Anal. Chem. 1994, 66, 4551-4556
Use of Hydrodynamic Chronocoulometry for Simultaneous Determination of Diffusion Coefficients and Concentrations of Dioxygen in Various Media Manabu Tsushima, Koichi Tokuda, and Takeo Ohsaka" Department of Electronic Chemistry, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 227, Japan
Hydrodyanmic chronocoulometry is theoretically developed such that the ditrusion codcient (0)and concentration (c*) (or nc*, where n is the number of electrons invoked in an electrode reaction) of an electroactive species can be simultaneouslydetermined without previous knowledge of either. The present technique involves measuring charge vs time curves after the electrode potential is stepped from an initial value, where no current flows, to a value at which the electrode reaction of the reacting species is controlled by mass transfer under hydrodynamic voltammetry using a rotating disk electrode. In principle, a single experiment, Le., measuring one charge vs time curve, allows simultaneous determination of D and c*. "his technique has been assessed by applying it to determine D and c* of a commonly used electrochemical test species, Fe(CN),j4-. The results indicated that the determination of D and c* using this method is straightforward, accurate, and rapid (within a few seconds). Further, this technique has been successfully applied to determine D and c* (saturated concentrations) of 0 2 in various 02-saturated media, demonstrating that the present technique is very useful in determination of D and c*, especially when preparation of standard solutions is impossible. A knowledge of the diffusion coefficient (0) and concentration (c*) (or nc*, where n is the number of electrons associated with an electrode reaction) of an electroactive species is essential to the analysis of the electrochemical system of interest from the viewpoints of electron-transfer kinetics and electroanalytical chemistry. Among various electrochemical techniques employed for determining D and c* (or nc*),l techniques which allow their simultaneous determination without previous knowledge of either are of great interest, especially when standard solutions are not available or their preparation is difticult, as in the case of an electroactive dissolved gas and an unstable species. Most of the ideas for this purpose are based on a combined use of transitent and steady-state and have been recently systematically (1) For example: Bard, A J.; Faulkner, L. R Electrochemical Methods, Fundamentals and Applications; John Wiley: New York, 1980. (2)Adams, R N. Electrochemistryat Solid Electrodes;Marcel Dekker: New York, 1969; Chapter 8. (3)Baranski, A S.;Fawcett, W. R; Gilbert, C. M. Anal. Chem. 1985,57,166. (4)Wipf, D.0.; Wehmeyer, K R; Wightman, R M. J. Org. Chem. 1986,51, 4760. 0003-2700/94/0366-4551$04.50/0 Q 1994 American Chemical Society
developed by Amatore and co-workers.6 In this case, at least two separate measurements are required. Much more convenient techniques, which enable one to simultaneously determine both D and c* without previous knowledge of either from a single measurement on a single analytical solution, are also a~ailable.~-l~ Techniques of this type are sinusoidal hydrodynamic voltammetry (SHV),7 potential-step chronoamperometry at microdisk electrodes or hanging mercury drop electrodes (HMDES),~-'~ and hydrodynamic chronocoulometry,18conducted under conditions where the rate of the process is controlled by mass transfer. The theory for the former two techniques has been rigorously de~eloped,'J~-'~ and their experimental applications have been often successf ~ 1 . 7 - 1 2 , ' 4 - ~ ~ Hydrodynamic chronocoulometry has recently been proposed by Morris1*for simultaneous determination of D and c*. Morris derived the charge (&)-time (t)relationship for this technique:18
Q = Qd
+ iLt
(1)
with
Qa = 1/3 nFAc*d
(2)
i, = nFAc*D/d
(3)
where i~is the Levich limiting current, Qd is the charge passed in electrolysis of species contained initially in the hydrodynamic ~~
(5)Malachesky, P. A Anal. Chem. 1969,41,1493. (6)Amatore, C.; Azzabi, M.; Calas, P.; Jutand, A; Lefrou, C.; Rollin, Y. J. Electroanal. Chem. 1990,288,45. (7) Tokuda, K.; Bruckenstein, S.; Miller, B.J. Electrochem. SOC. 1975,122,1316. (8)Brown, 0.R /. Electroanal. Chem. 1972,34,419. (9)Biondi, C.;Bellugi, L. J. Electroanal. Chem. 1970,24,263. (10) Ikeuchi, H.; Fugita, Y.; Iwai, K.; Sato, G. P. Bull. Chem. Soc.Jpn. 1976,49, 1883. (11) Kakihana, M.; Ikeuchi, H.; Sato, G. P.; Tokuda, K J. Electroanal. Chem. 1980,108,381. (12)Kakihana, M.; Ikeuchi, H.;Sato, G. P.: Tokuda, K. J. Electroanal. Chem. 1981,117,201. (13)Aoki, IC; Osteryoung, J. J. Electroanal. Chem. 1984,160, 335. (14)Winlove, C.P.; Parker, K H.; Oxenham, R K. C.J. Electroanal. Chem. 1984, 170,293. (15)Whiteley, L. D.;Martin, C. RJ. Phys. Chem. 1989,93,4650. (16)Lawson, D.R;Whiteley, L. D.; Martin, C. R; Szenirmay, M. N.; Song, J. I. J. Electrochem. SOC.1988, 135,2247. (17) Denuault, G.;Mirkin, M. V.; Bard, A J. J. Electroanal. Chem. 1991,308, 27. (18)Moms, S. E. Trends Anal. Chem. 1988, 7, 227. Analytical Chemistry, Vol. 66, No. 24, December 15, 1994 4551
u = c/c*
boundary layer, which has thickness 6 given by
t = Dt/8
z = Q,/6
F is the Faraday constant, A is the electrode area,
Y is the kinematic viscosity of the solution, and w is the electrode angular velocity (w = 2d where f is the frequency of the electrode rotation). However, the factor of l/3 in eq 2 is not one which has been derived on the basis of a rigorous theoretical treatment.The reason why self-consistency of these results was not adequate is probably associated with this fact. Furthermore, as will be stated below, Newman pointed out that neglect of higher terms in fluid velocity (see eq 6) results in 3%error in the convective diffusion Neglect of these terms by Morris may be another cause of the self-inconsistency in the evaluated data. The aim of the present study is first to derive a rigorous charge-time relationship for hydrodynamic chronocoulometryby taking the effect of higher terms in eq 6 into consideration and then to apply it to simultaneous determination of D and c* of 02 in various Orsaturated media.
with
The boundary value problem described by eqs 5 and 8 is then transformed into at&
u=l
Consider a simple electrode reaction, A f ne B, where A is soluble in solution containing a large excess of supporting electrolyte. For the time-dependent electrolysis at a RDE, the convective diffusion equation for species A is given by
where c and D are the concentration and diffusion coefficient of A, respectively, t is the time elapsed from the beginning of electrolysis, x is the distance from the electrode surface, and Vis the fluid velocity component normal to the electrode and is expressed by
+
V = (0~~)~'~(-0.510235~ 0.3333353 - 0.6159e
+
(14)
and
-
THEORY
= (dQ,/dx)2a2u/az2
at z = O
and O s z s l
u=O
at t > O and z = O
u = l
at t > O and z = 1
(15)
Though this boundary value problem has already been solved numerically by Halez1using the Crank-Nicholson method, Hale neglected all but the first term in eq 6. Newmanlg pointed out that the neglect of the higher terms in eq 6 leads to an error in the limiting current value of as much as about 3% for Schmidt number Sc = Y / D = 1000. Therefore, we took the iirst three terms of eq 6 into account. For convenience, we used a dimensionlessvariable?
E = [O.5l023(w3/v)'/'/3D) I ' l 3 x = 0.55405S~-'/~5 (16)
**a)
(6) Introducing eqs 6 and 16 into eqs 12 and 13 leads to
with
5
9 = 1.8049D'/3~'/6w-'/2~ exp(-e
+ 0.8843S~-"~P-
0
0.3932S~-~'~p) d t (17)
Lf the electrode potential is initially set so that no reaction of A occurs, and at time t = 0 it is stepped to a new value where conversion of A to B occurs at a convective diffusioncontrolled rate, the initial and boundary conditions are given by and xrO
c=c*
at t = O
c=O
at t > O and x = O
c=c*
and
at t > O and
x-00
(8)
According to Hale's procedure?O we employ the following dimensionless variables: (19) Newman, J. J,Phys. Chem. 1966,70,1327. (20) Hale, J. M. J. E l e c t r o a d Chem. 1963,6,187.
4552 Analyfical Chemistty, Vol. 66,No. 24, December 15, 1994
The latter expression was obtained by Newmanlgfor the correction of the kvich equation. (21) Hale, J. M.J. Electroanal. Chem. 1964,8,332.
n
21
Furthermore, if we take the ratio of the intercept to the slope, we obtain a quartic equation with respect to Sc-113:
I
(intercept)/ (slope) =
+
+
0.9757~-'Sc'/~(l 0.2980S~-'/~ 0 . 1 4 5 1 4 S ~ - ~ ' ~(23) )~ By solving eq 23, the Sc value is obtained, and then D is determined using the value of Y that has been known previously. The unknown value of nc* can then be obtained from either the intercept or the slope value. Thus, the present chronocoulometric measurement enables us to determine simultaneously D and nc* of the electroactive species. If the value of n is previously known, then c* is determined, and vice versa.
5
Figure 1. Plots of dimensionless charge G as a function of dimensionless time z. G = QhFAEG, t = DC'G2. The dotted line represents the G-t relationship for chronocoulometry at stationary disk electrode, and the dashed line is the straight line obtained by a linear regression of the G-r curve at rotating disk electrode.
The boundary value problem given by eqs 14 and 15 was solved by using the Crank-Nicholson h i t e difference method for various values of Sc ranging from 50 to 3000. The range of z was divided into 200 strips, Az = 0.005, and A t = 25 x was employed for discretization of t. Values of (dq/d2)2 were calculated and tabulated beforehand as a function of z for each value of Sc. Values of dimensionless current J and dimensionless charge G, defined by
J = id/nFADc* = (adaz),,
(19)
and
were calculated as a function of dimensionless time t for various values of Sc. Variations of G with t are plotted in Figure 1. It was found, fortunately, that the plots of the G against t for different values of Sc fall almost on the same curve. When t exceeds about 1.2, the slope of the plot of G against t becomes unity, indicating that the current reaches the steady-statevalue when t > 1.2d2/D. It is found that this linear part is expressed by
G = 0.3764
+t
(21)
for values of Sc ranging from 50 to 3000 within maximum error of 0.3%. Introducing eqs 10 and 20 into eq 21 and rearranging gives
Q = 0.3764nFAc*6
+ (nFADc*/d)t
(22)
This equation corresponds to eq 1 derived by Morris.'* Notice the difference in the numerical factors l/3 and 0.3764. We can expect from eqs 22 and 18 that the intercept and slope of the Q vs t plot are proportional to w-1/2 and UP, respectively.
EXPERIMENTAL SECTION Materials. Acetonitrile (ACN) , dimethyl sulfoxide (DMSO), NJV-diiethylformamide (DMFJ, and pyridine (Py) of spectre scopic grade (Kanto Chemical Co., Inc.) were used as received. NJV-Dimethylacetamide @MA) of spectroscopic grade and hexamethylphosphorictriamide (HMPA) (Eastmen Kodak Co.) were used after vacuum distillation. Water was purified by passage through a Milli-Q purification train. Deuterated acetonitrile (ACNd) , dimethyl sulfoxide 0MSO-d),pyridine (Py-4,and water (D20) (ISOTEC, Inc.) were used without further purification. All the solutions contained 0.1 M tetraethylammonium perchlorate W) or 0.1 M KC1 (Tokyo Kasei Co., Ltd.) of reagent grade as supporting electrolyte. &[Fe(CN)&3HzO (Kanto) of reagent grade was used as received. Glassy carbon (GC) disks (GC-20, Tokai Carbon Co., Ltd.) with diameter of 3 mm were used as the working electrodes. The exact areas of the GC electrodes were evaluated from their photographs. The surface of the GC electrode was polished with 0.3 ,um alumina powder (Marumoto Kogyo Co., Ltd.) on a microcloth wetted with Milli-Q water before use. The electrode was then carefully sonicated in water, and then it was rinsed successively with water, acetone, and finally with the solvent being used. Apparatus and Procedures. A computercontrolled electre chemical system (CS1090, Cypress Systems Inc.) and a rotating electrode system (Nikko Keisoku Co.) were employed for hydrodynamic chronocoulometric experiments. The electrolysis was carried out in a potential-step mode. The potential was stepped from an initial value, where no current flows, to a value which causes the electrode reaction product to be generated at a mass transfer-controlled rate. The chronocoulograms for Fe(CN)6*solutions or Orsaturated sample solutions were corrected for the residual current by subtracting the corresponding chronocoulogram recorded with deoxygenated supporting electrolyte solution. The electrochemicalcell was a conventional two-compartment Pyrex glass container with a GC working electrode, a spiral Pt wire auxiliary electrode, and an Ag/AgCl (KCl saturated) or Ag wire reference electrode. In the measurements in Orsaturated media, 0 2 gas (99.98%)was bubbled directly into the cell in order to obtain a saturated solution, and during the measurement 02 gas was flushed over the cell solution. Before entering the cell, 0 2 gas was passed through a concentrated HzS04 trap to eliminate trace water and then a trap containing pure solvents except for the cases in HzO and DzO solutions. The cell solution was deoxygenated with Nz gas in the experiments in Fe(CNh4solutions and the blank experiments. Except for the one using water as solvent, all the electrochemical measurements were Analytical Chemistry, Vol. 66, No. 24, December 15, 1994
4553
Table 1. Kinematic Viscosity Data of Various Solutions Measured by Ubbelohde Viscometer at 25.0 i 0.1 "C
solution0
v/cm2 s-1
HzO
0.009 132 0.008 844c 0.004 536 0.018 96 0.009 518 0.008 971 0.010 67 0.035 30 0.010 28 0.004 592 0.020 15 0.010 03
ACN DMSO Py
DMF
DMA
HMPA DzOd ACN-dd DMSO-dd Py-dd
b
Containing 0.1 M TEN. * For each solution, the measurements were repeated 3-5 times and the errors were less than 1%. Containing 0.1 M KC1. Deuterated solvents were used. a
-
O9.0
0.5
1.0
1.5
tis
Figure 2. Hydrodynamic chronocoulometric data for the oxidation of Fe(CN)& to Fe(CN)& at rotating GC disk electrode (4 = 3 mm) in aqueous solution containing 0.1 M KCI and 2.50 mM Fe(CN)64-. Electrode rotation rate: (1) 200, (2) 300,(3)400,(4)600,(5)800, and (6)1OOO rpm. The potential of the working electrode was stepped from 0.0 to 0.40 V vs Ag/AgCI.
performed at room temperature (25 f 1 "C) in a closed drybox flushed with air (or Nz gas) which was dried over silica gel and P2OS powder. The kinematic viscosities (v) of the solutions containing 0.1 M TEAP or 0.1 M KCl were measured using an Ubbelohde viscometer in a thermostated water bath (Coolnics Model CTR/ CTE;120, Komatsu-Yamato, Japan). The temperature of each solution was kept at 25.0 f 0.1 "C. The v values determined for the electrolyte solutions used in this study are summarized in Table 1. RESULTS AND DISCUSSION Evaluation of the Proposed Technique. The proposed
technique for simultaneously determining D and C was evaluated on the basis of results for the oxidation of Fe(CN)&- to Fe(CN)?, because the ferrocyanide/ferricyanide couple is one of the most commonly used electrochemical test systems. In carrying out hydrodynamic chronocoulometry,the potential was stepped from 0.0 to 0.4 V vs Ag/AgCl, held for 1.5 s, and returned to the initial value for various electrode rotation rates. The formal potential of the F ~ ( C N ) G ~ couple, - / ~ - estimated by cyclic voltammetry, was 0.21 V vs Ag/AgCl in 0.1 M KC1 aqueous solution. In Figure 2, the typical raw data of 9-t curves for the oxidation of Fe(CN)c4- are shown. A linear regression for each curve was carried out over the electrolysis time domain between 1.2 and 1.5 s, where a steady-state current condition was reached. The values of the slope i~ and intercept 98 of the straight lines thus obtained were plotted against u1/2and u-lI2, respectively (see Figure 3). These two kinds of plots gave straight lines passing through the origin, as is expected from eq 22. Thus, substituting the thus obtained values of i~and Qd into eq 23,the values of Sc were calculated, and then using the Y value (Table l), the D value could be obtained. In addition, using these values of Sc and D, the values of c* were determined from i~ or 96. The thus estimated values of D and c* for Fe(CN)c4- are summarized in Table 2. From this table, it is apparent that the c* values estimated by the present technique are in fair agreement with the concentrations (i.e., 2.50 and 5.00 mM) of the actually prepared solutions and that the values of D obtained in the Fe(CN)c4- solutions with different concentrations are almost the same. The average value 4554
Analytical Chemistry, Vol. 66, No. 24, December 15, 1994
o I n / (rad s-') 0.041
B
o -In / (rad s-')-In Figure 3. (A) i vs a~~~~ plots and (B) Qg vs a ~ - l / plots ~ for the ~ - Fe(CN)&. Concentration of Fe(CN)e4-: oxidation of F ~ ( C N ) B to (0)2.50 and (0)5.00 mM.
of D ((6.30 f 0.31) x cm2 s-l) was found to be satisfactorily consistent with the literature value ((6.50& 0.02) x cm s-1)22 obtained in the same electrolyte and concentration as used here. It is clear from these results that the technique described here provides a reliable, convenient method for simultaneously determ i n i D and c* of an electroactive species (without previous knowledge of either) on the basis of a single measurement. The (22) Von Stackelberg,M.;Pilgram, M.; Toome, V.2. Efectrochemistty 1953,57, 342.
Tabk 2. Simultaneous Determinationof Diffusion Coefficient and Concentration of Fe(CN)s4- by Hydrodynamic Chronocoulometryat 25 "C
c*/mMa
c*/mM
106D/cm2s-l
2.50
2.54 f 0.03 5.09 f 0.17
6.39 f 0.13 6.20 f 0.48
5.00
Concentration of the (containing 0.1 M KCl) . (I
actually
prepared solutions of Fe(CN),j4-
O*85'
"
'
0.5 '
"
'
1.0 I '
"
" 1.5 '
"
tis
Figure 5. Typical hydrodynamic chronocoulometric data for the reduction 0 2 to 0 2 - at rotating GC disk electrode (qj = 3 mm) in 0 2 saturated HMPA solution containing 0.1 M TEAP. Electrode rotation rate: (1) 200, (2) 300, (3) 400,(4) 600, (5) 800, and (6) 1000 rpm. The potential of the working electrode was stepped from -0.25 to -1.2 V vs Ag.
-0.3
-1.0
-0.5
E i V v s . Ag Figure 4.
Typical steady-state voltammograms for the reduction of
to 0 2 - at rotating GC disk electrode (qj = 3 mm) in On-saturated HMPA solution containing 0.1 M TEAP. Electrode rotation rate: (1) 200, (2) 300, (3)400,(4) 600, (5) 800, and (6) 1000 rpm. The voltammograms were recorded while the potential was scanned in a negative direction at 5 mV s-l. The inset shows Levich pot of i~ vs 0 2
tA
A
: I J/ I 1.5
. .-
1.0
U'E.
present technique can be expected to be especially useful in simultaneous determination of D and c* of an electroactive dissolved gas (e.g., OZ), where preparation of standard solutions is not easy and sometimes impossible. The successful application of this technique to determination of D and c* of 02 in various Orsaturated media will be described below. Simultaneous Determination of D and c* of 0 2 . Figure 4 shows the typical steady-statevoltammogramsfor the 02 reduction at rotating disk electrode in Orsaturated HMPA solution containing 0.1 M TEAP. It is well known that 02 is electrochemically quasireversibly (or reversibly) reduced to superoxide ion (OZ-) in aprotic media including HMPA (i.e., n = l).23-27 The linear Levich plot passing through the origin was obtained (see the inset in Figure 4), indicating that the limiting current is controlled by mass transfer of 02 from the bulk of solution to the electrode surface. The hydrodynamic chronocoulometric curves for the reduction of 02 to 0 2 - in the HMPA media are shown in Figure 5. For each curve, a linear regression was conducted over the electrolysis time between 1.2 and 1.5 s, and the slope and intercept estimated were plotted against w1j2 and w-lj2, respectively, as shown in Figure 6A and B. These figures also summarize the data for the media other than HMPA, i.e., DMSO, ACN, Py,DMA, DMF, and HzO. Here, it should be noted that two-electron (23)Ohsaka, T.; Tsushima, M.; Tokuda, K. Bioelechochem. Bioenerg. 1993,31, 289. (24)Sawyer, D.T.; Chiercato, G., Jr.; Angelis, C. T.; Nanni, E. J.; Tsuchiya, T. Anal. Chem. 1982, 54, 1720. (25)Hossain, M. S.;Tryk, D.; Yeager, E. Electrochim. Acta 1989, 34, 1733. (26)Tezuka, M.; Ohkatsu, Y.; Osa, T. Bull. Chem. SOC.Jpn. 1975, 48, 1471. (27) Sawyer, D.T.; Gibian, M. J. Tetrahedron 1979, 35, 1471.
w -" / (rad s -') -In
Figure 6. (A) k vs w1/2
plots and (6)Qd vs plots for the reduction 0 2 to 0 2 - or H 2 0 2 in various 02-saturated solutions containing 0.1 M TEAP. (0)ACN, (0)DMF, (0)DMSO, (0)Py, (A) DMA, (W) HMPA, (A)H20. reduction of 0 2 to HzO2 occurs at the GC electrode in aqueous media, i.e., n = 2. Similar data were also obtained for the deuterated solvents (i.e., DzO, ACN-d, DMSO-d, and Py-4. For every case, both i~vs w1j2and 96 vs w-1/2 plots were found to be satisfactorily linear and to pass through the origin, as expected from eq 22. Therefore, according to the abovementioned procedure, the values of D and c* (in this study, saturated concentrations) of 02 for all of the media examined could be Analytical Chemistry, Vol. 66, No. 24, December 15, 1994
4555
Table 3. Simultaneous Determination of Concentrations and Diffusion Coefficients of Solutions by Hydrodynamic Chronocoulometry at 25 "C
solutionu
values obtained in this work c*/mM 1 0 5 m m 2 s-1
literature values6 1 0 5 m m 2 s-1 1.5 (16) 1.65 (37) 1.7 (29,35) 1.94 (16) 2.22 (18) 2.29 (36) 2.45 (36)
1.28 f 0.11
2.07 f 0.66
1.0-1.3 (28) 1.25 (29, 30)
ACN DMSO
8.21 f 0.56 2.24 f 0.09
7.12 f 0.64 2.08 f 0.27
8.1 (24) 2.1 (24) 1.8 (32)
Py
4.50 f 0.25 4.72 f 0.12 4.64 f 0.18 3.80 f 0.15 1.32 f 0.04 7.66 f 0.26 2.44 f 0.08 4.66 f 0.26
5.91 f 0.38 4.76 f 0.24 5.39 f 0.18 3.59 f 0.36 1.89 f 0.12 8.36 f 0.36 2.09 f 0.10 5.44 f 0.55
4.9 (24) 4.8 (24) 0.923 (31)' 1.29 (31)c
DzOd ACNdd DMSO-dd @-dd
in Various OpSaturated
c*/mM
HzO
DMF DMA HMPA
0 2
1.93 (32) 2.76 (31) 3.23 (33) 7.44 (34) 5.85 (31) 1.67 (31)
Containing 0.1 M TEAP. The numbers in parentheses are the numbers of the references from which the values were taken. Air-saturated. Deuterated solvents were used.
estimated and are summarized in Table 3, together with the literature values. The c* values for the ACN, DMSO, Py,and DMF solutions are in fair agreement with literature valuesz4 determined by macroelectrolysis of 02. The value (1.28 mM) obtained for the HzO solution is also close to those (1.0-1.3 mM) often cited in literatu~-e.~~-~O No c* values are available for Orsaturated DMA and HMPA solutions. The values cited for these solvents are those obtained for the air-saturated solutions.31 These were determined from the limiting currents of the polarograms with use of the diffusion coefficients calculated using Walden's rule. Our c* value for DMA is fairly close to that (4.62 x cm2s-l) calculated for the Orsaturated solution assuming that 02 solubility obeys the well-known Henry's law, while the value calculated for HMPA (6.45 x cmz s-l) is largely different from our value (3.80 x cm2 s-9. The Devalues obtained in DMSO and DMA are relatively consistent with the literature v a l u e ~ , 3but ~ . ~those ~ in DMF and HMPA are largely different from the previously reported valu e ~ . The ~ ~value , ~ ~(2.07 x cm2 s-l) in the HzO solution is similar to those ((1.5-2.4) x cm2 s-l) reported by several other groups,16J8*29,35-37 although unfortunately the literature also (28) Shigehara, K; Anson, F. C. J. Phys. Chem. 1982,86, 2776. (29) Degrand, C. J. Electroanal. Chem. 1984,169, 259. (30) Pham, M.-C.: Dubois, J.-E. J Electroanal. Chem. 1986,199, 153. (31) Fujinaga, T.; Sakura, S. Bull. Chem. SOC.Jpn. 1974,47, 2781. (32) Tissot, P.; Yadav, A. IC Electrochim. Acta 1986,31, 71. (33) Goolsby, A D.; Sawyer, D. T. Anal. Chem. 1968,40, 83. (34) James, H. J.; Broman, R F. J. Phys. Chem. 1971,75,4019. (35) Durand, R R; Anson, F. C. J. Electroanal. Chem. 1982,134, 273. (36) Pletcher, D.; Sotiropoulos, S. J. Electroanal. Chem. 1993,356, 109. (37) Gubbms, K E.; Walker, R D. J. Electrochem. SOC.1965,112, 459. (38) Kinoshita, IC Electrochemical Oqvgen Technology;Wiley: New York, 1992. (39) Tsushima, M.; Tokuda, K; Ohsaka, T. Manuscript in preparation.
4556 Analytical Chemistry, Vol. 66, No. 24, December 15, 1994
contains some very varied values for the oxygen diffusion ~oefficients.~~ In addition, the c* and D values in the deuterated solutions were found to be almost the same as those in the usual solutions. Our and previous dataz3-37demonstrate a strong dependence of both D and c* (in this case saturated concentrations) of 02 upon solvent. The solvent dependence of c* will be discussed in some detail el~ewhere.3~ CONCLUSION
A theory of hydrodynamic chronocoulometry, which was originally proposed by Morris,18 has been rigorously developed. This technique allows simultaneous determination of D and c* (or nc*) values of an electroactive species without previous knowledge of either from a single experiment. The present technique has been successfully applied to determine D and c* (saturated concentrations) of 0 2 in various Orsaturated media. This study has demonstrated that the determination of D and c* using this technique is straightforward, accurate, and rapid and that this method is very useful in the determination of D and c*, especiallywhen standard solutions are not available, as in the case of an electroactive dissolved gas. ACKNOWLEDQMENT
The present work was financially supported by a Grant-in-Aid for Scientific Research (No. 05453117) and for Priority Area Research on New Development of Organic Electrochemistry (Nos. 05235214 and 06226222) from the Ministry of Education, Science and Culture, Japan, the Nakatani Electric Measuring Technology Foundation, and the Nissan Science Foundation. Received for review June 14, 1994. Accepted September 23, 1994.@ @
Abstract published in Advance ACS Abstracts, November 1, 1994.
