a standard deviation of 1670 over the frequency range of 50 to 14,000 c.p.s., and of magnitude 0.337 pa. per mv. with a probable error of not more than compared to the theoretical value (Equation 25) of 0.336. The theoretical value itself is not reliable to better than 5yo because of the uncertainty in II) and t , and a possible error in the value of the diffusion coefficient. This agreement between theoretical and observed values is more satisfactory than that observed in the study (6) where the frequency dependence was first considered. I n that paper the theoretical values of the current, and not the observed values, were corrected for the residual series resistances in the circuit (110 ohms) and for phase differences: the reported values of .f.lf (450 c.P.s.) and. hence, of k , (0.5 X 10-I em. see.-’) were therefore too lo^, as the apparent value of .f,,f decreases with increasing series resistances (20). The latter fact was realized by the authors ( G ) , d i o indicated that only relatiye signific:ince could be ascribed to the reported value of f w and k,. As the observed values in the present stud>- were corrected for the effects of series resistances and phase differences, tlic values of jlIand k , can be regarded as indicative of the absolute, rather than merely relative, magnitudes. Conclusions. T h e results obtained with cadmiuni(I1) in 0.5M hydrochloric acid are consistent u-itli Equntion 2 2 . The procedure evolved appears to ovmxmie most of the significant un-
certainties previously connected with the use of alternating current polarography. It may now be justifiable to regard the values of k, obtained by this technique as having absolute, rather than relative significance. The experimental error (10 to 15%) connected with the present results might be decreased by use of a low-resistance capillary of more stable characteristics, more precise temperature control, and use of more concentrated solutions to give a higher ratio of Rc/Rr, thus allowing results to be obtained a t even higher frequencies. Kork currently in progress is directed a t modification of the apparatus t o permit determination of transfer coefficients by the method suggested by van Cakenberghe ( l e ) , and to the application of the technique for investigating the reversibility of organic electrode reactions vith varying euperimental conditions. ACKNOWLEDGMENT
The authors wish to thank the Atomic Energy Commission, n-hich helped support the work described, and Carl Miller, mho constructed the electronic equipment. LITERATURE CITED
(1) Barker, G. C., Jenkins, I. L., Analyst 77, 685 (1952).
12) Boeke. J.. Suchtelen. H. van. Philim Tech. R e v . 4. 213 ’11939). ‘ (3) Boeke, J., S&ht&n, -H. van, Z. Elektrochem. 45, 753 (1939). (4) Breyer, B., Bauer, H. H.. Australian J . Chenz. 9, 437 (1956). \
,
(5) Breyer, B., Bauer, H. H., Hacobian, S . , Zbid., 7, 305 (1954). (6) Zbzd., 8, 322 (1955). (7) Breyer, B., Gutmann, F., Trans. Faraday SOC.42, 650 (1946). (8) Breyer, @,., Gutmann, F., Bauer, H. H., Osterr. Chemiker-Ztg. 57, 6 i (1956). (9) Breyer, B., Gutmann, F., Hacobian, S., Australian J . Chem. 6 , 188 (1953).
(10) Breyer, B., Gutmann, F., Hacobian, S., dustralzan J . S a . Research, Ser. A, 3, 567 (1950). (11) Ibzd., Ser. A, 4, 595 (1951). (12) Breyer, B., Hacobian, S., Bustralian J . Chem. 7, 225 (1954).
(13) Breyer, B., Hacobian, S., Azcstralian J: Scz. Research, A5, 500 (1952). (14) Cakenberghe, J. van, Bull. SOC. chim. Belges 60, 3 (1951). (15) Delahay, P., “Sew Instrumental
Methods in Electrochemistry,” Interscience, Sew York, 1954. (16) Delahay, P., Rec. trav. c h m 67, 165 (1948). (17) Drlahay, P., Adams, T J., J . Am. Chern. SOC.74, 5740 (1952). (18) Graharne, D. C., Zbid., 68, 301 (1946). (19) Grahame, D. C., J . Electrochem. SOC. 99. C370 11962). (20) Iial~anasundaram,A,, Proc. Indian =Icad. Sei. A33, 316 (1951). (21) Komyathy, J. C., llalloy, F., Elving, P. J., ASAL.CHEX.24, 431 (1952). Elving, P. J., Chun. (22) Loveland, J. IT,> Revs. 51. 67 11952). (23) Loveland, ’J, IT.>Elving, P. J., J. Phys. Chon. 5 6 , 250 (1952). Sichols, S.,Trans. (24) Matheson, L. -4.. Electrochenz. Soc. 73, 193 (1938). (25) Miller, D. AI., Can. J . Chern. 34, 942 (1956). (26) RIuller, R. H., Garman, R. L., Droz,
11.E , Petras, J., ISD.ENG.CHEM., AXAL.ED 10, 339 (1938).
RECEIVED for review July 22, 1957 cepted Sovember 27, 1967.
,4c-
AIternating Current Polarography Determination of Transfer Coefficient of Electrochemical Processes HENRY H.
BAUER and PHILIP J. ELVING
Universify of Michigan, Ann Arbor, Mich.
b The apparatus and technique described for use in sinusoidal wave alternating current polarography have been modified to permit determination o f the transfer coefficients for electrochemical reactions. The procedure i s a modification of that proposed by van Cakenberghe, which i s based on measurement of the even harmonics of the alternating current. The improved method i s simple and rapid, and permits determination o f the transfer coefficient to a precision o f about i0.01 or =k 0.02. The apparatus, operation, and critical features are described in some detail. The procedure was used to measure the transfer coefficients for
the reduction of cadmium(l1) a t the dropping mercury electrode in various media. A significant difference was observed between the values in potassium chloride and sodium sulfate solutions; the value in hydrochloric acid solution i s midway between the other two. N o significant changes in the transfer coefficient were apparent on varying the concentrations o f cadmium(11) or of background electrolyte, temperature, or amplitude and frequency o f the superposed alternating potential.
V
(6) has shown mathematically, from the theory of absolute reaction rates, that the alterAN C a K E N B E R G H E
nating current, produced under polarographic conditions as a result of a superposed alternating potential of small amplitude, should contain harmonics of the fundamental frequency. Furthermore, the even harmonics should disappear a t the point of symmetry of the polarographic curve-Le., a t the symmetry potential. For a perfectly reversible reaction, the latter would occur at the half-wave potential, E1 2 ; for other than a perfectly reversible reaction, the point of disappearance of the even harmonics would be a t some other potential, E z . The potential difference between Ell?and Ez can be used to culculate the ratio of Co’CR where Co and VOL. 30, NO. 3, MARCH 1958
341
CR represent the concentrations of the oxidized and reduced species in the electrode reaction O+ne=R
(1)
zt the potential Ez, provided that the potential difference is not too greati.e., does not exceed about 0.1 volt. The transfer coefficient can then be calculated from the ratio Co/CE. The transfer coefficient, CY,is defined as the coefficient of transformation of electrical energy into energy of activation or, as it is usually described, as the fraction of the applied potential effective in the forward reaction; (1 - CY)is then obviously the fraction of the applied potential effective in the reverse reaction. Van Cakenberghe reported values of the transfer coefficient a t the dropping mercury electrode for the reduction of phenosofranine and of four metal ions [cadmium(II), cobalt(II), nianganese(II), lead(I1); no value could be determined for cobalt(I1) under the experimental conditions used]. Despite the possibilities inherent in this approach as a rapid method for determining transfer coefficients, no other work with the method has been published since van Cakenberghe's paper (6). A previous study of alternating current polarography employing a superposed sinusoidal alternating potential of millivoltage amplitude ( 2 ) mentioned that the apparatus used could also be used to measure the transfer coefficient in the way suggested by van Cakenberghe, by the incorporation of a suitable frequency filter. Such a filter has now been found. The present paper describes the apparatus and method developed, and reports results obtained for the reduction a t the dropping mercury electrode of cadmium(I1) in a variety of media. APPARATUS SELECTION
Van Cakenberghe ( 5 ) used a tuned amplifier to transmit selectively the second harmonic of the alternating current to the screen of a cathode-ray oscillograph. Near the symmetry potential, the resulting current consisted of a very appreciable amount of the fundamental frequency as well as of the harmonics. Consequently, the potential of zero harmonics was determined by finding the potential a t which the current (fundamental frequency) displayed an undistorted sinusoidal form. I n the apparatus previously described ( 2 )for alternating current polarography, a vacuum-tube voltmeter was used to measure accurately the magnitude of the alternating current. If it were possible to obtain a frequency filter which would pass a negligible amount of the main frequency compared to the harmonic, this vacuum-tube voltmeter could be used to measure the actual magnitude of 342
ANALYTICAL CHEMISTRY
I' e2 Selectoject output
# I #2 Selectoiect Input Frequency Filter Master Switch
50" E t
-
output
7
Selectolect Unit
Figure 1.
Frequency filter
The two Selectoject units a r e identical. Current requirements are about 4 ma. for each unit. The 1 5 0 volt B + i s obtained from 400-volt power supply b y use of VR 1 5 0 and dropping resistor of about 2 7 K. Master switch positions
1. 2. 3.
4.
Frequency filfer shorted Selectoject No. 1 operating Selectoject No. 2 operating Both Selectojectr operating in series Selectoject circuit
c1.
Rp,
cp.
0.01 pf. 0.1 pf. 0.1 pf. 0 . 0 0 2 pf.
R1.
c4.
c3.
Cj. 0.05 pf. Cg. c7.
Ca. RI.
16"pf. 0.0002 pf. 0 . 0 0 2 pf. 1 megohm
1 kohmsb
Rii.
RJ. 1 kohmib
Rlp.
Rj. Rs. Ri. Rs. RQ. Rlo.
2 kohmsn 2 kohmsa 2 0 kohms 2 kohms 10 kohms 6 kohms 2 0 kohms
500 potd 5 megohmse R13. 5 megohmse R14. 1 2 0 kohms Vi, Vp. 1 2 A X 7 SI Sz. DPDT ganged positions ( 1 , selective amplifier; 2, rejection filter)
-
Electrolytic condenser. Matched pairs of resistors. Frequency control (carbon potentiometer with 5 : 1 vernier dial). e Amplification control (gonged carbon potentiometers with 5 : 1 vernier dial)
the harmonic current as a function of the polarizing potential. In this way, the potential of zero harmonics could be estimated with more certainty than is involved in deciding whether or not a particular wave form on the cathode-ray oscillograph is perfectly sinusoidal; this is particularly so because a dropping mercury electrode does not produce a steady trace on the screen. Furthermore, it seemed desirable for a t least t a o reasons to obtain a frequency filter which could be readily adjusted for work a t various frequencies: flexibility in permitting the choice of a suitable frequency, which choice could be critical because of the frequency dependence of the faradaic and capacitative impedances; and capability of investigating possible changes sf the meas-
ured transfer coefficient with frequency.
A filter satisfying these requirements has been found in the combination in series of two Selectoject units (1). The Selectoject circuit can be used either as a sharp amplifier or as a single frequency rejection filter. Frequency Filter. T W OSelectoject units constructed in accordance with the published circuit ( 1 ) (Figure 1) were placed between the first and second stages of the amplifier previously described-Le., between switch SI and tube V 2in Figure 8 of ( 2 ) . These units are connected to the amplifier via a fourposition switch, permitting the use of neither unit, of either one separately, or of the two in series. Other Electronic and Electrical Instrumentation. With the exception of the Selectoject units, the electronic
temperature variation runs, was used with a saturated calomel reference electrode for the runs in chloride solution and with a saturated mercurous sulfate electrode for the runs in sulfate solution.
0.5
% e
E CRITICAL FEATURES OF EXPERIMENTAL PROCEDURE
Use of Frequency Filter. It has been found more advantageous t o use both Selectojects as selective amplifiers of the second harmonic, rather than as narrowband rejectors of the fundamental frequency. The reason is t h a t in the latter case, and under the conditions used in the present study, 60-cycle stray current of magnitude
Frequency of Alternating Potential
Figure 2. Current passed b y frequency filter, as function of frequency, with filter set to amplify selectively a t frequency of 2F c.p,s.
0
0
f I
A
Steady Applied Potential, Volt
Figure 4. Selectojects properly adjusted A
B
G
D
Solution of 0.955 X 10-4M Cd(ll) in O.5M KCI Amplitude of alternating potential
A. 2 mv. B. 5 my.
Steady Applied Potential, V o l t
Figure 3.
Selectojects imperfectly adjusted
Solution of 9.55 X 1OW4MCd(l1) in 0.5M KCi. Curves drawn on different, arbitrory scales to show relative ease of location of minimum Amplitude of alternating potential across cell A. 2 mv. C. 15 mv. B. 5 mv. D. 30 mv.
instruments used werz the same as those previously described (2); the Fisher Elecdropode was replaced by a regular potentiometer-galvanometer arrangement. A 1-eeds 6: Northrup S o . 141023 potentiometer supplied the steady direct current polarizing potential. Its scale is marked in 1-mv. divisions, large enough to permit readings to be made to 0.2 nix-.; the slide-wire itself is sufficiently long to enable the polarizing potential to be changed by much smaller fractions of a millivolt. The Leeds 6: Northrup N o . 2430D galvanometer used had an internal resistance of 495 ohms and a period of 3.3 seconds. Its critical damping resistance of 23,000 ohms rvas effected by placing a 20,300-ohm resistor in series with an Ayrton shunt of 2000 ohms total resistance. The maximum sensitivity of the galvanometer was 0.46-pa. full scale (10 em.) deflection. Dropping Mercury Electrode. The capillary used !vas Corning marine barometer tubing, 6 cm. long, and had the following characteristics a t - 0.6 volt us. S.C.E.in 0.5M potassium chloride solution a t h = 26 cm.: t = 4.6 seconds and m = 2.52 mg. per second. Cell. -4 ITater-jacketed H-cell, maintained a t 25’ C. evcept for the
equal to or greater than that of the second harmonic is also passed by the filters I n the former approach, however, the second harmonic is amplified selectively with respect to the 60-cycle stray as well as with respect to the fundamental frequency. Adjustment of Frequency Filter. The Selectojects are adjusted in the following manner: The polarographic cell is replaced by a resistor of a few hundred ohms. The master switch (Figure 1) is put in position 2, and the ganged switch, SI- Szl of Selectoject 1 is put in the amplifier position. A potential of a few millivolts is applied across the resistor a t a frequency of 2F c.P.s., where F C.P.S. is the frequency which is to be used in the experiments. The amplification control, RI1,is put in an intermediate position; a t one extreme setting, no amplification results, while toward the other exheme, the unit oscillates. The frequency control, Ri2 - Rls,is then adjusted until there is a maximum current response on the output vacuum-tube voltmeter [K in Figure 2 of ( S ) ] . The alternating potential is then switched off and the amplification control is advanced until oscillation occurs, resulting in a large current read-
ing on the vacuum-tube voltmeter. the control is then turned back until the current just returns to zero. At this point, the Selectoject displays the maximum selective amplification. The setting of the frequency control, Rlz R13,is then checked; it may need slight readjustment. The adjustments outlined are highly critical and must be made very carefully. With the master switch in position 3, the same adjustments are made to Selectoject 2 . The switch is then put in position 4 and the oscillator is set to deliver the desired frequency of F C.P.S. The calibrated scale on the oscillator is not sufficient for this purpose. As a result of some harmonics being produced in the circuit itself, the curient response through the Selectojects passes through a maximum not only a t a frequency of 2F c.p.s. ( B ,Figure a), but also through a small. but usually easily discernible, maximum at the frequency of F c.p.s. ( A , Figure 2). The oscillator is set a t the peak of the latter maximum. The polarographic cell is now replaced in the circuit. Variation of Harmonics Current as Function of Steady Potential. Outside the potential range where a redox process occurs, t h e observed alternating current is due t o the capacity of the double layer a t the dropping niercury electrode and contains no appreciable amount of current due to harmonics. I n the potential region where a redox process occurs, the faradaic alternating current is due to harmonics, as well as to the fundamental frequency. These harmonics are a t a minimum at some potential in this range (5) (Figures 3 and 4). The magnitude of the harmonics increases more than linearly with increasing amplitude of the alternating potential (Figure 4). Quali’OL.
30,
NO. 3,
MARCH 1958
* 343
itatively, this can be readily explainedfor small amplitudes of the alternating potential, the current-potential characteristic (direct current polarographic curve) simulates linearity; with higher amplitudes, the section of the curve scanned by the alternating potential becomes increasingly nonlinear; the production of harmonics is presumably due to the same factors as the nonlinwrity of the curve. These facts are of great importance whtn measurements are made to locate E Z with the apparatus described. The adiiiatment of the frequency filter is so delicate that it is inadvisable to attempt to duplicate settings by dial calibration and reading; trial and error procedure, as described, is rapid and yields reproducible results. If the setting is not the best possible one, results are obtained as sliown in Figure 3: a t low amplitudes of the alternating potential, the minimum of the harmonics is not very pronounced, as the current being measured contains a very appreciable amount of the fundamental, and the magnitude of the latter reaches a maximum near the potential where the harmonics are a t a minimum (Figure 5 ) . At higher amplitides, the faradaic current contains a higher percentage of harmonics, as the latter increase more than linearly with amplitude while the fundamental increases only as tanh (TLFAT~~/~RT')Le., somewhat less than linearly ( 2 ) . Thus, the minimum of the harmonics cwrent at Ez can be more accurately loclated at higher amplitudes. Further, hecause the actual values of E z and Es (peak of the total alternating current) :we not exactly equal (Figure 5), incwasing the amplitude of the alternating potential results in a shift of the obs c v e d value of EZ until a limiting value is reached a t higher amplitudes (Figure 3). However, even a t amplitudes of the order of 30 or 40 mv., the minimum of the harmonics, EZ.can be located to nithin a fraction of 1 niv. If the setting of the frequency filter is the best obtainable, E ' Z can be located zwcurately even a t amplitudes of the alternating potential of the order of a few millivolts, and does not detectably change with changing amplitude (Figure 4). This is of practical importance; if the frequency filter setting is not quite i d d , Ez can still be accurately located by using alternating potential amplitudes of the order of 10 to 30 mv., provided that one is in the range of aniplitudes 11-here EZ is constant. However, the use of high amplitudes can produce disturbances in the dropping of the capillary electrode, which must be avoided
until the alternating current flw ing (due to the second harnionic) is a t a minimum in the potentidl range where the reduction occurs. The deflection of the direct current galvsnometer at this point then reprcsents the desired current, iz. This latter method does not depend on the reversibility of the process, but only on the validity of assuming diffusion control, ivhich can be readily verified by measuriiig the variation of tlie limiting current with tcmperature or \vith drop time. Knowing the ratio C0/Cz, the tranefer coefficient can be calculated from tlie equation ( 6 ) Steady Applied Potential, Volt
Figure 5. Total alternating current and harmonics current as function of steady applied potential Solution of 1.2 X 10-4M Cd(ll) in 0.5M HCI. Superposed alternating potential of 5-mv. amplitude across cell a t frequency of 200 c.p.s. A.C. polarogram (total alternating current flowing) Harmonics present in alternating current, measured b y use of frequency filter Difference between E, and E. i s less than 5 mv.
-.
-.
Table I. Diffusion Coefficients of Cadmium(l1) in Various Media a t
25' C. Base Solution 1 ,O M IiCl 0.5M KC1 0 1M IiCl 0.5M HC1
Diffusion Diffusion Coefficient," Current 105 Sq. Cm. Constant See.-' 3.90 3.77 3 56 3 73 2 43 2 72
0.84 0.77 0 70b 0 77 1 . O M NaoSOc 0 33 0 5M Na2S04 0 41 Calculated from diffusion current constant relative to value in 0.lM KC1. Value from literature (9). @
a t EZ. There are at least two possible ways of achieving this: Van Cakenberghe measured Ez accurately and tried to measure Ellz equally accurately from the polarographic curve. From the difference, Ellz-E z , the ratio CO/CRwas calculated by the Kernst equation. It is apparent that the latter will be justified only for reactions which are ideally reversible. A more generally valid method, which was used in the prtsent study, is to measure the direct current, iz, a t the potential E z and, by comparing this current with id from the direct current polarogram, to calculate the ratio Co/CB directly from the relation ( 7 )
(4, 10).
Determination of Transfer Coefficient. T o calculate the transfer coefficient, it is necessary t o know the relative concentrations of the oxidized and reduced species a t the electrode 344
ANALYTICAL CHEMISTRY
which may be written as follows h!. setting p = Co/CR
I n this procedure, EZ and Elizneed not be measured accurately. First, the direct current polarogram is plotted, and then the polarizing potential is adjusted
TRANSFER COEFFICIENT FOR CADMIUM REDUCTION
The experimental procedure outlined m-as used to determine the transfer coefficient for the reduction of cadmium(I1) at the dropping mercury electrodr. ill hydrochloric acid, potassium chloride, and sodium sulfate solutions under various experimental conditions. For the cdld a t i o n of Col'CRfrom Equation 2, the values of the diffusion coefficients used were based on Do = 0.70 X 10-5 sq. em. sec.-l in 0.1X potassium chloride (9); valucs of Do in other electrol) tcs nere calculated from the diffusion current constants observed in the present work relative to the value found in 0.1M potassium chloride (Table I ) ; a value of 1.61 X sq. cm. see.-' was used for DR [ ( S ) : mean of the five values quoted]. There is a possible uncertainty in using the latter value, which mas obtained for :t dropping amalgam electrode, for :t dropping mercury electrode. Variation with Amplitude of Alternating Potential. LIeasui enients could not be made accurately with alternating potentials of amplitude less than about 2 mv. or greater than about 40 niv. Within this range, there is no detectable variation in the magnitude of the transfer coefficlent-i e.. no change in Ez. Variation with Frequency of Alternating Potential. At frequencies below about 100 c.p.s.. the Selectojects do not discriminate sufficiently to allon useful measurements to he made. At frequencies above several hundi ed cycles, it n a s again not possible t o observe a sharp niinimum of the harnionics current: this limiting frequency n a s higher, the greater the concentration of the reducible species. The difficulty a t these highrr frequen-
cies resides not in the frequency filter, but in the electrochemical system itself. At higher frequencies, the major part of the current is not faradaic but capacitative, and consequently the harmonics of the faradaic current become a smaller and smaller fraction of the total current. As a result, the current passed by the filters contains an increasing amount of the fundamental frequency, and the minimum of the harmonics cannot be accurately located. Thus, the most useful measurements were possible only in a limited frequency ranqe, within which there was no detectahle variation of the transfer coefficient with frequency (Table 11). Variation with Temperature. Yo significant variation was observed in the transfer coefficient in t h e temperature range of 11' t o 45' C. (Table 111). Variation with Concentration. Over a tenfold range of cadmium(I1) conoentration in various media there was no significant change i n t h e value of t h e transfer coefficient (Table IV). Variation with Nature and Concentration of Base Electrolyte. There was no significant variation in t h e magnitude of the transfer coefficient with change in concentration of t h e background electrolyte for potassium chloride and sodium sulfate solutions. However, there was a definite difference betn-een the values found in chloride and in sulfate (Table T). I n potassium chloride, the transfer coefficient mas 0.44 to 0.45; in sodium sulfate, 0.37 to 0.38; and in hydrochloric acid. 0.41. The probable error in these values is about 0.02, as far as the reproducibility of the measurements is concerned. The uncertainty in the values of the diffusion coefficients used introduces a further possible inaccuracy. However. the possible variations in the values of Do will not be great, judging from values currentlv used in the literature. The error due to this uncertainty in the transfer coefficients calculated in the present study will not be greater than 0.01. ;iccordingly, the difference between the values found in potassium chloride and in sodium sulfate is almost certainly significant, whereas that between potassium chloride and hydrochloric acid solutions may not be significant. APPLICABILITY A N D LIMITATIONS
The method proposed by van Cakenherghe ( 6 ) for the determination of the transfer coefficient for an electrochemical reactioii b r means of measurement of the hnrnionics of the alternating current produced as a result of a superposed alternating potential has been thoroughly investigated and improved. An apparatus is described which can be used to measure the absolute magnitude
Table
II.
Transfer Coefficient of Cadmium(l1) as a Function of Frequency in Various Media at 25" C. Frequency, Transfer s o . of
System Studied 9.28 X lO-'M Cd(I1) in 1.0-44 Ka2S04
C.P.S. 100 200 350
Goefficien@ Detns.* 0.37 2 0.37 1 0.38 3 500 0.39 1 i50 0.35 1 0.38 1 1.86 X 10-'M Cd(I1) in 1.OM Na2SO4 200 0.36 1 350 2 0.37 500 4.64 X 10-4M Cd(I1) in 0.5M Sa2S04 100 0.41 1 200 0.38 2 350 0 38 3 500 0 39 2 650 0.38 1 3.7 X lO-'M Cd(I1) in 0.5.11 HCI 100 0 38 2 200 0 42 3 350 0.41 5 1.2 X lO-'M Cd(I1) in 0.531 HC1 0.41 2 100 0.39 3 200 0.43 1 350 9.55 X lO-'M Cd(I1) in 1.OM BCl 100 0.45 1 200 0.46 1 ~. 0.47 1 350 1 0.46 500 0.47 1 700 a Largest spread in any set of replicate determinations of transfer coefficient was 0.04. Maximum deviation of any individual result in a set from the mean for that set was 0.02. ~~
of the harmonics, rather than only to locate the potential of minimum harmonics. The technique described permits the latter potential t o be readily located to fractions of 1 mv. Calculation of the transfer coefficient from the experimental results requires knowledge of the diffusion coefficients of the oxidized and reduced species. However, a n error in these values does not produce an appreciable error in the magnitude of the transfer coefficient, as these quantities enter the calculation only as the square root of their ratio. The method has been applied to the study of cadmium(I1) in various media. A significant difference has been observed between the values of the transfer coefficient in potassium chloride solution, and those in sodium sulfate solution. KO significant changes in the transfer coefficient could be observed with amplitude of the alternating potential, with frequency, with temperature, with changing concentration of the reducible species, or with changing concentration of the background electrolyte. Unfortunately, entirely adequate data are not available for comparing the transfer coefficients determined in the present study with the results of other approaches. Van Cakenberghe (5) reported a to be 0.50 for cadmium(I1) reduction a t the dropping mercury electrode from 0.1M potassium chloride solution; 0.44 was found in the present study for a similar situation. Gerischer (8), who employed electrolysis with superimposed alternating potential, found a transfer coefficient
Table 111. Variation of Transfer Coefficient of Cadmium(l1) with Temperature"
Temperature,
c.
11
Transfer Coefficient 0.46
3-0.of Detns. 2
25 0.42 3 0.45 2 45 Data obtained at 350 C.P.S.for 0.955 X 10-4M cadmium(I1) in 0.5JT potassium chloride solution. Table IV. Variation of Transfer Coefficient of Cadmium(l1) with Concentration at 25" C.
Cadmium Transfer KO. Concn.. Coeffiof 104M cient Detns. 9 55 0 46 3 4 78 0 45 20 955 0 44 3 1 .OM Na2S04 9 . 2 8 0 37 8 3.72 0 33 1 1.86 0 31 4 0 531 HC1 3 i 0 41 1o Base Solution 0 5M KCl
0 40
1 2
6
Table V. Transfer Coefficient of Cadrnium(l1) in Various Media at
25" C. Base
Sohition 0 ldl KC1 0 5,l.r KCl 1 0.1l KC1
0 5Jf HC1 0 5'V n'aBO, 1 0.41 XanSOi
Transfer
Coefficient 0 0 0 0 0 0
44
45 46
Yo,of JMnq D
10 :i
41
16
38 37
13
VOL. 30, NO. 3, MARCH 1950
-7
345
*
of
0.17 0.02 for cadmium(I1) reduction a t a hanging drop cadmium amalgam electrode from 0.5M sodium sulfate solution; Berzins and Delahay (S), using potential-time curves, found CY for similar conditions, but in 1M sodium sulfate solution, to be 0.21 or 0.23, depending on the method of computation employed. Transfer coefficients found in the present study for cadmium(I1) reduction a t the dropping mercury electrode are 0.38 and 0.37 for 0.5M and 1.OM sodium sulfate solutions, respectively. It is apparent that future work with the method described in the present paper should include the investigation of cadmium(I1) solutions employing cadmium amalgam electrodes.
ACKNOWLEDGMENT
The authors wish to thank the Atomic Energy Commission which helped support the work described. Their debt to John Griffin should be acknowledged for pointing out the existence of the Belectoject, suggesting its use, and giving most helpful advice on its design and construction. They also wish to thank Carl Miller, who constructed much of the electronic equipment used.
Bauer, H. H., Elving, P. J., ANAL. CHEM.30, 334 (1958). Berzins, T., Delahay, P., J . Am. Chem. SOC.77, 6448 (1955). Buchanan, G. S., Australian J . Sei. 17, 103 (1954).
Cakenberghe, J. van, Bull. SOC. chim. Belges 60, 3 (1951). Cooper, W. C., Furman, N. H., J . Am. Chem. SOC.74, 6183 (1952). Delahay, P., “New Instrumental Methods in Electrochemistry,” p. 57, Interscience, New York, 1954. Gerischer, H., 2. Elektrochem. 57,604 (1953).
Rulfa, C. L., J . Am. Chem. SOC.76, LITERATURE CITED
(1) American
Radio Relay League, “Radio Amateur’s Handbook,” 33rd ed., p. 129, West Hartford, 1956.
2071 (1954).
Tachi, I., Okuda, M., Bull. Chem. SOC.Japan 27, 310 (1954).
RECEIVED for review August 8, 1957. Accepted November 22, 1957.
Voltammetry at Solid Electrodes Anodic Polarography of Sulfa Drugs JOHN D. VOORHIES and RALPH N. ADAMS’ Princeton Universify, Princeton, N. 1. ,The anodic oxidation of sulfa drugs was investigated a t a rotating platinum electrode b y a current-scanning technique. The sulfa drugs show anodic waves with EIiz(s from +0.75 to 1.05 volts vs. S.C.E. in the pH range 1 to 9. The formal oxidation-reduction potentials obtained in this study cannot be obtained by classical potentiometric methods. From the Eli* vs. p H curves one can obtain the dissociation constants of oxidized and reduced acidvalues of base species. The pK,’ reduced species are in good agreement with existing data obtained b y acid-base titrations. Similar comparison data for the oxidized forms are not available, as they are labile electrode species. The electrode reaction apparently is a 1-electron process at the amino (N4) group. Sulfapyridine, sulfisomidine, and sulfadiazine can b e quantitatively determined in the range of about 4 X loy5 to 1 X M with a reproducibility to f l to 3%. Determination in blood filtrates or urine is not satisfactory because of large background currents. The value of the present study lies in the potentialities of the method applied to other biologically important molecules,
T
determination of oxidation-reduction potentials of biological significance has long been a research area of vital interest. Although actual biological redox systems may be of extreme HE
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complexity due to enzyme interactions, much information can be obtained in the laboratory with regard to general levels of oxidation-reduction intensity. As hydrogen ions play an important part in almost all organic redox reactions, studies of the redox potentials as a function of the acid-base equilibria involved are important. Many of the early measurements involved interaction of the biological system with a highly colored (dyestuff) redox system. Although this method has distinct limitations, it is a valuable technique in certain situations. The schools of Michaelis and Clark developed potentiometric measurements to a high degree in their classical work on biological redox systems (5,IO). Polarography with the dropping mercury electrode has found some use, especially with redox systems of relatively low potential. The present study shows that voltammetry a t solid electrodes provides another valuable tool for investigation in this field. The aromatic amino group is susceptible to anodic oxidation a t platinum (7, 9, I S ) and other solid electrodes (9, 11). The group of sulfonamide derivatives known as sulfa drugs has the general structure: H ~ N ~ S O ~ N H - R
where R is generally a heterocyclic ring. A comparison of the current-voltage curves of aniline (I) and benzene sul-
fanilide (11) shows the amino group
H~NCI> C~>SO~-NH
I
I1
(N4) is electroactive a t a platinum electrode, while the amide (Nl) is inert. This primary amino oxidation accounts for well defined polarograms of dilute solutions of the sulfa drugs a t a rotating platinum electrode (RPE). It was decided to investigate the anodic polarography of the sulfa drugs over a wide pH range. As the EliZ of the polarographic wave can be closely identified with the formal redox potential, such studies provide information on the variation of oxidation-reduction intensity with pH. It is also possible to derive the formal acidity constants of many or all of the electroactive species involved in the electrode reaction. The sulfa drugs are still of considerable chemotherapeutic interest. They provide a model system to test the utility of the voltammetric technique. All polarograms reported herein were made by a recording current-scanning technique. The manual current-scan technique has been reported ( I , IS), and the details of the instrumentation for automatic recording have been presented (2). Present address, De artment of Chemistry, University of Ip&nm, Lawrence, Kan.
