Anal. Chem. 1088, 60, 1468-1472
1468
Electrochemical Oxidation of Nitrite on a Rotating Gold Disk Electrode: A Second-Order Homogeneous Disproportionation Process Xuekun Xing and Daniel A. &herson* T h e Case Center for Electrochemical Sciences and the Department of Chemistry, Case Western Reserve University, Cleveland, Ohio 44106
will be introduced that affords a simple criterion for identifying reactions proceeding by a second-order homogeneous DISP mechanism, and also a means of determining independently the rate constant for the disproportionation step, and the formal potential associated with the initial charge transfer step.
The rate of the homogeneous decomposttlon of nltrogen dloxkle, k , In acM medla has been determined from an analysls of the values of the diffusion controlled llmltlng currents for the oxldatlon of nltrlte on a rotatlng Au dlsk electrode. The methodology used Is based on the theory of second-order homogeneous dlsproportlonatlon processes and ylelded a which comvalue for k of (1.9 f 0.5) X 10" cm3~mol-'~s-', pares favorably wlth that reported earlier In the Ilterature. The lntroductlon of an approxlmate form for the currents below thelr dlffudon llmltlng values made lt posslMe to obtaln rather accurate analytlcal expresslons that relate E,,, wlth the rotation rate and the bulk concentration of the reactant, provldlng an expedlent diagnostic crlterlon for the Identification of secondorder homogeneous dlsproportlonatlonprocesses.
THEORY The system under consideration, represented in eq 3 and 4 below, involves a charge-transfer step followed by a second-order homogeneous disproportionation of either the oxidized or reduced species which regenerates the reactant. This
A f ne- + B
(3)
k
2B-+A+C
type of DISP mechanism has been treated theoretically for polarography (12-15), for cyclic voltammetry and double potential step chronoamperometry techniques in stagnant media (16-ZO), and also for a flow technique in a channel electrode configuration (21). In the case of rotating disk electrodes, DISP mechanisms involving both a homogeneous (22,23) and heterogeneous (Z4,25) disproprotionation have also been analyzed, and the results, in some cases, have been compared with experimental data (26-28). The differential equations that describe mass transport of A and B in the solution in the case of rotating disk electrode can be written as
The electrochemical oxidation of nitrite is of importance to analytical applications as it provides a basis for the quantitative determination of NO3- (1)and NOz (2) in aqueous media. Among the many reports published in the literature concerning this redox process (3-111, the most thorough investigation appears to be that of Guidelli et al. (7). On the basis of the results obtained from voltammetric and potential step experiments, these authors concluded that in the case of platinum electrodes in stagnant media, the most reasonable mechanism would be given by
NOz- + NO2 + e-
H ~ O+ 2NOZ h, NO3- + NO2- + 2H+
(4)
(1)
aA/at = Da2A/ax2 - vxaA/ax +
(2)
' / k ~ 2
aB/at = Da2B/ax2- uxaB/ax - kB2
The first step in this sequence involves a fast, heterogeneous one-electron transfer to form nitrogen dioxide which then undergoes homogeneous disproportionation regenerating partially the original reactant. In addition, a detailed quantitative analysis of the data enabled the rate constant for the disproportionation of NOz to be determined yielding a value of about 3.2 X loxocm3.mol-'.s-l. More recently, Erlikh et al. (10, 11) have reexamined the same electrochemical process on a rotating gold disk electrode. Plots of the diffusion limiting currents vs the square root of the rotation rate were found to be nonlinear and thus a t variance with the behavior expected for a simple redox reaction. These authors ignored the disporportionation reaction in eq 2, however, and attributed this phenomenon to the formation of some form of Au oxide on the electrode which would block a fraction of the active sites. This communication will present new experimental data for the oxidation of nitrite on a rotating Au disk electrode in acid media and show that the deviations observed by Erlick et al. referred to above not only are consistent with a second-order homogeneous disproportionation (DISP) mechanism but also provide a basis for evaluating the rate constant of disproportionation of NO2. In addition, a new formalism
(5) (6)
where x is the distance normal to the rotating electrode surface, D is the diffusion coefficient, which for simplicity has been assumed to be the same for both A and B, and k is the second-order homogeneous rate constant. The fluid velocity normal to the rotating surface ux,for sufficiently large Schmidt numbers, is given by -av-1/2u3/2x2 (29,30), where a = 0.51023, v is the kinematic viscosity, and w is the rotation rate of the disk. At steady state, equations 5 and 6 may be written in terms of the dimensionless variables
P = A/A*; Q = B/A* CY
=~A*/[(~V/~D)~/~(DW/Y)] (= (~Y/~D)'/~(W/V)~/~X
as follows: d2P/dE2 + 3f2dP/d(
+ '/,cyQ2
=0
d2Q/dt2 + 3t2dQ/d[ - CYQ'= 0 where the asterisk refers to bulk concentrations.
e
0003-2700/86/0360-1466$01.50/0 1986 American Chemical Society
(7) (8)
ANALYTICAL CHEMISTRY, VOL. 60, NO. 14, JULY 15, 1988
16
1489
4 /
,/'
10
Y
00
100
200
300
500
400
600
700
800
0
20
10
30
a
40
50
60
70
80
90
100
110
f'"/r pml"
Figwe 1. Plot of J vs a, from numerical results obtained in the present work (solid line) and those of Holub (77)(open circles).
Flgure 3. Plot of i , vs fl" for different values of kA *Is-': a, 0; b, 10; c, 50; d, 100; e, 500; f, 1000;g, m .
15
3
14
13 12 11
IO
Y 0
20
40
60
OOi 0
80
100
120
140
160
6
0
n
-
!
IO
,
, 20
30
40
50
l
I
,
,
I
60
70
80
90
100
f "'/ r p m
Figure 4. Plot of J vs f"'. The values of kA same as those in caption Figure 3.
IO
for a through g are the
current observed experimentally and that calculated by assuming k = 0, respectively, are given in Figure 1 (solid curve). These were found to be in excellent agreement with those reported earlier by Holub (23),which are represented by the open circles in the same figure. An analytical solution of the same system of differential equations was obtained by Ulstrup (22), who neglected the convection terms and assumed a sharply defined diffusion layer. Based on such formalism, the functional relationship between J and a may be shown to be given by
4 0
1 110
1 200
400
600
800
1000
1200
1400
1600
a Flgure 2. Plot of J vs a, from numerical results obtained in the present work (solid line) and those of Ultrup (76) (open circles).
The boundary conditions associated with the system under analysis are given by
at 5 = 0
P = Po = Ao/A* dP/df
+ dQ/df
=0
at 5 = 0
(9) (10)
and
P=l;Q=O
atf-m
(11)
where the subscript 0 refers to concentrations measured at the electrode surface. The system of differential equations (eq 7 and 8) with the boundary conditions in eq 9 through 11, for the limiting current case Po = 0, was integrated numerically by using a commercially available routine. The results obtained, presented in the form of J vs a , in which J is a dimensionless parameter defined as i,/io, where il and io are the limiting
an expression that affords very accurate results for J > 1.55 or for values of the characteristic parameter a greater than 50 (see Figure 2). It becomes evident from this analysis that the domain of validity of Ulstrup's treatment is determined by a and not only by the value of the rate constant k as was suggested in ref 22. A clear illustration of the effects of the rate constant associated with the second-order homogeneous disproportionation of the electrogenerated species is provided by a plot of the limiting current il vs f1I2, where f is the rotation rate in units of revolutions per minute. As shown in Figure 3, straight lines are obtained only for k = 0 and k = m , with slopes which differ by a factor of 2, whereas for other values of kA* the corresponding curves are found to bend downward as the rotation rate is increased. Another way of representing these data is by plotting J as a function of f112 (see Figure 4), in which case J becomes independent of the rotation rate only for the limiting values k = 0 and k = m . If the first electron transfer reaction is assumed to be fast, so that the electrode potential, E , and the relative concen-
1470
ANALYTICAL CHEMISTRY, VOL. 60, NO. 14, JULY 15, 1988
10 l5
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1
/
, ,
I
T 25uA
c
'
I
I
I
d C
b Q
I
-204 -08
-04
00
04
08
12
16
20
2 4
I
Flg~ue5. Plot of nF/RT(E - E o ) v s In [i11'3/2'3/(/1 - I)] for dlfferent values of a: a, 50; b, 100; c, 300.
Figure 6. Polarization curves for the electrooxidation of NO,- on a rotating Audisk electrode in a 0.1 M NaCIO, in 1 mM HCIO, solution containing'(a)0.1, (b) 0.2, (c) 0.3, (d) 0.4, (e) 0.5 mM NaNO,: f , 900 rpm; S , 0.196 cm2; scan rate, 10 mV.s-'.
trations of the readant and product at the interface are related through the Nernst equation, an analytic expression that relates the current and potential can be obtained within Ulstrup's formalism, namely
introduce large uncertainties in a. Based on the results presented in Figure 2, the simplest and most accurate approach for determining a would be to choose, if possible, experimental conditions such that 1.55 < J C 1.85.
1n[(l ,'la 1 */'))/(
1 ,-1)]
exp[-(nF/RT)(E - E"')] = 0.510c~~/~[2io - i]/[(2io)'/3i2/3] - 1 / 2 (13) where Eo' is the formal electrode potential for the redox process. It is often valuable to relate the half-wave potential, El/,, a parameter that can be easily determined experimentally, to the quantities being sought. Unfortunately, no analytic expressions can be derived based on Ulstrup's approach. A relationship of this type can be obtained, however, by assuming that the current for values smaller than i,, denoted as i, can be approximated by i = JnFSD(A* - Ao)/6,where S is the area of the electrode and 6 , the thickness of the diffusion layer for a rotating disk. In fact, a comparison of the values obtained from the strictly numerical calculations with those arising from this approximation were found to differ only by about 1% to 5% for values a > 100. On the basis of this approach, it may be shown that In [i11/3i2/3/(i1- i)]
+ -31 In [1.8793/a] (14)
Hence, the values of either k or Eo' can be determined from the intercept of the straight line obtained by plotting E vs In [il1I3i2l3/(i1- i)]. As shown in Figure 5, plots of this type for different values of a, based on the numerical calculations, yielded straight lines with slopes equal to one, as predicted by eq 14, providing a clear illustration of the accuracy of this approximation. Furthermore, an expression for the half-wave potential, Ell2, can be easily derived by replacing i by ill2 yielding Eli2
= Eo' F
RT/3nF[ln 3.75W - In 3.259D-1/3u1/3- In (kA*/w)] (15) Hence, plots of Ellz vs In w (or In A*) should give straight lines with slopes equal to +RT/3nF (or -RT/3nF) for an oxidation reaction, which may serve as a criterion for establishing the reaction mechanism. It is interesting to note that in the case of an E,Ci mechanism, the corresponding value for the slope is RTI2nF (30). From an overall perspective, the use of this rotating disk methodology for the evaluation of the rate constants for second-order disproportionation reactions may be restricted to values of J C 1.85, as for J > 1.85 slight variations in J
EXPERIMENTAL SECTION All electrochemical experiments were conducted in 0.1 M NaC104aqueous solutions at pH 3, adjusted with ultrapure HClO, (J. T. Baker). The rotating gold-ring gold-disk electrode as well as the instruments used in the measurements were the same as those employed in earlier studies ( I ) . Current-potential curves were recorded in the dynamic polarization mode at sweep rates of about 5-10 m V d . In order to minimize the effects associated with the spontaneous decomposition of NOz- (or "0,) (3),i.e. 3HN02 ---* 2N0
+ NO< + HzO + H+
(16)
the polarization curves were recorded immediately after introducing nitrite into the solution. Based on the time elapsed between the addition of NO; and the completion of the data acquisition, the decrease in the value of the limiting currents was estimated not to exceed 2-3%. This was determined based on the experimentally observed decrease in the value of the diffusion limiting current, measured at a constant rotation rate, as a function of time. The rate of disappearance of NOz-was also monitored by a standard spectrophotometric analysis method (31),for which similar changes in the concentration of NO2-were found for times comparable to the duration of the electrochemicalexperiments.
RESULTS AND DISCUSSION Typical dynamic polarization curves for the oxidation of nitrite on a rotating gold disk electrode in 0.1 M NaClO, at pH 3 as a function of [NO,-] and rotation rate are given in Figures 6 and 7, respectively. Fairly straight lines with a nonzero intercept were obtained by plotting the limiting currents for the oxidation of nitrite as a function of [NO,-] measured at constant rotation rate (slope, S = 0.31 f 0.02 A-M-'; intercept, I = (1.7 f 0.1) x lo4 A), and i vs at a fixed concentration of NO; (S = (4.6 f 0.1) X lo4 A-(rpm)1/2; I = (14 f 2) x lo4 A). The electron transfer number calculated from the slopes of these lines was found to be smaller than two, providing evidence that the overall reaction does not follow a simple 2e- oxidation. A clear indication that the decomposition of "0, could not by itself account for this effect was obtained from experiments in which the limiting currents were recorded sequentially in decreasing order for selected values off. Since the concentration of HN02 in solution will decrease in time, the observed currents at the lower rotation rates would be expected to be smaller than those calculated assuming a constant nitrite concentration in solution. As shown in Table I, however, the values of J measured experimentally were found to increase as the rotation rate was decreased, indicating
ANALYTICAL CHEMISTRY, VOL. 60, NO. 14,JULY 15, 1988 I
I
I
I
I
I
0 780
'0
w
1603
0 750
I
900
400
0.6
0.8
I
I
E I V vs SCE 10 I
I
I
Flgure 7. Polarization curves for the electrooxldation of NOz- on a rotating Au-disk electrode in a 0.1 M NaCIO, in 1 mM HCIO, solution containing 0.5 mM NaNO, at different rotation rates (rpm): (a) 400, (b) 900, (c) 1600, (d) 2500, (e) 3600. Other conditions are specified
in the caption of Figure 6.
0 780
-
W
u
m 090,
088
~~
-I
c
1
/
I
/ /
v)
0770 -
>
h>
,,
0 86
W
0 760
-
0 750
7
084
i
V" 4
074 000
I 050
100
150
250
200
1n[(111/31 2 ' 3 ) / ( 1 1 -
300 1)
400
350
1
Flgure 8. Plot of E v s In [il"3/2'3/(il - i ) ] for the electrooxidatlon of NO2- on a rotating Au disk electrode based on the data in Figure 7: 1, 400; 2, 900;3, 1600; 4,2500;and 5, 3600 rpm.
Table I. Values of the Limiting Current at Different Rotation Rates, and the Rate Constants for the Homogeneous Second-Order Disproportionation of NO2 as Determined from the Magnitudes of J and Q
CY
10-lOk/ cm3. mol-ld
1.80
6783 2990 1905 761
2.0 2.1 2.4 1.5
1.77
484
1.3
flrpm
i l / p A (at E = 0.95 V)
iO/pA
J
400 900 1600 2500 3600
104.0 153.5 202.5 246.0 290.0
54.8 82.2 109.6 136.9 164.3
1.90 1.87 1.85
that the observed deviation is due to a different phenomenon. The values of the parameter J calculated from the magnitudes of the experimental and theoretical limiting currents, given in Table I, were found to exceed 1.75. This makes it possible to calculate (Y from eq 12 and from these the actual values of k. The latter have been determined by using D(N0 2 - 1 = 1.73 X c m 2 d (32) and v = 0.01 cm2&, affording a value for k of (1.9 0.5) X 1O1O cm3.mol-'.s-l. Figure 8 shows a family of plots of E vs log [i11/3i2/3/(i1i ) ] . The average slope of the straight lines was 0.031 f 0.003 V, which compares well with the theoretically predicted value of 0.026 V, whereas the magnitude of E"' obtained from the
*
1471
,_________r_
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1472
Anal. Chem. 1988, 60, 1472-1474
Registry No. NOz-, 14797-65-0;NOz, 10102-44-0;Au, 744057-5.
LITERATURE CITED (1) Xing, X.; Scherson, D. A. Anal. Chem. 1987, 59, 962. (2) Parts, L.; Sherman, P. L.; Snyder, L. D.; Jaye, F. C. Anal. Instrum. 1972, 10, 157. (3) Plieth, W. J. I n €ncyclopedla of fhe Nectrochemlstry of fhe Nements; Marcel Dekker: New York. 1978; Vol. V I I I , pp 321-479. (4) Vetter. K. J. 2 . Phys. Chem. (Frankfurt am Main) 1950, 194, 199. (5) Tanaka, N.; Kato, K. Bull. Chem. SOC.Jpn. 1956, 2 9 , 837. (6) Raspi, G.; Guidelli, R . Chlm. Ind. (Milan) 1963, 4 5 , 1398. (7) Guidelli, R.; Pergola, F.; Raspi. G. Anal. Chem. 1972, 4 4 , 745. (8) Schmidt, G. 2 . Elekfrochem. 1959, 63, 1183. (9) Schmidt, G.; Lobeck, M. Ber. Bunsen-Ges. Phys. Chem. 1964, 6 8 , 677. (IO) Erlikh. Yu. I.: Anni, K. L.; Palm, U. V. Nekfrokhymiya 1979, 14, 925. ( 1 1 ) Erlikh, Yu. 1.; Anni, K. L.: Palm, U. V. Elekfrokhymiya 1980, 15, 1573. (12) Harris, W. E.; Kolthoff, I.M. J . Am. Chem. SOC. 1945, 6 7 , 1484. (13) Imai, H. Bull. Chem. Soc. Jpn. 1957, 3 0 , 873. (14) Oriemann, E. F.; Kern, D. M. H. J . Am. Chem. SOC. 1953, 7 5 , 3058. (15) Koutecky, J.: Koryta, J. Collect. Czech. Chem. Commun. 1954, 2 0 , 845. (16) Mastragostino, M.; Nadjo, L.; Saveant, J. M. Electrochim. Acta 1968, 13, 721. (17) Mastragostino, M.; Saveant, J. M. Nectrochim. Acta 1968, 13, 751. (18) Amatore, C.;Saveant. J. M. J . Hectroanal. Chem. 1977, 8 5 , 27.
(19) Amatore, C.; Saveant, J. M. J . Electroanal. Chem. 1980, 107, 353. (20) Amatore, C.; Gareil, M.; Saveant, J. M. J . Elecfroanal. Chem. 1983, 147, 1. (21) Compton, R . G.; Daly, P. J.; Unwin, P. R.; Waller, A. M. J . Elecfroanal. Chem. 1985, 191, 15. (22) Ulstrup, J. Necfrochlm. Acta 1968, 13, 1717. (23) Holub, K. J . Electroanal. Chem. 1971, 3 0 , 71. (24) McIntyre, J. D. E. J . fhys. Chem. 1967, 7 1 , 1196. (25) Mcintyre, J. D. E. J . fhys. Chem. 1989, 7 3 , 4102. (26) Kuta, J.; Yeager. E. J . Electroanal. Chem. 1971, 3 1 , 119. (27) Kuta, J.; Yeager, E. J . Electroanal. Chem. 1973, 46, 233. (28) Nekrasov, L. N.; Potapova. E. N. Nekfrokhimiya 1970, 6, 780. (29) Levich, V. G. Physicochemical Hydrodynamics : Prentice Hall: Englewood Cliffs, NJ, 1962. (30) Bard, A. J.; Faulkner, L. R. Nectrochemlcal Methods, Wiiey: New York, 1980. (31) Day, R. A., Jr.; Underwood, A. L. Quantitative Analysis, 5th ed.; Prentice Hail: Engiewood Cliffs, NJ, 1986. (32) Ehman, D. L.; Sawyer, D. T. J . Necfroanal. Chem. 1968, 16, 541. (33) Pourbaix, M. Afias d'Equilibres Nectrochimiques a' 25 "C; Gauthier Villars: Paris, 1963.
RECEIVED for review December 9, 1987. Accepted March 3, 1988. Support for this work was provided in part by IBM through a Faculty Development Award to one of the authors
(D.S.).
CORRESPONDENCE Nonspectroscopic I nterelement Interferences in Inductively Coupled Plasma Mass Spectrometry Sir: It has generally been reported that inductively coupled plasma mass spectrometry (ICP-MS) is more susceptible to nonspectroscopic interelement interferences ("matrix effects") by high concentrations of concomitant elements relative to inductively coupled plasma optical emission spectrometry (ICP-OES) (1-12). A recent paper by Beauchemin et al. (3) summarizes these reports. In most cases suppressions of analyte signals have been reported, but in a few cases ( I , 9) enhancements have been seen. The effects depend on both ICP operating conditions and lens settings. Different conditions have been used by various workers, which may explain reports of varied behavior. Nevertheless broadly similar effects have been reported for both SCIEX (1-6) and VG (7-12) commercial systems and for at least two "homemade" systems (2, 12, 13).
The mechanisms proposed thus far to explain these effects have focused on the ICP or the supersonic expansion, although several workers have suggested that some of the observed effects may arise in the ion optics. In this communication we will outline a new mechanism which qualitatively seems to account for many of the varied observations. The mechanism attributes the apparent matrix effects to changes in the flux and composition of the ion beam. These changes arise due to space charge effects within the skimmer. (Although Olivares and Houk (14) noted that space charge could be important in the optics of their ICP mass spectrometer, no connection between space charge and matrix effects was made.) Both ion current measurements and the behavior of ion signals a t the detector provide clues as to the origin of the matrix effects observed. Ion current measurements were made with a stainless steel collector consisting of three concentric rings and a central circular stop. (The overall diameter of the collector was 4.5 cm.) The collector was situated 1 in. from the base of the skimmer. All four elements of the collector
Table I. Equipment and Operating Conditions SCIEX ELAN 250 ICP-MS power 1.2 kW outer gas 12 L/min auxiliary flow 1 L/min nebulizer M e i n h a r d TR30-C3 Nebulizer flow" 0.85 L/min sample uptake 0.7 mL/min sampler/load coil separation 17 mm i o n lenses voltages adjusted t o give equal response for 100 ppb Li and U and maximal response for 100 ppb Rh sampling orifice 1.1 mm skimming orifice 0.9 mm skimmer tip located 7 mm downstream of sampling orifice Sensitivity a t this nebulizer gas flow was reduced ca. 5 times f r o m the m a x i m u m achieved a t 0.95 Limin.
were tied together and biased at -30 V through an electrically floating electrometer. A mesh lens between the skimmer and the collector was held at 0 V. Other equipment and operating conditions for all the measurements are listed in Table I. By use of these operating conditions, the ratios of analyte signals (Li+,Rb+, Th+) from solutions with and without a high concentration of matrix element were measured; the results are shown in Figure 1. Most striking are the mass effects. For equimolar solutions, heavy matrix elements give greater suppressions than light matrix elements and for a given matrix, light analytes are suppressed more than heavy analytes. Similar results have also been reported by Tan and Horlick ( 1 ) and Kawaguchi et al. (13). Other workers (9) have also reported that the extent of suppression depends on the settings of the ion lenses. This observation and the mass trends
0003-2700/88/0360-1472$01.50/0 C 1988 American Chemical Society
