(3) Nicholson, R. S., Shain, I., ANAL.
ing potential, and as mentioned above, the ratio ia/icis independent of electrode area, diffusion coefficient, and concentration of reactant. LITERATURE CITED
(1) Alberts, G. S., Shain, I., ANAL.
CHEM.35,1859 (1963).
( 2 ) Holleck, L., Schindler, R., 2. Elektrochem. 60, 1138 (1960).
CHEM.36, 706 (1964). (4) . , Nicholson. R. S.. S h a h, I.,. Ibid., 37. 178 (1965).' (5) Reinmuth, W. H., Columbia Univ., New York, unpublished results, 1964. (6) Schwarz, W. M., Shain, I., ANAL. CHEM.35, 1770 (1963). (7) Suzuki, M., Mem. Coll. Agr., Kyoto Univ. 67, (1954). (8) Testa, A. C., Reinmuth, W. H., ANAL. CHEM.33, 1320 (1961).
(9) Underkofler, W. L., Shain, I., Ibid., 35, 1778 (1963). RECEIVEDfor review September 21, 1964. Accepted December 7 . 1964. Presented in part at the Division of Analytical Chemistry, 148th Meeting ACS, Chicago, Ill., September 1964. Work %-as supported. @ part by the Atomic Energy No. Commission under Contract AT(ll-1)-1083. Other support was received from the National Science Foundation under Grant No. Gl5741.
Effect of a Coupled Chemical Reaction on the Faradaic Admittance GORDON H. AYLWARD and JOHN
W. HAYES
School o f Chemistry, University o f New South Wales, Kensington, Australia
b The application of a x . polarography to the measurement of the rate constant of a coupled chemical reaction by comparing faradaic admittances is demonstrated. The equation tested is restricted to fast electron transfer systems where the d.c. process is controlled by the kinetics of the chemical reaction but the periodic mass transfer remains diffusion controlled. The values of the rate constant for the reaction of cadmium ions with (ethylenedinitri1o)tetraacetic acid determined by d.c. polarography compare favorably with the values obtained by the a.c. method. The dependence of the admittance on frequency in the presence of the following reaction verifies diffusion controlled periodic mass transfer but apparently anomalous phase angle measurements are recorded.
E
to the theory of ax. polarography are opening up new possibilities for more exact studies of electrode reactions (3, 10, 11, 17). Smith has related the frequency and potential dependence of phase angles to the kinetics of electron transfer and (17 ) . coupled chemical reactions Recent publications and discuq-ions (1, 2,11, I 2 , 1 6 ) on the time dependence of a x . polarographic currents highlight some of the possible applications of the extended theories. I n a previous paper (3) an equation was derived for the amplitude of the peak height of an alternating current (ax.) polarogram for an electrode process involving a monomolecular chemical reaction following the electron transfer reaction. The expression was derived under the following assumptions: the electron XTEKSIONS
Present address, Department of ChemUniversity of North Carolina, Chapel Hill, N. C. 1
istry,
transfer reaction is reversible in d.c. polarography; the rate constant of the chemical reaction is greater than 10 second-1 ( I S ) but less than the angular frequency of the alternating voltage. I n this paper the equation is tested by comparing the values of the rate constants calculated from changes in the faradaic admittance with values obtained from the shift in the half-step potentials (E,/z) of the d.c. polarograms (14). For this study the oxidation of cadmium amalgam in acetate buffer solution containing (ethylenedinitri1o)tetraacetic acid (EDTA) was chosen as an example of an electron transfer process coupled to a following chemical reaction. Koryta and ZBbranski (14) have measured by the d.c. polarographic method the rate constant of this following reaction and have demonstrated that the predominant reaction in acetate buffer is Cd+2 HY-S --t CdHY(I)
+
where Y-4 is the tetravalent anion of EDTA. These authors assumed that only the aquo-cadmium ions react with HY-3; the concentration of cadmium ions was corrected for the formation of acetato-cadmium(I1) complexes. This simplifying assumption is accepted. EXPERIMENTAL
Cadmium amalgam was prepared and used in an all glass apparatus similar to that reported by Furman and Cooper (8). Preliminary a.c. polarograms were recorded on a modified Leeds & Northrup Electrochemograph Type E (9). The manual a.c./d.c. polarograph was of conventional design (6). A Philips GM6012/GM4574 combination voltmeter/preamplifier was used to measure the alternating current. A Hewlett Packard 200CD oscillator provided the source of alternating voltage which was kept a t 15 mv. root mean square. A Tektronix 502 dual beam
oscilloscope was used to measure the phase angles by observing the distance between corresponding maxima in the waveform of the applied alternating voltage and the polarographic alternating current. The series resistance was determined by measuring the current at a frequency of 50 kilocycles second-1 ( 5 ) . The faradaic admittance vas calculated in the conventional manner (5). The temperature of the polarographic cell was controlled a t 25' =t 0.2" C. The capillary used had an m value of 1.04 m?. second-1 and a drop time of 6.25 seconds a t a head of 50 em. (uncorrected) in 0.2X acetate buffer 0.4M KC1 a t a potential of -0.62 volt us. S.C.E. To test our equation the rate of the chemical reaction I must be reduced. This is achieved by adding excess calcium chloride to the system. The calcium-EDTA complex is known to be labile (20) and, from its stability constant and the ionization constants of the EDTA (7, 15, do), the concentration of free HY-3 is calculated. The solution also acts as a buffer with respect to EDTA and so the concentration of HY-3 a t the electrode surface is held constant. I n the measurement of the rate constant of the following reaction by the a s . polarographic method, the faradaic admittance a t the summit potential for a fast electron transfer process in the presence of the following reaction, Yj, is compared to the admittance, a t the summit potential, in the absence of the following reaction, Yd. Since, for a diffusion controlled process (4),
+
Yd
=
- n2F2AC;
(WDO)'/*
4RT
(1)
and, from the equation under test ( 3 ) , Yf
=
VOL. 37, NO. 2, FEBRUARY 1965
195
then the first order rate constant for the following reaction, k,, is given by
kf =
(2p1/2 1.34 t'
1)4
(3)
where p = Yd/Yf. Notations have the same meaning as used in a previous publication ( 2 ) . By comparing, in this way, admittances measured a t the same amalgam electrode, errors due to streaming effects and damping in the measuring circuit are reduced considerably.
Table 1.
Rate constant,* liter mole-' Solution composition Method" second-' Acetate buffer 0.1 AEliZ 6 . 4 x 109 Acetate buffer KC1 0.5 AEiiz 4.0 x 109 Acetate buffer KC1 CaClz 0.5 AEiiz 5.3 x 108 Acetate buffer KC1 CaClz 0.5 P 6.1 X lo8 AEIIZrefers to rate constant measurement from Ell2 shift. p refers to rate constant measurement from ratio of faradaic admittance (Equation 3). ' kz = kf/[HY]. Ionic strength
+ + +
Table RESULTS A N D DISCUSSION
The rate constants, determined for the formation of cadmium-EDTA in various electrolytes are listed in Table I. In calculating these rate constants, the effect of the concentrations of acetate and chloride ions on the aquo cadmium ion concentration (18, 21) is considered. The value obtained in acetate buffer is slightly higher than the result reported by Koryta and ZAbransk? (14). Tanaka, Tamamushi, and Kodama (20) have reported a rate constant for reaction I calculated from the rate constant for the dissociation of cadmium-EDTA in acetate buffer in the presence of calcium chloride. Their value, corrected for chloro- and acetatocomplexes of cadmium, is slightly higher than our figure. The plot of AE1i2 us. log [HYIt' deviates slightly from the theoretical 15-mv. slope in both Koryta and ZAbranski's (14) and our results. This may indicate that, while reaction I predominates, the assumption that the chloro- and acetato- cadmium complexes are not involved in the rate mechanism is invalid (19). Typical results for rate constants measured a t 60 cycles second-l and at different drop times are given in Table 11. Good agreement is obtained between the rate constants determined by the a.c. and the d.c. methods for drop times ranging from 2 to 12 seconds. According to our theory, the value of the rate constant should be independent of the frequency a t which the admittance is measured, provided k , < w . The results in Table I11 show no significant difference in the uncorrected values of the rate constants determined a t different frequencies. The measured phase angles between the faradaic current and the voltage across the electrode-solution interface are smaller in the presence of the following reaction (Table 11), and decrease with increase in frequency (Table 111). The experimental evidence, which includes linear relationships between YI and u1I2in the presence of the following reaction, suggests that these changes in phase angle, although not predicted by our present theory, do not affect the determination of the rate 196
ANALYTICAL CHEMISTRY
Summary of Rate Constant Measurements
Cadmium concentration x 104~ 1.96 1.96 1.96 4.99 4.99 4.99 1.96 1.96 1.96 1.96 1.96 1.96 CEDTA = 0
+ +
II.
Rate Constant Measurement at 60 Cycles Second-'
b;:[x 3.14 3.14 3.14 3.65 3.65 3.65 7.68 7.68 7.68 13.6 13.6 13.6
Drop time, second 2.52 3.71 5.62 2.32 3.16 4.80 3.00 4.25 7.66 2.78 3.57 5.70
k2
y, mmho 0.616 0,514 0.450 1.97 1.69 1.27 0.431 0.361 0.281 0.354 0.317 0.233
Phase angle, degree 23 21 10
40 40 37 16 14 10 17 11 10
x
liter mole-' second-' 3.22 3.31 2.61 1.65 1.66 2.10 2.76 3.06 2.63 2.81 2.82 3.24
CCB = 0
1.96 1.79 51 2.57 1.74 51 3.55 1.96 5.55 1.62 48 1.96 4.99 2.40 4.65 44 4.48 44 4.99 3.26 4.99 5.11 4.23 43 Mean value of k~ = (2.76 f 0.32) X IO7 liter mole-' second-' (go$&limits). Corrected mean value of k~ = 6.1 X IO* liter mole-' second-'. Supporting electrolyte: O.2M acetate buffer KC1 CaC12, CEDTA = 1.0 X 10-3M, pH 4.5, ionic strength 0.5 wlth KC1.
+
Table 111.
+
Effect of Frequency on the Measured Rate Constant When k,
