Theory of Alternating Current Polarography


forms at the electrode is equal to the initial bulkconcentration of the oxidized form (thereduced form beingassumed initially absent from the system)...
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Natural Abundance of Chlorine Isotopes SIR: Mass spectrometric determination of isotopic species in labeled compounds requires accurate knowledge of the natural isotopic abundances of all the elements in the compound (14). Correcting the parent peaks in lowvoltage spectra of p-chlorobiphenylordinary and deuterated-for naturally occurring isotopes (4) recently led to consistently negative residues at a mass two units above that of the most abundant species. The discrepancy suggested that the assumed distribution of the chlorine isotopes was in error. This distribution, 75.4% C135 and 24.6y0 Cln, obtained in 1936 ( f a ) , appears in four tabulations commonly referred to for such information (1, 7, 8, 10); two other such tabulations (6, 9) give 75.53% Cla6(3). The 1959 Nuclear Data Tables, issued by the United States Atomic Energy Commission ( I b ) , cite the latter as the best value but also list 75.4% and a third value, 75.8%,

Table 1.

which was reported by Owen and Schaeffer in 1955 ( I S ) . Independent recalculation from the intensities of ten pairs of peaks in the mass spectra (6) of three chlorine compounds gave the abundance shown in Table I. Correction factors for CIa and HZ were taken from the tabulation by McAdams (11). TWOvalues, shown in parentheses, are considered unreliable because of the low intensities of the peaks from which they were derived. The average of the other eight values is 75.80% C135, in agreement with Owens and Schaeffer’s value. The 0.06% average deviation measures solely precision, not accuracy. Mass discrimination in the spectrometer (0,a potential source of error, seems ruled out by the lack of measurable difference among values calculated trori peaks at masses ranging from 47 to 49 to 188 to 190. Improvements in instrumentation can account for some of the discrepancy but do not seem able to account for all of it.

Natural Abundance of Chlorine-35 Calculated from Mass Spectra

Abundance, 70 75.79 c1*+ (75.54”) CCl*+ 75.81 75,76 cc13+ 75.86 75.72 (75.873 o-Dichlorobenzene* CsH&12+ 75.72 75.95 p-Chlorobiphenyl Ci2HpC1+ 75.77 Average 75.80 Average deviation 0.06 Considered b Measured at low ionizing voltage. a Measured with 70-volt electrons. unreliable; not included in average value. Compound Carbon tetrachloride”

Ion cc1+

Masses Used 47-49 70-72 82-84 84-86 117-1 19 119-121 121-123 146-148 148-150 188-190

LITERATURE CITED

(I) American Institute of Physics Hand-

book, pp. 8-155, hlcGraw-Hill, New York, 1957. (2) Barnard, G. P., “Modern Mass Spectrometry,” pp. 69-85, Inst. of Physics, London, 1953. (3) Boyd, A. W., Brown, F., Lounsbury, M., Can. J . Phys. 33, 35 (1955). (4) Eliel, E. L., Meyerson, S., Welvart, Z., Wilen, S. H., J . Am. Chem. SOC.82, 2936 (1960). (5) General Electric Co., Knolls Atomic Power Laboratory, Schenectady, “Chart of the Nuclides,” 5th ed., 1956. (6) Grubb, H. M., Ehrhardt, C. H., Vander Haar, R. W., Moeller, W. H., 7th Annual Meeting, ASTM Committee E-14 on Mass Spectrometry, Los Angeles, May 1959. (7) Handbook of Chemistry and Physics, 41st ed., p. 453, Chemical Rubber Publ., Cleveland, Ohio, 1959-60. (8) ‘.‘Isotope Index,” 4th ed., p. 95, Scientific EouiDment co.. IndianaDob. . , Ind., 1959. (9) Lange, N. A.. ed., “Handbook of Chemistry,” 9th ed.,.p. 116, Handbook Publ., Sandusky, O h o , 1956. (10) Mattauch, “Nuclear Physics Tables” (translated by E. P. Gross and S. Bargmann), p. 111, Interscience, New York, 1946. (11) McAdams, D. R., “Isotope Correction Factors for Mass Spectra of Petroleum Fractions,’’ Esso Standard Oil Co., Baton Rouge, La., 1957,.distributed through ASTM Committee E-14 on Mass Spectrometry. (12) Nier, A. O., Hanson, E. E., Phys. Reu. 50. --.. ~.722 (1936). (13) Ow&, H.‘ RT, ’Schaeffer, 0. A., J . Am. Chem. SOC.77,898 (1955). (14) Stevenson, D. P., Wagner, C. D., Ibid.. 72, 5612 (1950). (15) U‘. S.’Atomic Energy Comm., “1959 Nuclear Data Tables,” p. 69, National Academy of Sciences-National Research Council, Washington, 1959. I

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SEYMOUR MEYERSON Research and Development Dept. American Oil Co. Whiting, Ind.

Theory of Alternating Current Polarography SIR: Works of Bauer and coworkers (4-7) have introduced into the recent literature a number of misconceptions with regard to the theory of alternating current polarography. Despite the fact that several general, and rigorous treatments of this theory predate the aforementioned papers, we fear that this erroneous work stands in danger of acceptance because of its currency and, therefore, feel compelled to point out its invalidity. Randles (19) and Ershler (11) considered the phase angle between current and potential at a faradaic impedance and derived an equation relating this angle to the parameters of the 964

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electrode process. Other authors have extended and elaborated on this theory (9, 19-16, 18, 24). In all cases the conclusions of these theoretical studies were in agreement with the earliest work. Many of the later studies concerned themselves specifically with the validity of Randles’ simple approach under conditions extant at the dropping mercury electrode. The effects of drop curvature ( f J ) , and change of characteristics of the diffusion layer due to drop growth (16,18) have been examined and found to be negligible under the conditions assumed in the derivation of the theorynamely, alternating potentials of fre-

quencies large compared to drop time, and of amplitudes small compared with

RT/nF. Other authors ( I S , 16, 23) have considered the case in which the rate of charge transfer is so large that the species a t the electrode obey the Nernst equation, the so-called reversible case. The earlier cited works also include this situation as the limiting case when the rate constant for charge transfer approaches infinity. Again there is no disagreement in the conclusions of the studies. Concurrently with these studies Breyer and coworkers have published a number of theoretical treatments relat-

ing to the same cases. The inadequacies of the earliest of these treatments have been pointed out by a number of authors (9, 11, 20). In 1955 Breyer and coworkers (8) produced a theory of the faradaic impedance which was a t variance with the above cited works of other authors as regards the wlation between phase angle and rate constant for charge-transfer. Since the assumptions in the derivation parallel those of the earliest work (19) and the mathematical functions considered are single valued and occur in linear equations, it is impossible on a priori mathematical grounds for both results to be correct solutions of the problem considered. Closer inspection verifies that the disagreement is due solely to inconsistency of sign in the derivation of Breyer and coworkers. Specifically, although earlier equations in their paper are consistent with the usual sign conventions (cathodic currents positive, potentials measured between indicator and reference), Equation 11 is not and subsequent conclusions are, therefore, in error. Aten (1) has apparently also reached this conclusion. This work of Breyer shares another defect with the later paper of Bauer (4). In the course of their derivation these authors find it convenient to assume that the sum of the time mean surface concentrations of the oxidized and reduced forms a t the electrode is equal to the initial bulk concentration of the oxidized form (the reduced form being assumed initially absent from the system). This assumption is unnecessary because these surface concentrations can be deduced from the treatment; moreover it is unjustified except in the special case in which the diffusion coefficients of the oxidized and reduced forms are equal. This assumption led Bauer ( 4 ) to the conclusion that the potential of minimum impedance for a reversible alternating current wave is not the same as the half wave potential for the corresponding direct current wave. This conclusion is a t variance with all other recent theoretical treatments of the case. While the difference between the predictions of the rigorous theory and those of Bauer’s treatment, in terms of experimentally measurable quantities, is too small t o be of significance in routine measurements, the fact that it arises from an arbitrary and unnecessary assumption in Bauer’s treatment places in doubt his conclusions with regard to the difference in potentials between alternating and direct current waves. In two recent works (6, 7 ) Bauer and c,oworkers, on the basis of their anomalous results in phase angle measurements, have been led to contend that the basic postulates of the theoretical treatments of alternating current polarography are in error. In the derivation of Matsuda ( I @ , for example, absolute

rate theory, Fick’s law of diffusion, and a somewhat idealized geometry of the dropping mercury electrode are the only postulates involved. Koutecky’s discussions indicate that geometric effects are of negligible importance. It would be a matter of concern if either of the other postulates were invalid, since a major portion of modern electrochemical theory rests on them. One of the major premises of the arguments of Bauer and Elving (6) is that previous theoretical studies have failed to take adequate account of faradaic rectification. I n some treatments less rigorous than that of Matsuda the presence of faradaic rectification has been ignored through the neglect of direct and higher harmonic components to the current rather than being demonstrated negligible on the basis of the postulates of the derivation. The results are substantially the same as those of the more sophisticated treatment. The validity of the simplified approach, however, can be demonstrated more directly by examining the predictions of the theory of faradaic rectification as given by Doss and Agarwal (IO),Barker (a), and Rangarajan (22). Under the experimental conditions employed by Bauer and coworkers (6) the direct potential change induced by the applied alternating potential is much less than the amplitude of the alternating potential and is, therefore, completely insignificant. The theory of faradaic rectification has been tested experimentally by Barker (2, 3). While in some cases his results have been anomalous, the magnitude of the effect observed has never been inconsistent with the assumption that it is negligible under conventional alternating current polarographic conditions. It is of interest that Randles (61)has indicated that Barker’s anomalous results are consistent with the theory of Laitinen and Randles (17) which takes account of adsorption of reactants a t the electrode-solution interface. Although Bauer and coworkers have rejected this explanation for their own data ( 7 ) , they appear to have done so on purely prejudicial grounds. On the basis of qualitative intuitive arguments, Bauer and Elving (6) have contended that there is no a priori basis on which to choose between the correctly and incorrectly derived expressions for phase angle. Indeed, they have postulated that one expression may be validly applicable to systems in which the oxidation reaction is “more hindered” and the other to systems in which reduction is “more hindered.” However, the power dissipated in an electrical circuit is a direct function of the cosine of the phase angle between current and potential. That a system should be more conservative of energy (greater phase angle) as it becomes less reversible

thermodynamically (is hindered) appears to violate the second law of thermodynamics. Yet, this is predicted by the incorrectly derived equation. Bauer and cpworkers (7) have reported experimentally measured phase angles between current and potential of greater than 90’. This is in apparent violation of the first law of thermodynamics, since it implies net production of energy in a cyclical process. We are led to suggest several possible sources of error in the method used by these workers to determine phase angle, since we can conceive of no acceptable theoretical explanation for some of the phenomena which they observed. The differential capacitance of the double layer may not have been accurately taken into account in their experiments for either of two reasons. The potential a t which the double layer capacitance was heasured may have differed significantly from the potential a t which the faradaic impedance was measured because of the. large ohmic potential drop in their circuitry. The differential capacitance of the mercury-electrolyte interface may have differed significantly from that of the electrolyte-amalgam interface produced on electrolysis. The current computed from measursment of the ohmic drop in their measuring resistor may not have been the same as that in the cell because of capacitive or resistive leakage to ground. We would further point out that even assuming the cadmium couple to be completely reversible the ratio of the admittances of the faradaic impedance and the double layer capacitance for a millimolar solution is of the order of 0.1 a t 1000 C.P.S. and 0.04 a t 5000 C.P.S. I n the experimental setup of Bauer and coworkers the error in the measurement of the total admittance was fully 50% of the faradaic admittance a t 1000 C.P.S. and exceeded the faradaic admittance a t 5000 c.p.5. We question the significance of data obtained under these conditions. Rigorous derivations indicate that Fick’s law diffusion coupled with reversible charge-transfer yields a phase angle of 45’ a t all frequencies. They further show that the presence of slow chemical or charge-transfer steps which participate to a significant extent in the over-all reaction tend to decrease the phase angle, as should be the case on the basis of the second law of thermodynamics. Since charge-transfer is a necessary step in the over-all reaction and cannot be “more than reversible,’’ observation of a phase angle greater than 45’ implies that the system is deviating from Fick’s law and reverting to an energetically more conservative form of mass transfer. As Laitinen and Randles pointed out, adsorption is a logical process for consideration since the excesses of oxidized and reduced VOL. 33, NO. 7, JUNE 1961

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forms built up on nitcrliate half cycles cannot be dissipated so readily as in the diffusion prow TKOother possibilitics would be ration in an ohmic potential gradient or non-Fickiaii diffusion causecl by ti,(, in~lonlogcneous Of electric'il layer. However, neither of tlic latter processes nould be eq>cctcd t o contribut,e sigcurnificantly at tilc frequel1(.ics rent-anililitudcs e~nployedby I3aui.r and con-orkcrs. LITERATURE CITED

(1) Aten, A . U o c t o r d thesis, Free University- of A i n ~ t c r d n m (1959), through H. H. Bxiier, private communlcation (1960). (a) Barlcer, G , c,, ..t,aal. ~ / ~ id c, t~a 18, ~ , 118 (1958). (3) Barker, G . c., i l l Yeager, E., Ed., "Transactions of the Symposium 011 Electrode Processes," Philadelphia, May 1959, \T'iley, S e w \-ark> in press.

(4) Bauer, H. H., J . Electrounal. C'hem. 1, (lY5').

(5) Bauer, H. H.. Elving, P. J . , J . A m .

them, sac, 82,2091 ( 1 9 ~ 0 ) . (6) Bauer, €1. H., Elving, P. J., U. S. Atoniic Energy Comm. Rept. Xo. 58, Contract .kT(11-1)-70, Project 8, July 1960; J . Ekefroanal. Cheui.in press. ( 7 ) 13nuerj H. H., Smith. 1). L., Elving, P. J., Ibid.,82, 2094 (1960). (8! Brrycr, B., Bnuer, H. H., Hacobian, b., A u s t r a l i a n J . Chem. 8 , 322 (1955). ( 9 ) Dclahay, P., "Sox Instrumental Methods in Electrochcmistr3," Chap. 7, Interscience, S e w York. 1954. (10) Doss, I Kandles, I., J. E. B., 1 rans. F a r a d q j Sac. 51, 54 (19%). (18) Matsuda, H., 2. Elektrochem. 61, 489 (1957); 6 2 , 977 (19581. (19) Randl(,s, J . E. B., Discussions F a m d a y Sac. 1, 11 (1947). (20) Ibid., 1, 47 (1947). (21) Ilnndles, J. E. B., in Yeager, E., Ed., "Transactions of the Symposium on

Electrode Processes,'' Philadelphia, May 1950. \\-iley, Kex York, in press. ( 2 2 ) Rangarajan, S. K., J . Electround. Indian A c a d . Sei. 35A, 43 (1952 j . C'henz. 1, 396 (1960). !VI.>Tachi, I., B~u l l . Cheuc.~ (11) Ershler, B, v,, ~ i ~~~~d~~ ~ ( 2 3 ) Senda, ~ ~ Sac. 1, 263 (1947); Zhur. Fir. Khini. Sac. J a p a n 28, 632 (1955). (24) Tachi, I., Kambara, T., Ibid., 28, 2 2 , 683 (1948), " (""). (12) Gerischer, H., 2.Elebtrochem. 5 5 , 98 W. H. REINYUTH (1951). D. E. SIIITH (13) Gerischcr, H., 2. p h w i k . Chel-ra. 198, 286 (1951). Department of Chemistry (14) Graharne, D. C., J . Electrochem. SOC. Colunlbia University 98,370C (1952). New York 2 7 , K. Y.

Determination of Surface Area by Gas Chromatography SiR:

A method has bcen described

( 3 , 4) for the detelmin:tticn of surface

area which involves the measurement of the uplake of nitrogen from a nitrogen-helium gas stream. A chromatographic column packed n ith the test material and cooled to -196" C. is used. To obtain sufficient data for the calculation of a surface area several adsorption-desorption runs are necessary, each run giving one point on the adsorption isotherm. The object of this communication is t o suggest a similar method for determining the surface area but needing only one chromatographic experiment. The method resembles that described by Gregg and Stock ( 2 ) and the suggested procedure is outlined belon-. A small, weighed amount of the adsorbent is used to pack a short gas chromatographic column and is de-

gassed in a stream of helium as described by Kelsen and Eggertsen (3). While continuing the flow of helium the column is cooled to - 196" C. Neat the gas stream is changed to a heliumnitrogen mixture whose composition is such that the relative nitrogen pressure, p,, a t the temperature of the column is approximately 0.5-Le. about 30 to 40 em. of mercury. When the column has been completely saturated nith nitrogen at this pressure, as nill be shown by a constant deflection on the recorder used to indicate the composition of the effluent gas, the gas stream is changed again to pure helium. The adsorbed nitrogen nill be eluted and the complete isotherm up to the pressure p , can now be calculated from the elution curve. ProvidPd that the isotherm is not Type I11 or V in the B E T (Brunauer-Emmet-Trller)

TIME

Figure 1 . Chromatogram obtained by saturating the column with nitrogen at pressure pa and then eluting with pure helium

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classification, a record will be obtained similar to that shown in Figure 1. It is assumed that a differential type of detector cell is used-e.g., a thermal conductivity cell. The amount of nitrogen adsorbed a t the pressure p , corresponds to the area ABCD when this has been suitably corrected for the dead volume of the apparatus. The amount eluted corresponds to the area EFHJ and obviously ABCD 3 E F H J ; homeever, the pronounced tailing will make it difficult t o measure the area under the curve H F where this approaches the baseline. To calculate a point on the isotherm

I PRESSURE Figure 2.

Adsorption isotherm

~