Anal. Chem. 1983, 55,2063-2066
2063
Direct and Titrimetric Determination of Hydrogen Peroxide by Reverse Pulse Polarography Alicia Brestovisky and Emilia KirowaEisner
Department of Chemistry, Tel-Aviv University, Rnmat-Aviv, Tel-Aviv, Israel J a n e t Osteryaung*
Department of Chemistry, State University of New York ut Buffalo, Buffalo, New York 14214
Hydroxide produced In the polarographic reduction of hydrogen peroxlde gives rise to an anodlc wave for mercury. I n the reverse pulse polarographic mode this wave Is strictly proportional to concentration of hydrogen peroxide In the range 0.007-1.5 mM with dlffusion current constant 6.5 /*A s112 ,,,~-l mg-2J3. This wave may be used analytlcally for direct determlnatlon of hydrogen peroxlde or It may be used as the lndlcator current for an lndlrect determinatlon employing amperometrlc tltratlon In the dlffuslon layer with strong acid.
Reverse pulse (RP) polarography is a technique for examining the products of electrochemical reactions (1). In its most usual application the potential is held at an initial value at which the substance OF interest is reduced under diffusion control. Then once in the life of each mercury drop a pulse is applied in the positive direction and the current is sampled near the end of the pulse width. Pulses are applied to successively more positive values, and the resulting curve of current vs. pulse potential is an RP polarogram of the product of the electrode reaction which takes place at the initial potential. Reverse pulse polarography has been used to study the mechanism of electrode reactions (2-9), to determine diffusion coefficients ( l o ) ,and for analytical purposes (11). The RP technique can be especially useful analytically when the voltammetric properties of the reaction product are more favorable than those of the reactant itself or when the reduction of the reactant is not well-separated from reduction waves for other substances in solution. The determination of the product may be carried out directly by measuring the height of the RP wave, or it may be done indirectly by titration in the diffusion layer using the RP limiting current for amperometric detection of the end point. An additional feature of this approach is that a wide variety of substances, all of which have the same product, may be determined by use of the same voltammetric wave. In general these classes of compounds are reduced totally irreversibly, and the product is not reoxidized to the starting material on the RP wave. An example of such a class is HzO, IlzOz, 02, and other peroxides or superoxides which generally produce hydroxide on c?lectrocliemical reduction. These reductions are generally irreversible and the resulting waves are poorly suited for direct voltanimetric determinations. However, the hydroxide produced readily depolarizes mercury, according to the reaction Hg 20H- = Hg(OH), 2e-
+
+
and under well-defined ranges of pulse widths and concentrations the resulting (anodicwave is diffusion controlled in hydroxide concentration (12). Here we report on the direct and titrimetric determination of HzOzin unbuffered aqueous solution by using the IRP wave of hydroxide for direct mea-
surement or as an indicator of the end point of an acid-base titration in the diffusion layer. The direct determination based on the height of the RP wave relies on calibration curves obtained for known concentrations of hydroxide using NP polarography under the same electrochemical conditions. Standard addition methods may also be employed, in which known concentrations of hydroxide are added to the unknown solution of hydrogen peroxide. Titration in the ddfusion layer consists of titration of species formed in that layer as a result of electrochemical reaction. In the present case, hydroxide formed according to reaction 1 is titrated by adding strong acid to the bulk solution. The end point for the titration is determined amperometrically from the limiting current for reaction 1as a function of volume of titrant added. The end point is reached when the flux of hydroxide at the electrode surface is equal to the flux of strong acid added as titrant in the bulk of solution. The possibility of titrations in the diffusion layer is by no means a new ildea (13), but pulse voltammetric techniques make their implementation easier than before. The diffusion layer titration is an attractive alternative to direct titration in cases whlere (1)the product of an electrode reaction can be titrated conveniently, but the reactant cannot, and (2) the amperometric end point detection works better for the titration of prodluct than for titration of reactant. In the present case the acid-base titration works well, and the only substantial drawback is that the solution must be unbuffered. Detection of the end point can be carried out as described here, or by following the increase of the current due to the reduction of excess Hf to Hz.The latter approach is inherently more sensitive to1 interference from other species in solution and therefore only the former is pursued here. Hydrogen peroxide is a convenient example for demonstrating these points, but also the type of determination proposed here may have substantial practical utility for measuring or controlling the concentration of hydrogen peroxide in reaction mixtures, because it is difficult to maintain solutions of knowin concentration. This can be especially important for organic reactions in which the distribution of products depends strongly on concentration of hydrogen peroxide. Althouglh the work reported below was carried out exclusively in aqueous solution, thermodynamicconsiderations suggest that it may be broadly applicable to nonaqueous solvents in which hydroxide ion is stable. EXPERIMENTAL SECTION The electrocheimical equipment and procedures were straightforward and have been described in detail elsewhere (12, 14). The head of niercury of the dropping mercury electrode was 46 cm, and the flow rate (in the range 0.297-0.735 mg/s) is specified as necessary below. All potentials were measured and are quoted here vs. Hg/HgS04(s),K2S04(sat)reference electrode. Stock solutions of 0.05 mM HzOz(stored under refrigeration) and 0.02 M KMn04were standardized according to classical proce-
0003-~700/83/0355-~063$01.50/0 0 1983 American Chemical Society
2064
ANALYTICAL CHEMISTRY, VOL. 55,NO. 13, NOVEMBER 1983
I'
I
,
I
I
I
,
r l
05-
4c
:-I.I 0
-2
-
-3b
I -40
I
0
-05
E, 0
-0 4
-I 2
-08
-1 6
E, V
and RP polarograms of 93.7 pM H,O, in 0.1 M NaCIO,: 7 = 1.1 s; t , = 11.1 ms. The currents i w , iRp,H202, and are illustrated. Figure 1. DC
dures. The source of HzOzwas Mallinkrodt AR 3% Hz02(0.02% acetanilide). Titration Procedures. A known volume of sample 0.1 M in NaClO, was introduced into a tightly sealed cell and well deaerated. Polarograms were then recorded in the RP mode with initial potential -1.9 V after successive additions of known amounts of HC104in deaerated solution. The solution was stirred briefly after each addition. Before the titration the sample must be neutralized. If the concentration of H20zis greater than 100 pM this is not a critical step, and the neutralizationcan be carried out by convenient but less precise methods, such as adjusting the pH to 7.0. For lower concentrations the neutralization must be carried out by pretitration. The pretitration is carried out exactly as the titration itself, except that the initial potential for the RP polarograms is set at -1.0 V, at which value no reduction of Hz02 occurs.
RESULTS AND DISCUSSION Sampled DC and R P waves for the reduction of HzOzin 0.1 M NaC104are shown in Figure 1. The DC wave is totally irreversible, and the rising portion is spread over a potential range of 0.6 V. However the region of the limiting current is well-defined, and the limiting current, iDc, is diffusion controlled. The R P wave is typical of that expected for an irreversible process. The cathodic branch of the wave arises from the reduction of HzOzdiffusing to the electrode during the time of the pulse according to the reaction
H 2 0 + 2e-
-
20H-
(2) Two waves are observed on the anodic branch. The wave appearing at more negative potentials is not well-defined and merges into the larger wave. However, measurements a t a variety of drop times, 7, and pulse widths, t,, showed that the height of this wave, iRp,H202,is equal within experimental error to the height of the DC wave for reduction of H202. This indicates that this wave is due to oxidation of Hz02diffusing to the electrode during the time of the pulse according to the equation H202 20HO2 -t2 H 2 0 2e(3)
+
-
+
It might be asked why, if this identification of the small wave is correct, this wave does not appear in the DC polarogram. The answer is quite simple. Under DC conditions in neutral solution the wave does not appear because no hydroxide is present. In the RP mode, the hydroxide formed according to reaction 2 at the initial potential is available in the diffusion layer, so reaction 3 can occur. Addition of hydroxide in the bulk solution gives rise to the anodic wave in the DC mode in the presence of HzOz. The larger wave appearing a t more positive potentials is due to the oxidation of mercury in the presence of hydroxide
I
-15
I -20
v
Flgure 2. RP polarcgrams of 0.14 rnM HO , , in 0.1 M NaCIO, at various pulse widths: 7 = 1.11 s; t , (ms) In order of increasing limiting current 40.4, 20.1, 11.3, 5.6.
according to reaction 1. This wave has been well characterized in previous work (12). Assuming both of the anodic waves (reactions 1and 3) have the stoichiometry l(OH-)/le- the total wave height is directly proportional to hydroxide concentration. However it is of some interest to see the relation between the wave heights for these two waves. The total anodic wave height, iRp,T, is given by the Sum iRp,OH + iRp,H202where iRp,OH is the height O f the hydroxide wave and iRP,H202 the height of the peroxide wave (Figure 1). As described above iRp,H2O2 = -iDc. Also, provided 7 2 400t,, iNP/iDC = (3r/7tP)'/', and iNp = iDc- iRp,T, where i N p is the height of the NP wave for reduction of HzOz( I ) . Combining these relations ~ R P , o H / ~ R P , H ~ o=~
(4) Large ratios of 7 / t , increase the concentration of hydroxide in the diffusion layer relative to HzOzon the pulse time scale and result in larger currents for the hydroxide wave. For 7 / t , = 400, iRp,OH/iRP,H2O2 = 11. The dependence on t, is shown explicitly in Figure 2. Clearly iRP,H2O2 is independent of t, and equals iDc. The experimental ratios of iRp,OH/iRp,H2O2 deviate somewhat from the value predicted by eq 4,because of geometrical considerations not taken into account in this simplified treatment (1, 10). Data from experiments similar to those of Figure 2 which include variation of T as well may be analyzed as described previously (1) to yield the value of the stoichiometric coefficient, p , for hydroxide in reactions 2 and 3. The result is p = 2.01 f 0.02. It has been noted previously that the NP limiting current due to hydroxide according to reaction 1is strictly linear only for [OH-] I 0.4 mM (12). That is true also for the total RP limiting current in this case. For CH202 in the range 0.007-0.39 mM, iRp,T is linear in CHZo2with intercept 3.2 gA, slope (sensitivity) 89.1 pA/mM, and correlation coefficient (r)0.9998 (for 7 = 2.22 s, t, = 10.7 ms, m = 0.735 mg/s). However, adequate linearity is maintained at higher concentrations for most analytical purposes. For example, in the range 0.007 < CH2O2 C 1.46 mM, the slope is 85.5 pA/mM and r = 0.998. A reasonable average value for the diffusion current constant is I i R p , T t , 1 / 2 / C ( m 7 ) 2 ~ 3 = 6.5 pA s1/2mM-' mg-2/3. At concentrations above 1.46 mM the linearity of the current-concentration relationship is no longer maintained, and the apparent value of the diffusion current constant decreases. At 1.1 mM H20zthe reproducibility of iRp,T is 0.2%. When pretitration is employed, the intercept at CHz02 = 0 is reduced to 0.16 PA. The detection limit, defined as 3sb/m, where s b is the standard deviation of the background current and m the sensitivity, is 0.8 gM. Acid-Base Titrations i n t h e Diffusion Layer. Hydroxide produced in the RP reduction of H202can be de-
( 3 ~ / 7 t , ) ~-' 2~
AN ALYTICAL CHEMISTRY, YOL. 55, NO. 13, NOVEMBER 1983 V, mL
20615
Table I. Amperometric Titration for H,O,' CHZO,,
mM
taken
found
error, %
0.0226 0.0570 0.114 0.228 0.456
0.0234 0.0540 0.112 0.221 0.448
+ 3.5 -4.6 -1.8 -3.1 -1.8
a 0.1 M NaClQ,, T '= 1.1s, tp = 10.7 ms, m = 0.376 mg/s. Samples pretitrated.
-5t 0
-0 4
-0 8
E,
-4 2
-I 6
v
Figure 3. RP polarograms for 0.25 mM H,O, in 0.1 M NaCIO, and the resulting titration curve: titrant, 3.9 mM HCI04; lnltial solution volume, 50.38 mL; 7 = 1 s; t , = 10 ms. The currents used in the titration curve have been corrected for dilution. The end point occurs at 2.38
mL.
termined also by titration in the diffusion layer. The initial potential is maintained on the limiting current plateau for reduction of H202,,and the pulse potential is maintained on the limiting current plateau for oxidation of mercury in the presence of hydroxide, reaction 1. The titration is carried out by measuring the resulting current as a function of added hydrogen ion. The equivalence point is reached when the flux of hydrogen ion diffusing toward the electrode equals the flux of hydroxide ions diffuriing from the electrode. Because of the stoichiometry of reaction 2, at this point the flux of hydrogen ions is exactly twice the flux of hydrogen peroxlde, and thus the flux condition at the equivalence point is CbHDH1i2= 2 C b ~ z ~ z D ~ z ~ z 1 / 2 (5) and the unknown concentration of H202is given by
CbHzoz= (1/2)CbH(DH/D~,~,)'/2
(6)
where CbHzOz and CbHrefer to the bulk concentrations of H202 and H+, respectively, and DHzOzand DH are the corresponding diffusion coefficients. RP polarograms taken after successive additions of acid and the resulting tilration curve are shown in Figure 3. The intersection point of the two curves, corrected for dilution, occurs at V = 2.38 mL (the left part of the titration curve is a straight line with correlation coefficient 0.9996 and intercept a t V = 2.38 mL). In order to calculate the proper concentration of H202from thle known concentration of HS added according to eq 6, it is necessary to know the ratio DI{202/L)H. In fact the proportionalitybetween the quantity of titrant and the concentration of analyte may be determined empirically by titration of Ekandarcls. However, especially for purposes of method development, it is more satisfying to determine each value of D directly from the limiting NP current. These were measured for 0.14 mM Hz02in 0.1 M NaC104,7 = 1.11s, 5.6 < t , < 90.7 ms and, using the same DME under the same conditions, for 0.9 mM HC104. The resulting individual values were DH = 8.7 X cm2s-l and DH202= 1.2 X cm2 d. The value of the ratio in eq 6 can be obtained directly from the limiting current ratios without introducing uncertainties in electrode area, etc., and is given by (DH20,/DH)1'2 = CHiNP,H202/2CH202iNP,H = 0.36
((7)
The value of ( D ~ z ~ z / Dwas ~ ~ also ) 1 ~determined 2 by carrying out titrations of solutions of H202of known concentration and
using eq 6. Plots of CbH vs. CbHzOzfor C b ~ zin~the z range 0.01-1.3 mM yield the value (DHzoz/DH)1/2 = 0.360 from the slope with a correlation coefficient of 0.9998. Table I gives representative results for titrations in this concentrationrange. Titration of five samples 0.11 mM in H202under the same conditions yielded a standard deviation of 0.9%. The systematic negative error of Table I may be attributable in part to systematicpositive! standardization error due to acetanilide. Interferences. Interfering substances include those which might react with hydroxide or react electrochemically to produce hydroxide or hydrogen ions. ( a ) p H and Buffer Capacity. Hydrogen peroxide can be determined,in aqueous solutions of any pH by employing t'he pretitratjon procedure, provided the buffer capacity is sufficiently low. Concentrationsof weak acids or bases in soluti'on that could'react with OH- or with H+ must be negligible in comparison with the concentration of H202to be determined. ( b ) Metal Ions. Interference due to metal ions may occur because of the current due to electrochemical reactions of the metal or because of reaction of the metal with hydroxide in the diffusion layer. Consider first electrochemical interferences. Metal ions which are reduced more easily than hydrogen peroxide can form an amalgam while the potential is held on the limiting current plateau for hydrogen peroxide reduction. Then during the pulses,the amalgam can be oxidized to form the metal ion. This changes the magnitude of the pulse current but does not cause any interference with the titration procedure (unless the metal ion reacts with hydroxide). Furthermore, direct measurement based on the height of the wave due to hydroxide is unaffected as long as that wave is well separated from the metal oxidation wave, and the limiting current for metal oxidation provides a good base line for measurement of the height of the wave due to hydroxide. Reaction of metal ions in the diffusion layer with electrogenerated hydroxide is a well-known phenomenon (15). Interference with either the direct or titrimetric determinatiion of peroxide will result if the reaction products are stable with respect to Hg(OH),(aq) or inert on the time scale of the lexperiment. If the metal is reduced at potentials more negative than that for peroxide reduction, then metal hydroxide can be generated while hydroxide is being generated. If, on the other hand, the metal is more easily reduced than peroxide, the concentration of metal ion in the diffusion layer while hydroxide is being generated should be insignificant and no metal liydroxide will form. During pulses to potentials where the, metal is reoxidized, however, metal hydroxides could form. It might be expected that the former would cause more severe interference, because the time scale is much greater than that of the pulse. ,We carried out interference studies with Pb2+,Cd2+,Z I P , and Cu2+in solutions 0.07 mM in H202. Under these conditions the surface concentrationof OH- during the generation step is 0.14 mM; the estimated solubilities of the hydroxides, M(OH),(s), at this concentration are 0.6,0.002, 1 X and 0.12 mM, respectively, while the estimated solubility of Hg(I1)
2066
ANALYTICAL CHEMISTRY, VOL. 55, NO. 13, NOVEMBER 1983
Table 11. Effect of Metal Ions on Relative Limiting Current for RP Wave of Hydroxidea ! ~ R P , TZRP,M(II)
Pb(I1)
15 0.02 0.12 0.22 0.93
Cd(I1) 0.03 0.06 0.36 0.66 Zn(I1)
Cu(I1)
-0.81 1.06 1.06
0.01
1.11
1.57 14.4
-0.99 1.02 1.00 1.13 1.14
17 0.02 0.03 0.16 0.32 0.01
-1.40 0.96 0.85 0.54 0.51
18.2
-6.43 C
a t = 10.7 ms; T = 1.1s; [H,O,] = 0.07 mM; [NaClO,] = 0.1 M. RP wave of H,O, ( E , ,JH 0 = -1.56 V. decreased and distol?ted.
is 2.5 mM (16). Hg(I1) at pH 10.1 exists as Hg(OH),(aq) and the principal soluble forms of the other metals would be M(OH)+ or M(OH)z(aq). The formation constant for Hg(OH),(aq) is given by log Pz = 22, and, therefore, as suggested by the solubility products given in Table 11, any hydroxides that form should be unstable with respect to formation of M2+and Hg(OHI2(aq). The soluble hydroxides are all labile; however, reactions involving precipitation are frequently not in equilibrium. In the case of Pb(II), as shown in Table 11, there is no interference at moderate concentrations. At 0.12 mM Pb(I1) it is rather difficult to measure accurately the small wave due to OH- on top of the large wave due to Pb(Hg). However the titration procedure works well even at 0.12 mM Pb(I1). The solubility calculations suggest that interference due to Cd(I1) might be greater, but the results of Table I1 show it is less. To examine this case more closely we carried out RP polarogram~of 0.3 mM Cd(I1) in 0.07 mM HzOz. At short pulse widths (tP 5 10 ms) semilogarithmic analysis of the wave according to the equation for the reaction Cd(Hg) + 20H- = Cd(OH)2(aq)+ 2e-
times is apparently a kinetic phenomenon. For Cu(11) even 0.01 mM concentration causes a severe diminution and distortion of the limiting current for HzOz. Presumably this is due to the fact that the rate of precipitation of Cu(OH), is larger than that of Pb(OH)2or Cd(OH)z. Zn(I1) is much less soluble than Cu(I1) because the soluble hydroxides are less stable (16). Furthermore, Ell2for Zn(I1) is near that for HzOz,sa the concentration of Zn(I1) in the diffusion layer when OH-is being generated is much greater than that of Cu(I1) under the same conditions. Thus Zn(I1) diminishes the limiting current for hydroxide significantly even at a concentration of 0.03 mM. But at 0.02 mM, the effect is minor, indicating again that slow kinetics of precipitate formation decrease the extent of interference. In summary,metal ions that form insoluble hydroxides may interfere in this determination, depending on the exact chemical conditions. ( c ) Oxygen. Oxygen is of course reduced simultaneously with hydrogen peroxide, producing hydroxide, and therefore interferes. However normal procedures for deaeration are sufficient to achieve the reproducibility of blank values reported here. (d) Anions That Depolarize Mercury. Any anion, X-, that depolarizes mercury with the formation of insoluble products may interfere. However the interference has nothing to do with the peroxide reduction, only with the anodic wave for mercury. This type of interference has been investigated thoroughly for halides already (12). The results are that the bromide concentrationmay be as large as 0.05CHz02 and iodide or chloride concentrations may be as large as 4CHzo2without interference. Registry No. Hydrogen peroxide, 7722-84-1.
LITERATURE CITED
.
E = Eo - (RT/nF) In ( ~ C ~ ~ ( ~ ~ ~ ~ -~ ~ , / ~ ~ H ) (RT/nF) In (2(id- i ) z / i $ ) (8) yields a straight line with slope 29 mV. Other assumptions about the product yield curved semilogarithmic plots. Thus at sufficiently short pulse widths only the soluble neutral complex, Cd(OH)2(aq),is formed, and there is negligible interference at moderate concentrations. For longer pulse widths insoluble products are formed with resulting interference with determination of H202. The well-behaved oxidation at short
Osteryoung, Janet; Kirowa-Eisner, E. Anal. Chem. 1980, 52,62-66. Kashti-Kaplan, S.; Hermolln, J.; Kirowa-Eisner, E. J . Nectrochem SOC. 1981, 128,802-810. Osteiyoung, Janet; Talmor, D.; Hermolin, J.; Klrowa-Elsner, E. J . Phys. Chem. 1981, 85, 285-289. Webber, A.; Kirowa-Eisner, E.; Hermolin, J.; Osteryoung, Janet J . Nectrochem. SOC. 1982, 129. 2725-2730. Stojek, 2.;Osteryoung, Janet J . Nectroanal. Chem. 1981, 127, 67-74. Wolclechowskl, M.; Osteryoung, Janet Anal. Chem. 1982, 54, 1713-1719. , Hermolin, J.; Kirowa-Elsner, E.; Kosower, E. M. J . Am. Chem. SOC. 1961, 103,1591-1593. Hermolin, J:; Kashti-Kapian, S.; Kirowa-Eisner, E. J . Nectroanal. Chem. 1981, 123,307-322. Linga, H.; StojYk, 2.;Osteryoung, R. A. J . Am. Chem. SOC. 1981, 103,3754-3760. Brumleve, T. R.; Osteryoung, Janet J . Phys. Chem. 1982, 8 6 , 1794-1801. Wojclechowski, M.; Osteryoung, Janet, unpublished results. Kirowa-Eisner, E.; Osteryoung, Janet Anal. Chem. 1978, 50, 1062-1066. Kolthoff, I. M.; Lingane, J. J. "Polarography", 2nd ed.; Interscience: 1 ' York, 2 ) 1952; p 110. New Brestovisky, A. M.Sc. Thesls, Tel-Aviv University, 1979. Kolthoff, I. M.; Llngane. J. J. "Polarography", 2nd ed.; Interscience: New York, 1952; p 106. Sillen, L. 0.; Martell, A. E. "Stability Constants of Metal-Ion Complexes"; The Chemical Soclety: London, 1964; Spec. Pubi. 17; 1971; Suppl 1, Spec. Publ. 25.
RECEIVED for review May 9, 1983. Accepted August 1, 1983. This work was supported in part by the National Science Foundation under Grant No. MPS75-00332 and CHE7917542.
