Anal. Chem. 1987, 59, 154-156
154
A
¡
electrodes are virtually equivalent to previous three-step methods at Au electrodes. However, because of the elimination of the adsorption period, deviation from linearity of the i-C response is less severe with the two-step method. With the greatly improved detection limits at Au as compared to Pt electrodes and ease of application of the two-step waveform utilizing existing instrumentation, it is anticipated that this method will find increasing application for carbohydrate detection in liquid chromatographic and flow injection systems.
Glucose
Registry No. Glucose, 50-99-7; sucrose, 57-50-1; sorbitol, 50-70-4.
LITERATURE CITED (1) Textbook of Pediatrics, 10th ed.; Auerback, V. H., DIGeorge, A. M„ Nelson, W. E.; Eds.; Saunders: Philadelphia, PA, 1975; p 432. (2) Kaplan, A.; Szabo, L. L. Clinical Chemistry: Interpretation and Techniques: Lea & Flblger: Philadelphia, PA, 1979; Chapter 8. (3) Jandera, P.; Churacek, J. J. Chromatogr. 1974, 98, 55. (4) Havllcek, J.; Samuelson, O. J. Inst. Brew. 1975, 81, 466. (5) Linden, J. C.; Lawhead, C. L. J. Chromatogr. 1975, 105, 125. (6) Conrad, E. C.; Palmer, J. K. Food Technol. (Chicago) 1976, 30, 84. (7) Scobell, H. D.; Brobst, K. D.; Steele, E. M. Cereal Chem. 1977, 54(4),
8) Sucrose
905.
(8) Altzelmuller, K. J. Chromatogr. 1978, 156, 354. (9) Binder, H. J. Chromatogr. 1980, 189, 414. (10) D'Ambolse, M.; Noel, D.; Hanai, T. Carbohydr. Res. 1980, 79, 1. (11) Petchey, M.; Crabbe, M. J. C. J. Chromatogr. 1984, 307, 180. (12) Rocklin, R. Liq. Chromatogr. 1983, 7(8), 504. (13) Davies, A. M. C.; Robinson, D. S.; Couchman, R. J. Chromatogr.
I0
mm
(14) (15) (16) (17) (18) (19)
Figure 5. Multiple flow injection peaks with pulsed amperometrlc detection utilizing a Princeton Applied Research Model 174A potentiostat for glucose and sucrose: (waveform) E1 = 0.15 V (f, = 300 ms) and E¡ = 0.75 V (f2 = 200 ms); samples injected, 50 µ of 1.0 mM carbohydrate in 0.20 M NaOH; carrier stream, 0.20 M NaOH at 0.5 mL min"1; (A) glucose and (B) sucrose.
(20) (21) (22)
The 5 for 50 µ of 1.0 mM glucose and sucrose. base-line currents are shown in parentheses. The relative standard deviation of peak height over an 8-h period was less that 2%.
in Figure
(23) (24) (25) (26)
SUMMARY The method of PAD is now applicable for the detection of carbohydrates at Au electrodes utilizing commercially available potentiostats with asymmetric square-wave potential waveforms. Detection limits with the two-step waveform at Au
1974, 101, 307. Kuo, J. C.; Yeung, E. S. J. Chromatogr. 1981, 223, 321. Hyakutake, H.; Hanai, T. J. Chromatogr. 1975, 108, 385. Hughes, S.; Johnson, D. C. Anal. Chim. Acta 1981, 132, 11. Hughes, S.; Johnson, D. C. J. Agrie. Food Chem. 1982, 30, 712. Hughes, S.; Johnson, D. C. Anal. Chim. Acta 1983, 149, 1. Johnson, D. C.; Polta, J. A.; Polta, T. Z.; Neuburger, G. G.; Johnson, J.; Tang, A. P.-C.; Yeo, I.-H.; Baur, J. J. Chem. Soc., Faraday Trans. 1 1988, 82, 1081. Hughes, S.; Meschi, P. L.; Johnson, D. C. Anal. Chim. Acta 1981, 132, 1. Polta, J. A.; Johnson, D. C. J. Liq. Chromatogr. 1983, 6, 1727. Polta, J. A.; Johnson, D. C.; Merkel, K. E. J. Chromatogr. 1985, 324, 407. Polta, T. Z.; Johnson, D. C. J. Electroanal. Chem. 1986, 209, 159. Polta, T. Z.\ Luecke, G. R.; Johnson, D. C. J. Electroanal. Chem. 1986, 209, 171. Edwards, P.; Haak, K. Am. Lab. (Fairfield, Conn.) 1983, (April), 78. Rocklin, R. D.; Pohl, C. A. J. Liq. Chromatogr. 1983, 6(9), 1577.
Received for review June 4,1986. Accepted Augest 25,1986. This work was supported by the National Science Foundation through Contract CHE-8312032.
Redox Reaction Rates Using Potentiostatic Coulometry R. W. Ramette,* R. Z. Harris, A. A. Bengali, and R. J. Noll
Department of Chemistry, Carleton College, Northfield, Minnesota 55057
While developing precise coulometric methods for the determination of oxidants, we noted recent references (1, 2) to a report (3) that the reaction of chlorate ion with iodide ion followed an unusual rate law
A new method based on potentiostatic coulometry was used to study the kinetics of the aqueous redox reactions between the Ions chlorate/lodlde, bromate/lodlde, and bromate/bromIde. The halogen product was continuously and rapidly reduced back to halide at a large platinum gauze cathode, the current being a direct measure of reaction rate and the accumulated charge serving to measure the extent of reaction. The reactions were studied at several temperatures, and activation entropies and enthalpies were calculated. 0003-2700/87/0359-0154$01.50/0
-d[C103-]/dí
=
fe[C103-][I-]15[H+]2
(1)
ionic strength 1.0. This half-life of a few seconds in 0.1 M HI, but simple experiments show that the reaction is much slower than that.
with k implies
©
35 M"3,5 s"1 at 30 °C and
=
a
1986 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 59, NO. 1, JANUARY 1987
The early work of Bray (4) shows a first-order dependence on the iodide ion concentration rather than 1.5, and we have confirmed this. It is possible that the high value of the above rate constant is caused by the presence of a high concentration of hydrochloric acid, resulting in chlorate oxidation of chloride. However we have been unable to obtain the experimental data on which the report of ref 3 is based. Therefore it seemed worthwhile to determine the rate constant for the chlorate/iodide ion reaction in the absence of chloride ion. The direct cathodic reduction of chlorate ion is also extremely slow at a platinum electrode held at +0.1 V vs. SCE, compared to the rapid reduction of triiodide ion. We chose the chlorate/iodide ion reaction to test a novel coulometric method for studies of certain redox kinetics. We then extended the work to the brómate/iodide and brómate/bromide ion reactions. In a solution that is well-stirred and in contact with a large area platinum gauze electrode held at a suitable potential, the triiodide ion formed by the homogeneous reaction is rapidly reduced at the electrode to iodide ion. Similar behavior is shown by bromine/bromide ion. The combined reactions are represented as follows: (Pt working electrode)
i--------------j ,
CIO3- + 6H+ +
t
91"
K
1
31s" + 3H20
--
+ Cl
The rate of change in triiodide ion concentration is the difference between its rate of homogeneous formation and its rate of cathodic reduction. The potentiostatic reduction of triiodide ion follows the typical first-order behavior explained by Lingane (5), so we write
d[I31/dt
=
3fe[H+]2[I-][C1031
-
fce[I3"]
(2)
The triiodide concentration will go through a maximum at a time depending on the values of the two rate constants (6). The electroreduction may be monitored by potentiostatic coulometry, recording both the cathodic current and the accumulated charge, the latter serving as a measure of extent of the reaction. The cathodic current is proportional to the rate of reduction, the proportionality constant being 2FV. Since i = 2FVke[lf], we may express the rate of change of triiodide ion concentration by differentiation
d[Lf] dt
_ ~
di/dt
( ’
2FVke
where F
= 96 487 C and V is the cell solution volume. Substitution and rearrangement give
k
Í/2FV + (di/dt)/2FVke 3[H+]2[I-][C103-]
(4)
The concentration of iodide ion remains essentially constant and the chlorate ion concentration can be calculated by using the relationship [CIO3-]
=
C0
-
Q/6FV
+
i/6FVke
(5)
where C0 is the initial concentration, the first correction term is simply an expression of Faraday’s law, and the second term is a measure of the (small) amount of triiodide ion present in essentially steady-state concentration. Similarly, the acid concentration can be calculated by using the 6:1 stoichiometric
ratio. Equation 4 has essentially the same form as required for the widely used method of initial rates. The numerator is the instantaneous rate of formation of triiodide ion, and the denominator is the stoichiometric part of the rate law. What distinguishes this technique from the method of initial rates
·
155
is that the actual rate (current) may be measured at many successive times during the course of the reaction, while the accumulated charge provides accurate data for correcting the changing concentrations. The method of initial rates does not measure rate directly, but infers the initial rate by extrapolating data to zero time, providing only one value for the reaction rate, and therefore only one value for the rate constant per kinetics run. The present method allows many repeated determinations of the rate constant per run and is not re-
stricted to using data acquired during the first few percent of the reaction. This implies great improvement in the statistical reliability of the rate constant. Also, should the solution contain small impurities that might affect the data at the start of the run, such effects will disappear as the reaction proceeds.
During the electrolysis any unbalance of charge is continuously prevented by migration of anions out of and cations into the working electrode compartment. Thus, there will be some loss of iodide ion and some gain of hydrogen ion, minimized by using 5 M sodium perchlorate in the auxiliary compartment. Simulation of the experiment by numerical integration using a BASIC computer program called coulkin shows that these effects are negligible. However, migration corrections may be made by considering limiting conductivities. A computer program calcko carries out the calculations related to eq 4.
EXPERIMENTAL
SECTION
Sodium chlorate was recrystallized from hot water, and other chemicals were analytical reagent grade. Solutions were prepared with water redistilled from an all-glass still. The electrochemical equipment consisted of PAR/EG&G Model 371 potentiostat, Model 379 digital coulometer, and Model 377A cell assembly with a Model K0027 platinum gauze electrode. The PAR glass coulometric cell was replaced by a standard weighing bottle bottom and was suspended in a constant-tem-
perature water bath. In a typical run, sodium halide and perchloric acid were placed in the cell, and the Pt electrode was maintained at +0.1 V vs. SCE until the background current reached a constant low value of a few microamperes. Nitrogen gas constantly flowed over the surface of the solution to avoid oxidation of iodide ion by oxygen. Then a small volume of sodium chlorate (or brómate) solution was added from a dispensing pipet to start the reaction. The current increases as the halogen concentration builds up and then begins a slow decrease as the oxidant is used up. Current was recorded vs. time on a Houston 2000 recorder. At regular intervals the accumulated charge was simply read from the digital output on the coulometer. Thus, the assembled data for a kinetics run were a set of time, charge and current values, typically spaced at 60-s intervals for up to 30 min. Separate experiments, where a small amount of triiodide ion solution was added in the absence of oxidant, showed that with our combination of electrode and stirrer the rate constant ke for the potentiostatic reduction of iodine has a reproducible value of 0.041 M”1 s_1 at 25 °C. This value is not critical in the calculations as long as the cathodic reduction is fast compared to the homogeneous redox reaction. As a check the rate constant for the chlorate/iodide ion reaction was also determined spectrophotometrically, using a Perkin-Elmer Lambda 5 instrument equipped with a constant-temperature cell holder. The solution was prepared by mixing solutions as described above, except that the individual solutions were first deaerated with nitrogen. Absorbances were determined at 1-min intervals for 30 min at 445 nm, where separate measurements on a known triiodide ion solution showed the molar absorptivity to be 1732 L moT1 cm-1. In this time period the reaction went only about 0.23% toward completion, so the slope of a plot of absorbance vs. time was linear and suitable for the method of initial rates.
In the study of the brómate reactions it was necessary to use low concentrations of acid and brómate to decrease the rate. Typical concentration conditions and maximum currents at 25
156
ANALYTICAL CHEMISTRY, VOL. 59, NO.
·
1,
JANUARY 1987
Table I. Typical Conditions for the Kinetics Experiments'1 reaction
^halate
0.1
chlorate/iodide brómate/iodide bromate/bromide
0.00035 0.002
‘Concentration units
are
^halide
Cacid
¿max/mA
0.5 0.1 0.1
0.4 0.02 0.02
1.3 10 3.5
mol/L.
Table II. Rate Constants (Units of M Entropies and Enthalpies
temp/°C
and Activation
X X X X
45
2.7 8.4 2.7 8.7
10~6
ASgctiy
-56 ± 8
J/K
-61 ±
3
J/K
45 ±
1
kJ
10"6 10"6 10"5
86 ± 3 kJ
Afíggtiv
CONCLUSION
brómate/ bromide
We have also used this “method of instantaneous rates” with
1.03 2.39 5.74 13.2
-28 ±
5
J/K
63 ±
1
kJ
summarized in Table I. In all cases the ionic strength adjusted to 1.0 with sodium perchlorate.
are
RESULTS AND DISCUSSION Table II summarizes the values of the rate constants at various temperatures and shows the calculated activation entropies and enthalpies. The latter were obtained by nonlinear regression fits of the following equation (7) to the experimental data: k
=
oscillating reactions. Its use for an instructional kinetics experiment was reported by Clarke (11), who used a “clock” reaction with phenol to measure the rates. His rate constants over a temperature range from 0 to 30 °C are reasonably consistent with those in Table II, considering that his work was at ionic strength 0.3. From his results we calculate the activation entropy and enthalpy to be -67 J/K and 51 kJ, respectively.
for the oxidation of iodide ion by peroxydisulfate ion and hydrogen peroxide. The technique cannot be as broadly used as the method of initial rates. It is applicable only to redox reactions comprising one electrochemically reversible couple (i.e., having rapid redox kinetics) and one completely irreversible couple. In addition to iodide and bromide ions, possible reversible reducíante include ferrous and ferrocyanide ions. It is not necessary that the reversible couple be the source of the reducing agent. For example, it may prove possible to study oxidations of electrochemically irreversible couples by ferric ion, bromine, or iodine, in which case it would be necessary to poise the working electrode at potentials sufficiently positive to maintain constant concentration of the success
12.0 23.7 47.0 92.2 155
5
°C
s *)
chlorate/iodide brómate/iodide
15 25 35
was
3
Bromate/Bromide Ion Reaction. This reaction has long been used as a source of bromine for precise titrations and more recently (10) has been of vital interest in the study of
RT/Nh exp(AS/R) exp(-AH/RT)
(6)
where R is the gas constant, N is Avogadro’s number, and h is Planck’s constant. In a typical run values for the rate constant were determined at 20-s intervals for 900 s with a standard deviation of 2%. Chlorate/Iodide Ion Reaction. Runs with varying concentrations confirmed the form of the rate law proposed by Bray (4). The results correspond to values of 0.98,1.99, and 1.02 for the orders for chlorate ion, hydrogen ion, and iodide ion, respectively. From the spectrophotometric data we found the rate constant to be 1.0 X 1CT5 at 25 °C, in fairly good agreement with the electrochemical results. The slightly higher value may be due to incomplete removal of oxygen from the solution during the measurement.
Bromate/Iodide Ion Reaction. This has been thoroughly
discussed by Barton and Wright (8), who used an amperometric method to find k = 49 M~3 s"1 at 25 °C and reported an activation energy of 9.9 kcal/mol based on the early work of Clark (9). This is consistent with our results.
oxidant.
ACKNOWLEDGMENT We thank Mark Rhodes and Douglas McGuire for assistance in developing the techniques for the spectrophotometric
work.
Registry No. C103", 14866-68-3; Br03", 15541-45-4; 20461-54-5; Br", 24959-67-9.
,
LITERATURE CITED (1) Ikeda, Y.; Tang, T.; Gordon, G. Anal. Chem. 1984, 56, 71-73. (2) Miller, K. G.; Pacey, G. E.; Gordon, G. Anal. Chem. 1985, 57,
734-737.
(3) Nlkolelis, D.; Karayannls, M.; Hadjlloannou, T. P. Anal. Chim. Acta
1977, 94, 415-420.
(4) Bray, W. C. J. Phys. Chem. 1903, 7, 92-117. (5) Lingane, J. J. Electroanalytlcal Chemistry, 2nd ed.; Interscience Publishers: New York, 1958; p 224. (6) Benson, S. W. The Foundations of Chemical Kinetics; McGraw-Hill: New York, 1960; p 35. (7) Espenson, J. H. Chemical Kinetics and Reaction Mechanisms; McGraw-Hill: New York, 1981; p 117. (8) Barton, A. F. M.; Wright, G. A. J. Chem. Soc. 1968, 1747-1753. (9) Clark, R. H. J. Phys. Chem. 1906, 10, 679. (10) Cltri, O.; Epstein, I. R. J. Am. Chem. Soc. 1986, 108, 357-363. (11) Clarke, J. R. J. Chem. Educ. 1970, 47, 775-778.
Received for review July 24, 1986. Accepted September 9, 1986. This research was supported by NSF-RUI Grant No. CHE-8418616.
