. A. Mahlman, R. W. Matthews,
250
Reduction of Cerium(IV) by Hydrogen Peroxide, Reaction Rate
on
and
T. J. Sworski
Dependence of
Hammett’s Acidity Function12
by . A. Mahlman, R. W. Matthews,38 and T. J. Sworski*3b Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee
37880
(Received June IB, 1970)
Publication costs assisted by the V, S. Atomic Energy Commission
The rate of cerium(IV) reduction by hydrogen peroxide adheres well to d[CeIV]/d< = 2fc0bsd [CeIV]2 [H202 ]/ [Cem]. A marked decrease in k0bad with increase either in sulfuric acid concentration from 2.0 to 8.0 M or in ammonium bisulfate concentration from 1.0 to 5.0 M is consistent with an equilibrium between H02 and H202+. A marked increase in Jfc„b»d with further increase in sulfuric acid concentration from 8.0 to 13.0 M is consistent with an equilibrium between H202 and H302+. The dependence of k0bad on sulfuric acid concentration is expressed quantitatively as a function of Hammett’s acidity function Ho.
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Introduction Reduction of cerium(IV) by hydrogen peroxide in aqueous solutions has been postulated4·8 to proceed through two consecutive one electron transfer reactions. Sigler and Masters6 obtained kinetic evidence CeIV
+ HA
CeIV
-X
Cem + H+ + H02
+ H02 ~^*· Cem + H+ +
02
(1)
(2)
for the HOa radical as an intermediate in their study of isotopic exchange between cerium(IV) and radioactive cerium(III) in 0.4 M sulfuric acid solutions induced by hydrogen peroxide. They postulated the reverse of reaction 1 Ce111
+ H+ + H02
CeIy + H202
and determined fc_i[H+]/fc2 = 0.129 ± 0.013 at 0°. Direct evidence for the H02 radical as an intermediate was obtained7·8 by electron spin resonance spectroscopy. Reduction of cerium(IV) by hydrogen peroxide is fast, the reaction reportedly8 being complete within a few seconds even at micromolar reagent concentrations. Therefore, dynamic-flow methods9 were used by Czapski, Bielski, and Sutin10 to study the kinetics of this reaction. They confirmed the reaction mechanism of Sigler and Masters and determined h = (1.0 ± 0.1) X 10« M~l sec"1 and W(fc-i[H+]) = (1.28 ± 0.1) X sec-1 in 0.4 M sulfuric acid at 25°. 107 In a preliminary communication11 on our study of cerium(III) oxidation in 4.0 M sulfuric acid induced by 60Co y radiation, we reported the rate of cerium(IV) reduction by hydrogen peroxide to be much slower in 4.0 M sulfuric acid with fciAV(fc-i[H+]) = 2.15 X 108 M~x sec”1. In this paper, we report a kinetic study of the reduction of cerium(IV) by hydrogen peroxide both in sulfuric acid solutions from 2.0 to 13.0 M and in ammonium bisulfate solutions from 1.0 to 5.0 M. The Journal of Physical Chemistry, Vol. 75, No. B, 1971
Experimental Section Materials. Water from a Barnstead still was further purified by successive distillations from an acid dichromate solution, from an alkaline permanganate solution, and from an all-silica system to be stored in silica vessels. Solutions were prepared using reagent grade chemicals: G. Frederick Smith ceric ammonium sulfate and cerous sulfate, Baker and Adamson ammonium bisulfate, E. I, du Pont de Nemours and Co. sulfuric acid, and J. T. Baker Chemical Co. hydrogen peroxide. The cerous sulfate was further purified by a procedure which we previously reported.12 Analytical Procedure. Cerium(IV) concentrations in all solutions were determined by absorbance measurements with a Cary Model 15 recording spectrophotometer. For sulfuric acid solutions, the molar extinction coefficients reported by Boyle13 were used. For ammonium bisulfate solutions, the following molar ex(1) Research sponsored by the U. S. Atomic Energy Commission under contract with Union Carbide Corp. (2) Presented at the 157th National Meeting of the American Chemical Society, Minneapolis, Minn., Apr 14-18, 1969. (3) (a) Guest Scientist from (he Australian Atomic Energy Research Establishment, Sydney, Australia, (b) To whom correspondence should be addressed. (4) S. Baer and G. Stein, J. Chem, Soc., 3176 (1953). (5) J. H. Baxendale, Special Publication No. 1, The Chemical Society, London, 1954, p 40. (6) P. B. Sigler and B. J. Masters, J. Amer. Chem, Soc., 79, 6353
(1957). (7) E. Saito and B. H. J. Bielski, ibid., 83, 4467 (1961). (8) B. H. J. Bielski and E. Saito, J. Phys. Chem., 66, 2266 (1962). (9) H. Harridge and F. J. W. Roughton, Proc. Roy. Soc., Ser. A, 104, 376 (1923). (10) G. Czapski, B. H. J. Bielski, and N. Sutin, J. Phys. Chem., 67, 201 (1963). (11) R. W. Matthews, . A. Mahlman, and T. J. Sworski, ibid., 72, 3704 (1968). (12) R. W. Matthews, . A. Mahlman, and T. J. Sworski, ibid., 74, 2475 (1970). (13) J. W. Boyle, Radiat. Res., 17, 427 (1962).
Reduction
of
Ce(IV)
tinction coefficients 6498 for
by
were
HA
251
determined for cerium(IV) at
1.0 M NH4HS04, 6996 for 3.0 M and 7472 for 5.0 M NH4HS04. CeriumNH4HS04,
320 nm:
(III) concentrations in cerium(III) and cerium(IV) stock solutions were determined by oxidation of cerium(III) by argentic oxide14 followed by spectrophotometric analyses for cerium(IV). Experimental Procedure.
The experimental procedure was similar to that which we previously used to study the kinetics of cerium (IV) reduction by nitrous acid in sulfuric acid solutions.16 All kinetic studies were made with air-saturated solutions in a 2-cm cylindrical spectrophotometer cell at ambient room temperature of about 25°. The synchronous drive feature of the spectrophotometer was used to record the solution absorbance as a function of time. A negligibly small volume of stock hydrogen peroxide solution was injected by a micropipet into the cerium(IV)-cerium(III) solutions in a 2-cm cell, and the chart drive was simultaneously activated. The cell was then capped, shaken vigorously with a small air space present, and placed into the sample cavity of the spectrophotometer; the decreasing absorption due to cerium(IV) was recorded as a function of time.
Results We assume that the stoichiometry for the reduction of cerium(IV) by hydrogen peroxide is well established. Two cerium(IV) ions are reduced by each molecule of hydrogen peroxide.4 All experiments were conducted with initial concentrations of hydrogen peroxide that were insufficient to reduce all of the cerium(IV). The reaction kinetics could then be studied by monitoring only the cerium(IV) concentration. Hydrogen peroxide concentrations were not determined, but inferred. Typical experimental data that demonstrate the feasibility for a kinetic study using classical spectrophotometric techniques are shown in Figure 1. First, the initial solution absorbance was recorded. After hydrogen peroxide was added, about 7 sec was consumed in capping, shaking, and placing the 2-cm cell in the spectrophotometer before the solution absorbance could be recorded as a function of time. The dotted line in Figure 1 indicates the amount of reaction that occurred during this 7-sec period. The solid line from 7 to 163 sec is the recorded solution absorbance that shows the decrease in cerium(IV) concentration with time. Many hours later, when the reaction is sensibly complete, the final solution absorbance is recorded. The reaction mechanism of Sigler and Masters requires that the rate of reaction adhere to eq I. We cond TCeIV i =
—
2fci [Ce1
v ]
[HA
]
//
1.
Reduction of cerium(IV) by hydrogen peroxide in
5.0 M ammonium bisulfate solutions. Solid curve is cerium(IV) absorbance in a 2.0-cm cell; initial [CeIV] = 19.7 X 10-5 M; initial [Cem] = 52.35 X "5 M; aobsd = 5.43 X 10~5 M; “5 Qoaiod = 5.20 X 10 ; O, data selected at 10-sec intervals
for computer analysis.
firm the approximation10 that &_i[H+][CemJ is much greater than &2[CeIV] since all of our data adhere well to eq II. Since [CeIV], [HA], and [Cein] all change with d[CeIV] df
2/cob8d
[CeIV]2[HAJ
j
(
[Ce111]
time, we must obtain relations between them in order to integrate eq II. Let a denote the concentration of cerium (IV) when reaction is complete, x denote [CeIV] a, and c denote the sum of the initial concentrations of cerium (IV) and cerium(III). Then [CeIV] = a + x, [HA] c a 0.5z due to stoichiometry, [Ce111] x, and the rate of reaction is given by eq III. Integration —
=
=
—
—
da:__lc0bSdx(a + x)2 a -x) dt (c
(
~
'
-
yields eq IV in which Ci is the constant of integration.
-i__ o
_
+ a:\
_
cj
in(í±A \ /
,
c
+
,
(IV) Figure 2 shows the applicability of eq IV, specifically for the experimental data also shown in Figure 1. A computer program SLOPULSE, previously used15 in a kinetic study of cerium (IV) reduction by nitrous acid, was adapted for use in this study. The experimental data were fit to eq IV by the method of least squares using our laboratory’s IBM 360/75 computer. (14) J. J. Lingane and D. J. Davis, Anal. Chira. Acia, 15, 201 (1956).
,
V
Figure
fc2[CeIV]
(15) T. J. Sworski, R. W. Matthews, and . A. Mahlman, Advances in Chemistry Series, No. 81, American Chemical Society, Washington, D. C., 1968, p 164.
The Journal of Physical Chemistry, Vol, 75, No.
%,
1971
. A. Mahlman, R. W. Matthews,
252
T. J. Swobski
and
Table II: Reduction of Cerium(IV) by Hydrogen Peroxide in Ammonium Bisulfate Solutions [CeUI],« X 10"
[NHiHSCb], M
1.0 1.0 3.0 3.0 5.0 5.0 5.0 5.0 5.0 5.0
Figure 2. Test for applicability of eq IV: O, ordinate values for selected data shown in Figure 1.
Aobsd seo"*1 X 10~8
766 ± 4 (2)6 621 ± 9 (2)
648 324 324 162 104
17.6 ±0.3 (2) 15.4 ±0.4 (2) 1.19 ±0.09 (4) 1.21 ±0.06(4) 1.22 ±0.09(4) 1.19 ±0.10 (3) 1.33 ±0.12 (2) 1.21 ±0.01 (2)
52.0 26.0 13.0 6.5 0
Additional cerium (III) (0.35 X 10_5 M) present in 5.0 M ammonium bisulfate solutions due to presence of cerium (III) in 6 Number of experiments indicated cerium(IV) stock solution. “
At first, the observed values for
used.
Later, the computer program was modified to determine that value for a which would give the best fit of the data to eq IV. The results from the use of this modified computer program are listed in Table I for sulfuric acid solutions and in Table II for ammonium bisulfate solutions. a were
Table I: Reduction of Cerium(IV) by Hydrogen Peroxide in Sulfuric Acid Solutions HjSO.I, M
“
[Ce”l] X
2.0 2,0 3.0 3.0 4.0 4.0 4.0 6.0 6.0 8.0 8.0 8.0
324 162 388 194 339
10.0 10.0 12.0 12.0 12.0 13.0 13.0 13.0
162
10»
169.7
42.4 324 162 162
32.4 9.7
32.4 162
97.2 32.4 648 486 324
fcobsd,
AT"1 sec"1 X 10
123 ± 2 (5)“ 129 ± 6 (2)
43.4 ± 1.6(4) 43.3 ±1.3 (4) 22.5 ±0.9 (4) 22.2 ±0.9 (4) 21.2 ± 0.1 (2) 5.62 ±0.04 (2) 4.70 ±0.21 (4) 2.83 ±0.35 (6) 2.52 ±0.16 (4) 3.20 ±0.09 (2) 4.50 ±0.02 (3) 4.21 ±0.06 (2) 27.0± 1.3(4) 50.4 ±8.2 (4) 49.9 ±2.8 (2) 441 ± 133 (4) 461 ± 42 (4) 394 ± 134 (7)
Number of experiments indicated within parentheses.
Comparison of observed (o0bsd) and calculated values of a proved to be instructive. For 1.0 M ammonium bisulfate solutions and 2.0-4.0 M sulfuric acid solutions, o0tti0ll was randomly either slightly larger or slightly smaller than o0bed· For 3.0 and 5.0 M ammonium bisulfate solutions and 6.0 to 10.0 M sulfuric acid solutions, tWd was generally smaller than a„bsd· For 12.0 and 13.0 M sulfuric acid solutions, ocaiod was always larger than o0bad· (Ocaiod)
The Journal of Physical Chemistry, Vol. 75, No. 8, 1971
within parentheses.
The lower values of ocai0d for 6.0 to 10.0 M sulfuric acid solutions were dramatically called to our attention. Results from seven experiments had to be withdrawn from inclusion in Table I because no best fit of the data to eq IV was indicated for any positive value of The solutions for these seven experiments must aoaiodhave contained excess hydrogen peroxide. The lower values of ooaiCd probably result from recording of a„bsd before reactions were truly complete. The higher values for aoaiod in 12.0 and 13.0 M sulfuric acid solutions suggested an interfering reaction. This may be the formation of peroxymonosulfuric acid from hydrogen peroxide, recently investigated16’17 in 5.012.0 M sulfuric acid solutions. To test this possibility, we conducted some experiments in which cerium (IV) was added to sulfuric acid solutions at varying delay times after addition of hydrogen peroxide. The results for 8.0 and 10.0 M sulfuric acid solutions are listed in Table III.
Table III: Effect of Delay Time for Cerium(IV) Addition after Hydrogen Peroxide Addition [HiSO.], M
[CeUI],
8.0 8.0 8.0 8.0 10.0
0.013 0.013 0.013 0.013 0.052 0.052 0.052 0.052 0.052 0.052
10.0 10.0 10.0 10.0 10.0
M
Delay time, min
0 5 10 120 0 5 10 120
1080 1080
fcobad
tlcalod
X
Gobsdi 108
1.9 2.6 2.4 3.1
3.7 8.9 8.9 16.0 15.5
25.0
M~l see-: X 10-4
3.97 3.94 4.19 3.79 9.33 10.3 9.21 9.12 9.08 9.58
(16) J. M. Monger and O. Redlich, J. Phys. Chem., 60, 797 (1956). (17) O. Redlich and W. E. Gargrave, ibid., 72, 3045 (1968).
Reduction
of
Ce (IV) by H202
253
The effect of delay times for cerium(IV) addition was examined qualitatively for hydrogen peroxide solutions in 13.0 M sulfuric acid containing no cerium(III) initially. An initially fast reduction of cerium(IV) was followed by slow reduction. The fraction of cerium(IV) reduction by the slow reaction increased with increase in delay time. The rate of this slow reaction was not markedly affected by the presence of 0.052 M cerium(III). Since reaction of cerium(IV) with peroxymonosulfuric acid is inhibited18 by high concentrations of cerium(III), the slow reaction results from slow hydrolysis of peroxymonosulfuric acid to yield hydrogen peroxide as reported by Boyle.13 For the experiments summarized in Tables I and II, the cerium (IV) solutions were prepared the previous day to allow reduction of cerium (IV) by the impurities in sulfuric acid to go to completion. In 8.0 M sulfuric acid solutions, the amount of cerium(IV) reduced by impurities in one day amounted to about 3 X 10-6 M. We attribute the small values of ctoaicd a0bsd listed in Table III for zero delay times to reduction of cerium(IV)
value of 12.8 determined10 in 0.4 M sulfuric acid solutions. Therefore, the marked decrease in fcobsd with increase either in ammonium bisulfate concentration from 1.0 to 5.0 M or in sulfuric acid concentration from 0.4 to 8.0 M can be attributed to a marked decrease in fc2/(fc-i [H+])·
Protonation of The dependence of fc0bsd on . sulfuric acid concentration from 0.4 to 8.0 M can be quantitatively explained by assuming a sensible equilibrium between H02 and H202+ with AH,oz+ hr [H02]/[H202+]. The function h0 is related to Hammett’s acidity function Ho by the relationship Ho —log fc0·19 The experimental data are consistent with the following reaction mechanism. =
=
CeIV
CeIV
—
The lowest value for fcobsd was observed for 5.0 M ammonium bisulfate solutions. Then, as indicated in Table II, the rate of cerium(IV) reduction is so slow that it is unnecessary to purposefully add cerium(III) initially to be able to monitor the reaction. Our objective for the experiments with no cerium(III) added initially was to determine both /q and fc2/(fc_i[H+]) through the use of eq V which results from the integraa
+
x
X a2fcifc2£
cfc_i[H+]
tion of eq I.
+ H02
CeIV
+
H2022+
(4)
Ceni + H02+
(5)
H+ + 02
—>
H202+
H+ + H02
—>
Ce111
+
(6) H2022+
H+ + H02+
—
(3)
(7)
(8)
Kno2+ and KH2o2=+ are assumed to be so large
that
reactions 5-8 are sensibly irreversible. The rates of reaction of H02 and H202+ with cerium(III) and cerium(IV) are assumed to be negligibly small compared with the rates of protonation of H02 and dissociation of H202+ so that virtual equilibrium exists between H02 and H202+. The rates of reduction of cerium (IV) by H02 and H202+ are assumed to be negligibly small compared with the rate of oxidation of cerium(III) by H202+. The rate of cerium(IV) reduction is then given
by eq II with
Discussion
a
< =?I
ho2+
—
Cem + H202+
H202
h2o2+
—
by impurities. The very large values of acaiCd aobSd for 10.0 M sulfuric acid solutions with long delay times, listed in Table III, are attributed to formation of peroxymonosulfuric acid from hydrogen peroxide prior to addition to cerium(IV). Despite the presence of peroxymonosulfuric acid, use of the modified computer program yielded values for fcobSd which are essentially independent of delay time. Therefore, the positive values of aoaicd «obsd observed for 12.0 and 13.0 M sulfuric acid solutions do not invalidate the values for fcobsd listed in Table I but only indicate a cause for the inthat is pronounced for crease in experimental error 13.0 M sulfuric acid solutions.
+
+
Ci
(V)
However, the result was only to further establish the validity of eq II and IV. Comparison of eq IV and V reveals the reason for the validity of eq IV in 5.0 M ammonium bisulfate solutions with no cerium(III) added initially. fc2/(fc_i [H+]) must be much less than 1 in marked contrast with the
fcsfciZ rCobsd
i
—
fc-3
l
\
11 T"
ks,KuM,
hh 7
i
I 1
(VI)
There should be a linear correlation between log fcobsd and Hammett’s acidity function Ho when H202+ is essentially completely dissociated. Figure 3 does indicate just such á correlation at low sulfuric acid concentrations. Log fcobsd Ho approaches a limiting conwith stant value decreasing sulfuric acid concentration. obtained by interpolation from the were Ho values data of Ryabova, Medvetskaya, and Vinnik.20 The experimental data for sulfuric acid solutions from 2.0 to 8.0 M were fit to eq VI by the method of least squares Using the computer program of Lietzke21 and assuming that all determinations had a constant —
. H. Mariano, Anal. Chem., 40, 1662 (1968). (19) L. P. Hammett, “Physical Organic Chemistry,” New York, N. Y., 1940, Chapter 9. (18)
McGraw-Hill,
(20) R. S. Ryabova, I. M. Medvetskaya, and . I. Vinnik, Russ. J. Phys. Chem., 40, 182 (1964). (21) . H. Lietzke, ORNL-3259, Mar 21, 1962. The Journal of Physical Chemistry, Yol. 76, No. £, 1971
. A. Mahlman, R. W. Matthews,
254
and
T. J. Sworski
attributed the influence of pH
on the dependence of and iron(II) iron(III) concentrations to (?(Fem) of oxidation iron(II) by H202+ and reduction of iron(III) by HO2. The apparent validity of eq VI for sulfuric acid solutions from 0.4 to 8.0 M is considered further evidence for the existence of H2O24". Pucheault, Ferradini, and Buu24 assumed that H02 and H2O24" were not in equilibrium owing to reactions of HO2 and H2O2+ with iron(II) and iron(III). A similar approach for the reduction of cerium (IV) by
on
Figure 3. Test for correlation between log acidity function H0: O, data of this paper; Bielski, and Sutin.10
fcobsd
and Hammett’s Czapski,
·, data of
hydrogen peroxide would predict a complex dependence of fcobsd on cerium(III) and cerium(IV) concentrations. The independence of fc0bsd on both cerium(III) and cerium(IV) concentrations as originally reported by Czapski, Bielski, and Sutin10 is justification for our assumption of virtual equilibrium between H02 and H202+. Protonation of HfOt. As shown in Table I and Figure 4, fcobsd has a minimum value at a sulfuric acid concentration near 8.0 M and then increases with further increase in sulfuric acid concentration. There may be a correlation between this increase in fc0bsd and the reported increase in rate of peroxymonosulfuric acid formation from hydrogen peroxide for the same concentration range. Although Redlich and Gargrave17 support the original proposal16 that peroxymonosulfuric acid formation results from reaction of hydrogen peroxide with undissociated sulfuric acid molecules, they do admit a possible linear correlation for 9.0-12.5 M sulfuric acid solutions between the rate of peroxymonosulfuric acid formation and Hammett’s acidity function Ho. Such a correlation suggests the existence of H302+. The increase in fc0bsd with increase in sulfuric acid concentration from 8.0 to 13.0 M can be quantitatively explained by assuming a sensible equilibrium between H2O2 and H302+ with fco[H202]/[H302+]. The experimental data are consistent with inclusion of reactions 9-11 in our proposed reaction mechanism. =
Figure 4. Dependence of fc„bsd on ammonium bisulfate and sulfuric acid concentrations: , ammonium bisulfate solutions; O, sulfuric acid solutions, data of this paper; ·, sulfuric acid solutions, data of Czapski, Bielski, and Sutin;10 A, computed curve using eq VI; B, computed curve using eq VII.
The data adhere well to eq VI as indicated by the computed curve A in Figure 4 with percentage
error,
(2.8 ± 0.2) X 104 M~l sec"1 and hKm
