve. A three-electrode configuration with a platinum plate counter electrode of 10 cm2 area was employed in a 1 experiments summarized in Table I except No. 7,in which the reference electrodes also served as the counter electrode, so that the current flowed through the reference electrode and its junction with the sample solution. The maximum iR drop across the cell, under the conditions of No. 7, was 0.04 mV, so that no correction for it was necessary. Liquid junctions were made, except where noted, through a few strands of asbestos fiber sealed into the end of a piece of glass tubing. In some experiments, the junctions were 4% agar bridges (10-mm length) of the type frequently used in polarography, contained in the cross bar of an H-cell following a 10-mm diameter medium-porosity sintered glass disk. The resistance of the cell with such an agar bridge, measured by a bridge operating at 1 Hz, was 32.2 ohms, when the agar contained saturated KC1 and the solutions in the compartments were saturated KC1 and I F HCl, and 65.9 ohms when the agar contained 1F K S 0 4 and the solutions were 1 F K2S04and 1F HCl. Potentials were measured with a precision potentiometer. All experiments were made at 25 “C, with reagent grade chemicals and normally accepted procedures. RESULTS AND DISCUSSION
Table I summarizes the data obtained where reference electrode A is generally the MSE with varying solution composition and reference electrode B is always the SCE. Potential values E,* are the measured emf of the galvanic cells consisting of electrodes A and B, which are virtually in direct contact with each other through saturated KC1 solution, and potentials E, are the similar emf‘s of the cell with the two electrodes connected to each other through the sample solution. The differences of these two potential values are given as AE, while the calculated values of AE, are based on the individual liquid-junction potentials calculated on the basis of Hender(4) D. A. MacInnes, “The Principles of Electrochemistry,” Dover, New York, N. Y. 1961
son’s equation (3, 4). The latter equation was used rather than Planck’s equation on the basis that the potentials of continuous mixture junctions and of free diffusion junctions, such as those formed with a congealed salt-agar bridge, are given by the Henderson equation (cy. reference (3), especially pages 2656). Conductances of ions necessary for the calculation were taken from MacInnes (4). It is apparent that conversion of half-wave potentials measured us. A to values us. B, using E,, gives values in excellent agreement with those found experimentally. In contrast, the use of E,* for the conversion gives inconsistent results. 7 he values of AE,, therefore, represent the error introduced when E,* is used. These errors are large enough to damage the usefulness of the converted potential values, The use of a KNOBbridge with electrode A reduces the error, but does not eliminate it. Experiment 5 explicitly shows that a SCE with a KNOs bridge can not be regarded as equivalent to the SCE without the bridge; such presumption would introduce an error of 21 mV in the recorded value, when the sample solution is 1F HCI. Effect of Current Flow. The usual concept of liquidjunction potential strictly applies to liquid junctions without current flow, which is approached in potentiometry and in polarography with a three-electrode system. For twoelectrode polarography, however, current flow through the liquid junction may possibly alter the distribution of ions at the junction and hence the potential, so that the usual concept of liquid-junction potential is not applicable. Examination of the Table I data focusing on No. 7 suggests that the effect of the current flow on the junction potential may not exceed the usual polarographic experimental error, at least under the experimental conditions employed. This point was further investigated, using the KC1-agar bridges of No. 7. Currents up to 100 PA, in both directions, were passed through the agar bridge, which was the junction between saturated KCl and 1F HC1 solutions, by means of large spiral AgAgCl electrodes in each solution. The potential difference between the ends of the bridge was measured, using two AgAgCl electrodes in saturated KCl with capillary tips which were placed at 2-mm distances from the ends of the bridge. VOL. 41,
NO. 1,
JANUARY 1969
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An essentially similar experiment was also made with a 1F K&04 agar bridge and 1FK2S04 and 1FHC1solutions. The rate of the potential change was in agreement with the expected iR drop, was reversible, and was reproducible within 0.2 mV. Consequently, under the usual polarographic conditions, the effect of current flow on the junction potential is smaller than the polarographic experimental error, at least for the combinations of solutions and agar bridges employed.
CONCLUSIONS It is recommended that the emf of a galvanic cell consisting of two reference electrodes, which are connected to each other through the sample solution, be used to convert polarographic and other types of electrochemical potentials measured against
one reference electrode to values us. the other reference electrode. Use of the emf of a cell consisting of the two reference electrodes, which are in direct or virtually direct contact with each other, produces significant errors in the converted potential values, which are larger than polarographic experimental errors and which cannot be predicted by calculation based on Henderson’s equation. The above conclusions may be even more important in polarography in nonaqueous media, where the liquid junction potentials are larger than in aqueous media and where a considerable variety of reference electrodes is currently used. RECEIVED for review July 31, 1968. Accepted September 30, 1968. The authors thank the National Science Foundation, which helped support the work described.
CORRESPONDENCE Controlled Surface Porosity Supports for High Speed Gas and Liquid Chromatography SIR: The advantage in carrying out gas chromatographic separations using packed columns with particles consisting of solid cores and a thin porous coating was first suggested by Golay ( I ) . Subsequent studies have verified that highefficiency gas chromatographic analyses can be made with this approach (2, 3). The desirability of performing liquid chromatographic separations wherein the solute-sorbent interactions occur to only a limited depth in the outer shell of the sorptive particle was pointed out by Weiss (4). Earlier, Pepper indicated the benefits of confining ion exchange interactions to the surface of the sorbent (5). Rapid ion exchange separations have now been carried out using this basic approach (6, 7). Recently, Horne, Knox, and McLaren (8) have suggested that high-speed separations by liquid chromatography should be possible using nonporous supports with thin, uniform surfaces of sorbent and high carrier fluid velocities. This paper will describe some preliminary gas and liquid chromatographic results obtained using columns prepared with a controlled surface porosity (CSP) support (9). By varying the dimensions of the overall particle and the thickness and porosity of the surface, this support can be optimized for use in both gas and liquid chromatography. (1) M. J. E. Golay in “Gas Chromatography 1960, Edinburgh,” R. P. W. Scott, Ed., Butterworths,London, 1960, p 139. (2) J. J. Kirkland, ANAL.CHEM., 37, 1458 (1965). (3) I. Haliisz and F. Holdinghausen, J . Gas. Chromafogr.,5, 385 (1967). (4) D. E. Weiss, Aust. J . Appl. Sci., 4, 510 (1953). (5) K. W. Pepper, “Chemistry Research,” Her Majesty’s Stationery Office, London, England, 1952. (6) J. R. Parrish, Nature, 207,402 (1965). (7) . , C. G . Horvath, B. A. Preiss, and S. R. Lipsky, ANAL. CHEM., 39,1422 (1967). (81 . , D. S. Horne. J. H. Knox, and L. McLaren, Sep. Sci.,1, 531 (1966). (9) J . J. Kirkland, Patents applied for.
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ANALYTICAL CHEMISTRY
The support developed for this investigation consists of spherical siliceous particles with a porous surface of controlled thickness and pore size. The support is hard, mechanically stable, and its porous surface is characterized by being uniform and of predetermined porosity and thickness. A cross section of the porous surfaces of two support particles used for liquid chromatography is shown schematically in Figure 1. A comparison of the gas chromatographic characteristics of untreated glass beads and the CSP support is illustrated by the HETP vs. carrier velocity plots in Figure 2. The significantly higher efficiency of the column made with the CSP support is due to the elimination of the relatively large stationary liquid pools which occur at the contact points of the untreated glass beads and the distribution of this liquid evenly throughout the porous surface of the CSP support. In contrast to the data obtained with the untreated glass bead column, the CSP column shows only minor differences in the slope of the HETP plots for two solutes having dissimilar partition ratios (decane, 16; naphthalene, 49). The CSP column also shows very slight decrease in efficiency with a large increase in carrier flowrate, a condition conducive to high speed analyses. For instance, the CSP column illustrated by the data in Figure 2 can be operated at a carrier velocity four times that of the optimum velocity with a decrease of only about 30% in the efficiency of the column for naphthalene. The reduced plate height (plate height/average particle diameter) for naphthalene at the optimum carrier velocity for the CSP column is 3.8. This value compares favorably with results of Dal Nogare and Chiu (IO), who used high performance columns packed with diatomaceous earth particles. Presumably, even lower reduced plate heights could be obtained for the CSP supports by using columns of (10) S. Dal Nogare and J. Chiu, ANAL.CHEM., 34,890 (1962).
