- Email: [email protected]
Hydrogen isotope and temperature effect upon oxygen and hydrogen peroxide reduction at the mercury electrode
J. Electroanal. Chem., 191 (1985) 175-183
175
Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
H Y D R O G E N I S O T O P E AND T E M P E R A T U R E E F F E C T U P O N O X Y G E N AND H Y D R O G E N P E R O X I D E R E D U C T I O N AT T H E M E R C U R Y E L E C T R O D E
C.J. VAN VELZEN, J.M. OOSTVEEN, M. SLUYTERS-REHBACHand J.H. SLUYTERS Van 't Hoff Laboratory of Physical and Colloid Chemistry, State University, Padualaan 8, 3584 CH Utrecht (The Netherlands)
(Received 2nd January 1985; in revised form 8th March 1985)
ABSTRACT A comparative study has been made on the reduction of oxygen to hydrogen peroxide and of hydrogen peroxide to water in H20 and D20. The first electron transfer does not show an isotope effect. A considerable isotope effect occurs for the subsequent protonation of the 0 2 ion. From the temperature dependence of the pertinent rate constants, activation parameters are evaluated. It is concluded that the reduction of hydrogenperoxide is slow due to the low value of the pre-exponential factor, the activation energy being surprisingly small for this irreversible reduction.
INTRODUCTION In organic chemistry much attention has been focussed on the hydrogen isotope effect [1-3] because of its application in the elucidation of reaction mechanisms. Two different effects are recognized: the primary or kinetic isotope effect and the secondary or solvent isotope effect. In electrochemistry these effects have received attention mainly in proton reduction. Some time ago, primary as well as secondary H / D isotope effects on hydrogen and oxygen evolution and,oxygen reduction were Studied [4-6]. It was shown that along with other studies such as pH effect, H / D isotope effects can be used as additional criteria for the elucidation of these electrode reactions. In the electrochemical reduction of oxygen to hydrogen peroxide a very small isotope effect has been found [5]. More recently, Weaver and co-workers have studied the solvent isotope effects upon the reduction of some simple electrode reactions. They found substantial changes in the kinetics as well as in the thermodynamics of transition-metal redox couples [7]. Recently we reported an extensive study on oxygen reduction at the mercury electrode [8,9]. In contrast with other studies, it was found that not only the first electron transfer to 0 2 is rate-determining but also the protonation of the superoxide ion 0 2 by water molecules and protons. Since this protonation is rate-determining, one would expect a kinetic H / D isotope effect on the overall kinetics of the oxygen reduction. Only a secondary isotope effect on the first step c a n be expected if oxygen interacts with the solvent. We carried out the study in neutral solutions in which the reduction is known to be 0022-0728/85/$03.30
© 1985 Elsevier Sequoia S.A.
176
completely dc-irreversible. Thus the experiments will not be complicated by the isotope effects on the inverse reaction, i.e. the oxidation of hydrogen peroxide. Since this reaction involves OH- or OD- ions and OD- is a stronger base than OH-, the solvent isotope effect will be significant. Measurements of the activation parameters of electrode reactions from the temperature effect are rare due to doubt over how to control the electrical variable on temperature change. Weaver showed the possibility and significance of such measurements in non-isothermal cells for simple electrode reactions [10,11]. For more complex reactions with more steps, as in the present case, one will find the temperature effects upon the rate-determining steps only. However, as will be shown in this paper, the significance of the activation parameters of steps other than the first one can be quite small. In this paper the hydrogen isotope and temperature effects on the reduction of hydrogen peroxide are also reported. THEORY
From earlier investigations on oxygen reduction at the mercury electrode [8,9] it is found that the mechanism can be described by kl
Oa + e02- + H 2 0
~-02
k_! kz ~ HO 2 + OH-
+ H O 2 + H20
HO ~ H2024- OH--,
kf
02 + 2 H 2 0 q- 2 e - --* H 2 0 2 q- 2 O H In neutral solutions the inverse reaction is negligible, so the rate equation is independent of the standard potential of the reduction and therefore pH-independent: (l)
i = - nFkfco~
It was shown that the rate constant kf does not obey the Butler-Volmer equation kf = ksh exp(--a4,), but that the rate constant as a function of potential obeys l/k~ = 1/k I + k_~/kak 2
Since the first step is a "simple" electron transfer: k, = k ° exp[ ( alr/RT
)( E - El°)]
and
k_
/kl = exp[ ( r / R r
)( E -
(2)
177
eqn. (2) yields 1
exp[(alF/RT)(E
kf
k0
- E~)]
exp[(F/RT)(E k2
- E~')]
exp(lal~b) + exp(½~) ksl
kc
(3) where E~' is the standard potential of the 0 2 / 0 ~- couple, ~ = 2 F / R T ( E - E °) and E ° is the standard potential of the couple O 2 / H O ~ at pH 14. It will be clear that the value of the rate constant k 2 of the chemical step can be evaluated from the experimental values of k c only if the standard potential of the first step, E~', is known. The values of E ° reported in the literature show considerable variation [12]. The most reliable value seems to be E~' = - 0 . 3 3 V vs. SHE (defined with p O 2 = 1 atm. and Co~ = 1 M ) or E~' = - 0 . 3 9 V vs. SCE ( c % = Co~). This value of E~ explains why this proton transfer reaction, which will be fast, can be rate-determining. Although k 2 will be high, as for most proton transfer reactions, the term exp[(F/RT)(E-E?)]/k 2 in eqn. (3) can dominate or be significant because ( E - E~') appears to be sufficiently positive. The reduction of hydrogen peroxide is known to be completely irreversible irrespective of pH. The standard potential of the H 2 0 2 / O H - couple in a neutral solution is E ° = 1.15 V vs. SCE [13], while the faradaic region is found at E < - 0 . 4 0 V vs. SCE. So eqn. (1) will hold for this reaction. The rate constant of reduction, k R, obeys the Butler-Volmer equation, with a low transfer coefficient [14]. EXPERIMENTAL
The experiments on the isotope and temperature effects on oxygen reduction were performed using the impedance method as described earlier [8]. The temperature effect on hydrogen peroxide reduction was studied by means of pulse polarography with pulse widths of 0.05-4 s. The isotope effect on hydrogen peroxide reduction was determined from the second polarographic wave of the reduction of oxygen [14]. A static mercury drop electrode (SMDE) was used as the working electrode. D20 (Fluka Garantie) and n202 (Baker Analyzed Reagent) were used without further purification. The reference electrode (an aqueous saturated calomel electrode, SCE) was maintained at 25°C in all experiments and was connected to the cell via a Vicor frit [15] mounted on a salt bridge filled with the cell solution. In this way the liquid-junction potential between the reference and working electrodes will be constant within a few millivolts [16]. RESULTS
Reduction of oxygen
From the impedance measurements performed with the automatic network analyzer the charge transfer resistance Rct as a function of potential is calculated. A
178
8OO
~600 ~° D20
400 20O .
I
I
oo 5
I
0 "
I
I
-Q05 -010 -015 E I V vs. SCE
I
~020
Fig. 1. The charge transfer resistance Rct as a function of potential for the reduction of oxygen. Experimental data obtained in (e) H20 and (O) D20. Drawn lines were calculated with the parameters of Table 1 for ( ) H20 and (- - -) D20.
fit procedure is used to find the rate constants as a function of potential which describe the experimental values of Rct as well as possible according to the theoretical equation [8]:
2)(l/akfEo) 0 In kJOep. In this equation
Rot = ( R T / n 2 F
(4)
with a = t o is the surface concentration of O, which can be calculated with the exact solution of the stationary spherical diffusion problem [17]. In Fig. 1 the effect of using heavy water instead of water as the solvent on Rot is shown. The potential-dependent rate constants calculated from the data in Fig. 1 are plotted in Fig. 2. The ratio of the diffusion coefficients in both solutions is taken to be Dn2°/nD2°02 /'-'02 = 1.2 [7]. Figure 2 shows that the isotope effect on the kinetics is negligibly small in the negative potential region, but significant in the positive
4 E
l
// Q~
& ,-
-065 -QIO ' E l Y vs. SCE
-o.1'~ -Q20 '
Fig. 2. Ln kf vs. E for the reduction of oxygen in (
) H20 and ( - - - ) D20.
179 TABLE 1 Kinetic parameters of the reduction of oxygen to hydrogen peroxide Solvent H20 H20 H20 H 20 D20
Temperature/ K
k~l /
274 298 318 323 298
0.021 0.10 0.43 0.53 0.09
a1
cm s -~
k2/
105 D o / c m 2 s -1
c~)2/mM
1.1 1.8 2.5 2.8 1.5
1.2 0.87 0.68 0.64 0.90
cm s -1 0.34 0.36 0.41 0.38 0.34
2.5 3.0 2.8 3.2 1.5
potential range. The experimental kinetic parameters according to eqn. (3) are given in Table 1. The isotopic ratio of the standard rate constants found for the electron transfer reaction equals "~s,/~n~°/t'o~O/~s,= 0.9 for the protonation k ~ ° / k D2° = 2.0. The effect of temperature on the charge transfer resistance is presented in Fig. 3. The diffusion coefficients of oxygen at the different temperatures are calculated from the limiting currents. The solubility of oxygen at the different temperatures was estimated from literature data [18]. Accurate impedance measurements at high temperature are hampered by the strong decrease of the viscosity of the solution, resulting in an increasing instability of the diffusion layer. The potential dependence of the rate constants found from Fig. 3 are shown in Fig. 4. Table 1 contains the kinetic parameters describing these rate constants as a function of potential, again according to eqn. (3).
SO0
6O0 u -~ 400 rY
-
20O
Q ,5
-
0
~bO ' ".o.o.o~aa.om ~.o-a-
~
.a \
-.~"
-Q05 -0.10 -Q15 -Q 0 - E / V vs. S C E (25~C)
Fig. 3. Potential dependence of the charge transfer resistance Rot for the reduction of oxygen at different temperatures. Experimental data: (©) 274 K, (e) 298 K and ( + ) 323 K. Drawn lines were calculated with the kinetic parameters of Table 1.
180
f
-2
/
_
./
I/
/
~I
li
I~1 II / i X I"
-8
I I
Q 5
I
0
I
I
I
- 0 0 5 -0.10 -O15 -O20 E / V vs. SCE (25"C)
Fig. 4. Potential dependence of In k r for the reduction of oxygen at the temperatures indicated.
Reduction of hydrogen peroxide From the polarograms the rate constant k~ of the reduction of hydrogen peroxide as a function of potential has been obtained using the exact solutions of the mass transport. The plots of In k R vs. E are shown in Fig. 5. As can be seen, the temperature affects the rate constant only slightly. The hydrogen isotope effect on the hydrogen peroxide reduction appears to be negligibly small. DISCUSSION
Hydrogen isotope effect The effects of the substitution of 1320 for H20 and of temperature upon the kinetics of the reduction of oxygen to hydrogen peroxide are given in Table 1. Since these parameters are found by using eqn. (3) with a constant value of E ° irrespective of solvent and temperature, these parameters are in fact the rate constants observed
f"
2
J
,.',7,"
..'" J/l" -~ i -8
/ i"
//x
/ "
". t. "i" / y/ ,1 ~ /, "i
-lO: J / ' -Q4
-0.6
.
-08
.
.
-1.0 E/V
.
-1.2 -1.4 SCE (25°C)
vs.
Fig. 5. Ln k R vs. E for the reduction of hydrogen peroxide in D20 at T = 298 K and in H 2 0 at the temperatures indicated.
181 at a stated potential of E = E~2/HO~ = - 0.216 V vs. SCE. In order to determine the isotope effect one should correct for difference in double-layer structures. As this correction is most probably of minor importance [7], we did not perform it. From Table 1 it is seen that the isotopic rate ratio for the first one-electron transfer is found to be almost unity. This result indicates that the Gibbs energies of activation for this reaction in D20 and H 2 0 are actually the same. Therefore it can be concluded that the interaction between the dissolved oxygen and the solvent is negligibly small or the same. The apparent rate ratio of the protonation of O [ is found to be (k~2°/kD2°)app = 2. Thus, as could be expected, a kinetic isotope effect on the oxygen reduction shows up only in the protonation step. Since (kH20//kD20)app > 1 the isotope effect is found to be "normal". However, interpretation should be done with care. As can be seen from eqn. (3), the absolute value of this rate constant can be determined only if the standard potential difference of the O 2 / O ~- couple in H 2 0 and D20 is known. The true ratio is given by
( k ~ 2 ° / k D2°) = ( k ~ 2 ° / k ~ 2°) exp( ~ T (E~ "D2° - E~''H~°)
(5)
where E? "n2° and E~''D~° are the standard potentials of the O2/O / couple in solutions of H 2 0 and D20, respectively. It seems reasonable to assume the correction to be small, giving (k~2°/k°2~°)= 2. Compared to primary isotope effects found for homogeneous reactions [1-3], this value is somewhat low. Normal hydrogen isotope effects are found to be in the range 3-7. In semi-classical treatments the isotope effect is explained by the difference in Gibbs energy of activation due to the difference in zero-point energies of the transition state and reactants [2]. This treatment gives a maximum value of about 8. A value of 2 would mean that the difference in activation enthalpy has a value of about 1.7 kJ m o l - ' . The isotope rate ratio found for the reduction of hydrogen peroxide is very small. This result indicates only that the O - D or the O - H bond in the activated complex of the rate-determining step does not change in the course of the reaction.
Temperature effect Weaver et al. have described the determination of the activation parameters for simple electrode reactions. They defined the ideal enthalpy of activation AH~ea , as AHi~ea, = - R [ 3 (ln( k / T '/2 ) ) / 3 ( 1 / T )]
(6)
In this equation k is the experimental rate constant, uncorrected for double-layer differences, as a function of temperature at a fixed non-isothermal cell potential. In eqn. (6) k is divided by T 1/2 because of the expected temperature dependence of the collision frequency factor Z e [11]. It should be noted that at these temperatures this temperature dependence of Z e is only of minor importance quantitatively (about 1% in AH *). With the values found for the first electron transfer to oxygen, a simple electron transfer reaction, the ideal enthalpy of activation is found to be 48 O kJ mol-1 at E -- - E 02/HO; -- --0.216 V vs. SCE (Fig. 6), which is a moderate value.
182
~.~
-3
E -4 ..,~ -5
l -o -7 3,0
'
3I2
3.4 '
' 3.'6 l o o o T-~/~C~
'
Fig. 6. in(ksl/T 1/2) vs. T-t for the reduction of oxygen. With the equation
k = Zerp exp( ASi~eal/R ) exp( - A Hi~eal/RT )
(7)
the ideal entropy of activation is found to be 60 J K - ] mo1-1 (independent of temperature), on the assumption that ~O = 1 and Z e = (kT/2"rtm*) 1/2 = 2.2 X 104 cm s - i at 25°C. The apparent temperature dependence of k c is found to be small, but cannot be interpreted in terms of activation parameters of the protonation because the temperature dependence of the standard potential E~ is unknown. However, the activation enthalpy will be low. The rate constant of protonation by water molecules is found to be k~CH2o = 2.9 cm s -~. With E~ = - 0 . 3 9 V vs. SCE it follows that k2CH2o = 3000 cm s-1. The rate constant of the homogeneous secondorder protonation of O 2 by water equals 109 M -1 s -1 [19]. Comparison of these rate constants shows that if the protonation step in the oxygen reduction is really homogeneous, the reaction layer thickness would be about 1 nm. The ideal enthalpy of activation of the reduction of hydrogen peroxide is found to be about A H i ~ l = 48 kJ mo1-1 at E = - 0 . 0 0 V vs. SCE (Fig. 7), AHi~a I = 27 kJ mol-1 at E = 1.00 V vs. SCE, and AHidea * j = 72 kJ t o o l - ] at the standard potential -
"~"
-14
E
% ~ -~(
1
-18
3'.0
A
A •-
3'.6
x)OO l~'/K"
Fig. 7. Ln(kR/T 1/2) vs. T-1 for the reduction of hydrogenperoxide at E = 0 V vs. SCE.
183 E °. T h e s e v a l u e s are s u r p r i s i n g l y l o w for a c o m p l e t e l y i r r e v e r s i b l e e l e c t r o d e r e a c t i o n w i t h s u c h a h i g h o v e r v o l t a g e n e e d e d for r e d u c t i o n . I n s e r t i n g this v a l u e i n t o e q n . (7) yields ZeKp exp(ASi~eal/R)= 500 c m s -1. T h i s result i n d i c a t e s t h a t rp exp(ASi-~eal/R ) is low, w h i c h w o u l d m e a n t h a t e i t h e r r p << 1, i.e. the e l e c t r o n t r a n s f e r is n o n - a d i a b a t i c [20], o r t h e i d e a l e n t r o p y o f a c t i v a t i o n is n e g a t i v e . REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
R.P. Bell, The Proton in Chemistry, 2nd ed., Chapman and Hall, London, 1973. A.V. Willi, Isotopeneffekte bei Chemische Reaktionen, Thieme Vedag, Stuttgart, 1983. R.P. Bell, Chem. Soc. Rev., 3 (1974) 513. B.E. Conway in E. Yeager (Ed.), Transactions of the Symposium on Electrode Processes, Wiley, New York, 1961, p. 267; Proc. R. Soc. London, A256 (1960) 128; A247 (1958) 400. M. Salomon, J. Electrochem. Soc., 114 (1967) 922. J.D.E. McIntyre and M. Salomon, Am. Chem. Soc., Div. Fuels Chem., Preprints, 11 (1967) 209. M.J. Weaver, P.D. Tyma and S.M. Nettles, J. Electroanal. Chem., 114 (1980) 53. C.J. van Velzen, M. Sluyters-Rehbach, A.G. Remijnse, G.J. Brug and J.H. Sluyters, J. Electroanal. Chem., 134 (1982) 87. C.J. van Velzen, M. Sluyters-Rehbach, A.G. Remijnse and J.H. Sluyters, J. Electroanal. Chem., 142 (1982) 229. M.J. Weaver, J. Phys. Chem., 80 (1976) 2645. M.J. Weaver, J. Phys. Chem., 83 (1979) 1748. W.H. Koppenol, Dissertation, Utrecht, 1978. M. Pourbaix, Atlas of Electrochemical Equilibria in Aqueous Solutions, Pergamon Press, Oxford, 1966. C.J. van Velzen, M. Sluyters-Rehbach and J.H. Sluyters, J. Electroanal. Chem., to be published. Manual of the SMDE, Model 303, EG&G Princeton Applied Research, Princeton, 1978. E.L. Yee, R.J. Cave, K.L. Guyer, P.D. Tyma and M.J. Weaver, J. Am. Chem. Soc., 101 (1979) 1131. A.J. Bard and L.R. Faulkner, Electrochemical Methods, Wiley, New York, 1980. R. Battino (Ed.), Solubility Data Series, Vol. 7, IUPAC, Pergamon Press, Oxford, 1981. H. Bitchier and R.E. Bi~hler, Chem. Phys., 16 (1976) 9. R.A. Marcus, Electrochim. Acta, 13 (1968) 995.
175
Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
H Y D R O G E N I S O T O P E AND T E M P E R A T U R E E F F E C T U P O N O X Y G E N AND H Y D R O G E N P E R O X I D E R E D U C T I O N AT T H E M E R C U R Y E L E C T R O D E
C.J. VAN VELZEN, J.M. OOSTVEEN, M. SLUYTERS-REHBACHand J.H. SLUYTERS Van 't Hoff Laboratory of Physical and Colloid Chemistry, State University, Padualaan 8, 3584 CH Utrecht (The Netherlands)
(Received 2nd January 1985; in revised form 8th March 1985)
ABSTRACT A comparative study has been made on the reduction of oxygen to hydrogen peroxide and of hydrogen peroxide to water in H20 and D20. The first electron transfer does not show an isotope effect. A considerable isotope effect occurs for the subsequent protonation of the 0 2 ion. From the temperature dependence of the pertinent rate constants, activation parameters are evaluated. It is concluded that the reduction of hydrogenperoxide is slow due to the low value of the pre-exponential factor, the activation energy being surprisingly small for this irreversible reduction.
INTRODUCTION In organic chemistry much attention has been focussed on the hydrogen isotope effect [1-3] because of its application in the elucidation of reaction mechanisms. Two different effects are recognized: the primary or kinetic isotope effect and the secondary or solvent isotope effect. In electrochemistry these effects have received attention mainly in proton reduction. Some time ago, primary as well as secondary H / D isotope effects on hydrogen and oxygen evolution and,oxygen reduction were Studied [4-6]. It was shown that along with other studies such as pH effect, H / D isotope effects can be used as additional criteria for the elucidation of these electrode reactions. In the electrochemical reduction of oxygen to hydrogen peroxide a very small isotope effect has been found [5]. More recently, Weaver and co-workers have studied the solvent isotope effects upon the reduction of some simple electrode reactions. They found substantial changes in the kinetics as well as in the thermodynamics of transition-metal redox couples [7]. Recently we reported an extensive study on oxygen reduction at the mercury electrode [8,9]. In contrast with other studies, it was found that not only the first electron transfer to 0 2 is rate-determining but also the protonation of the superoxide ion 0 2 by water molecules and protons. Since this protonation is rate-determining, one would expect a kinetic H / D isotope effect on the overall kinetics of the oxygen reduction. Only a secondary isotope effect on the first step c a n be expected if oxygen interacts with the solvent. We carried out the study in neutral solutions in which the reduction is known to be 0022-0728/85/$03.30
© 1985 Elsevier Sequoia S.A.
176
completely dc-irreversible. Thus the experiments will not be complicated by the isotope effects on the inverse reaction, i.e. the oxidation of hydrogen peroxide. Since this reaction involves OH- or OD- ions and OD- is a stronger base than OH-, the solvent isotope effect will be significant. Measurements of the activation parameters of electrode reactions from the temperature effect are rare due to doubt over how to control the electrical variable on temperature change. Weaver showed the possibility and significance of such measurements in non-isothermal cells for simple electrode reactions [10,11]. For more complex reactions with more steps, as in the present case, one will find the temperature effects upon the rate-determining steps only. However, as will be shown in this paper, the significance of the activation parameters of steps other than the first one can be quite small. In this paper the hydrogen isotope and temperature effects on the reduction of hydrogen peroxide are also reported. THEORY
From earlier investigations on oxygen reduction at the mercury electrode [8,9] it is found that the mechanism can be described by kl
Oa + e02- + H 2 0
~-02
k_! kz ~ HO 2 + OH-
+ H O 2 + H20
HO ~ H2024- OH--,
kf
02 + 2 H 2 0 q- 2 e - --* H 2 0 2 q- 2 O H In neutral solutions the inverse reaction is negligible, so the rate equation is independent of the standard potential of the reduction and therefore pH-independent: (l)
i = - nFkfco~
It was shown that the rate constant kf does not obey the Butler-Volmer equation kf = ksh exp(--a4,), but that the rate constant as a function of potential obeys l/k~ = 1/k I + k_~/kak 2
Since the first step is a "simple" electron transfer: k, = k ° exp[ ( alr/RT
)( E - El°)]
and
k_
/kl = exp[ ( r / R r
)( E -
(2)
177
eqn. (2) yields 1
exp[(alF/RT)(E
kf
k0
- E~)]
exp[(F/RT)(E k2
- E~')]
exp(lal~b) + exp(½~) ksl
kc
(3) where E~' is the standard potential of the 0 2 / 0 ~- couple, ~ = 2 F / R T ( E - E °) and E ° is the standard potential of the couple O 2 / H O ~ at pH 14. It will be clear that the value of the rate constant k 2 of the chemical step can be evaluated from the experimental values of k c only if the standard potential of the first step, E~', is known. The values of E ° reported in the literature show considerable variation [12]. The most reliable value seems to be E~' = - 0 . 3 3 V vs. SHE (defined with p O 2 = 1 atm. and Co~ = 1 M ) or E~' = - 0 . 3 9 V vs. SCE ( c % = Co~). This value of E~ explains why this proton transfer reaction, which will be fast, can be rate-determining. Although k 2 will be high, as for most proton transfer reactions, the term exp[(F/RT)(E-E?)]/k 2 in eqn. (3) can dominate or be significant because ( E - E~') appears to be sufficiently positive. The reduction of hydrogen peroxide is known to be completely irreversible irrespective of pH. The standard potential of the H 2 0 2 / O H - couple in a neutral solution is E ° = 1.15 V vs. SCE [13], while the faradaic region is found at E < - 0 . 4 0 V vs. SCE. So eqn. (1) will hold for this reaction. The rate constant of reduction, k R, obeys the Butler-Volmer equation, with a low transfer coefficient [14]. EXPERIMENTAL
The experiments on the isotope and temperature effects on oxygen reduction were performed using the impedance method as described earlier [8]. The temperature effect on hydrogen peroxide reduction was studied by means of pulse polarography with pulse widths of 0.05-4 s. The isotope effect on hydrogen peroxide reduction was determined from the second polarographic wave of the reduction of oxygen [14]. A static mercury drop electrode (SMDE) was used as the working electrode. D20 (Fluka Garantie) and n202 (Baker Analyzed Reagent) were used without further purification. The reference electrode (an aqueous saturated calomel electrode, SCE) was maintained at 25°C in all experiments and was connected to the cell via a Vicor frit [15] mounted on a salt bridge filled with the cell solution. In this way the liquid-junction potential between the reference and working electrodes will be constant within a few millivolts [16]. RESULTS
Reduction of oxygen
From the impedance measurements performed with the automatic network analyzer the charge transfer resistance Rct as a function of potential is calculated. A
178
8OO
~600 ~° D20
400 20O .
I
I
oo 5
I
0 "
I
I
-Q05 -010 -015 E I V vs. SCE
I
~020
Fig. 1. The charge transfer resistance Rct as a function of potential for the reduction of oxygen. Experimental data obtained in (e) H20 and (O) D20. Drawn lines were calculated with the parameters of Table 1 for ( ) H20 and (- - -) D20.
fit procedure is used to find the rate constants as a function of potential which describe the experimental values of Rct as well as possible according to the theoretical equation [8]:
2)(l/akfEo) 0 In kJOep. In this equation
Rot = ( R T / n 2 F
(4)
with a = t o is the surface concentration of O, which can be calculated with the exact solution of the stationary spherical diffusion problem [17]. In Fig. 1 the effect of using heavy water instead of water as the solvent on Rot is shown. The potential-dependent rate constants calculated from the data in Fig. 1 are plotted in Fig. 2. The ratio of the diffusion coefficients in both solutions is taken to be Dn2°/nD2°02 /'-'02 = 1.2 [7]. Figure 2 shows that the isotope effect on the kinetics is negligibly small in the negative potential region, but significant in the positive
4 E
l
// Q~
& ,-
-065 -QIO ' E l Y vs. SCE
-o.1'~ -Q20 '
Fig. 2. Ln kf vs. E for the reduction of oxygen in (
) H20 and ( - - - ) D20.
179 TABLE 1 Kinetic parameters of the reduction of oxygen to hydrogen peroxide Solvent H20 H20 H20 H 20 D20
Temperature/ K
k~l /
274 298 318 323 298
0.021 0.10 0.43 0.53 0.09
a1
cm s -~
k2/
105 D o / c m 2 s -1
c~)2/mM
1.1 1.8 2.5 2.8 1.5
1.2 0.87 0.68 0.64 0.90
cm s -1 0.34 0.36 0.41 0.38 0.34
2.5 3.0 2.8 3.2 1.5
potential range. The experimental kinetic parameters according to eqn. (3) are given in Table 1. The isotopic ratio of the standard rate constants found for the electron transfer reaction equals "~s,/~n~°/t'o~O/~s,= 0.9 for the protonation k ~ ° / k D2° = 2.0. The effect of temperature on the charge transfer resistance is presented in Fig. 3. The diffusion coefficients of oxygen at the different temperatures are calculated from the limiting currents. The solubility of oxygen at the different temperatures was estimated from literature data [18]. Accurate impedance measurements at high temperature are hampered by the strong decrease of the viscosity of the solution, resulting in an increasing instability of the diffusion layer. The potential dependence of the rate constants found from Fig. 3 are shown in Fig. 4. Table 1 contains the kinetic parameters describing these rate constants as a function of potential, again according to eqn. (3).
SO0
6O0 u -~ 400 rY
-
20O
Q ,5
-
0
~bO ' ".o.o.o~aa.om ~.o-a-
~
.a \
-.~"
-Q05 -0.10 -Q15 -Q 0 - E / V vs. S C E (25~C)
Fig. 3. Potential dependence of the charge transfer resistance Rot for the reduction of oxygen at different temperatures. Experimental data: (©) 274 K, (e) 298 K and ( + ) 323 K. Drawn lines were calculated with the kinetic parameters of Table 1.
180
f
-2
/
_
./
I/
/
~I
li
I~1 II / i X I"
-8
I I
Q 5
I
0
I
I
I
- 0 0 5 -0.10 -O15 -O20 E / V vs. SCE (25"C)
Fig. 4. Potential dependence of In k r for the reduction of oxygen at the temperatures indicated.
Reduction of hydrogen peroxide From the polarograms the rate constant k~ of the reduction of hydrogen peroxide as a function of potential has been obtained using the exact solutions of the mass transport. The plots of In k R vs. E are shown in Fig. 5. As can be seen, the temperature affects the rate constant only slightly. The hydrogen isotope effect on the hydrogen peroxide reduction appears to be negligibly small. DISCUSSION
Hydrogen isotope effect The effects of the substitution of 1320 for H20 and of temperature upon the kinetics of the reduction of oxygen to hydrogen peroxide are given in Table 1. Since these parameters are found by using eqn. (3) with a constant value of E ° irrespective of solvent and temperature, these parameters are in fact the rate constants observed
f"
2
J
,.',7,"
..'" J/l" -~ i -8
/ i"
//x
/ "
". t. "i" / y/ ,1 ~ /, "i
-lO: J / ' -Q4
-0.6
.
-08
.
.
-1.0 E/V
.
-1.2 -1.4 SCE (25°C)
vs.
Fig. 5. Ln k R vs. E for the reduction of hydrogen peroxide in D20 at T = 298 K and in H 2 0 at the temperatures indicated.
181 at a stated potential of E = E~2/HO~ = - 0.216 V vs. SCE. In order to determine the isotope effect one should correct for difference in double-layer structures. As this correction is most probably of minor importance [7], we did not perform it. From Table 1 it is seen that the isotopic rate ratio for the first one-electron transfer is found to be almost unity. This result indicates that the Gibbs energies of activation for this reaction in D20 and H 2 0 are actually the same. Therefore it can be concluded that the interaction between the dissolved oxygen and the solvent is negligibly small or the same. The apparent rate ratio of the protonation of O [ is found to be (k~2°/kD2°)app = 2. Thus, as could be expected, a kinetic isotope effect on the oxygen reduction shows up only in the protonation step. Since (kH20//kD20)app > 1 the isotope effect is found to be "normal". However, interpretation should be done with care. As can be seen from eqn. (3), the absolute value of this rate constant can be determined only if the standard potential difference of the O 2 / O ~- couple in H 2 0 and D20 is known. The true ratio is given by
( k ~ 2 ° / k D2°) = ( k ~ 2 ° / k ~ 2°) exp( ~ T (E~ "D2° - E~''H~°)
(5)
where E? "n2° and E~''D~° are the standard potentials of the O2/O / couple in solutions of H 2 0 and D20, respectively. It seems reasonable to assume the correction to be small, giving (k~2°/k°2~°)= 2. Compared to primary isotope effects found for homogeneous reactions [1-3], this value is somewhat low. Normal hydrogen isotope effects are found to be in the range 3-7. In semi-classical treatments the isotope effect is explained by the difference in Gibbs energy of activation due to the difference in zero-point energies of the transition state and reactants [2]. This treatment gives a maximum value of about 8. A value of 2 would mean that the difference in activation enthalpy has a value of about 1.7 kJ m o l - ' . The isotope rate ratio found for the reduction of hydrogen peroxide is very small. This result indicates only that the O - D or the O - H bond in the activated complex of the rate-determining step does not change in the course of the reaction.
Temperature effect Weaver et al. have described the determination of the activation parameters for simple electrode reactions. They defined the ideal enthalpy of activation AH~ea , as AHi~ea, = - R [ 3 (ln( k / T '/2 ) ) / 3 ( 1 / T )]
(6)
In this equation k is the experimental rate constant, uncorrected for double-layer differences, as a function of temperature at a fixed non-isothermal cell potential. In eqn. (6) k is divided by T 1/2 because of the expected temperature dependence of the collision frequency factor Z e [11]. It should be noted that at these temperatures this temperature dependence of Z e is only of minor importance quantitatively (about 1% in AH *). With the values found for the first electron transfer to oxygen, a simple electron transfer reaction, the ideal enthalpy of activation is found to be 48 O kJ mol-1 at E -- - E 02/HO; -- --0.216 V vs. SCE (Fig. 6), which is a moderate value.
182
~.~
-3
E -4 ..,~ -5
l -o -7 3,0
'
3I2
3.4 '
' 3.'6 l o o o T-~/~C~
'
Fig. 6. in(ksl/T 1/2) vs. T-t for the reduction of oxygen. With the equation
k = Zerp exp( ASi~eal/R ) exp( - A Hi~eal/RT )
(7)
the ideal entropy of activation is found to be 60 J K - ] mo1-1 (independent of temperature), on the assumption that ~O = 1 and Z e = (kT/2"rtm*) 1/2 = 2.2 X 104 cm s - i at 25°C. The apparent temperature dependence of k c is found to be small, but cannot be interpreted in terms of activation parameters of the protonation because the temperature dependence of the standard potential E~ is unknown. However, the activation enthalpy will be low. The rate constant of protonation by water molecules is found to be k~CH2o = 2.9 cm s -~. With E~ = - 0 . 3 9 V vs. SCE it follows that k2CH2o = 3000 cm s-1. The rate constant of the homogeneous secondorder protonation of O 2 by water equals 109 M -1 s -1 [19]. Comparison of these rate constants shows that if the protonation step in the oxygen reduction is really homogeneous, the reaction layer thickness would be about 1 nm. The ideal enthalpy of activation of the reduction of hydrogen peroxide is found to be about A H i ~ l = 48 kJ mo1-1 at E = - 0 . 0 0 V vs. SCE (Fig. 7), AHi~a I = 27 kJ mol-1 at E = 1.00 V vs. SCE, and AHidea * j = 72 kJ t o o l - ] at the standard potential -
"~"
-14
E
% ~ -~(
1
-18
3'.0
A
A •-
3'.6
x)OO l~'/K"
Fig. 7. Ln(kR/T 1/2) vs. T-1 for the reduction of hydrogenperoxide at E = 0 V vs. SCE.
183 E °. T h e s e v a l u e s are s u r p r i s i n g l y l o w for a c o m p l e t e l y i r r e v e r s i b l e e l e c t r o d e r e a c t i o n w i t h s u c h a h i g h o v e r v o l t a g e n e e d e d for r e d u c t i o n . I n s e r t i n g this v a l u e i n t o e q n . (7) yields ZeKp exp(ASi~eal/R)= 500 c m s -1. T h i s result i n d i c a t e s t h a t rp exp(ASi-~eal/R ) is low, w h i c h w o u l d m e a n t h a t e i t h e r r p << 1, i.e. the e l e c t r o n t r a n s f e r is n o n - a d i a b a t i c [20], o r t h e i d e a l e n t r o p y o f a c t i v a t i o n is n e g a t i v e . REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
R.P. Bell, The Proton in Chemistry, 2nd ed., Chapman and Hall, London, 1973. A.V. Willi, Isotopeneffekte bei Chemische Reaktionen, Thieme Vedag, Stuttgart, 1983. R.P. Bell, Chem. Soc. Rev., 3 (1974) 513. B.E. Conway in E. Yeager (Ed.), Transactions of the Symposium on Electrode Processes, Wiley, New York, 1961, p. 267; Proc. R. Soc. London, A256 (1960) 128; A247 (1958) 400. M. Salomon, J. Electrochem. Soc., 114 (1967) 922. J.D.E. McIntyre and M. Salomon, Am. Chem. Soc., Div. Fuels Chem., Preprints, 11 (1967) 209. M.J. Weaver, P.D. Tyma and S.M. Nettles, J. Electroanal. Chem., 114 (1980) 53. C.J. van Velzen, M. Sluyters-Rehbach, A.G. Remijnse, G.J. Brug and J.H. Sluyters, J. Electroanal. Chem., 134 (1982) 87. C.J. van Velzen, M. Sluyters-Rehbach, A.G. Remijnse and J.H. Sluyters, J. Electroanal. Chem., 142 (1982) 229. M.J. Weaver, J. Phys. Chem., 80 (1976) 2645. M.J. Weaver, J. Phys. Chem., 83 (1979) 1748. W.H. Koppenol, Dissertation, Utrecht, 1978. M. Pourbaix, Atlas of Electrochemical Equilibria in Aqueous Solutions, Pergamon Press, Oxford, 1966. C.J. van Velzen, M. Sluyters-Rehbach and J.H. Sluyters, J. Electroanal. Chem., to be published. Manual of the SMDE, Model 303, EG&G Princeton Applied Research, Princeton, 1978. E.L. Yee, R.J. Cave, K.L. Guyer, P.D. Tyma and M.J. Weaver, J. Am. Chem. Soc., 101 (1979) 1131. A.J. Bard and L.R. Faulkner, Electrochemical Methods, Wiley, New York, 1980. R. Battino (Ed.), Solubility Data Series, Vol. 7, IUPAC, Pergamon Press, Oxford, 1981. H. Bitchier and R.E. Bi~hler, Chem. Phys., 16 (1976) 9. R.A. Marcus, Electrochim. Acta, 13 (1968) 995.