LITERATURE CITED
(1) Ilreiter, M., Iileinerman, M., Delahay, P., J . Am. Chem. SOC.80,5111 (1958). (2) Cardwell, H. AI. E., Dunitz, J. D., Orgel L. E., J . Che,n. SOC.1953, 3740. (3) CoAdit, P. C., I n L Eng. Chem. 48, 1252 (1956). (4) DeFord, D. D., 133rd Meeting, ACS, San Francisco, Calif , April 1958. (5) Elving, P. J., Rcsenthal, I., ANAL. CHEM.26, 1454 (1954). (6) Furman, N. H., Bricker, C. E., J. Bm. Cheni. Soc. 64, 560 (1942). ( 7 ) Gierst, L., Hurwitz, H., 2. Elektroc h i n . 64, 36 (1960); Hurwitz, H., Ibid., 65,178 (1961).
(16) Koutecky, J., Brdicka, R., Ibid., 12. 337 (1947). (17) ’Matsuda, ’H., J. Phys. Chem. 64, 336 (1960). (18) Paul, M. A., Long, F. A., Chem. Rev. 57, 15 (1957). (19) Ross, J. W., DeMars, R. D., Shain, I., ANAL.CHEM.28, 1768 (1956). (20) Ryvolova, A., Hanus, V., Coll. Czech. Chem. Comm. 21, 853 (1956). (21) Weber, J., Koutecky, J., Ibid., 20, 980 (1955).
(8) Hamer, W. J., Acree, S. F., J . Res. Nut. Bur. Std. 35, 381 (1945). (9) Hammett, L. P., “Physical Organic Chemistry,” p. 271, McGraw-Hill, New York, 1940. (10)Hanus, V., Brdicka, R., Chern. Listy 44,291 (1950). (11) Harned, H. S., Owen, B. B., “The Physical Chemistry of Electrolyte Solutions,” 3rd ed., p. 678, Reinhold, New York, 1958. ( 1 2 ) Ibid., pp. 716,731. (13) Korvta. J.. Electrochim. Acta 1, 26 . (1959)” ’ ‘ (14) Koutecky, J., Coll. Czech. Chem. Comm. 18, 597 (1953). (15) Ibid., 19, 1093 (1954).
RECEIVEDfor review April 23, 1963. Accepted August 19, 1963. Division of Analytical Chemistry, 144th Meeting, ACS, Los Angeles, Calif., April 1963.
Electrochemical Study of Kinetics of a Chemical Reaction Coupled Between Two Charge Transfer Reactions Potentiostatic Reduction of p-Nitrosophenol GENE S. ALBERTS and IRVING SHAlN Chemistry Department, University o f Wisconsin, Madison, Wis.
b Theoretical relations were derived for electrolysis experiments at constant potential (potentiostatic method). The experiments describe an electrochemical system in which a homogeneous chemical reaction is coupled between two charge transfer reactions. Included were systelns with reversible and irreversible chemical reactions, for both plane and spherical electrodes. The method was used to investigate the coupled chemical reaction in the reduction of p-nitrosophenol, the dehydi+ation of the phydroxylaminophencl intermediate. The results were compared with the rate constants obtained by the chronopotentiometric method, and the applicability of the two methods was critically evaluated. The first-order rate constant in buffered (PH 4.8) ethanol-water solution with gelatin present is 0.60 set.-' In buffered aqueous solutions without gelatin present, the rate constanl is 1.30 set.-'
I
STUDY of chemical reautioris coupled to electron transfer processes, the ECE (22) meohanism (chemical reaction interposed between two charge transfer reactions) has received little attention. The kinetic scheme can be represented by:
N TIE
and the effect of thcs coupled chemical reaction depends on the reduction
potentials of A and C. Frequently C is more easily reducible than A , and in such a case, the polarographic current (at potentials corresponding to the reduction of A ) is enhanced by the simultaneous reduction of a portion of the C produced by the chemical reaction. It is possible to calculate the rate constant for the homogeneous chemical reaction from the enhanced polarographic current, and the theoretical relations have been discussed by Koutecky (12) and by Tachi and Senda (20). However, no application has been made in the actual determination of a rate constant, probably because of the complexity and approximate nature of the theoretical relations. In chronopotentiometry, an analogous effect is observed, in that the transition time is longer than expected on the basis of the stoichiometric concentration of A alone. The rate constant can be determined from this increased transition time, and the theory for the chronopotentiometric behavior has been derived by Testa and Reinmuth (22). The ECE mechanism is an important class of coupled chemical reactions because it may include most electrode reactions in which more than one electron is transferred. Not many cases have been detected, however, because the chemical reaction is usually extremely fast. Only two examples in which the reaction is fairly slow have been studied extensively: the reduction of o-nitrophenol (2, 16, 18, 23) and the reduction of p-nitrosophenol
(f 1, 19). All polarographic studies have been qualitative, and only in the chronopotentiometric study (23) was a rate constant calculated. In this work, the potentiostatic method has been extended to the investigation of the ECE mechanism. The effect of the coupled chemEa1 reaction is that a t short times, the current corresponds to the reduction of A to B by n1 electrons, but as the concentration of C is increased by the chemical reaction, there is a gradual transition to a current corresponding to the reduction of A to D by (nl nz) electrons. The time a t which this change occurs is a function of the rate constant of the homogeneous chemical reaction. Part of the theory for the potentiostatic method is implicit in Koutecky’s treatment (12) but only for plane electrodes. In this work, the theory was extended for both plane and spherical electrodes, and explicit relations were derived. The derivations for spherical eleotrodes made it possible to use the hanging mercury drop electrode (16) for the investigation. Experimental data were obkained for the potentiostatic reduction of p-nitrosophenol, and the results %-ereused to calculate the rate constan6 of the homogeneous chemical reaction coupled between the two charge transfer reactions. In addition, the reaction was investigated by chronopotentiometry and the range and applicability of the two methods in obtaining rate constants were compared.
+
VOL. 35, NO. 12, NOVEMBER 1963
1859
Figure 2. A. 8. C. D.
Behavior of the ECE mechanism at a plane
Figure 1. electrod e
E.
-----
Theory for k = 0.1 limiting slopes
F.
ret.-'
CU - kbCc/k,) since Equations 9 and
The current is given by
THEORY
In considering the current-time relations for the investigation of the ECE mechanism using the potentiostatic method, it is useful to divide the problem into four cases. That is, the coupled chemical reaction could be reversible or irreversible, and the electrode could be a plane or a sphere. Actually, three of these are special cases ot the fourth, but for ease of computation and convenience in use the cases were considered separately. Plane Electrode, Irreversible Chemical Reaction. I n the simplest of these cases, the experiment is performed at a plane electrode, and the coupled chemical reaction is irreversible (kb equals zero or is much Under diffusion smaller than k,). controlled conditions, the boundary value problem is described by the Fick's law equations modified by suitable kinetic terms:
(z)=-~ -t
i = nlFAD bCA
t = 0, z
2
0: C A =
CA*;
CC =
0 (4)
CB, C C - 0
(5)
CB
t
> 0, x
+
a:
f > O , Z = O :
+
The effect of the coupled chemical reaction can be seen readily from a plot of i us. t - 1 1 2 as is normally used in the presentation of potentiostatic data (Figure 1). A t short times the current is dependent only on the reduction of A to B and the elope of the plot is determined by nl electrons. At long times the current corresponds to the reduction of A to D and the slope is determined by (a na) electrons. During intermediate times the current ahifts from one limit to the other, and the time a t which this change occurs is a function of the rate constant of the coupled chemical reaction. Plane Electrode, Reversible Chemical Reaction. If the coupled chemical reaction is assumed to be reversible, the same boundary value problem applies except that the Fick's law Equations 2 and 3 must be modified to include the reverse chemical reaction:
C A + CA*; C A = C C = O
(6)
Two changes of variable must be used CC and Y = in this case (C = C B
+
1860
ANALYTICAL CHEMISTRY
10 each contain two Concentration variables ( I S ) . The problem then can be solved by a similar application of the Laplace transform.
Aftcr introducing the usual change in variable (C = CB CC) to simplify Equation 3 which contains two concentration variables ( I S ) , this boundary value problem was solved by R straightforward application of the Laplace transform:
+
where k, is the first order rate constant and it is assumed that the diffusion coefficients of all species are equal. The initial and boundary conditions are :
Cell and lid construction
Reference electrode compartment Hanging mercury drop electrode Dropping mercury electrode capillary scoop Deaerator Counter electrode comportment
-
Here, z2 = Z/(K2 I), 1 = kl -k kb, and I< = kb/k,. The upper sign is used if K is greater than one, the lower if K is less than one. With an approach similar to that of Koutecky and Brdicka ( I S ) , Equation 11 predicts, for all values of K , that for both !ong and short times, the limiting slopes of i us. t - 1 / * plots are the same as those predicted by Equation 8. When the curve is changing from one limit to the other, there is only a small difference between Equations 8 and 11 and thus it is difficult to distinguish between the two mechanisms by the potentiostatic behavior. This is consistent with the assumption that C is reduced as fast aa it arrives a t the electrode surface, because the rate of production of C will depend almost entirely on the rate constant k,. Although equilibrium is approached further out in the solution, it is the chemical reaction taking place near the electrode that has the major effect on the current. Thus, to a first approximation, all potentiostat,ic ECE investigations may be correlated with the theory for systems having an irreversible coupled chemical reaction.
Spherical Electrode, Irreversible Chemical Reaction. The third E C E case involves an irreversible chemical reaction with the experiment cartied out a t a spherical electrode. The boundary value problem is similar t o the previous two cases except the Fick’s law equations and the initial and boundary conditions must be written for sphericrilly symmetrical diffusion :
nz FAD
(7;)
r=m
(1s)
Here, r is the distancla measured from the center of the spherical electrode and TQis its radius. To simplify this boundary value problem, an additional change in variable was required to convert Equations 12, 13, and 14 t o the form of the linear diffusion equations (4). This reduced the problem to the same form as the first case considered and it could be solved by a similrw application of the Laplace transform :
+
Here p = nz/(nI nz),bz = k r - D/rzo, the upper sign applies if b2 > 0 and the < 0. Io is the modified lower if Bessel function, and the other terms have their usual significance. This equation qualitatively predicts the same behavior LLS the equations
+*
derived for plane electrodes, except for an upward displacement of the curves. At short times, the limiting slope of the i us. t-’I2 plot has an intercept of nlFADCA*/ro, while a t long times the intercept becomes (nl nz)FADCA*/ro. The shape of the curve also will be different due to this change in intercept. ,4t short times, Equation 19 reduces to the form of Equation 8, and the latter can be used for spherical electrodes if the rate constant is high enough. Using typical values for the diffusion coefficient and the radius of the electrode, the spherical contribution to the current is less than 10% of the total current flowing a t times less than about 0.8 second. Thus, the plane equation can be used with spherical electrodes for systems with rate constants larger than about 10 sec.-l Spherical Electrode, Reversible Chemical Reaction. A boundary value problem describing the E C E reaction with a reversible coupled chemical reaction taking place a t a spherical electrode could be set up and solved in the same manner as the other three cases. However, because the difference between a reversible coupled chemical reaction and an irreversible one is very small when investigated using the potentiostatic technique, and because the increased complexity of the answer which can be expected would make it cumbersome to use, this problem was not considered further.
+
EXPERIMENTAL
Apparatus. All measurements were made on a n instrument based on the analog computer amplifiers manufactured by G. A. Philbrick Researches, Inc. (Boston), incorporating some of the ideas first suggested b y Booman (3) and DeFord (6). This instrument was built in modular form and could be used for all of the electroanalytical techniques including polarography, linearly varying potential, chronopotentiometry, constant potential, etc. All experiments were performed with a three-electrode cell configuration. The cell (Figure 2) used for all experiments except coulometry consisted of a borosilicate glass weighing bottle with a 50/12 joint. A Teflonlid was machined to fit snugly to the joint, and holes were provided to allow insertion of the various electrodes, the nitrogen inlet, and the scoop. The glass counter electrode compartment was separated from the solution by an ultrafine fritted disk. The counter electrode itself was 3.5 feet of 26-gauge platinum wire wound on a Teflon rod. In use, this counter electrode compartment was filled with the solution under investigation. The glass reference electrode compartment contained three sections separated by fine fritted glass disks. The
left compartment was a saturated calomel electrode, the middle section contained saturated potassium chloride, and the right compartment contained the solution to be investigated. The outer compartments were provided with T joints a t the top for closing while the middle compartment was closed with rubber policemen. Also, the right compartment could be disassembled at the center joint to allow two different means of contacting the solution. A Luggin capillary was used in the experiments with the dropping mercury electrode. In most experiments with the hanging mercury drop electrode, however, a tube ending with an ultrafine fritted disk was used since the “convection shield” prevented bringing the Luggin capillary close to the electrode (see below). The dropping mercury electrode assembly was conventional. A capiilary with a drop time in the range of 3 to 5 seconds was used. The hanging mercury drop electrode nas constructed in the same manner as described previously ( 2 4 except 5-mm. soft glass tubing was used. Usually, three drops of mercury from the dropping mercury electrode capillary were collected in the scoop and transferred t o this electrode. A typical value of the electrode area was 0.07 em.* To investigate the effect of shielding of the drop by the mercury-glass interlace on the hanging mercury drop electrode, several electrodes were constructed by grinding the glass on the tip of the electrodes to varying sharpness. The scoop was made from a short section of Teflon rod drilled crosswise and mounted on a glass rod bent a t a right angle. The deaerator was made from a coarse fritted disk sealed to glass tubing and bent 180”. It could be raised out of the solution to provide a blanket of nitrogen over the solution while running an experiment. The cell used for coulometry was similar except that a mercury pool working electrode was used. The bottom of the weighing bottle-cell was formed into a conical shape, provided with a Teflon stopcock, and connected to a mercury reservoir. The level of the mercury could be varied to give the desired area. To minimize the effect of vibrations, the entire cell assembly, including the water bath, was mounted on a heavy platform supported by an inner tube. Convection currents in the solution were further minimized by hanging a 14-mm. glass tube on the hanging mercury drop electrode support so that the mercury drop was inside this tube (Figure 2). The bottom of this “convection shield” was closed by the scoop. All experiments were carried out in a thermostat controlled at 25.0 f 0.1’ C., and all solutions were deaerated 15 minutes with high purity nitrogen. Spectrophotometric measurements were made under air-free conditions on a Cary Model 14 recording spectrophotometer. VOL 35, NO. 12, NOVEMBER 1963
1861
Table I. Polarographic Behavior of p-Nitrosophenol Buffer First wave Second wave PH EIO id, Eiiz id, Composition Meas. Calcd. us. SCE pa. us. SCE pa. H3PO4 NaH2P04 0.2M 0.1M 0.02M
0.02M 0.1M 0.2M
HOAc
KOAc
0.2M 0.1M 0.02M
0.02M 0.1M 0.2M
SaH2P04
NazHP04
0.2144 0.1M 0 02M
0.02144 0.1M 0.2M
I
1.7 2.4 3.4
1.0 2.0 3.0
3.9 4.9 5.9
3.7 4.7 5.7
5.9 7.0 8.0 9.7
0.152 0.094 0.018
10.9 10.7 10.2
-0.75 -0.80 -0.90
14.3 14.1 13.7
-0.019 -0.079 -0.141
10.1 10.3 10.9
-0.97 -1.20 -1.42
13.9 13.9 13.3
6.1 7.1 8.1
-0.139 -0.207 -0.282
11.1 12.1 12.4
-1.42
13.6
9.2
-0.426
13.3
l\;a2Ba07 0.025-%?
Na2HPOI
KarPOa - . 0.01M 0.05*44 0.1M
0.1M 10.7 11.3 -0.513 12.1) 0.05M 11.6 12.3 -0,587 12.9 0 .0 l'Zl 12.1 13.3 -0,632 12.8 911 solutions contained 10-3M p-nitrosophenol, 20'34 ethanol, and 0.005'x gelatin, with the ionic s rength adjusted to 0.3M with KN03.
Materials. The sodium salt of p nitrosophenol (Eastman Kodak Co.) was purified by first dissolving in water, filtering through charcoal, precipitating with acid, and filtering to get the acid form. Then the solid acid was recrystallized twice from benzene and dried under vacuum. Analysis (Huffman AMicroanalytical Laboratories, Wheatridge, Colo.) , Calcd. for CsH6NO: C, 58.54; H, 4.09; 0, 25.99; K, 11.38. Found: C, 58.64; H, 4.15; 0 , 25.80; N, 11.48. Rtelting point 130.5' C. Although the electrochemical behavior was not affected, solutions of p-nitrosophenol slondy changed color on standing. Therefore, fresh amounts were weighed out and dissolved just before running each experiment. All other chemicals were reagent grade and were used without further purification. All solutions were buffered with various combinations of acetate, phosphate, and borate buffers and in each case the ionic strength was adjusted to 0.30M with potassium nitrate. RESULTS AND DISCUSSION
The polarographic reduction of pnitrosophenol has been investigated by Suzuki (19) and by Holleck and Schindler (11). Although there were some inconsistencies in the two investigations, the results were qualitatively the same and the following mechanism for the first wave was proposed: OH
OH
0
OH
"OH
NH
"1
The p-hydroxylaminophenol is not elcctroactive a t these potentials, but it can split out water to form the p-benzoquinoneimine which is reduced to 0
ANALYTICAL CHEMISTRY
OH
0
OH
I:
OH
OH
A=o
N=o
1862
p-aminophenol. The rate of the coupled chemical reaction increases with pH, and as the solution is made more basic, the polarographic limiting current approaches that of a direct four electron reduction. At this point, the effect of the coupled chemical reaction cannot be detected polarographically. At low pH values, a second polarographic wave appears a t more negative potentials where the p-hydroxylaminophenol is presumably electroactive and thus corresponds to the direct reduction of p-nitrosophenol to p-aminophenol. This mechanism is supported by the fact that in the reduction of nitrobenzene, which has been studied extensively (@, the first reduction stage is the formation of nitrosobenzene, which in turn is reduced to phenylhydroxylamine and finally to aniline. In this analogous reaction, the presence of the two intermediate compounds has been demonstrated. The sequence has been regarded as typical of the reduction of all nitro and nitroeo compounds. However, an alternate mechanism, still consistent with an ECE scheme, would be that suggested by a mechanism postulated for the oxidation of p-aminophenol (17, 21). If applied to this case, the hydroxylaminophenol instead of splitting out water, would lose ammonia to form p-benzoquinone which would be reduced to hydroquinone.
"OH
I
This alternate suggestion is based on a report that in acid solution, p-benzoquinoneimine is unstable and loses ammonia to form p-benzoquinone (25). However, the rate of loss of ammonia is
very low, requiring times equivalent to overnight, while in the electrochemical oxidation of p-aminophenol, the pbenzoquinoneimine disappears much more rapidly. It is also possible that side reactions such as the formation of compounds like azobenzene may take place (9). However, most of these reactions are second order and if present would be detected polarographically through a nonlinear relation between current and concentration, or by anodic shifts in the half wave potential. Because of the reported inconsistencies in the polarographic behavior of pnitrosophenol, and to select experimental conditions for which this reaction would be most suitable for the evaluation of the potentiostatic method, an investigation of the polarographic behavior was repeated in this work. In addition, to help settle the problem of the mechanism of the reaction, large scale coulometric reductions a t both high and low pH values were used to prepare the products for spectrophotometric examination and also to determine the total number of electrons involved in the reduction. Polarography. The polarographic behavior of p-nitrosophenol as a function of p H is presented in Table I. All solutions contained gelatin t o suppress the large maxima and ethanol to increase the solubility of the p-nitrosophenol. Because the height of the first wave is a t a minimum a t about pH 4.8 (indicating the rate of the coupled chemical reaction is lowest here), this pH was selected for determination of the rate constant and for evaluation of the potentiostatic method. Therefore, the effect of alcohol concentration was studied a t this acidity. For the first polarographic wave, increasing the alcohol concentration by 10% lowers the limiting current about 10%. This could be due to several effects, among them a change in the apparent rate constant, or a change in the diffusion coefficient. Because the p-nitrosophenol is more soluble in alcohol, while the buffers are less soluble, a comproniise alcohol concentration of 20% was selected for further experiments. The dependence of the height of the first polarographic wave on concentration of p-nitrosophenol was investigated to ensure that the reaction is first order. The results of these experiments indicate that the diffusion current constant, (id/C), is constant over the concentration range of 10-4M to 2 x 10+M to about 5%. Thus, any second order processes occurring as side reactions probably are of minor importance. Coulometry. In order to show that the total reduction of p-riitrosophenol
involved four electrons in both acidic and basic media, large scale coulometric reductions \+ere performed. At both pH 12.3 and pH 4.8 the total number of electrons was 4.0 & 0.1. Thus, even though the polarographic limiting currents at these two p H values are different (Table I), the total reduction of the p-nitrosophenol requires the same number of electrons. This is consistent with an ECE mechanism. Spectrophotometric Investigation. T o help identify the product obtained on reduction of p-nitrosophenol (postulated as being either p-aminophenol or hydroquinone), samples which \%eretaken from the electrolysis cell after total reduction were investigated spectrophotometrically. I n basic solutions (pH 12.3) the spectra of the two proposed products are quite similar. However, there is a slight difference beta een the spectra at about 260 mp and comparison nith the spectrum of the actual product indicated that p-aminophenol is the more likely produci,. At p H 4.8, however, there was n i doubt that the product is p-aminophenol and not hydroquinone. The :tbsorption maximum for p-aminophmol a t 275 mM was matched exactly by the reduction product M hile the absorption maximum for the hydroquinone ic a t 290 mp. From these studies it was concluded that the reduction corresponds to the Equation I1 and not 111-ie.. hydroxylaminophenol splits out water and not ammonia. T ius, in the studies of the electro-oxidation of p-aminophenol (17, 21) the ra lid disappearance of the yuinoneimine E i probably caused by the rexerse of the coupled chemical reaction in the ECI3 mechanism of Equation I1 and the formation of the quinone by loss of rinimonia is slow compared to the hydration reaction. Gelatin. Since glllatin had been uacd in all previoLis polaiograpliic .tudies to suppress the large insxima observed on the rcduction of p nitrosophcriol, its cffc:t on thc hanging niercury drop elec ,rode also was investigated. Stationary electrcde polarogranis (voltammetry with linearly varying potential) with gelatjn in the system exhibited normal peak-shaped curves. However, without gelatin, erratic behavior was observed. The curves, run one after another on newly formed electrodes, could no, be reproduced either with respect to potential or current. It was suspected that this behavior was related to adsorption of impurities and/or reactant during the nonreproducible intervals of catching the drops, transferriqg them to the hanging mercury drop electrode, and waiting for convection to die out. To investigate this behavior further,
E
Figure 3. Reduction of p-nitrosophenol at a slowly dropping mercury electrode, using voltammetry with linearly varying potential A. 8.
With gelatin Without gelatin
current-potential cur\ es were measured on the last few seconds of a slowly dropping mercury electrode (ca. 15-second5 drop time) using rapid rates of voltage bean. With this technique the surface conditions of the electrode (age of drop and convection) could be reproduced, and on scanning the potentials, reproducible results aere obtained. With gelatin in the system normal curves were obtained (Curve A in Figure 3). Hol%ever,without gelatin a large spike nas observed just cathodic of the normal peak potential. This can be explained by an increased supply of reducible material a t the electrode surface a t potentials where the large spike is observed. The source of this increased availability of reducible material is probably related to the streaming phenomena which cause polarographic maxima, since the magnitude of the spike decreases on increasing thc rate of voltage scan. Analogous beha\ ior is obsen ed using chronopotentionietry. With gelatin in the system, normal potential time curves are obtained and the transition time is well defined. Without gelatin, however, the cuiies start out the same but when the potential starts to increase a t the ehpected transition time, it suddenly returns to the potential obseri ed before the transition and stays there 10 to 20 tinies longer than normal. Again, as nith stationary electrode polarography, this phenomenon rcult': from an increased supply of reducible material a t the electrode surface, and the rhronopotentiometric investigation of p-nitrosophenol is difficult \\ithout gelatin in the system. For comparison of the major techniques, therefore, it &as necessary to run all experiments nith 0.005% gelatin present. On the other hand, current-time or potentiostatic experiments behave nornially nithout gelatin in the sybtem
because no data are t'aken in the potential region where the strange behavior is observed in stationary electrode polarography, chronopotentiometry, and polarography. This is a major advantage of the potentiostatic technique, and therefore in addition to the potentiostatic experiments above, it was also possible to determine IC for p-nitrosophenol without gelatin present. Determination of Diffusion Coefficients. In order to correlate the experimental results with theory, it was necessary to assume that the hanging mercury drop electrode closely approximated a sphere. This assumption was investigated by determining the diffusion coefficient of iodate ion from potentiostatic data (16) u4ng electrodes nith differing amounts of shielding a t the mercuryglass interface. The most pointed of these gave agreement to about *2y0 between values of the diffusion coefficient calculated from slope and intercept of i LIS. t-lIz plots. However, the electrode was too fragile for normal use and a sturdier electrode which gave agreement of 10 to 15% between slope and intercept values of the diffusion coefficient was used for further investigations. Gsing this technique, the diffusion coefficient of p-nitrosophenol was determined for use in theoretical calculations. Although it would be desirable to determine the diffusion coefficient under the same experimental conditions as used for the determination of the rate constant, the limiting slopes necessary for such calculations are observed only a t very short times, or very long t'imes, depending on the value of k. Values of the diffusion coefficient would be more accurate if determined under conditions where t'he kinetic complicat'ions cause no observable deviation. For this reason the diffusion coefficient' was determined a t pH 12.3 and compared with values estimated from the limiting slopes of i us. t-1'2 plots a t pH 1.8. These values agreed closely (h47,) and thus, although the ionic form of p-nitrosophenol is not the same a t these two pH values (IO), the diffusion coefficient apparently is not markedly different. The diffusion coefficient for p-nitrosophenol a t pH 12.3 with gelatin and alcohol in the system was 4.8 X 10-6 sq. cm. per second, while without gelatin and alcohol present, the diffusion coefficient was 8.5 X 10-6 sq. cm. per second. Chronopotentiometric Determination of the Rate Constant. For a system such as p-nitrosophenol where the potential of the second charge transfer reaction is assumed to be anodic of the first reduction, a single transition time will be observed which varies as a function of the rate constant and the current density VOL. 35, NO. 12, NOVEMBER 1963
0
1863
In spite of the large variation in the rate constants determined chronopotentiometrically, they should be a t least of the correct order of magnitude and thus give a value with which to compare rate constants determined by the potentiostatic technique. Potentiostatic Determination of the Rate Constant. For the potentiostatic investigation, Equation 19 was divided by the equation for the case where the rate constant is infinite (6) to obtain a dimensionless form analogous to that used in chronopotentiometry :
p = 2/3
-2 0
1 -I 0
0
I
1
10
2.0
LogikTl
Figure 4. Theoretical curves for the chronopotentiometric investigation of the ECE mechanism at plane electrodes P = nz/h
between the limits determined by nl and (nl n2) electrons (22). Although this derivation is strictly applicable only for plane electrodes, it was used here because the corresponding derivation for a spherical electrode would be very complicated. Furthermore, by varying the current density so that the transition times are very short, the effects of spherical diffusion should be minimized. For accurate evaluation of chronopotentiometric data, plots (Figure 4) of the theoretical relations are required [reference (.@), Equation 24 and reference (BS), Equation 1; note typographical errors in both]. Because of the complexity of the equation, these were calculated on a Bendix G-15 digital computer. Tables of the data required for construction of large scale plots were prepared (I) and are available on request. The rate constant c m be obtained by measuring i , , ~ 1 / 2 and comparing that product with i o ~ mwhere l'* r m is the transition time which would be observed if the rate constant were very large. One of the serious limitations in applying this method to an actual case involves the determination of & T m 1 / 2 1 and three different estimates were made here. The first involved calculation from the equation for a direct (n, n2) electron reduction a t a plane
+
+
Table II.
+ nz) electrode (7) using the value of the diffusion coefficient obtained from potentiostatic experiments. The results using this technique of determining & T , ~ / ~are given in the third and fourth columns of Table 11. Because of the large variation in the rate constant obtained with varying current densities, an attempt was made to improve the results by calculation of 6rm1/2from the equation for a direct (nl nJ electron reduction a t a spherical electrode (14). Since the electrode used in this work was a sphere, and since the ratio of an experimental &+ to a computed value of &,rrn1l2is used in the correlation, it was expected that deviations caused by the spherical electrode would be minimized. This approach (fifth and sixth columns of Table 11) did not markedly decrease the variation in rate constant with current density. A third method of determining &rml/*, experimental determination a t pH 12.3, was used as a check on the values calculated from the spherical electrode equation. Since the transition times measured experimentally agreed to about 4% with those calculated from the spherical equation, it was concluded that the large variation in k with current density could not be accounted for by geometrical considerations.
+
Chronopotentiometric Determination of Rate Constant for Homogeneous Chemical Reaction Coupled to Reduction of p-Nitrosophenol
hSml l z / ~ 7 1 12 io, Ira. 20 25 30 40 50 60
T,
sec.
calcd. ' from plane
4.50 2.45 1.43 0.706 0.420 0.281
1.28 1.38 1.51 1.61 1.67 1.70
ior,"2/iorl'~
k, sec.-l
calcd. from sphere
0.77 0.86 0.89 1.19 1.57 2.05 Av. 1 . 2 1 t O . 8
1.36 1.47 1.58 1.67 1.71 1.74 ''
Iz, sec.-l 0 50 0.61 0.68 0.95 1.31 1.71 Av. 1 . 0 1 t 0 . 7
10-JM p-nitrosophenol,pH = 4.8, 20% alcohol, and 0.005% gelatin.
1864
0
ANALYTICAL CHEMISTRY
(20)
+
p = nd(nl n2), B = Dt/ro2, klt, $ = a - 8, i is the observed current, i, is the current that would be observed with an infinite rate constant, and the other terms have their usual significance. The upper sign is used if +>O, the lower if $
