5414
J . Phys. Chem. 1992, 96, 5414-5419
(2) Tague Jr., T. J.; Wight, C. A. Chem. Phys. 1991, 156, 141. (3) Tague Jr., T.J.; Wight, C. A. J . Photochem. Photobiol. A , submitted
for publication. (4) Tague Jr., T. J.; Wight, C. A. Unpublished results. ( 5 ) Benderskii, V. A.; Misochko, E. Ya.; Ovchinnikov, A. A.; Philippov, P. G.Pis’ma Zh. Exp. Teor. Fiz. 1988, 32, 429. (6) Misochko, E. Ya.; Titov, V. A.; Philippov, P. G.; Benderskii, V. A. Khim. Fir. 1988, 7, 1559. (7) Benderskii, V. A,; Ovchinnikov, A. A,; Philippov, P. G. React. Solids 1985, 4, 409. ( 8 ) Kimerfeld, I. M.; Lumer, E. V.; Shwedchikov, A. P. Chem. Phys. Lett. 1973, 21, 429.
(9) Pouchert, C. J. The Aldrich Library of IR Spectra; Aldrich Chemical Co.: Milwaukee, WI, 1970. (10) Sedlacek, A. J.; Mansueto, E. S.;Wight, C. A. J . Am. Chem. SOC. 1987, 109, 6223. (11) Lias, S.G.; Bartmess, J. E.; Liebman, J. F.; Holm-, J. L.; Levin, R. D.; Mallard, W. G. J . Phys. Chem. ReJ Data 1988, 17 (Suppl. I). (1 2) Benson, S.W. Thermochemical Kinetics, 2nd ed.; Wiley-Interscience: New York, 1976; p 63. (13) Benderskii, V. A.; Titov, V. A.; Philippov, P. G. Dokl. Akad. Nuuk 1984, 278, 1157. (14) Barelko, V. V.; Barkalov, I. M.; Goldanski, V. I.; Kirykhin, D.P.; Zanin, A. M. Adu. Chem. Phys. 1988, 74, 339.
A Model for the pH-Regulated Oscillatory Reaction between Hydrogen Peroxide and Sulfide Ion‘ Gyula Riibai,” Miklds Orbiin,2band Irving R. Epstein* Department of Chemistry, Brandeis University, Waltham, Massachusetts 02254-91 10 (Received: February 1 1 , 1992; In Final Form: March 18, 1992)
An empirical rate law model consisting of 6 protonation equilibria and 12 redox reactions is proposed for the oscillatory reaction between S2-and H202. The 14 species whose concentrations are explicitly taken into consideration are S2-,HS-, H2S, HOSH, S42-,HS4-, SS2-,HSOg, SO?-,H202,HOT, H’, and OH-. The key to the pH-regulated oscillatory behavior is the H+-autocatalysisin the overall reaction HS- + 4H202 SO:- + 4H20 + H+ that results from the more rapid oxidation by H202of the protonated than of the unprotonated form of the sulfite intermediate in this pathway. Simulations give excellent qualitative agreement with both the closed system behavior and the oscillations observed in a flow reactor, though some quantitative discrepancies remain.
-
The oxidation of sodium sulfide with a large excess of hydrogen peroxide in unbuffered aqueous solution is a very complex reaction, which exhibits bistability and sustained oscillations in a continuous-flow stirred tank reactor (CSTR).3 This reaction constitutes the first member of the family of pH-regulated oscillator^.^ In the pH-regulated oscillators, the concentration of hydrogen ion, or that of its counterpart hydroxide ion, plays a critical governing role in the dynamical behavior of the reaction. Hydrogen ion can accelerate or inhibit key steps in the reacting system, while it is consumed or produced in those steps, thereby creating autocatalytic or autoinhibitory feedbacks in unbuffered solution. At least one of these kinetic effects is believed to be essential for chemical oscillation to occur. Since the discovery of oscillation in the sulfide-hydrogen peroxide reaction, many new pH oscillators have been reported, and either detailed mechanisms or empirical rate law models have been proposed for nearly all of them. Two simple, general models for pH-regulated oscillators have also been s u g g e ~ t e d . ~ , ~ All the proposed models share a common core in that each contains at least two component processes, one that produces hydrogen ions and another that consumes them. If one of these processes is lacking, pH-regulated oscillations cannot occur either in a closed system or in a CSTR. One of the two necessary component reactions must be autocatalytic in H+ (or in OH-). Surprisingly, despite the apparent simplicity of its constituents, neither a mechanism nor an empirical rate law model has yet been proposed for the hydrogen peroxidesulfide oscillator. The hydrogen peroxide oxidation of sulfide has been of interest for some time, because this reaction has been suggested for the treatment of odors resulting from the generation of HIS in sewer lines. The stoichiometry, kinetics, and mechanism of the reaction have been investigated by several authors. Hoffmann7 has reported the most thorough study, the results of which imply that the requirements for pH-regulated oscillation are fulfilled by the hydrogen peroxidesulfide reaction. The H+-consuming process is the partial oxidation of hydrogen sulfide ion to elementary sulfur:
On the other hand, the total oxidation of hydrogen sulfide to sulfate ion leads to the formation of hydrogen ions:
HS-
-
+ 4H202
S042-
+ 4 H 2 0 + H+
(2)
In the acidic pH range, reaction 1 predominates. In basic solution, and in excess hydrogen peroxide, sulfate is the final product, according to reaction 2. During the oscillation, the pH changes from acidic to basic;3 consequently both reactions may be expected to take place. In order to fulfill the kinetic requirements for oscillation, the rates of reactions 1 and 2 should increase with increasing [H+]; otherwise the system will not be autocatalytic in H+. Both Hoffmann7 and Satterfield et a1.8 found experimentally that the overall rate of consumption of hydrogen sulfide decreases with increasing hydrogen ion concentration. Their result is just the opposite of the desired kinetic effect. It is, however, obvious that reactions 1 and 2 represent net stoichiometries, which may have very complex kinetics, and the desired feedback can be hidden within the overall kinetics. We attempt in this paper to dissect reactions 1 and 2 into simpler steps and thereby to find the steps responsible for the oscillations and other peculiar dynamical behavior in this reaction. While sufficient kinetic data to construct a mechanism for this reaction based on a set of elementary steps are not yet available, we believe that enough is now known so that an empirical rate law model, based largely on Hoffmann’s experimental work and our own, can shed important light on the workings of this system. Experimental Background The experimental results to be considered here are primarily those obtained by Orbtin and Ep~tein.~ A few additional data were collected during the present study. Most of the kinetic runs were carried out without a buffer. We found that dissolved oxygen affects the rate of the reaction and modifies the shape of the kinetic curves. In order to eliminate this effect, the reagent solutions were deoxygenated with argon after preparation and were then kept
0022-3654/92/2096-5414$03.00/00 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 13, 1992 5415
Oscillatory Reaction between H202and S2-
1
5.00
{
o.6
1
0.4
7.00
I a
Q 0.2
9.00
0
560
I
1000
time, (s)
0.0 0
500
1000
time, (s)
Figure 1. Measured pH vs time curves in a closed reactor at different [Na,S],: [H,O,], = 0.020;[H+], = 0.0020;[Na,S], = 0.0015 (a), 0.002 (b), and 0.0025 (c) M; T = 25 O C . White sulfur precipitated in the later stages of the reaction.
Figure 2. Measured absorbance in a 1-cm cell at 372 nm. The initial concentrations and the temperature are the same as in Figure 1. The second increase in absorbance is due to the increasing turbidity.
from oxygen before use. The reactions were started by adding oxygen-free hydrogen peroxide solution to the reaction mixture, which was stirred with a magnetic stirring bar. The CSTR studies in ref 3 were not performed with deoxygenated solutions, because preliminary studies indicated that the oscillatory behavior was not affected by the presence of oxygen. When Na2S, H202,and dilute H2S04solutions are combined in a thermostated closed reactor, the mixture initially turns clear yellow as the result of transient formation of polysulfides (mainly Sq2-)’v9 and the p H rises rapidly from the acidic to the alkaline range. The yellow polysulfides are then oxidized further to colorless sulfate. If the initial [H+] is sufficiently high, instead of sulfate formation one observes the precipitation of white elementary sulfur. The potential traces for Pt, glass pH, and sulfide ion selective electrodes exhibit multiple inflection points, strongly suggesting that the reaction takes place in several distinct steps. Typical measured pH-time curves are shown in Figure 1. Potential traces for Pt and sulfide ion selective electrodes can be found in Figure 1 of ref 3. We followed the transient formation of the yellow tetrasulfide ion with a Varian DMS 200 spectrophotometer at 372 nm (c = 1140 M-l cm-’).l0 The measured a h o r b a n e t i m e curves are presented in Figure 2. Fast formation followed by autocatalytic consumption of tetrasulfide ion is clearly seen. The second, slow increase in absorbance is due to the formation and coagulation of colloidal sulfur. Note that in the presence of dissolved oxygen the development of the yellow color is preceded by a short (1-2-min) lag period, and the maximum value of the absorbance is smaller. Thus oxygen delays and reduces the formation of tetrasulfide. When the reaction is camed out in the CSTR, one may observe, depending upon the flow rate and input concentrations, either of two steady states, bistability between them, or sustained oscillations. The oscillations are marked by visible changes in the state of the reactor. In the high p H phase, the solution is clear and colorless. Then, colloidal sulfur begins to appear, sometimes accompanied by a pale yellow color of the solution, and turbidity increases until the pH passes its minimum. The solution then clears again.
(i) they can act as acid-base buffers, thereby controlling the concentration of hydrogen ion; (ii) since the reactivity of the protonated and unprotonated species can differ significantly, they affect the rates of the component reactions. All the protonation constants used in the model are taken from the literature. The sequence of redox reactions is derived from Hoffmann’s careful mechanistic study.’ Most of the numerical values of the rate constants for the component redox reactions were estimated from our computer simulations. We first consider the important variable species. We then discuss both series of reactions. Variable Species. The following reactive species are considered to be the most important ones in this very complex reacting system. Sz-, H S , and H#. Unprotonated sulfide was taken into account as an input species only. Its concentration is always very low in aqueous solutions of pH < 12; therefore it cannot have any significant role in the component redox reactions. The two protonated sulfides are, however, important reacting species. HOSH. This intermediate species is a hydrated elementary sulfur with zero oxidation state, formation of which has been suggested by H ~ f f m a n n .We ~ assume that it does not precipitate from the aqueous reacting mixture. S4z-,HS,-, and Sa2-.The transient formation of tetrasulfide ions during the oxidation of sulfide has been proven experimentall^.^^^ We need to assume the transient accumulation of at least one other polysulfide species, which we take to be . : S The other polysulfides are assumed to be very reactive. They do not participate in the rate-determining steps of the component reactions so that their concentrations never reach stoichiometrically important values. Our model does not include them explicitly. The protonation constants for the polysulfide species decrease as the degree of polymerization increases, and the protonated form of SB2-does not exist in the p H range of the oscillations. Sa. The oxidation state of sulfur in S8 is the same as that in HOSH. However, S8 is less reactive and is present as a colloid. The observed turbidity of the solution in slightly acidic medium can be explained by the formation of S8. Colloidal S8 is treated in numerical simulations of the model as a homogeneous reactant. and HSO,. S(1V) is always an important intermediate when a sulfur compound of low oxidation state is oxidized to sulfate. The further protonation of hydrogen sulfite does not take place in the pH range of the oscillation. HzOz and H02-. Hydrogen peroxide is an input species. Its deprotonated form is also of importance in the present system. H+ and OH-. These are key species in every pH-regulated oscillator. Protonation Equilibria. Since the pH change seems to be the most important regulator of these oscillations, all protonation
Constructhg the Model We do not aim at constructing a complete mechanism of elementary steps but rather focus on complex component reactions and overall stoichiometric pracesses as building blocks of a model. Where possible, we propose submechanisms for the complex component reactions, but the simulation is not based on the submechanisms. Our model consists of two main groups of processes: a series of protonation equilibria and a sequence of redox reactions. The role of the protonation equilibria is two-fold:
5416 The Journal of Physical Chemistry, Vol. 96, No. 13, 1992
equilibria of the above listed species taking place in the pH range covered by the oscillations must be taken into account. Either the measured (if available) or estimated values of rate constants for both directions of the equilibria have been used in our computations. We consider the protonation of sulfide ion. The value of its protonation constant is very high and has been subject to considerable uncertainty.13 This uncertainty does not cause any problem in our calculations, because the same simulated pH-time curves are obtained with the lowest (10l2 M-I) and the highest ( 1017 M-I) published values. It seems clear that S2-is never a principal species in aqueous solution. It hydrolyzes completely according to reaction 3 to form SH- and OH-. Instead of the simple protonation, we consider reaction 3, which expresses the protonation of S2-in an indirect way and is more realistic chemically than the simple bimolecular reaction between S2-and H+.
S2-+ H 2 0= SH-
+ OH-
(3)
Under our experimental conditions, the equilibrium in reaction 3 is shifted almost completely to the right. There is therefore no need to consider further reactions of S2-. The second protonation equilibrium of sulfide ion (reaction 4) takes place at around pH 7. Eigen and KustinI4 measured the rate constants for both forward and reverse reactions.
SH- + H+ + SH2
(4)
The first protonation of S42- (reaction 5 ) occurs a t pH =6.15 We do not consider the second protonation of tetrasulfide ion, because pKa2falls outside the pH range covered by the oscillations. S42-
+ H+ + HS4-
(5)
The protonation of sulfite ion is a key contributor to the oscillatory character of the model. Equilibrium 6 plays a similar role in a number of pH-regulated oscillatory reactions described earliera6
S032-+ H+
HS03-
(6)
We include in the model equilibrium 7, although the degree of deprotonation of hydrogen peroxide is low even in the upper pH region of the oscillatory curves, and equilibrium 7 is not essential for simulating the oscillation. However, hydrogen peroxide is always present in large excess, and the small extent of its deprotonation is enough to modify the shape and period of the calculated oscillations. HOz-
+ H++ H202
+ OH- + H2O
(8)
The equilibrium and rate constants of the protonation equilibria 3-8 are summarized in Table I. The ratios of rate constants are consistent with the known values of the equilibrium constants. Each forward and reverse reaction is treated here as a pseudoelementary step having a mass action rate law. Redox Reactiom. Hoffmann7 has suggested that the initial step in the oxidation of HS-by H 2 0 2is the formation of hydrated elementary sulfur in the form of HOSH. SH- + H202
-
HOSH
+ OH-
TABLE I: Equilibria, Redox Reactions, Equilibrium Constants, and Rate Constants Used in Simulations of the Kinetic Behavior of the Hydrogen PeroxideHydronen Sulfide System equilibria K kf, M-’ s-’ k,, S-’ (3) S2- + H 2 0 * SH- + OH(4) SH- + H + + SH2 : + H+ * HSC (5) -s (6) S032- H+ HSOC (7) H02- + H+ HZ02 ( 8 ) Ht OH-+ H20
+
+
(9)
The rate law of this step was found to be
+ k9/[H2S][H202] (9’)
ug = -d[H202]/dt = k9[HS-][H202]
Hoffmann7 and Satterfield et aL8 concur that HS- reacts faster with H202than does H2S, so we have neglected the second term of eq 9’. According to Hoffmann’ and Resch et al.,” the value for k9 is 0.48 M-l s-I. It is very likely that reaction 9 is not an elementary step. The fate of HOSH depends on the composition of the reaction mixture. It can either (i) be oxidized further by the excess hy-
1.0 M6
100
100
1.78 X lo7 M-Ib 7.5 X 2 x 106 M - I ~ 1 x 107 7.1 X lo6 M-Ib 5 X 1OIo
4.3 X 5 7 X lo3
4.5 x 10” M-Ib
1 x 1O1O
2.2 x
6.0 X loi5M-Ib
1.5 X 10Ilb 2.85 X
redox reactions
+
k.“ M-I s-’
(9) SH- H202 HOSH + OH(10) HOSH + 2 H202 SO?- 2H+ 2H20 (1 1) S032- H202 SO:H20 (12) HSOC + H202 S042- + H20 Ht HSC + 3H20 (13) 3HOSH + HS(14) 3HOSH HIS HSC 3H20 + Ht (15)-:S + 4HOSH Ss2- + 4H20 (16) HSI- + 4HOSH Ss2- + 4H20 + Ht (17) Ss2- + H202 Sa + 2OH(18) HSC 9H202 4S032- 6H20 7H+ (19)-:S + 9H202 4SOj2- + 6H20 + 6H+ (20) l/sSs 2H202 OHHSOC + 2H20
+ + --+ + + +
+
+
+
0.48b 0.04 0.206 7.00b 10.0 100
+
4.00 2.00 0.20 0.065
-+ -
+
0.01 1 X lo6 M-2
(third order)
“All reactions assumed first order in each reactant. bExperimentally determined, see text for references.
drogen peroxide, producing H+, or (ii) react with the unreacted sulfide, leading to formation of polysulfide accompanied by consumption of H+. (i) If the reaction of HOSH with H202occurs (eqs 10-12), the total oxidation of sulfide to sulfate will take place along with formation of H+. Again, reaction 10 is a net stoichiometry
HOSH
-
+ 2H202
S032-+ 2H+
+ 2H20
(10)
assumed to have the kinetics of the rate-determining step (loa), which is followed by the fast oxidation of the unstable HSO, (lob). Sulfite accumulates as a transient species. The final step
--
HOSH + H202
(7)
Our model contains the well-known water dissociation equilibrium (8), which controls the ratio [H+]/[OH-1.
H”
Rabai et al.
~
HS02- + H 2 0
+ H+
HS02- + H 2 0 2 S032-+ H 2 0 + H+ 1= 0 -d[HOSH]/dt = k,,[HOSH] [H202]
(loa) (lob) (10’)
in this pathway, the oxidation of sulfite to sulfate, is autocatalytic in hydrogen ion,12because the protonated form of sulfite can be oxidized faster than the unprotonated form. M a d e P investigated
-
S032-+ Hz02 HS03- + H202
S042-
S042-
+ H20
(11)
+ H 2 0 + H+
(12) reaction 11 in alkaline medium and found a simple rate law (1 1’). Ul1
= -d[SO3’-]/dt
= kll[S032-][H20J
(11’)
In an earlier study,12the kinetic experiments suggested a two term rate law of the form of (12”) for reaction 12. In the present study, u I 2 = -d[HS03-]/dr = k,2[HS03-1 [H+l[H2021+ k12WS03-I [H2021 (12” ) we found the first term to be negligible in the pH range of the oscillations, so we use eq 12’ in our simulations. Reactions 10-12 = k12’[HS03-1 W 2 0 2 1
(12’) generate H+. When the rate laws 10’-12’ together with the fast protonation equilibrium of the sulfite ion (eq 6 ) are taken into account, this process is seen to be autocatalytic in H+, as required 012
The Journal of Physical Chemistry, Vol. 96, No. 13, 1992 5417
Oscillatory Reaction between H202and S2by the general models for pH-regulated oscillator^.^^^ On adding reactions 9-1 1, we obtain the stoichiometry of reaction 2, which was found experimentally in basic solution by H ~ f f m a n n . ~ (ii) The hydrogen ion-consuming pathway leading to the formation of elementary sulfur starts with the reaction between HSand HOSH. 3HOSH
+ HS-
-w
HS4- + 3H20
(13)
In order for the mechanism to account for the change in the concentration of colloidal sulfur, which is easily visible during the oscillation, a sulfur (s8)consuming process must be taken into consideration. As possible routes for the chemical removal of colloidal sulfur, we considered the known reactions between sulfur and sulfite (or hydrogen sulfite) ions and the hydrolysis of sulfur. Both possibilities were discarded as being too slow. It is more likely that reaction 20 occurs. The [OH-]-dependence in rate
l/gSg + 2H202 + OH-+ HSO3-
Stepwise formation of tetrasulfide ion is reasonable to assume. However, accumulation of di- and trisulfide ions is not expected. HOSH
+ HS-
HS2- + HOSH
HS3-
+ HOSH
slow
+ H20
(13a)
HS3- + H 2 0
(13b)
HS4- + H20
(1 3c)
HS2-
fast
The rate law of reaction 13 is given by = -d[HS-]/dt = k13[HS-][HOSH]
013
(13’)
which is consistent with the mechanism described by reactions 13a-13c. Since the H+-consuming pathway is dominant in acidic medium, where the concentration of H2S is higher than that of HS-, the following reaction along with reaction 13 must be taken into account. 3HOSH
+ H2S
-
HS4-
+ 3H20 + H+
(14)
The submechanism and the rate law are similar to those of reaction 13. 1114 -d[H,S]/dt = k14[H2S][HOSH] (14’) Both the protonated and unprotonated forms of the accumulated tetrasulfide ions react further with HOSH to form Sa2-. S42-
+ 4HOSH
HS4- + 4HOSH
-m
-
-d[S,’-]/dt
016
= -d[HS,-]/dt
+ 4H20 + H+
(16)
in acidic solution
= klS[S42-][HOSH]
(15’)
= k16[HS4-][HOSH]
(16’)
017
-
s8
+ 20H-
= -d[Sg2-]/dt = k17[Sa2-][H202]
(17) (17’)
Reaction 17 is unlikely to be an elementary step, because H202 is not known to act as a two-equivalent oxidant by transfer of two electrons to the 0-0bond. The sum of reactions 7 X (9) (13) + (5) (15) + (17) yields the overall stoichiometry of reaction 1, which was found experimentally by Hoffmann7 for the oxidation of HS- by H202in the acidic pH range. There is a common point where the hydrogen ion-producing and the hydrogen ion-consuming pathways merge. Tetrasulfide ions can react not only with HOSH but also with hydrogen peroxide. In reactions 18 and 19, both the protonated and the unprotonated tetrasulfide ion are oxidized by H202with simple rate laws v18and vI9. We shall not speculate here on the possible detailed mechanism of these obviously very complex component reactions.
+
+
-
HS4- + 9H202
-
s42-+ 9 H 2 0 2 018
+ 6 H 2 0 + 7H+ 4S032- + 6 H 2 0 + 6H+
= -d[HS,-]/dt
019
eq 20‘ reflects that Sa disappears and the solution clears up when the pH is high. At low pH the solution remains turbid. Reactions 18-20 result in further H+ production. Furthermore, reaction 20 eliminates the colloidal sulfur from the reaction mixture, explaining the experimentally observed periodic precipitation and dissolution of sulfur in a CSTR. Elemental S8 is present as a colloid in the reacting mixture, and the rate of its oxidation can only be approximated by a simple form like eq 20‘. Since the eight sulfur atoms in a sulfur molecule end up in eight different product molecules, reaction 20 can only take place as a succession of steps. The first and rate-determining step is probably the ring opening of Sa by nucleophilic attack of H20< Similar ring-opening processes have long been postulatedI7 in the reactions of Sg. T h e d y n a m i c Comideratiom. Consideration of the relevant reduction potentials shows that all the redox reactions in Table I are favored thermodynamically. Since the pH changes by several units during the oscillation, it is necessary to consider how the oxidizing properties of hydrogen peroxide and the reducing power of the sulfur species depend on pH. The reduction potential of hydrogen peroxide is given by l a E / V = 0.84 - 0.0509pH The following schemes show the reduction potentials of the sulfur species in acidic and alkaline solution^.'^
The final step in this pathway leading to the formation of colloidal sulfur is reaction 17, which we assume to have rate law 17’.
sa2-+ H202
= -d[sal/dt = ~ ~ o [ S ~ I I H ~ O ~ I [ O H(20’) -I
(15)
Reactions 15 and 16 have stepwise mechanisms similar to reactions 13a-13c. The corresponding rate laws are 015
(20)
+ 4H20
Sa2-
Sa2-
020
+ 2H20
4s032-
(18) (19)
= kia[HS4-][H202]
(18’)
= -d[Sd2-]/dt = kIg[S42-][H202]
(19’)
0.16 I
-0.07
s042---s,o:-
0.40
0.57 I
I -0.07
-H%o,-
-H2S03
’
0.87 -%0,2-
0.6
0.14
-S
-H,S
I
L 0.50
in alkaline solution 4.66
-0.94
I
-0.58
-0.74
SO,^- - s * o ~ ~ --S
1
-0.45
-SZ-
We see that the oxidation of sulfide ion by hydrogen peroxide, reaction 9, is favored thermodynamically in both acidic (H,S) and alkaline (HS-) solutions. We assume that the thermodynamic properties of S are very similar to those of HOSH, a hydrated form of elementary sulfur produced in reaction 9. Since the oxidation of elementary sulfur is favored, reaction 10 should take place over a wide pH range. Reactions 13-16, leading to the formation of polysulfide ions from elementary sulfur and sulfide ions, are known to take place in aqueous solution.20 The standard reduction potentials of the polysulfide couples are very similar to those of S/S2- (-0.45 V), which means that their oxidation by hydrogen peroxide, reactions 17-19, should be favored as well.
Results of the Calculations Siulstiolrs of the Closed System Kinetics. The model proposed here contains 6 protonation equilibria ((3)-(8)) and 12 redox reactions ((9)-(20)). The system of differential equations based on the rate laws of the component reactions in Table I was solved numerically by the Runge-Kutta method. As a comparison of calculated pH-time curves (Figure 3) with their measured counterparts (Figure 1) demonstrates, the simulations are able to reproduce the shape of the experimental curves. An increase in the pH from its initial value, which is determined
5418 The Journal of Physical Chemistry, Vol. 96, No. 13, 1992
5.0-
7.0
I
a
/
-
I I
bl
1
1
J
I
/
/
/ C /
r \
,I '--
I
I
1
I
\
I
/
I
I
!
\ 11.0
/
I
\
-
I
I
\
I
/ /
/
/
.7*:
1
/
/
I
Q
5'0
t
I
/
9.0 -
RBbai et al.
I
7
/
I
/
, 1000
1
I
I
I
I
2000
time, (s)
Figure 5. Calculated oscillatory curves in a CSTR. Input concentrations: [S2-l0= 0.0167 M;[H2O2Io= 0.40 M; [H'], = 0.002 M. Flow rbte: ko = 6 X lo4 s-l.
Figure 3. Calculated [H'] vs time curves in a closed reactor. Initial conditions as in Figure 1 .
*9
15 20 25 30 T l m r , min Figure 6. Measured oscillatory curves in a CSTR.' Input concentrations and flow rate as in Figure 5.
0
time, (s) Figure Calculated [S:-] conditions as in Figure 1. I
vs time curves in a closed reactor. Initir
by the ratio [S2-IO/[H+],,, can be seen in the first stage of the reaction. The first redox reaction (9) produces OH- and explains the early pH increase. Later the hydrogen ion-producing component reactions overcompensate reaction 9, forcing the pH to decrease. The calculated concentrations of tetrasulfide ion as a function of time are presented in Figure 4. There is impressive agreement between the shapes of the experimental absorbancetime curves shown in Figure 2 and the calculated [St-]-time curves. Reactions 13 and 14 explain the fast formation of the tetrasulfide intermediate in the early phase of the reaction. Its apparently autocatalytic consumption in the second part of the reaction results from the component reactions 18 and 19. Since the protonated form of tetrasulfide can be oxidized faster by hydrogen peroxide (reaction 18) than its unprotonated form (reaction 19), the overall rate of Sd2-consumption increases with increasing hydrogen ion concentration. The major quantitative discrepancy between the calculated and measured kinetic curves in the closed reactor is that the time scale of the calculated curves in Figures 3 and 4 is twice as long as that of the measured curves in Figures 1 and 2. This discrepancy can be eliminated by increasing the rate of component reaction 9. This rate was, however, measured' and confirmed" earlier, and we are reluctant to change it. We have searched, thus far unsuccessfully, for other modifications of the model that will give a comparable acceleration of the simulated kinetics.
5
IO
Simulations of the Osciitions in CSTR. In order to simulate the kinetic behavior of the oxidation of sulfide by hydrogen peroxide in an open reactor, we added appropriate flow terms to the model discussed above. Introduction of input flows of H202, S2-,and H+ and output flows of all the variable species should lead to an oscillatory model, if the reactions listed in Table I are indeed the major processes occurring. Figure 5 shows the results of a simulation of [H+] under the oscillatory conditions reported by OrMn and E p ~ t e i n .The ~ experimental behavior with the same input concentrations and flow rate is illustrated in Figure 6. The agreement between the experimental and simulated oscillations is quite good. The experimental and calculated periods are essentially the same, and the calculated amplitudes of the pH oscillations are very similar to the measured ones. There is, however, a significant discrepancy between the calculated and measured oscillatory phase diagrams in the [Na2S],-k, plane (Figure 7), and we also had difficulty in accurately reproducing the shape of the experimental phase diagram in the [H2OJo-[S2-], plane. Discussion The sulfur-based oscillators have been among the last to yield to mechanistic analysis. Because of the large number of possible intermediates and the difficulty in monitoring these species spectrophotometrically or potentiometrically, investigation of these oscillating reactions has been a considerable challenge. The first such system to be subjected to mechanistic analysis, the chlorite-thiosulfate reaction,*I has to date yielded only partial mechanistic results,22 with no complete explanation of its ability to oscillate. More recently, mechanisms that account for oscillatory behavior have been proposed for the methylene bl~e-sulfide-oxygen~~ system and for the copper catalyzed oscillatory reaction between
J. Phys. Chem. 1992, 96, 5419-5424
5419
sulfur containing chemical oscillators. Acknowledgment. This work was supported by the National Science Foundation (Grant CHE-9023294), by the Hungarian Academy of Sciences (OTKAGrant I/3 No. 2275 to M.O.), and by a US.-Hungarian cooperative grant from the NSF and the Hungarian Academy. We thank Richard Noyes for several enlightening suggestions and Kenneth Kustin for helpful discussions. Registry No. Hydrogen peroxide, 7722-84-1; sulfide, 18496-25-8.
8.0 A
I
W
0
6.0
N
cn
L
N
0 7
References and Notes
4.0
2.0
0.0
Figure 7. Measured (from Figure 5 of ref 3) and calculated oscillatory phase diagrams in the [NazS],-ko plane with [H2Ozlo= 1.0 M, [H+], = 0.002 M.
hydrogen peroxide and t h i o c ~ a n a t e .The ~ ~ present mechanism, despite some remaining quantitative discrepancies, goes a step further toward solving the mechanistic problem for sulfur-based oscillators by successfully addressing two major questions. First, we have shown how autocatalysis by hydrogen ion may be accounted for if one considers the appropriate protonation equilibria and reactive intermediates, even though in the overall reactions 1 and 2 protonated hydrogen sulfide reacts less rapidly than unprotonated HS-. Second, we have for the first time in a study of a chemical oscillator shown how polymeric sulfur species may be introduced in a fashion consistent with experimental data and how these species can influence the behavior of the system. The empirical rate law approach utilized here has proved valuable in other and its application is particularly appropriate in the present case, where both the hydrogen peroxide and the sulfur moieties still hold unsolved mysteries for the kineticist. We have been able for the first time to put to a quantitative test the ideas about this system derived by Hoffmann' from his experimental work, and his notions have stood up well. It seems likely that these ideas will prove useful in deciphering the mechanisms of other
(1) Paper no. 77 in the series Systematic Design of Chemical Oscillators. Paper no. 76: Lengyel, I.; Epstein, I. R. Proc. Narl. Acad. Sei. U.S.A. 1992, 189, 3977. (2) Permanent addresses: (a) Institute of Physical Chemistry, Kossuth Lajos University, H-4010 Debrccen, Hungary. (b) Institute of Inorganic and Analytical Chemistry, L. E6tv6s University, H-1518 Budapest 112, Hungary. (3) Orbin, M.; Epstein, I. R. J . Am. Chem. SOC.1985, 107, 2302. (4) Ribai, Gy.; Orbin, M.; Epstein, I. R. Ace. Chem. Res. 1990,23,258. ( 5 ) Gisplr, V.; Showalter, K. J . Phys. Chem. 1990, 94, 4973. (6) Luo, Y.; Epstein, I. R. J . Am. Chem. SOC.1991, 113, 1518. (7) Hoffmann, M. R. Enuiron. Sei. Technol. 1977, 1 1 , 61. (8) Satterfield,C. N.; Reid, R. C.; Briggs, D. R. J . Am. Chem. Soc. 1954, 76, 3922. (9) Schwarzenbach, G.; Fischer, A. Helo. Chim. Acta 1960, 43, 1365. (10) Lessner, P.; Winick, J.; McLarnon, F. R.; Cairns, E. J. J . Electrochem. SOC.:Elecirochem. Sei. Technol. 1986, 133, 2510, 2517. (11) Resch, P.; Field, R. J.; Schneider, F. W.; Burger, M. J . Phys. Chem. 1989, 93, 8186. (12) Ribai, Gy.; Kustin, K.; Epstein, I. R. J . Am. Chem. SOC.1989,111, 3870. (13) Myers, R. J. J . Chem. Educ. 1986, 63, 687. (14) Eigen, M.; Kustin, K. J . Am. Chem. SOC.1960, 82, 5952. (15) Feher, F.; Berthold, H. J. Fresenius' Z . Anal. Chem. 1953,138,245. (16) Mader, P. M. J . Am. Chem. SOC.1958,80,2634. (17) (a) Bartlett, P. D.; Meguerian, G. J. Am. Chem. Soc. 1956, 78, 3710. (b) Bartlett, P. D.; Cox, E. F.; Davis, R. E. J . Am. Chem. Soc. 1%1,83, 103. (c) Bartlett, P. D.; Colter, A. K.; Davis, R. E.; Roderick, W. R. J. Am. Chem. SOC.1961, 83, 109. (18) Bockris, J. 0. M.; Oldfield, L. F. Trans. Faraday Soc. 1955,51,249. (19) Bard, A. J.; Parsons, R.; Jordan, J. Standard Potentials in Aqueous Solution; Dekker: New York, 1985. (20) Pryor, W. A. Mechanisms of SulJur Reactions; McGraw-Hill: New York, 1962; pp 11-14. (21) Orbin,M.; De Kepper, P.; Epstein, I. R. J . Phys. Chem. 1982,86, 431. (22) (a) Nagypil, I.; Epstein, I. R.; Kustin, K.Int. J. Chem. Kinet. 1986, 18, 345. (b) Nagypil, I.; Epstein, I. R. J . Phys. Chem. 1986, 90, 6285. (c) Peintler, G.; Nagypil, I.; Epstein, I. R. J . Phys. Chem. 1990, 94, 2954. (23) Resch, P.; Field, R. J.; Schneider, F. W. J . Phys. Chem. 1989, 93, 2783. (24) Luo, Y.; Orbin, M.; Kustin, K.; Epstein, I. R. J . Am. Chem. SOC. 1989, 111,4541. (25) Gdspir, V.; Showalter, K. J. Am. Chem. SOC.1987, 109,4689.
Characterization of the Cationic Exchanges in A Zeolites by Means of the Vibrational Frequencies of the Cations A. Boumiz, J. Cartigny, and E. Cohen de bra* Laboratoire de Recherches Physiques, associC au CNRS, UniversitC Pierre et Marie Curie, 4 Place Jussieu, Tour 22, 75252 Paris Cedex 05, France (Received: July 24, 1991)
The far-infrared spectra of A-type zeolite samples show broad bands sensitive to cationic exchange. We present the far-infrared spectra of five A zeolites with Li+, Na+, K+,or Ca2+cations. The vibrational frequencies of the exchangeable cations with respect to the anionic framework have been calculated, taking in account the ions of eight sodalite units. In the potential interaction between cation and framework (electrostatic, polarization, dispersion, and repulsion), the repulsion constants are determined by a combination method, and the effective ionic charges by the orbital electronegativity method.
Introduction Far-infrared spectroscopy can be a method for the characterization of cationic exchange since the spectral range below 400 cm-1 presents bands which are sensitive to the exchangeable cations. The NaA zeolite framework is built of and A D 4
So4
tetrahedrons, which form (SiOzA102)12sodalite units. These later are distributed on a cubic network. When silicon and aluminum are not differentiated, the unit cell has a 12.3-A parameter and the large (Y cavity has a mean diameter of about 11.4 A diameter. By exchange of Na cations by monovalent or divalent cations, one
0022-36S4/92/2096-5419$03.00/00 1992 American Chemical Society
