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Electroreduction of periodate at a platinum electrode
Electroanalytical Chemistry and InterJ?tcial Electrochemistry, 54 (1974) 351-359 ~i:) Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
351
E L E C T R O R E D U C T I O N O F P E R I O D A T E AT A P L A T I N U M E L E C T R O D E
F. SECCO and M. VENTURINI
Istituto di Chimica Analitica ed Elettrochimica, Universit& di Pisa, Via Risorgimento 35, 56100 Pisa (Italy) (Received 5th February 1974; in revised form 20th March 1974)
INTRODUCTION
The voltammetric behaviour of periodate has scarcely been investigated. From the few papers published on this topic 1-3, which are referred to polarographic measurements at the DME, it is inferred that the reduction of periodate takes place through two consecutive irreversible steps (1) and (2): IO2 + 2 H + + 2 e ~ IO3 + H 2 0
(1)
IO3+6H++6e-~
(2)
I-+3H20
Whereas the characteristics of the wave corresponding to reaction (2) are well known since thorough investigations have been carried out on iodate reduction 4 8, the knowledge of the electrochemical reduction of periodate to iodate is quite incomplete because the wave corresponding to step (1) falls into a range of potentials in which the anodic dissolution of mercury occurs. The platinum electrode, by allowing work at more positive potentials, enabled us to obtain voltammetric curves showing two complete waves. In connection with investigations on reaction mechanisms of oxidizing agents in solution and at the electrode surface 9-11 we report now a voltammetric study of the periodate reduction at a platinum microelectrode with periodical renewal of the diffusion layer ( D L P R E ) 12. EXPERIMENTAL
Chemicals were of analytical grade and conductivity water was used to prepare t h e s o l u t i o n s and as a medium for the electrochemical reaction. The desired acidities were obtained by means of suitable buffers and whenever necessary by adding HC104 or NaOH. The ionic strength was kept constant at 0.2 M with NaC104. The pH values were measured directly into the polarographic cell by using a combined glass electrode and a Metrohm E388 potentiometer. All measurements have been done at 25°C. The current-potential curves were recorded with a three-electrode system using a Polarecord E261 Metrohm connected with an I R compensator E446 Metrohm 9-a 1. The platinum microelectrode was platinized and both reference and auxiliary electrodes were saturated mercurous sulphate joined to the polarographic cell by bridges consisting of a solid mixture of silica gel and NaC104 (3:2). Current-time curves were measured oscillographically keeping constant the potential with a 68 TS 1 Wenking potentiostat. All the potentials reported in this work are however referred to SCE.
352
F. SECCO, M. VENTURINI
RESULTS
A typical current voltage curve for periodic acid is represented in Fig. 1. This curve shows two well separated waves (a) and (b) the height of the first, which falls at more positive potentials, being ½of the height of the second. Coulometric measurements 13 enabled us to establish that the process giving wave (a) involves two electrons and the process connected with wave (b) involves six electrons overall. The temperature coefficient of the limiting current of wave (a) is 1.060/o per degree gnd for wave (b) is 1.10°o per degree. This suggests that both steps of the reduction are diffusion controlled13. The oscillographic analysis of single oscillations confirmed this assumptfon 13. The mean current of both waves, i, at any fixed potential increases proportionally to the concentration of periodate, whereas addition of increasing amounts of iodate produces a proportional growth of wave (b) and the height of wave (a) remains unchanged.
:
:::
:
-
1
E/V(SCE) Fig. 1. Voltammogram of 10 3 M KIO~ at pH=6.40 (NaH2PO~ Na2HPO~ buffer) and ionic strength 0.2 M (NaC104). Curve (c) represents a voltammogram in the absence of KIO4. The curves have been recorded toward more positive potentials.
These results enabled us to state that the reduction of periodate on platinum electrode occurs through two consecutive steps represented by eqns. (1) and (2), as on DME. The proportionality between the diffusion limiting current, ia, and the concentrations of periodate and iodate, is of importance for the analytical determination of the components of periodate-iodate mixtures.
REDUCTION OF IOn- AT Pt
353
Logarithmic analysis, performed on the ascending part of waves (a) and (b), leads to the conclusion that both steps of the reduction are irreversible. The familiar E vs. l o g [ ( i d - i ) / i ] plot yields straight lines with slopes of 0.230 V for step (1) and of 0.100 V for step (2) instead of 0.03 V and 0.01 V as expected if the two processes were reversible. It follows that ne=0.26+0.02 for step (1) and n~= 0.57_+0.07 for step (2). The same results 9 have been obtained by plotting log 2 against E. In Fig. 2 is shown the dependence of half-wave potentials against log [H +] for step (1) and in Fig. 3 an analogous plot for process (2) is represented. Hydrogen ion concentrations have been obtained from pH by using the Davies equation 14.
0.8-_
•
•
oU3 0.6
0.4
0.2
2
4
lO
8
6
-log
EH+?
12
Fig. 2. Plot of E~ against -log [H +] for the reduction step of periodate to iodate.
0.2
0.0-
. ~ - 0.2 -
" ~
-0.4 -
~
I
2
I
4 -Iog[H~
I
6
I
8
I
10
I
12
Fig. 3. Plot of E~ against -log [H +] for the reduction step of iodate to iodide.
354
F. SECCO, M. VENTURINI
DISCUSSION The good separation of waves (a) and (b) enabled us to obtain independent results about the two consecutive steps (1) and (2) of the periodate electroreduction so that they will be discussed separately and the first wave will be referred to as the periodate wave and the second as the iodate wave. Periodate wave The linear dependence of the mean current on the periodate concentration at any given potential means, on the basis of diffusion layer approximation, that the order of the reaction with respect to periodate is unity 15. The value of 0.26 for n~ strongly suggests that only one electron is involved in the rate-determining step. Moreover the dependenc e of the half-wave potential on log [H +] shown in Fig. 2 leads to the conclusion that hydrogen ion is involved in the reduction process. In the range of pH explored the equilibrium between two hydrated forms of periodate, H4IO 6 and H3IO ~- is mainly established. The two approximately linear portions of the curve intersect at a pH value corresponding to pK of H4IO 6 ( K = 3 . 1 x l 0 -8 at •=0.2 M (ref. 16)). At p H < p K , where the H4IO6 ion is predominant, the electrode reaction is independent of hydrogen ion concentration, and at pH > pK, where H3IO ~ is the prevailing species in solution one hydrogen ion seems to be involved in the electrode process. This could be rationalized by assuming that the fast equilibrium (6) is preceding the rate-determining step:
H,~IO~ + e --* products
(3)
On the basis of this mechanism a relationship between E+ and [H + ] can be derived in the formaT: , E~ = const. +
2.3RT [H +] ~ log K + [H +]
(4)
The slope of the pH dependent portion of the curve represented in Fig. 2 (plotted for [ H + ] ~ K) yields for 2.3 RT/coTF the value of 0.1l V instead of 0.23 V as obtained from the logarithmic analysis. Such a large difference suggests that the reaction pathway must be more complex and probably a parallel reaction, involving the reduction of H3IO62-, occurs. If the half-wave potentials are plotted against log{([H+]+3.1 x 10-11)/([H+]+3.1 x 10-s)} a straight line is obtained with a slope in agreement with the value of 2.3 R T/enF given by E vs. log {(id- i)/i} plots. This plot is shown in Fig. 4. This Figure also shows that strong deviations from linearity occur at low acidities when E½ is plotted against log {[H+]/([H +] +K)} according to eqn. (4). One can therefore write: 2.3RT ]-H+]+3.1 x 10 -11 E~ = const. + ~ log [H+]+3.1 x 10 - 8
(5)
A mechanism which gives a good explanation of the experimental results and allows eqn. (5) to be rationalized is the following (see Appendix):
355
REDUCTION OF 10 2 AT Pt log ~,.0 I
([H~+3.1~10-%
XO
2.0
I
I
t.0 I
0.0 ~
0.6-
~0.4 oa
o2.zo.~_ O.O ~.0
I
I
I
I
~.o
~.o
~.0
0.0
d-H~+ 3.1. Io-") - -
log ~
@ ~3, 3.1 ,, lo-~
Fig. 4. ( ) represents a plot of E i against l o g ( [ H + ] + 3 . 1 x l 0 - U ) / ( [ H + ]+3.1 x l 0 8). ( represents a plot of E} against log [H +]/([H +] + 3.1 x 10-8) (upper abscissa).
)
H4106 ~ H3IO~ + H + (fast equilibrium)
(6)
H4106 +e -~ products
(slow)
(7)
H3IO 2- +e ~ products
(slow)
(8)
It is of interest to compare the electroreduction of periodate with its reduction by iodide ion. In particular an examination of the results obtained by Abel and Ffirth 18 and by Indelli e t al. 19 for the periodate-iodide reaction shows that in the range of acidities in which H4IO 6 is the prevailing species in solution, the ratedetermining step is represented by the equation: H4106 + I- ~ [H4106 I2- ]* -~ products
(9)
This step is analogous to the potential-determining step given in eqn. (7) in which the transition state might be depicted as in the scheme:
J!\o
ol
where Pt means participation of the charged electrode. Since this reaction involves a structural change from the octahedral geometry of periodate to the pyramidal one of iodate ion, the breakdown of transition state in favour of the products probably consists of the transfer of one OH group from the periodate to the electrode and the H3IO 2- species, which is leaving, is rapidly converted to 103 ion by loss of one O H - and one water molecule.
356
F. SECCO, M. VENTURINI
This sort of bimolecular mechanism is valid also for the parallel path involving H3IO 2- ion (eqn. 7). In this case the transition state is H3IO~- and its decomposition to products again involves transfer of one O H to the electrode and the leaving species H2IO~- is converted to iodate ion by loss of two O H - ions. The parallelism between the mechanism of reduction of oxidizing agents by iodide ion and on the electrode 9-* 1 holds for the periodate system too. Finally it is worth commenting that, in analogy to the Br6nsted theory of general acid catalysis, the ratio (log k ° z - l o g k ° l ) / A p K (where k°l and k°2 are the rate constants of reactions (7) and (8) respectively, pK is the difference of pK's of periodic acid) should give the transfer coefficient, ~, of the electrochemical process 2°. This relationship yields k12/kll .0 0 ~ 10 -3 which corresponds to the value obtained as shown in the Appendix if the usual value of 0.5 is used for ~, but with the experimental value of 0.26 one obtains k lo2 / k l0l = 1.8 x 10 -2 . This difference might be ascribed to the fact that when the reactions to be compared involve ions bearing different charges, as H4IO 6 and H3IO~ , the ratio of rate constants is smaller than expected because of the electrostatic repulsion which in a reaction involving a species of charge - 2 and the other of charge - 1 is higher than in a reaction involving two species both of charge - 1. The effect of the electrostatic repulsion on the two reactions (7) and (8) is expressed by the factor 21 exp [(eZ/DkT)(1/r11 - 1/r12)] and its value can be calculated only after an arbitrary choice of the reaction distances rl 1 and rl 2lodate wave The linear dependence of the mean current, L upon the depolarizer concentration at any given potential allows us to state that the potentialdetermining step involves only one iodate. The value of n~ (0.57) is approximately twice the corresponding value for the periodate reduction. Our value is to be compared with n~=0.5 found by Orlemann and Kolthoff5 for the electroreduction of iodate at the D M E in the range 1 ~< pHi< 5.5, and with the results of Delahay and Strassner 6 who found n~=0.6 in the range of pH 2-6 and 8-14. The latter authors found n~ = 0.3 at 6 ~< pH ~< 8 in agreement with the value of 0.26 obtained by Shain et al. 7"s. This makes doubtful the determination of n, the number of electrons involved in the slow step. If we consider'that for most reactions the most probable value of the transfer coefficient, ~, is 0.5, an experimental value of 0.57 for n~ leads to the conclusion that n = 1. On the contrary, if we assume that the value is the same as in the periodate reduction, then n = 2. That protons are participating in the electrode reaction is clearly indicated by half-wave potential dependence on pH. The plot of Fig. 3 consists Of two linear portions intersecting at pH-~ 6.5. The slope of the first portion yields R Tm/F~n = 0.07 V and the slope of the second 0.043 V. By using the experimental value of n~ a reaction order in H +, m, ranging between 0.7 and 0.4 is obtained a3. This means that there are probably two parallel paths operative, the first independent of hydrogen ion concentration and the second first-order in H +.
ACKNOWLEDGEMENTS Thanks are due to M.. L. Fernandez Castafion for help in the polarographic measurements. This work has been supported by Italian C.N.R.
REDUCTION OF IO~ AT Pt
357
SUMMARY In connection with studies on mechanisms of reaction of oxidizing agents at the electrode surface, the reduction of periodate at a platinum electrode with periodical renewal of diffusion layer has been studied. The process is represented by two irreversible consecutive steps IO2+2e +2H + ~IO~+HzO I O 3 + 6 e - + 6 H + ~ 1 - + 3 HzO
(i) (ii)
which have been separately investigated. The mechanism of reaction (i) involves two paths in which H4IO 6 and H3IO62 are simultaneously reduced through oneelectron potential-determining steps. Reaction (ii) is also interpreted on the basis of two parallel paths of order 1 and 0 respectively in hydrogen ion. The number of electrons involved in the slow steps of iodate reduction is uncertain. APPENDIX If two parallel paths do contribute to the electrode reaction as in the following scheme: Ox + H + ~ HOx
fast equilibrium
(10)
HOx+ne
~ Red
(11)
Ox+ne
~ Red
(12)
the current for the irreversible overall electroreduction process is given by the sum of two contributions: i = i11+i12
(13)
If [HOx]*, [Ox]* are the concentrations of the protonated and unprotonated forms of the depolarizer in the bulk of the solution and [HOx], [Ox] the corresponding concentrations at the electrode surface then: il, =/~,1 { [HOx]* - [ ~ ]
}
i12 =/~12 { [Ox]* - [ O ~ ] }
(14) (15)
On the other hand the theory of irreversible electrode processes and eqn. (13) yield: i = nF A {k~l [FIOx] +k,2[OX]}
(16)
where kl 1 and ka 2 are the rate constants of the heterogeneous processes (11) and (12) respectively. In well buffered solutions the H + concentration at the electrode surface can be considered equal to the concentration in the bulk of the solution. Moreover it is reasonable to set [Ox]/[HOx]=[Ox]*/[HOx]* so that the dissociation constant, K , of reaction (10) is equal to the concentration quotient at the electrode surface. Under these conditions eqn. (16) becomes: i = n F A ( kla + k I 2 K / [ H + ] ) [nOx]
and from eqns. (14) and (15) it follows that:
(17)
358
F. SECCO, M. VENTURINI i = { k l l ']- ]~12K/[ H + ] } { [ H O x ] * - [H~Ox] }
Taking into account that [ ~ ]
(18)
= 0 when i= id one can write:
id-i
[HOx] = kla+k12K/[ H+]
(19)
Introduction of eqn. (19) in (17) gives:
i nFA ia--i -- kll + k , 2 K / [ H +] {k,, +kx2K/[H+]}
(20)
After introducing : k l a = k ° l exp [ - ~~ -n F ( E - E ° ) I
(21)
( E - E °)
(22)
k12 = k°2 exp
- ~
the following equation is obtained:
RT
nFAk° 1
E=E °+~ln
kll
RT [ H + ] + k12K/kal o o RT I n - i + ~ F In [H+]+~12K/~11 - c~n~ id--i
(23)
and therefore for i = id/2 :
RT
E~ -- const. + ~
In
[H +] + k 1o2 K / k l l o
[ H+] + k,2 K/Yq,
(24)
k12/kll=(D12/D11) ½, where D12 and Dll are the diffusion coefficients of Ox and HOx respectively, it is reasonable, in the case of periodate reduction, to assume this ratio to be unity. Equation (24) is therefore reduced to the empirical eqn. (5) when k ° 2 / k ° 1 is set equal to 10 -3. S i n c e 12
REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14
J. Heyrovsk), Polarography, Springer, Viermar, 1941, p. 75. P. Souchay, Anal. Chim. Acta, 2 (1948) 17. R. H. Coe and L. B. Rogers, J. Amer. Chem. Soc., 70 (1948) 3276. E. F. Orlemann and I. M. Kolthoff, J. Amer. Chem. Soe., 64 (1942) 1044. E. F. Orlemann and I. M. Kolthoff, J. Amer. Chem. Soc., 64 (1942) 1070. P. Delahay and J. E. Strassner, J. Amer. Chem. Soc., 73 (1951) 5219. R. D. Dernars and I. Shain, J. Amer. Chem. Soc., 81 (1959) 2654. I. Shain, K. J. Martin and J. W. Ross, J. Phys. Chem., 65 (1961) 259. M. Venturini, A. Indelli and G. Raspi, J. Electroanal. Chem., 33 (1971) 99. M. Venturini, F. Secco and D. De Filippo, J. Electroanal. Chem., 40 (1972) 339. M. Venturini and F. Secco, J. Chem. Soc., Perk. 11, (1973)491. D. Cozzi, G. Raspi and L. Nucci, J. Electroanal. Chem., 12 (1966) 36. J. Heyrovsk~¢ and J. Kfita, Principles of Polarography, Academic Press, New York, 1966, pp. 88, 276. C. W. Davies, lon Association, Butterworths, London, 1962, p. 39.
REDUCTION OF IO~ AT Pt
359
15 G. Raspi, F. Pergola and R. Guidelli, Anal. Chem., 44 (1972) 472. 16 J. Bjerrum, G. Schwarzenbach and L. G. Sillen, Stahility Constants, Special.Publ., No 7, The Chemical Society, London, 1958, Part II, p. 125. 17 P. Zuman in A. Streitwieser and R. W. Taft (Eds.), Progress in Physical Organic Chemistry, Vol. 5, Interscience, New York, 1967, p. 81. 18 E. Abel and A. Fiirth, Z. Phys. Chem., 107 (1924) 313. 19 A. Indelli, F. Ferranti and F. Secco, J. Phys. Chem., 70 (1966) 631. 20 C. L. Perrin in A. Streitwieser and R. W. Taft (Eds.), Progress in Physical Organic Chemistry, Vol. 3, Interscience, New York, 1965, p. 165. 21 E. A. Moelwyn-Hughes in Kinetics of Reactions in Solution, Clarendon Press, Oxford, 2nd edn., 1947, p. 82.
351
E L E C T R O R E D U C T I O N O F P E R I O D A T E AT A P L A T I N U M E L E C T R O D E
F. SECCO and M. VENTURINI
Istituto di Chimica Analitica ed Elettrochimica, Universit& di Pisa, Via Risorgimento 35, 56100 Pisa (Italy) (Received 5th February 1974; in revised form 20th March 1974)
INTRODUCTION
The voltammetric behaviour of periodate has scarcely been investigated. From the few papers published on this topic 1-3, which are referred to polarographic measurements at the DME, it is inferred that the reduction of periodate takes place through two consecutive irreversible steps (1) and (2): IO2 + 2 H + + 2 e ~ IO3 + H 2 0
(1)
IO3+6H++6e-~
(2)
I-+3H20
Whereas the characteristics of the wave corresponding to reaction (2) are well known since thorough investigations have been carried out on iodate reduction 4 8, the knowledge of the electrochemical reduction of periodate to iodate is quite incomplete because the wave corresponding to step (1) falls into a range of potentials in which the anodic dissolution of mercury occurs. The platinum electrode, by allowing work at more positive potentials, enabled us to obtain voltammetric curves showing two complete waves. In connection with investigations on reaction mechanisms of oxidizing agents in solution and at the electrode surface 9-11 we report now a voltammetric study of the periodate reduction at a platinum microelectrode with periodical renewal of the diffusion layer ( D L P R E ) 12. EXPERIMENTAL
Chemicals were of analytical grade and conductivity water was used to prepare t h e s o l u t i o n s and as a medium for the electrochemical reaction. The desired acidities were obtained by means of suitable buffers and whenever necessary by adding HC104 or NaOH. The ionic strength was kept constant at 0.2 M with NaC104. The pH values were measured directly into the polarographic cell by using a combined glass electrode and a Metrohm E388 potentiometer. All measurements have been done at 25°C. The current-potential curves were recorded with a three-electrode system using a Polarecord E261 Metrohm connected with an I R compensator E446 Metrohm 9-a 1. The platinum microelectrode was platinized and both reference and auxiliary electrodes were saturated mercurous sulphate joined to the polarographic cell by bridges consisting of a solid mixture of silica gel and NaC104 (3:2). Current-time curves were measured oscillographically keeping constant the potential with a 68 TS 1 Wenking potentiostat. All the potentials reported in this work are however referred to SCE.
352
F. SECCO, M. VENTURINI
RESULTS
A typical current voltage curve for periodic acid is represented in Fig. 1. This curve shows two well separated waves (a) and (b) the height of the first, which falls at more positive potentials, being ½of the height of the second. Coulometric measurements 13 enabled us to establish that the process giving wave (a) involves two electrons and the process connected with wave (b) involves six electrons overall. The temperature coefficient of the limiting current of wave (a) is 1.060/o per degree gnd for wave (b) is 1.10°o per degree. This suggests that both steps of the reduction are diffusion controlled13. The oscillographic analysis of single oscillations confirmed this assumptfon 13. The mean current of both waves, i, at any fixed potential increases proportionally to the concentration of periodate, whereas addition of increasing amounts of iodate produces a proportional growth of wave (b) and the height of wave (a) remains unchanged.
:
:::
:
-
1
E/V(SCE) Fig. 1. Voltammogram of 10 3 M KIO~ at pH=6.40 (NaH2PO~ Na2HPO~ buffer) and ionic strength 0.2 M (NaC104). Curve (c) represents a voltammogram in the absence of KIO4. The curves have been recorded toward more positive potentials.
These results enabled us to state that the reduction of periodate on platinum electrode occurs through two consecutive steps represented by eqns. (1) and (2), as on DME. The proportionality between the diffusion limiting current, ia, and the concentrations of periodate and iodate, is of importance for the analytical determination of the components of periodate-iodate mixtures.
REDUCTION OF IOn- AT Pt
353
Logarithmic analysis, performed on the ascending part of waves (a) and (b), leads to the conclusion that both steps of the reduction are irreversible. The familiar E vs. l o g [ ( i d - i ) / i ] plot yields straight lines with slopes of 0.230 V for step (1) and of 0.100 V for step (2) instead of 0.03 V and 0.01 V as expected if the two processes were reversible. It follows that ne=0.26+0.02 for step (1) and n~= 0.57_+0.07 for step (2). The same results 9 have been obtained by plotting log 2 against E. In Fig. 2 is shown the dependence of half-wave potentials against log [H +] for step (1) and in Fig. 3 an analogous plot for process (2) is represented. Hydrogen ion concentrations have been obtained from pH by using the Davies equation 14.
0.8-_
•
•
oU3 0.6
0.4
0.2
2
4
lO
8
6
-log
EH+?
12
Fig. 2. Plot of E~ against -log [H +] for the reduction step of periodate to iodate.
0.2
0.0-
. ~ - 0.2 -
" ~
-0.4 -
~
I
2
I
4 -Iog[H~
I
6
I
8
I
10
I
12
Fig. 3. Plot of E~ against -log [H +] for the reduction step of iodate to iodide.
354
F. SECCO, M. VENTURINI
DISCUSSION The good separation of waves (a) and (b) enabled us to obtain independent results about the two consecutive steps (1) and (2) of the periodate electroreduction so that they will be discussed separately and the first wave will be referred to as the periodate wave and the second as the iodate wave. Periodate wave The linear dependence of the mean current on the periodate concentration at any given potential means, on the basis of diffusion layer approximation, that the order of the reaction with respect to periodate is unity 15. The value of 0.26 for n~ strongly suggests that only one electron is involved in the rate-determining step. Moreover the dependenc e of the half-wave potential on log [H +] shown in Fig. 2 leads to the conclusion that hydrogen ion is involved in the reduction process. In the range of pH explored the equilibrium between two hydrated forms of periodate, H4IO 6 and H3IO ~- is mainly established. The two approximately linear portions of the curve intersect at a pH value corresponding to pK of H4IO 6 ( K = 3 . 1 x l 0 -8 at •=0.2 M (ref. 16)). At p H < p K , where the H4IO6 ion is predominant, the electrode reaction is independent of hydrogen ion concentration, and at pH > pK, where H3IO ~ is the prevailing species in solution one hydrogen ion seems to be involved in the electrode process. This could be rationalized by assuming that the fast equilibrium (6) is preceding the rate-determining step:
H,~IO~ + e --* products
(3)
On the basis of this mechanism a relationship between E+ and [H + ] can be derived in the formaT: , E~ = const. +
2.3RT [H +] ~ log K + [H +]
(4)
The slope of the pH dependent portion of the curve represented in Fig. 2 (plotted for [ H + ] ~ K) yields for 2.3 RT/coTF the value of 0.1l V instead of 0.23 V as obtained from the logarithmic analysis. Such a large difference suggests that the reaction pathway must be more complex and probably a parallel reaction, involving the reduction of H3IO62-, occurs. If the half-wave potentials are plotted against log{([H+]+3.1 x 10-11)/([H+]+3.1 x 10-s)} a straight line is obtained with a slope in agreement with the value of 2.3 R T/enF given by E vs. log {(id- i)/i} plots. This plot is shown in Fig. 4. This Figure also shows that strong deviations from linearity occur at low acidities when E½ is plotted against log {[H+]/([H +] +K)} according to eqn. (4). One can therefore write: 2.3RT ]-H+]+3.1 x 10 -11 E~ = const. + ~ log [H+]+3.1 x 10 - 8
(5)
A mechanism which gives a good explanation of the experimental results and allows eqn. (5) to be rationalized is the following (see Appendix):
355
REDUCTION OF 10 2 AT Pt log ~,.0 I
([H~+3.1~10-%
XO
2.0
I
I
t.0 I
0.0 ~
0.6-
~0.4 oa
o2.zo.~_ O.O ~.0
I
I
I
I
~.o
~.o
~.0
0.0
d-H~+ 3.1. Io-") - -
log ~
@ ~3, 3.1 ,, lo-~
Fig. 4. ( ) represents a plot of E i against l o g ( [ H + ] + 3 . 1 x l 0 - U ) / ( [ H + ]+3.1 x l 0 8). ( represents a plot of E} against log [H +]/([H +] + 3.1 x 10-8) (upper abscissa).
)
H4106 ~ H3IO~ + H + (fast equilibrium)
(6)
H4106 +e -~ products
(slow)
(7)
H3IO 2- +e ~ products
(slow)
(8)
It is of interest to compare the electroreduction of periodate with its reduction by iodide ion. In particular an examination of the results obtained by Abel and Ffirth 18 and by Indelli e t al. 19 for the periodate-iodide reaction shows that in the range of acidities in which H4IO 6 is the prevailing species in solution, the ratedetermining step is represented by the equation: H4106 + I- ~ [H4106 I2- ]* -~ products
(9)
This step is analogous to the potential-determining step given in eqn. (7) in which the transition state might be depicted as in the scheme:
J!\o
ol
where Pt means participation of the charged electrode. Since this reaction involves a structural change from the octahedral geometry of periodate to the pyramidal one of iodate ion, the breakdown of transition state in favour of the products probably consists of the transfer of one OH group from the periodate to the electrode and the H3IO 2- species, which is leaving, is rapidly converted to 103 ion by loss of one O H - and one water molecule.
356
F. SECCO, M. VENTURINI
This sort of bimolecular mechanism is valid also for the parallel path involving H3IO 2- ion (eqn. 7). In this case the transition state is H3IO~- and its decomposition to products again involves transfer of one O H to the electrode and the leaving species H2IO~- is converted to iodate ion by loss of two O H - ions. The parallelism between the mechanism of reduction of oxidizing agents by iodide ion and on the electrode 9-* 1 holds for the periodate system too. Finally it is worth commenting that, in analogy to the Br6nsted theory of general acid catalysis, the ratio (log k ° z - l o g k ° l ) / A p K (where k°l and k°2 are the rate constants of reactions (7) and (8) respectively, pK is the difference of pK's of periodic acid) should give the transfer coefficient, ~, of the electrochemical process 2°. This relationship yields k12/kll .0 0 ~ 10 -3 which corresponds to the value obtained as shown in the Appendix if the usual value of 0.5 is used for ~, but with the experimental value of 0.26 one obtains k lo2 / k l0l = 1.8 x 10 -2 . This difference might be ascribed to the fact that when the reactions to be compared involve ions bearing different charges, as H4IO 6 and H3IO~ , the ratio of rate constants is smaller than expected because of the electrostatic repulsion which in a reaction involving a species of charge - 2 and the other of charge - 1 is higher than in a reaction involving two species both of charge - 1. The effect of the electrostatic repulsion on the two reactions (7) and (8) is expressed by the factor 21 exp [(eZ/DkT)(1/r11 - 1/r12)] and its value can be calculated only after an arbitrary choice of the reaction distances rl 1 and rl 2lodate wave The linear dependence of the mean current, L upon the depolarizer concentration at any given potential allows us to state that the potentialdetermining step involves only one iodate. The value of n~ (0.57) is approximately twice the corresponding value for the periodate reduction. Our value is to be compared with n~=0.5 found by Orlemann and Kolthoff5 for the electroreduction of iodate at the D M E in the range 1 ~< pHi< 5.5, and with the results of Delahay and Strassner 6 who found n~=0.6 in the range of pH 2-6 and 8-14. The latter authors found n~ = 0.3 at 6 ~< pH ~< 8 in agreement with the value of 0.26 obtained by Shain et al. 7"s. This makes doubtful the determination of n, the number of electrons involved in the slow step. If we consider'that for most reactions the most probable value of the transfer coefficient, ~, is 0.5, an experimental value of 0.57 for n~ leads to the conclusion that n = 1. On the contrary, if we assume that the value is the same as in the periodate reduction, then n = 2. That protons are participating in the electrode reaction is clearly indicated by half-wave potential dependence on pH. The plot of Fig. 3 consists Of two linear portions intersecting at pH-~ 6.5. The slope of the first portion yields R Tm/F~n = 0.07 V and the slope of the second 0.043 V. By using the experimental value of n~ a reaction order in H +, m, ranging between 0.7 and 0.4 is obtained a3. This means that there are probably two parallel paths operative, the first independent of hydrogen ion concentration and the second first-order in H +.
ACKNOWLEDGEMENTS Thanks are due to M.. L. Fernandez Castafion for help in the polarographic measurements. This work has been supported by Italian C.N.R.
REDUCTION OF IO~ AT Pt
357
SUMMARY In connection with studies on mechanisms of reaction of oxidizing agents at the electrode surface, the reduction of periodate at a platinum electrode with periodical renewal of diffusion layer has been studied. The process is represented by two irreversible consecutive steps IO2+2e +2H + ~IO~+HzO I O 3 + 6 e - + 6 H + ~ 1 - + 3 HzO
(i) (ii)
which have been separately investigated. The mechanism of reaction (i) involves two paths in which H4IO 6 and H3IO62 are simultaneously reduced through oneelectron potential-determining steps. Reaction (ii) is also interpreted on the basis of two parallel paths of order 1 and 0 respectively in hydrogen ion. The number of electrons involved in the slow steps of iodate reduction is uncertain. APPENDIX If two parallel paths do contribute to the electrode reaction as in the following scheme: Ox + H + ~ HOx
fast equilibrium
(10)
HOx+ne
~ Red
(11)
Ox+ne
~ Red
(12)
the current for the irreversible overall electroreduction process is given by the sum of two contributions: i = i11+i12
(13)
If [HOx]*, [Ox]* are the concentrations of the protonated and unprotonated forms of the depolarizer in the bulk of the solution and [HOx], [Ox] the corresponding concentrations at the electrode surface then: il, =/~,1 { [HOx]* - [ ~ ]
}
i12 =/~12 { [Ox]* - [ O ~ ] }
(14) (15)
On the other hand the theory of irreversible electrode processes and eqn. (13) yield: i = nF A {k~l [FIOx] +k,2[OX]}
(16)
where kl 1 and ka 2 are the rate constants of the heterogeneous processes (11) and (12) respectively. In well buffered solutions the H + concentration at the electrode surface can be considered equal to the concentration in the bulk of the solution. Moreover it is reasonable to set [Ox]/[HOx]=[Ox]*/[HOx]* so that the dissociation constant, K , of reaction (10) is equal to the concentration quotient at the electrode surface. Under these conditions eqn. (16) becomes: i = n F A ( kla + k I 2 K / [ H + ] ) [nOx]
and from eqns. (14) and (15) it follows that:
(17)
358
F. SECCO, M. VENTURINI i = { k l l ']- ]~12K/[ H + ] } { [ H O x ] * - [H~Ox] }
Taking into account that [ ~ ]
(18)
= 0 when i= id one can write:
id-i
[HOx] = kla+k12K/[ H+]
(19)
Introduction of eqn. (19) in (17) gives:
i nFA ia--i -- kll + k , 2 K / [ H +] {k,, +kx2K/[H+]}
(20)
After introducing : k l a = k ° l exp [ - ~~ -n F ( E - E ° ) I
(21)
( E - E °)
(22)
k12 = k°2 exp
- ~
the following equation is obtained:
RT
nFAk° 1
E=E °+~ln
kll
RT [ H + ] + k12K/kal o o RT I n - i + ~ F In [H+]+~12K/~11 - c~n~ id--i
(23)
and therefore for i = id/2 :
RT
E~ -- const. + ~
In
[H +] + k 1o2 K / k l l o
[ H+] + k,2 K/Yq,
(24)
k12/kll=(D12/D11) ½, where D12 and Dll are the diffusion coefficients of Ox and HOx respectively, it is reasonable, in the case of periodate reduction, to assume this ratio to be unity. Equation (24) is therefore reduced to the empirical eqn. (5) when k ° 2 / k ° 1 is set equal to 10 -3. S i n c e 12
REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14
J. Heyrovsk), Polarography, Springer, Viermar, 1941, p. 75. P. Souchay, Anal. Chim. Acta, 2 (1948) 17. R. H. Coe and L. B. Rogers, J. Amer. Chem. Soc., 70 (1948) 3276. E. F. Orlemann and I. M. Kolthoff, J. Amer. Chem. Soe., 64 (1942) 1044. E. F. Orlemann and I. M. Kolthoff, J. Amer. Chem. Soc., 64 (1942) 1070. P. Delahay and J. E. Strassner, J. Amer. Chem. Soc., 73 (1951) 5219. R. D. Dernars and I. Shain, J. Amer. Chem. Soc., 81 (1959) 2654. I. Shain, K. J. Martin and J. W. Ross, J. Phys. Chem., 65 (1961) 259. M. Venturini, A. Indelli and G. Raspi, J. Electroanal. Chem., 33 (1971) 99. M. Venturini, F. Secco and D. De Filippo, J. Electroanal. Chem., 40 (1972) 339. M. Venturini and F. Secco, J. Chem. Soc., Perk. 11, (1973)491. D. Cozzi, G. Raspi and L. Nucci, J. Electroanal. Chem., 12 (1966) 36. J. Heyrovsk~¢ and J. Kfita, Principles of Polarography, Academic Press, New York, 1966, pp. 88, 276. C. W. Davies, lon Association, Butterworths, London, 1962, p. 39.
REDUCTION OF IO~ AT Pt
359
15 G. Raspi, F. Pergola and R. Guidelli, Anal. Chem., 44 (1972) 472. 16 J. Bjerrum, G. Schwarzenbach and L. G. Sillen, Stahility Constants, Special.Publ., No 7, The Chemical Society, London, 1958, Part II, p. 125. 17 P. Zuman in A. Streitwieser and R. W. Taft (Eds.), Progress in Physical Organic Chemistry, Vol. 5, Interscience, New York, 1967, p. 81. 18 E. Abel and A. Fiirth, Z. Phys. Chem., 107 (1924) 313. 19 A. Indelli, F. Ferranti and F. Secco, J. Phys. Chem., 70 (1966) 631. 20 C. L. Perrin in A. Streitwieser and R. W. Taft (Eds.), Progress in Physical Organic Chemistry, Vol. 3, Interscience, New York, 1965, p. 165. 21 E. A. Moelwyn-Hughes in Kinetics of Reactions in Solution, Clarendon Press, Oxford, 2nd edn., 1947, p. 82.