(3) Aylward, G. H., Hayes, J. W.,
Tamamushi, R., “Proceedings of the First Australian Conference on Electrochemistry,” J. A. Friend, F. Gutmann, eds., Pergamon Press, Oxford, 1964; in press. (4) Bauer, H. H., J . Electroanal. Chem. 3, 150 (1962). (5) Bauer, H. H., Elving, P. J., ANAL. CHEM.30, 334 (1958). (6) Breyer, B., Bauer, H. H., “Alternab
ing Current Polarography and Tensammetry,” p. 96, Interscience, New York, 1963. (7) Carini, F. F., Rlartell, 8. E., J . Am. Chem. SOC.74, 5745 (1952).
(8) Furman, N. H., Cooper, W. C., Ibid., 72, 5667 (1950). (9) Hayes, J. W., Aylward, G. H., ANAL. CHEM.34, 1039 (1962). (10) Hung, H. L., Delmastro, J. R., Smith, D. E., J . Electroanal. Chem. 7, 1 (1964). (11) Hung, H. L., Smith, D. E., ANAL. CHEM.36, 922 (1964). (12) Ibid., p. 2218. (13) Kern, D. M. H., J . Am. Chem. SOC. 75, 2473 (1953). (14) Koryta, J., ZBbransk?, Z., Collection Czech. Chem. Commun. 25, 3153 (1960). (15) Schwarzenbach, G., Ackermann, H., Helv. Chim. Acta. 31, 1029 (1948).
(16) Senda, bl., Kagaku S o Ryoiki, “Zokan 50,” 15 (1962). (17) Smith, D. E., ANAL.CHEM.36, 602 (1964). (18) Tanaka, N., Kamada, N., Osawa, H., Sato, G., Bull. Chem. SOC.Japan 33. 1412 119601. (19) ‘Tanaka, K.,bgino, H., Ibid., 36, 175 (1963). (20) Tanaka, N., Tamamushi, R., Kodama, M., 2. Physik. Chem. N . F . 14, 141 (1958). 121) Vanerzee. C. E.. Dawson. H. J.. J . Am. Chem. hoc. 75; 5629 (lLk3). ~
RECEIVED for review August 13, 1964. *4ccepted Xovember 9, 1064.
A.C. and D.C. Polarographic Study of the Rate of a Substitution Reaction G O R D O N H. AYLWARD and JOHN W. HAYES’ School of Chemistry, Universify o f New South Wales, Kensington, Australia
b A rate constant of 1580 180 liters mole-’ second-l is reported for the substitution reaction between calcium ions and (ethylenedinitrilo) tetraacetatoeuropate(II) ions in ammonia buffer a t p H 9.3. The rate constant is calculated from the shift in the half-step potential of the reduction of europium(ll1)-EDTA in the presence of excess calcium ions. A value of approximately one tenth this figure is obtained by the a x . polarographic method in which the faradaic admittances are compared in the absence and presence of calcium ions. The values calculated from a.c. measurements vary with ionic strength and decrease with increase in frequency and in calcium ion concentration. An explanation is offered which relates these discrepancies to the effect of the double layer structure on the magnitude of the phase angle and the faradaic admittance.
I
N A PREVIOUS paper ( I ) , the validity
of an equation (2) for the alternating current polarographic wave for a fast electron transfer process coupled to a following chemical reaction of limited rate has been demonstrated. I n this paper, the d.c. and a.c. methods of measuring the rate of a following reaction are compared using a system in which a substitution reaction follows the electron transfer process. iit the surface of the dropping mercury electrode, (ethylenedinitrilo) tetraacetatoeuropate (11) (Eu(I1)EDTA) complex is generated by re1 Present address, Department of Chemistry, University of North Carolina, Chapel Hill, N. C.
duction of europium(II1)-EDTA. This is followed by substitution of calcium ions for the europium(I1) in the complex. The reaction scheme may be represented as Eu(II1)-YEu(II)-Y-Z
+ e - ~ tEu(II)-Y-* l + Ca+2 E u ++ ~
(I)
+
(11)
where Y-4 represents the tetravalent anion of EDTA. Several papers have been published on the reduction of europium(II1)EDTA (3, 9, 16, 16). Eckardt and Holleck (3) reported a reversible reduction to europium(I1)-EDTA, in the presence of excess EDTA, occurring a t a half-step potential (E14 of -1.1 volts us. S.C.E. These authors show that in the p H range 7 to 10 the reduction proceeds by reaction I and that Eu(II1)-Y- is the predominant species in the solution. For this reason we have chosen to work within this pH range, but first it was necessary to re-examine the polarographic reduction in the absence of excess EDTA; for our purpose, excess of free calcium ions is required to make reaction I1 pseudo-monomolecular. EXPERIMENTAL
High purity europium(II1) oxide (Johnson Matthey and Co., Ltd., London) was heated to 900’ C. for 6 to 7 hours and dissolved in stoichiometric amount of 1N hydrochloric acid (8). Unless otherwise stated, the results reported below were obtained using solutions of the following composition: 2 m M europium(II1)-EDTA, lOmJ4 calcium EDTA, 2 X low4% Triton x-100, 0.2M ammonia-ammonium chloride
buffer, pH 9.3; the ionic strength was adjusted with potassium chloride; the free calcium ion concentration was varied as shown in the tables. All chemicals were of analytical reagent grade. The capillary electrode had a flow rate of 2.79 mg. second-’ and a drop time of 3.20 seconds a t a height of 50 em. of mercury in 0.2Af ammonia buffer and 0.4M potassium chloride a t a potential of - 1.1 volts OS. S.C.E. The same apparatus and methods of measuring admittances and phase angles were used as reported earlier (1). RESULTS
-.
Polarographic Reduction of EuY I n the absence of free EDTA, a reversible d.c. polarogram is not obtained for the reduction of europium (111)-EDTA. When the solution is made 1 0 m X with respect to calciumEDTA, the reduction becomes reversible giving a slope of 60 mv. for the plot of potential vs. log (id - i)/i. It appears that the calcium-EDTA serves to keep the surface concentration of EDTA constant during the reduction process (14). All further experiments were carried out in the presence of calcium-EDTA since the d.c. limiting current and the height of the a.c. polarographic wave are not altered by its addition. EFFECTOF FREECaLcIuni ION. I n the presence of free calcium ions, the half-step potential ( E m ) shifts to more positive potentials as expected in the presence of a following reaction, However, the diffusion current constant increases and becomes drop time dependent; a maximum of the second kind is observed; and the log-plot slope decreases. VOL. 37, NO. 2, FEBRUARY 1965
197
- 16
I
I
- 1.2
I
- 0.8
[cd
iog (0,785
- 0.4
I
0.0
('J
Figure 1 . Dependence of shift of halfstep potential on concentration of free calcium ions
fx
Figure 2.
The faradaic admittance decreases with increasing concentration of free calcium ions. The phase angle, 9, between the alternating potential and faradaic current increases from 30 degrees in absence of free calcium ions to 45 degrees in the presence of 0.1M calcium chloride. EFFECTOF SURFACTANT.On adding 2X % Triton X-100, the diffusion current constant does not vary with drop time or with the concentration of free calcium ions. The maximum disappears and the log-plot slope remains a t 60 mv. The a x . polarographic wave and the phase angle are not affected by this concentration of surfactant. Rate Constant by D.C. Method. The shifts in the Em with increasing free calcium ion concentration and
Table 1.
IO3 d 6 '
Temperature dependence of rate constant
00
AA
From shift in half-step potential
From faradaic admittance
with variation in drop time are shown in the plot (6) in Figure 1. The slope of 31 mv. is in good agreement with the theoretical, 59.2/2n mv. The mean rate constant for the substitution reaction, calculated from the E1i2 values for 12 different conditions, is 1580 =t 180 liters mole-1 second-' (90% limits). The rate constant is independent of the concentration of europium(II1)EDTA, but the slight decrease in the value with decrease in pH indicates that the mechanism is not so simple as proposed; further evidence for this comes from the slight dependence of the rate constant on drop time. Rate Constant by A.C. Method. The rate constant can be measured
from the a.c. polarographic waves by comparing the faradaic admittances in the presence of, Y I ,and in the absence of, Yd, the following reaction. The second-order rate constant of the chemical reaction, k2, is calculated by substituting these values in the following equation (1):
k2[Ca] =
(2p*/2 1.34 t'
114
(1)
where p' = Yd/Yf. In Table I the results are given for frequencies of 60, 200, and 500 C.P.S. The values for the rate constant decrease with increase in frequency. This trend is confirmed for higher frequencies using an a s . bridge circuit.
Rate Constant Determination from Faradaic Admittance
(at Ionic strength 0.5) 60 C.P.S.
y, mmho
degrees
4,
liters mole-' second-1
0,920 0.877 0,835 0.763 0.612 0.560 0.514 0.461 0.564 0.517 0.465 0.396
38 39 42 40 42 43 44 45 42 42 42 42
348 316 270 226 224 226 204 204 144 142 136 136
Drop
x
time, [Cal I O ~ M seconds 1.0 1.0 1.0 1.0 5.0 5.0 5.0 5.0 10.0 10.0 10.0 10.0
3.36 4.25 5.80 9.10 3.22 4.28 5.94 7.89 3.31 4.20 5.76 8.96
200
Mean value k ~ , liters mole-' second-' ~~
215 i 37
500 c.p.5.
C.P.S.
kg,
k2,
Y, mmho 1.64 1.56 1.41 1.31 1.01 0.935 0.826 0.763 0.935 0.847 0.760 0.670
4,
degrees 16
17
20 18 40 39 39 37 _. 40 42 42 37 140 zk 14
liters mole-' second-1
Y, mmho
degrees
liters mole-1 second-'
187 171 171 136 156 151 153 142 97 102 154 135
2.16 2.01 1.92 1.80 1.47 1.37 1.25 1.11 1.41 1.36 1.33 1.02
16 16 14 11 22 22 22 23 21 20 20 21
214 203 176 137 134 127 112 116 103 68 47 63
$1
125 f 25 ~
198
0
ANALYTICAL CHEMISTRY
~~
Table II.
Effect of Ionic Strength on A.C. Polarograms
60 c.p.8.
[Ca] M
Ionic strength
y, mmho
degrees
0.0 0.0 5 x 10-2 5 x 10-2
0.5 1.0 0.5 1.0
2.06 2.08 0.612 0.660
30 31 42 47
4,
(Drop time: 3.22 seconds) 200 C.P.S. k2, k2, liters liters 4, mole-1 y, mole-’ second-’ mmho degrees second-’
500 c.p.6. k2,
y, mmho
41 degrees
4.10 4.85 1.47 15.8
10
liters mole -1 second-]
POTASSIUM CHLORIDE
... 224
2.98 3.18 1.01
187
1.59
20 23 40 43
...
...
156 150
19 22 24
i34
173
SODIUM CHLORIDE 0.0 0.0 0.0 5 x 10-2 5 x 10-2 5 x 10-2
0.5 1.0 2.0 0.5 1.0 2.0
1.47 1.89
Temperature Effects. Variations with temperature of the rate constants determined by d.c. and a.c. methods are presented as separate Arrhenius plots in Figure 2. According to the transition state theory (6),the heat of activation, AH:, and the entropy of activation, AS:, can be calculated from the slopes and intercepts of these lines. The d.c. method gives a AH: value of 11 kcal. mole-’ and a AS$ value of -8 entropy units. The values coincide within the experimental error with the ax. results of 9 kcal. mole-’ and -20 entropy units. Effect of Ionic Strength. The rate constant determined by the d.c. method decreases from 1420 to 840 liters mole-’ second-’ for an increase in ionic strength, with sodium chloride, from 0.5 to 2.0. I n the absence of free calcium ions, an increase in ionic strength produces an increase in the faradaic admittance and in the phase angle. This increase is significantly greater in solutions containing potassium chloride than in sodium chloride (Table 11). I n the presence of free calcium ions, these changes are less, particularly in solutions containing sodium chloride. DISCUSSION
An explanation of the differences in the value of the rate constant determined by d.c. and a.c. polarography may be found in the extent of the influence of the double layer structure on the various measurement)s. A number of authors (7, 8, 10-18) have shown that repulsive and attractive double layer effects can influence the magnitude of the faradaic admittance and the phase angle between the faradaic admittance and the alternating potential. At the potential of the reduction of europium(II1)-
19 39
... ...
2.48 3.18
12 32
EDTA, the electrode is negatively charged and the depolarizer ion, EuY-, will experience a repulsion from the double layer. As the concentration of cations around the electrode surface is increased, by increasing the ionic strength, this repulsive effect will be weakened. Repulsion causes a decrease in the magnitude of the phase angle and the faradaic admittance while attraction causes an increase. Also, the magnitude of these effects increases with increasing frequency. The results in Table I1 show higher values for the phase angle and the faradaic admittance as the increase in the ionic strength decreases the repulsive effect of the double layer. The effectiveness of the cations in opposing the repulsive effect of the electrode increases in the series Li+ < Na+ < K+ (4). Thus, in the presence of potassium ions, the values of the faradaic admittance and the phase angle are greater than in the presence of sodium ions (Table 11). The effectiveness of cations also increases with increasing charge. I n the presence of free calcium ions the attractive effect is greatly increased (IS). Thus, increasing the sodium ion concentration in the presence of free calcium ions does not result in a large change in the faradaic admittance and the phase angle (Table 11). Measurements of rate constants, which rely upon comparison of &.e. polarograms in the absence and presence of free calcium ions, can give a result lower than expected since the ratio of the admittances, p , in Equation 1 will be smaller than expected. The double layer effects become more pronounced as the frequency is increased, p is decreased, and a lower value of the rate constant will be obtained. This explanation accounts qualitatively for the apparently anomalous phase angles, the observed frequency
...
3.19 4.65
...
10 17
... ...
dependence of the measured rate constants, and thus the difference in the magnitude of the rate constant measured by d.c. and a x . polarography. But it has a number of short comings, and it must remain tentative until a detailed study of the mechanism of the substitution reaction and of the structure of the double layer is completed. LITERATURE CITED
(1) Aylward, G. H., Hayes, J. W., ANAL. CHEM.57, 195 (1965). (2) Aylward, G. H., Hayes, J. W.,
Tamamushi, R., “Proceedings of the First Australian Conference on Electrochemistry,” J. A. Friend, F. Gutmann, eds., Pergamon Press, Oxford, 1964,
in nress.
(3)Eckardt, D., Holleck, L., 2. Elektrochem. 59, 202 (1954). (4) Frumkin, A. N., Nikolaeva-Fedoro-
vich, N., “Progress in Polarography,” P. Zuman, I. M. Kolthoff, eds., Vol. 1, p. 229, Interscience, London, 1962. (5) Glasstone, S., Laidler, K. J., Eyring, H., “The Theory of Rate Processes,” pp. 195, 417, McGraw-Hill, New York, 1941. (6) Koryta, J., ZAbransk?, Z., Collection Czech. Chem. Commun. 25, 3153 (1960). ( 7 ) Matsuda, H., J. Phys. Chem. 64, 339
(imn). \ - - - - I .
(8) Narayanan, K., Rangarajan, S. B., Australian J . Chem. 16, 565 (1963). (9) Onstott, E. I., J. Am. Chem. SOC. 74. 3773 (1952). (10) ‘Rangarajan,‘S. K., Can. J. Chem. 41, 983, 1007 (1962). (11) Rangarajan, S . K., J. Electroanal. Chem. 5, 253 (1963). (12) Senda, M., Delahav. P..’ J. Phws. ‘ Chem. 65, 1580 (1961).” ’ (13) Schmid, R. W., Reilley, C. N., J . Ani. Chem. SOC.80, 2101 (1958). (14) Tanaka, N., Tamamushi, R., Kodama, M., 2. Physik. Chem. N . F . 14. 141 - - - (1958). \----,. I
(15) VlEek, A. A., Collection Czech. Chem. Commun. 20, 1507 (1955). (16) VlEek, A. A., Ibid., 24, 181 (1959).
RECEIVED for review September 2, 1964. Accepted October 23, 1964. VOL. 37, NO. 2, FEBRUARY 1965
199
