trolyte. Any Np(1V) formed may then be reversibly reduced to Np(II1) a t the electrode. When a large amount of Np(1V) relative to the amount of uranium is present, a separate peak for the reduction of Np(1V) may be observed a t about -0.3 V vs. the SCE. The effect of an amount of neptunium (added as Np(V) sulfate) sufficient to cause slight interference with the uranium peak height is shown in Figure 2. Note the broadening of the uranium peak toward a more negative potential. The possible interference of fourteen other cations was investigated and the results are summarized in Table 111. Zinc(II), Mo(V), Ti(IV), and Pt(1V) were found to interfere a t the levels tested. The effect of chromium is not clear. By itself Cr(II1) did not affect the uranium peak height; however, addition of Cr(II1) in the presence of molybdenum caused a significant increase in peak height. No interference from Th(1V) was observed. This is important because 23sPu metal is often cast into thorium oxide crucibles, and thorium is a common impurity. I t is important to note that the oxidation states given for ions listed in Tables I1 and I11 are the nominal oxidation state in which the ions were added to the electrolyte, which is a combination of a mild complexing agent and a reducing agent, Le., sulfate and ascorbic acid. Americium was not tested separately; however, all samples contained some americium. For most samples, the weight percent of americium was about one-tenth that of the uranium. No evidence of americium interference was noted as evidenced by the agreement between D P P results and the results of other methods of uranium analysis. Americium(II1) is not considered to be electroreducible in aqueous solutions, and it is likely that any reasonable amount of americium could be tolerated. Several anions were checked for interference. A fivefold concentration excess of ClOa- or NOS- over uranium had no effect. Phosphate and F- interfere strongly even in small amounts and must be excluded. Chloride interferes by increasing the level of residual current in the region of the uranium peak.
The method of analysis described works equally well for determination of uranium in compounds of 239Puprovided uranium is present a t about 500 ppm or higher so that the concentration of plutonium in the electrolyte does not need to exceed about 1 mg ml-l, in which case the peak due to the oxidation product of ascorbic acid may interfere. Because the concentration of uranium in many 239Pusamples is well below 500 ppm, a t least a partial separation of uranium from plutonium would often be required. However for 238Pusamples, where the uranium concentration is almost always 500 ppm or higher, the present method offers the advantages of simplicity and directness combined with relative freedom from interferences. The method is especially convenient when a coulometric determination of plutonium is to be carried out on the same sample, because aliquots of the same sample solution serve for both procedures without additional dilutions.
ACKNOWLEDGMENT The helpful interest of R. Gillette Bryan is gratefully acknowledged.
LITERATURE CITED (1) L. J. Mullins, Los Alamos Sci. Lab. Rep, LA-4940, Oct. 1972. (2) G. W. C. Milner, J. D. Wilson, G. A . Barnett, and A. A . Smales, J. Electroanal. Chem., 2, 25 (1961). (3) Y . Chapron, Commis. Enerq. At. (Fr.) Rapp., CEA-R 3299, 1967. (4) J. H. Christie, J. Osteryoung. and R. A. Osteryoung, Anal. Chem., 45, 210 ( 1973). - -, (5) J W. Dahlby, R. R Geoffrion, and G. R. Waterbury, Los Alamos Sci. La6 Reo.. LA-5776. Jan. 1975. (6) I. Hodara and I.'Balouka, Anal. Chem., 43, 1213 (1971). (7) R. K. Skogerboe and C. L. Grant, Spectrosc. Lett., 3, 215 (1970). (8) Mound Laboratory Report, MLM 1996, 1964. (9) J. C. Hindrnan, D. Cohen, and J. C Sullivan, Proc. Conf. Peaceful Uses At. Energy, 7955,7, 345 (1956) \
RECEIVEDfor review August 4, 1975. Accepted September 19, 1975. Work done under the auspices of the Division of Space Nuclear Systems of the Energy Research and Development Administration.
Digital Simulation of Differential Pulse Polarography James W. Diliard and K. W. Hanck" Department of Chemistry, North Carolina State University, Raleigh, N.C. 27607
Digital simulation is used to evaluate the effects of moduiation amplitude, number of electrons transferred, and charge transfer kinetics (a,ko) on differential pulse poiarograms. The combined use of least squares curve fitting routines and digital simulation allows heterogeneous charge transfer rate constants In the range 10-1-10-4 cm/sec to be measured using differential pulse polarography. Kinetic studies may be M. Experimental performed on solutions as dilute as data are reported for Cd2+/Cd, Ti+/Ti, Zn2+/Zn, and Eu3+/ Eu2+.
Differential pulse polarography (DPP) has proved to be a versatile and reliable trace analytical tool. Although there are several instrumental variations of DPP ( 2 - 4 ) , in its most common form, a small amplitude voltage pulse of short duration is superimposed on the slowly increasing 218
ANALYTICAL CHEMISTRY, VOL. 48, NO. 1, JANUARY 1976
linear voltage ramp applied to the cell. Timing circuits ensure that the pulse is applied a t the same point in the life of each mercury drop; the output current is the difference between the current flowing just prior to the end of drop life and the current flowing just prior to the application of the voltage pulse. Unlike other electroanalytical methods, very few investigations of the theory behind D P P have been made. Parry and Osteryoung (5) used a rather simple subtractive model to evaluate the analytical current of DPP. Their model assumes Nernstian behavior and ignores the hydrodynamic peculiarities of the dropping mercury electrode. To evaluate the use of D P P in speciation studies involving complexes of trace metal ions, we have found it necessary to investigate the theoretical behavior of D P P in systems complicated by rate determining chemical and electrochemical steps (6). We have elected to apply digital simulation to D P P rath-
1:
0
-6 3
2 3
-' C E-E'
j/ R T
Flgure 2. Simulated differential pulse polarogram for a reversible two-electron transfer (-): calculated polarogram from Parry and Osteryoung (0)
-
P
0
P
E,
v)
Table I. Variation of Peak Height and Half Width
Y
.
L
C
Peak height
Y
L
a
U
Eniod(mV) U
U I
- 1
I
0
I
I I
116
50 25
I I
117
118
119
10 5
l i m e l o o p N u m b e r (Simulator)
-k 0
I
I
1926.6
i
I
16.7
40.0
16.7
l i m e in m r e c . (Polarograph)
Figure 1. Differential pulse polarographic timing sequence for a
2.000-second drop er than a closed form solution to the appropriate set of differential equations. The effect of heterogeneous charge transfer parameters will be described here; the effects of homogeneous chemical reactions will be discussed in a future publication. THEORETICAL The basic theory of digital simulation is based on a model in which the solutioii around an electrode is divided into volume elements of thickness Ax and area equal to that of the electrode. Diffusion is the movement of species from one volume element to an adjacent one during a time increment At as governed by Fick's second law. The details of the method have been thoroughly described by Feldberg (7). We have adapted Feldberg's approach to the requirements of DPP. The timing sequence employed was a close approximation to that used in our commercially available instrument (8);see Figure 1. Parameters for an expanding planar electrode and hydrodynamic corrections for the DME as described by Feldberg (7) were included. Heterogeneous charge transfer kinetics were introduced through Equations 1 and 2
ht,=k"exp(
n=l 100
(n - U ) F ( E - EO)
RT
where k f is the forward rate constant for the simultaneous transfer of n electrons, k b is the analogous backward rate constant, and k o is the standard heterogeneous charge transfer rate constant for the couple; the remaining symbols have their usual significance.
n = 2 100 50 25 10 5 n = 3 100 50 25
10 5
Simulator
Parry and Osteryoung
Half w i d t h , mV Simulator
Parry and Osteryoung
1.000
1.000
0.601 0.317 0.128 0.064
0.602 0.318 0.129 0.065
123.4 99.0 92.5 90.3 89.4
123.4 99.1 92.7 90.9 90.6
1.000
1.000 0.781 0.470 0.200 0.101
102.0 61.7 48.5 45.9 45.2
102.0 61.7 49.5 46.. 0 45.4
1.000
1.000
0.902 0.626 0.284 0.145
0.903 0.627 0.286 0.146
102.7 53.4 36.5 31.2 30.3
100.2 53.4 36.5 31.2 30.4
0.781 0.470 0.199 0.100
During the simulation, the potential was advanced a t a rate of 2 mV/drop. The concentrations of all species were reset to the bulk concentration with the termination of each drop sequence to simulate the action of the drop timer on the DME. The FORTRAN program as used on an IBM 370/165 is available on request. The basic construction of the program is similar to that used by Feldberg ( 7 , 9 ) . EXPERIMENTAL Cadmium and zinc stock solutions were prepared from 99.999% and 99.95% pure wire respectively by dissolution in Ultrex nitric acid (J. T. Baker Chemical Co., Phillipsburg, N.J.). T h e thallium solutions were prepared from analytical grade TlN03; reagent grade Eu203 was dissolved in Ultrex perchloric acid (J. T. Baker) to prepare the europium standards. All stock solutions were apM and prepared using doubly deionized water. proximately T h e supporting electrolyte for cadmium and zinc was 1 M K N 0 3 and 1 M KC1 for thallium and europium. Both were prepared with deionized water and reagent grade chemicals. T h e PAR Model 174 Polarographic Analyzer (Princeton Applied Research Corp.) and the PAR 172 drop timer were used in the differential pulse mode with a 2-sec drop time. The electrometer and current output were multiplexed and displayed on a DTC Model 3312 digital panel meter (Data Technology Corp.). All experimental data were collected a t zero scan rate to minimize instrumental artifacts ( 1 0 ) . Data computation and curve fitting were performed in double precision using the IBM 370/165 and associated peripherals. A Beckman fiber tipped saturated calomel reference electrode, a platinum wire auxiliary electrode, and a standard D M E (SargentWelch S-29417 capillary, m = 3.896 mg Hg/sec) were used in the 3-electrode cell. The solutions were deoxygenated by purging with purified nitrogen which had been passed through a Ridox scrubber. (Fisher Scientific Co., Fairlawn, N. J.) ANALYTICAL CHEMISTRY, VOL. 48, NO. 1, JANUARY 1976
219
1 2-
e
H
' 0 s-
H
P -
\
c
2.11
10.c
-5.0
nF(E-E3>/RT Figure 3. Current I ( A ) , current II (B)and the current difference of a two-electron reversible simulated polarogram
5 0
-5 0
3 0
nF ( E-? 1 / R T Figure 6. ( A ) Effect of heterogeneous charge transfer rate constant ( n = 1, LY = 0.5). Rate constant: (1) 1.0, (2) lo-', (3) lo-*, and (4) 10-3 cm/sec. Peak current normalized to totally reversible value. (€3) Effect of transfer coefficient ( n = 1, ko = cm/sec). Transfer coefficient: (1) 0.7, (2) 0.6, (3) 0.5, (4) 0.4, and (5) 0.3. Peak current normalized to that of a = 0.5
,.,>
., .^ -z(r-r:~ ~-
,^
- . I
~
1
2~
~
0.5A
Figure 4. Simulated differential pulse polarogram of a reversible experimental polarogram of cadmium two-electron transfer (-); (4.00 X M) in 1 M KN03 (0). Drop time = 2 sec; modulation amplitude: ( A ) 100 mV and (6) 50 mV
0 0w e
'
c
, 34
c 5I
0 c3
:
2
3
'
-LOG
q0
1
5
Figure 7. Variation of /peak with /to.( A ) One-electron transfer. (6) Two-electron transfer Modulation amplitude: (1) 100 mV, (2) 50 mV, (3) 25 mV, (4) 10 mV, and (5)5 mV. Peak currents normalized to reversible value 8
c .
1 r-
I
t
?-
Figure 5. Simulated differential pulse polarogram of a one-electron transfer ( k o = 0.15 cmlsec, a = 0.9) (-); experimental polarogram of thallium (4.45 X 10-5 M) in 1 M KCI (0) Drop time = 2 sec; modulation amplitude: ( A ) 100 mV and (6)50 mV
RESULTS AND DISCUSSION Since the simulator input/output operations must be in terms of dimensionless parameters, the current is normalized either with the peak maximum or with a specified current such as the peak maximum of a totally reversible system. The potential is normalized and plotted as nF(E E o ) / R T . In Figure 2, a totally reversible simulated polarogram is plotted along with points calculated from Parry and Osteryoung's equation. The relative peak currents and peak width as a function of modulation amplitude for the totally reversible case are compared in Table I with data 220
ANALYTICAL CHEMISTRY, VOL. 48, NO. 1, JANUARY 1976
tabulated by Parry and Osteryoung. The close agreement indicates the simple model of Parry and Osteryoung to be in excellent agreement with our more detailed simulations of reversible systems. Current I, current 11, and the current difference are plotted in Figure 3. Current I would be that obtained for a Tast or "sampled dc" polarogram. The enhanced sensitivity and characteristic curve shape of differential pulse polarography are due mainly to current 11. Christie and Osteryoung (11) treated current I1 for a reversible system as the sum of two currents: a pulse current resulting from the voltage pulse and a dc faradaic current which is the current that would flow if the pulse were not applied. The magnitude of the pulse current is determined by the degree of concentration polarization prior to the application of the pulse. Initially, the pulse current increases as the potential scan proceeds since little electrolysis takes place prior to the application of the pulse. The degree of concentration polariza-
F
1.0-
0.5-
E C
-.*
-4 0
-'C E-E')
I1
0.0I 3
12.0
/RT
-12.0
0 0
nF(E-Eo)/RT
Figure 8 .
Simulated differential pulse polarogram of europium (-): experimental polarogram (1.23 X M Eu3+ in 1 M KCI) (0). Drop time = 2 sec; modulation amplitude: ( A ) 100 mV and (6)50 mV; kinetic parameters given in Table II
Figure 9. Simulated differential pulse polarogram of zinc (-); experimental polarogram (4.01 X M Zn2+ in 1 M K N 0 3 ) (0). Drop time = 2 sec; modulation amplitude: ( A ) 100 mV and (6)50 mV; kinetic parameters given in Table II
tion prior to pulse application increases as the potential scan proceeds, eventually the pulse current reaches a maximum and begins to decrease with potential. The pulse current is zero when the electrode is completely concentration polarized prior to the application of the pulse. At this point, current I and current I1 are in most instances equal; Christie and Osteryoung have discussed the factors and situations which may cause current I and I1 to differ slightly a t potentials cathodic of the peak potential. The potential dependence of experimentally measured values of current I and current I1 for cadmium closely agree with that of the simulator (12). In Figure 4, an experimental polarogram of 4.00 X M cadmium is compared to a totally reversible simulated polarogram. A similar comparison is shown in Figure 5 for 4.45 X 10-5 M thallium; in this case, the literature kinetic values (k" = 0.15, a = 0.9) were employed in obtaining the simulated polarogram ( 1 3 ) . Characteristic DPP curves for quasireversible systems were obtained by varying the heterogeneous rate constant and the transfer coefficient in the simulator. The polarograms shown in Figure 6 A illustrate the effect of varying the heterogeneous rate constant while holding the transfer coefficient at 0.5. With increasing irreversibility, the current decreases, the shape broadens, and the peak potential shifts in a negative direction. Variation of the transfer coefficient while holding the rate constant at cm/sec is illustrated in Figure 6B. Changes in a have a pronounced effect on the curve symmetry. The ratio of peak current to totally reversible peak current is plotted against (-log k") for the transfer of one and
two electrons in Figure 7 . The effect of modulation amplitude is also shown. From this plot, one can estimate k" by experimentally determining the current ratio. The peak current ratios of Eu to T1 and Zn to Cd were used to graphically estimate k o for Eu3+/Eu2+ and Tl+/Tl (Table 11). The discrepancies with the literature values may be due to the assumption that a was 0.5 or that corrections for differences in diffusion coefficients, solution concentrations, or blank currents were not sufficiently taken into account. The simulator was used as a subroutine in conjunction with a standard, in-house, nonlinear least squares program (14) to obtain refined kinetic parameters. Initial guesses of k o ,a , and E" were converted by the simulator into current ratios (Le., I / I J for each of a t least 30 values of potential distributed along an experimental polarogram. The calculated current ratios were compared with the experimental values and the initial guesses of k", a , and E" were modified automatically until the best fit was obtained. Approximately five minutes of CPU time were needed to obtain values of h " , a , and E" valid to three significant figures. The resulting fits for europium (1.23 X M ) and zinc M )are plotted in Figures 8 and 9; the experi(4.01 X mental values for k" and a are compared to literature values in Table 11. Both the graphical and least squares procedure yield kinetic parameters in good agreement with literature values, especially when it is noted that the DPP values were obtained using solutions 100 times more dilute than those cited in the literature. The least squares procedure, however, yields parameters which are less dependent on modulation amplitude than does the graphical approach. As may
Table 11. Kinetic Parametersa E u 3 + / Eu '+
k', cm/sec
Zn2+/Zn
k",cmjsec
Q
...
...
7.94 x 10-3 3.71 x 10-3
... ...
0.536 i 0.018 0.536 t 0.011 0.49
(3.18 i 0.22) x 10-3 (3.00 i 0.06) x 5 . 4 x 10-3
0.450 i 0.030 0.423 t 0.013 0.39
I/Irev method
100-mV modulation 5.01 x 10-4 50-mV modulat,ion 4.79 x 10-4 Least squares f i t 100-mV modulation (2.6 i 1 7 ) x 50-mV modulation (2.4 i 8.4) x 1 0 - 4 Literature values (13) 2.1 x 10-4 a Uncertainties are 95% confidence intervals.
-__
01
ANALYTICAL CHEMISTRY, VOL. 48, NO. 1, JANUARY 1976
221
be seen from Figure 7, couples with rate constants larger than 0.1 cm/sec are effectively reversible while polarograms of couples with rate constants smaller than cm/sec are rather insensitive to variations in k " . This insensitivity is responsible for the large uncertainty in the values of k" found for Eu3+/Eu2+. As the modulation amplitude is decreased the uncertainty in k " also decreases, implying that peak shape is more sensitive to kinetic parameters at low modulation amplitude. DPP using the commercial PAR 174 instrument is best suited for studying reactions with rate constants in the 10-1-10-4 cm/sec range. The shorter pulse widths available with certain custom designed instruments should permit the study of faster reactions. Either the graphical or the curve fitting technique offers a means for studying the kinetics of charge transfer reactions involving species a t the 10-5-10-6 M level. This is two orders of magnitude lower than now possible. This should aid in studying the concentration dependence of kinetic parameters and in studying materials of limited solubility. Digital simulation is an effective tool for investigating the effects of less than ideal red/ox reactions on differential pulse polarographic analysis. The effects of homogeneous
chemical kinetics (e.g. preceding, following, or catalytic reaction) are currently under examination in our laboratory.
LITERATURE CITED ( 1 ) D. E. Burge, J. Chem. Educ., 47, A 8 1 (1970). (2) J. B. Flato, Anal. Chem., 44 (1 l ) , 75A (1972). (3) A . M. Bond and R. C. Boston, Rev. Anal. Chem., 11, 129 (1974). (4) N. Klein and Ch. Yarnitzky, J. Electroanal. Chem., 61,1 (1975). (5) E. P. Parry and R. A. Osteryoung, Anal. Chem., 37, 1634 (1965). (6) K. W. Hanck and J. W. Dillard, Water Resources Research Institute Re-
port 85, Raleigh, N.C., Dec. 1973. Feldberg in "Electroanalytical Chemistry", Vol. 3, A. J. Bard, Ed., Marcel Dekker. New York, N.Y., 1969, pp 199-296. (8) "Instruction Manual Polarographic Analyzer Model 174", P.A.R. Gorp., Princeton, N.J., 1971. (9) I. Ruzic and S. W. Feldberg, J. Electroanal. Chem., 63, 1 (1975). (10) J. H. Christie, J. Osteryoung, and R. A. Osteryoung, Anal. Chem., 45, 210 (1973). ( 1 1 ) J. H. Christie and R. A . Osteryoung, J. Electroanal. Chem., 49, 301 (1974). (12) T. P. Hoit, Ph.D. Thesis, University of North Carolina, Chapel Hill, N.C., 1972. (13) N. Tanaka and R. Tamamushi. Electrochim. Acta, 9,983 (1964). (14) Triangle Universities Computation Center, Rep. LSR-89-1, Research Triangle Park, N.C., 1972. (7) S.W.
RECEIVEDfor review August 13, 1975. Accepted September 29, 1975.
Polarographic Determination of Chloride, Cyanide, Fluoride, Sulfate, and Sulfite Ions by an Amplification Procedure Employing Metal Iodates Ray E. Humphrey* and Stanley W. Sharp Department of Chemistry, Sam Houston State University, Huntsville, Texas 77340
The anions CI-, CN-, F-, Sod2-, and SO02- were determlned polarographically by reaction of a 1:l ethanol-water solutlon wlth a relatively insoluble metal Iodate. Iodate ion is released and Its reduction current measured at the dropping mercury electrode. Mercuric iodate is used to determine CI-, CN-, and SO02-, barium iodate for SOP2-, and thorium Iodate for F-. Ions were determined in the range of approximately 2-50 ppm.
Certain anions have been determined chemically by reaction with an insoluble metal iodate to release iodate ion followed by reduction of the iodate to iodine and titration of the iodine with sodium thiosulfate solution. This results in a chemical amplification as six iodine atoms result for each monovalent anion and twelve iodine atoms for each divalent anion. Chloride ( I ) , fluoride (2), and sulfate ( 3 ) have been determined in this way. Polarographic measurement of the reduction current for iodate ion should also result in considerable gain in sensitivity since six electrons are involved. Fluoride ( 4 ) is apparently the only anion which has been determined by the measurement of iodate reduction current. The procedure was developed for the determination of fluorine in organic compounds. The anions investigated in this study are difficult to determine by a polarographic reduction procedure. Exchange reactions involving metal chloranilates and measurement of the reduction current of the chloranilate anion have been used for determination of several anions ( 5 ) . Ex222
ANALYTICAL CHEMISTRY, VOL. 48, NO. 1, JANUARY 1976
change of these ions for iodate and measurement of its reduction current results in essentially a six-electron reduction for monovalent anions and a twelve-electron reduction for divalent anions and allows the determination of these species in the low parts-per-million range.
EXPERIMENTAL Apparatus. Polarographic data were obtained with a SargentWelch Model XVI recording Polarograph. A conventional H-cell with a saturated calomel electrode was used and was mounted on a Sargent-U'elch constant head dropping mercury electrode assembly. T h e H-cell might be impractical for trace analysis in some instances because of the possibility of adsorption on the fritted glass and difficulty of cleaning. The dropping mercury electrode had a drop time of 4.11 sec and a flow rate of 2.10 mg of mercury per sec. Solutions were agitated with the insoluble iodate compounds on a Lab-Line Junior Orbit Shaker. Reagents. Mercuric iodate, used to determine chloride, cyanide, and sulfite, was obtained from City Chemical Co., New York, N.Y. Barium iodate. used for sulfate ion, was precipitated by reaction of a solution of barium nitrate and potassium iodate. Thorium iodate for determination of fluoride was prepared from reaction of thorium nitrate and potassium iodate. The relatively insoluble iodates were washed with distilled water and dried. Stock solutions of the anions to be determined, prepared from the best available sodium or potassium salt, were made up in 1:1 ethanol-water solvent. T h e solutions of sodium sulfite contained 5% glycerol to retard air oxidation. Procedure. Solutions containing the anion to be determined in the 1:l ethanol-water solvent were mixed thoroughly with the appropriate insoluble iodate compound by shaking for 20 min. After filtering, 0.30 rnl of concentrated perchloric acid was added, the hydrogen ion concentration being approximately 0.12 M . Solutions
