Electrochemical kinetic study of the Fe3+Fe2+ system in oxalate medium

ELECTROCHEMICAL KINETIC STUDY OF THE Fe3+-Fez+ SYSTEM IN OXALATE MEDIUM V.LOPEZand Departamento

de Ektroqnimica, Departamento C.S.I.C., Universidad Autbnoma,

M. J. PE~A*

de Investigaciones Quimicas, Centco Canto Blanco, Madrid 34, Spain

Coordinado

(Receiued 9 July 1980) Abstract-The overall proasses were determined for the reduction of Fe?* to Fe”, in an oxalate medium and at oxalate concentrations of less than 0.5M. The coordination numbers of the oxidized and reduced species were calculated, together with the number of intervening protons that depend on the oxalate concentration and the pH. Inaddition, the species that reducesat the electrode is determined, together with the intensity equations for each process. INTRODUCTION

pH is close to 2, Fe3 ’ can exist as Fe(C,O,); and Fe’ + and even as free Fe’+. Using the Lingane method, we calculated (p-q) = 2. From the Rabko and Dubohenko diagrams[6], we also established the coordination number of the oxidized and reduced species, according to the working conditions. Once we had determined the distinct overall processes dependent on the pH value and the oxlate concentration, we then calculated the species that reduces at the electrode. Calculations were abo made for the electrochemical orders with respect to the complex Fe ion, oxalate ion and pH for each process together with the corresponding intensity equations.

as Fe(C,O,) It has been proved that the Fe3 +-Fe’ + -oxalate system is a quasi-reversible process at oxalate concentrations of less than O.SM[l]. We found an electrode rate constant of about 0.3.10-’ cm/s and an average transfer coefficient, 01,of 0.8. Fir&t we established the overall electrachemical reactions that take place depending on the pH and the oxalate concentration. We then calculated the electrochemical orders and their corresponding intensity equations. In order to determine the overall reactions we calculated the variation in E , ,2 with the pH, and consequently we could determine the number of protons taking part. Likewise, we could calculate the (p - q) values, ie the difference between the coordination number of the oxidized and reduced species at each pH interval and the number of transferred electrons. Various authors, using diverse methods, have studied the iron-oxalate ion complexes. Early studies were based on the neutralization curves of ferric solutions containing varying quantities of oxalate. It was found that the complex with the highest coordination number was Fe(C,O,);’ and the different Fe3+-oxalate equilibria were established. From an electrochemical point of view, the study of the complex iron-oxalate species was initiated by Stakelberg and Freyhold[Z], Toropova[3] Kolthoff and Lingone[4] and later work was carried out by Latinen et &[5]. Theseauthors found (w) values of 1 and 0 for oxalate concentrations of < 0.2M and > 0.2M respectively, that correspond to the processes:

Fe(C,O,);

3 + le- eFe(C,O,);“+C,O;

for (p-q) = 1 and Fe(C,O,);

3 + le- + Fe(C,O,);”

for (P-q) = 0. According to literature, however, other complex species can exist. Thus, if the oxalate concentration is stnall, but always in excess of the Fe3+ ions, and if the l

To whom correspondence

should be addressed.

EXPERIMENTAL Method In order to calculate (w), the difference between the coordination number of the oxidized and reduced forms;we have used Lingane’s equation (7): RT BMXP E l,r=E”-~logBMX,-(W)~loB(X)

RT

The (w) value is derived from the slope of the graph, Ei,, us log concentration of complexing substance. Matsuda and Ayabe[8] established that a study can be carried out for quasi-reversible reactions similar to that for reversible ones. This involves the substitution of E,,,, read straight off the polarogram, by the reversible half-wave potential (E,,,) calculated by the aforementioned method[l]. We used the Rabko and Dubohenko diagrams[6] in the determination of the p and q values. These diagrams represent the distinct forms in which Fe”+ and Fe’+ appear, depending on the oxalate concentration and pH. The number of electrons transferred during the electrodic process was calculated by the microcoulombimetric method as described by Meites, Gilbert and Rideal[P, lo]. 8.57

V. LOPEZANDht. J. PEkA

858

2.1O-2 M, we obtain three distinct intervals. In the first, pH 1.8-2.8, the slope is - 120 mV and therefore the number of protons taking part in the overall a reaction would be 2. The interval, pH 2.8-4, has a slope --log& = p-i dlag(X) of - 53 mV and the number of protons is 1. For pH values greater than 4, the slope is zero and therefore no where p is the coordination nuntber of the predominprotons take part in the overall reaction. ant species, and i the coordination number of the With increase in the oxalate concentration, these species that reduces at the electrode. The transfer coefficient was calculated from the changes in slope take place at more acidic pH values. In order to establish the various species, we caicuexpression: lated the m) values. A series of experiments were 0.048 carried out, maintaining constant the ferric ion con(12) centration in the cell (lo-’ M) and varying the oxalate nm=E, ion concentration. where E, is the peak potential and E,,, the i,,, Figure 2 shows the variation of E,,, us the log of the potential. oxalate concentration at different pH values. At pH 1.8, the slope is - 130 mV and corresponds to a (w) value of 2 for all oxalate concentrations studied. A radiometer PO4C polarograph was used to At pH 2, there are two interval% (1)corresponding to obtain polarograms. The working electrode was a oxalate concentrations lower than 0.1 M and @-q) Radiometer R405 mercury drop. Capillary charac= 2, and (2) oxalate concentrations greater than 0.1 M teristics were: a = 0.100 V, drop time = 6.1 s and and (w) = 1. mercury flow = 1.51 mg/s. The saturated calomel reAt pH = 3.5, there are three intervals: (1) for oxalate ference electrode was a Radiometer E-65. concentrations of less than 5.10-‘M, where (p-q) = 2, pH measurements were made using a Reckman, (2) oxalate concentrations between S.lO-*M and Expandomatic SS-2-pH meter. The temperature was O.lM, (p -4) = 1, and, (3) oxalate concentrations maintained constant at 25°C by means of a Colora greater than O.lM with zero slope and (w) = 0. M.B. ultra-thermostat. At pH greater than 4, intervals 2 and 3 also appear Voltammograms were obtained by means of a three within the same oxalate concentration ranges ie (p-q) electrode potentiostatic system Amel, model 563. The = 1, at oxalate concentrations less than BiM and working electrode was an Ingold 490 mercury drop, (w) = 0 for higher oxalate concentrations. the drop time being approximately 40 s. The auxiliary We have used the Rabko and Dubovenko diagrams electrode, was platinum, model lngold 303 NS. to evaluate p and q_ These diagrams indicate the The curves were recorded during the drop life time. distinct forms in which Fe3+ and Fez* appear dependThe scan rate in the applied potential remained ing on the oxalate concentration and the pH of the constant at 2OtnV/s. solution_ Table 1 shows the predominant species of Fe3 f and Fe*+ for the pH and concentration ranges studied. RESULTS Figure 3 is a plot of log i/id--i us log of the oxalate concentration at fixed potential and pH 3.5. The slope gives the value of pi. The values for i are given in Figure 1 shows the variation in E, ,2 with the pH for different oxalate concentrations. Three intervals of Table 1. different slope are observed. Although the pH value, An average value of u = 0.8 was obtained inwith which the slope varies, depends on the oxalate dependently of the oxalate and Fe”+ concentration concentration, if we consider a concentration of and the pH. The complex species that reduces at the electrode is determined from the following expression:

-0.24 -

-0.16 -

Fig. 1. Variation of E,,,

with pH

at different oxalate concentrations.

859

Electrochemical kinetic study of the Fe’+-Fe*+ system in oxalate medium

-ZdI 0.06

I

L 0

I

I -0.B

1

I -0.16

I -024

1

EL

Fig. 2. Variation of E;,L with log (C,Ot) for different pH values.

Table 1. Coordination number of species

that reducea at electmde

PH 1.8 2

lo- 2 - 0.2 lo-’ -0.1 0.1 -0.3 10-a -5.10-’ s.10-* -0.1 0.1 - 0.36 10-J -0.1 0.1 - 0.36

3.5

>4

.-I!0.2 J

0

? 4, Y / // 0 2OOmV

-02 1

t

Fe+2 Fe+’ FeWA) Fe+1 FeGO,) FeWL); Fe(C,O,); Fc(C,O,);”

WGO,); FeGO,); FWA); FeGW; FeWA); FeWA); Fe(C,O,);’ Fc(C,O.,);’

A 190 mV

*/I

-0.6 . t

1.4

l

0 If5 mv I 170 RN

16

I

-oz-

l _.-•-

180 mV

-04 /-

l-•

-02 -

.,.A-*-*

02mrw A 210 mv l

200

lw-04

0255 -

mv

4245mV l 235 mV

z

-kg

cc,oq*1

Fig. 3. Plot of log i/id-i USlog (C,O;) at fixed potential and pH = 3.5.

The behaviour of the E-i curves was studied for different oxalate concentrations and pH values. In the study of those potentials corresponding to the foot of the E-i curve it is deduced that the Tafel law is obeyed for the concentrations considered. It is observed that the curve of E/log i is practically independent of the Fe’+ and oxalate concentrations and pH values. An average value of 67 mV is calculated as shown in Table 2. The electrochemical orders were calculated taking

into account the ferric ion and oxalate concentration and the pH value. Table 2 gives a summa ry of the variation in the Tafel slope and electrochemical order with the Fe3+ concentration at two different oxalate concentrations. A value of 1 was obtained in all cases. Likewise, the electrochemical orders were calculated with respect to the pH, for the tbrec sections of the E,,, trs pH plot. Rwults are given in Table 3. Table 4 gives the electrochemical orders with respect to the oxalate concentration.

v.

860

LOPEZ

AND

Table 2. Tafel slopes and electrochemical order with respect to the ferric ion concentration (pH = 4) (C,O,=)

(Fe”)

M. J. PEkA

reduces at the electrode), in this case 0, we can assume that the mobile equilibria would be

WGO,),

+ I-I*

kFe(C,O,)+ +CtO,H

WV) 4.10-Z

0.2

0.4.10-3 0.8.W3 1.2.10-3 l.6.1O-3 2. 10-3

68 70 66 68 68

0.8.10‘” 1.2.10-3 l.6.1O-3 2. 10“

70 66 66 68

k, IL +H+ Fe3+ + C204HFe3 + is the reduced species

1.00

Fe’+ + le- ?.Fer+ 1.00

and the overall process would be: Fe(C,O,);

+ 2Hf + 2e- + Fe’* + ZC,O,H-

(1)

and the intensity equation would be: DISCUSSION

i = Fk,K,K,C~2,~o,,..C~~.CFS~C~oI~~exp~.

From the results, we determined the overall reactions for the different pH intervals. At pH 1.8-2.8, the predominant overall process is: Fe(C,O,);

+ 2H’ + le- -+ Fez+ + 2C20,H-

(1)

This process is in agreement with the (w) value of 2, with the values of p and 4, with the calculated number of protons = 2, with the number of electrons = 1 for every interval studied and also with the dominant species of the oxalate ion in this pH range. In this same range, but with oxalate concentrations greater than 0.1 M, this other process appears:

- uFAd RT

This equation is in agreement with the aforementioned points, the electrochemical orders, Tafel slopes = - 67 mV and a = 0.8, In the same pH range but at oxalate concentrations greater than 0.1 M, the order with respect to the proton concentration is 1 and to the oxalate concentration - I. The overall process that takes place is expressed by: Fe(Cr0.J;

+ W* + FeC,O,+C,O,H-.

(2)

The mobile equilibrium would be A,

Fe(C,O,);

+ H+ + le + Fe(C,O,) + C,O,H

(2)

where (w) = 1 and number of protons = 1. At pH 3.5, together with (1) and (2) the following process takes place, at oxalate concentrations greater than 0.1 M: Fe(C,O,);

+ le 4 Fe(C,O&

(3)

which agrees with (~9) = 0, p and 4 = 2 and number of protons = 0. At higher pH’s the foIlowing processes take place: (a) at oxalate concentrations Fe(C,O,):-

~0.1 M

+ le- -+ Fe(C,O&

+CsO;

(4)

which agrees with the p and q values, (w) = 1, number of protons = 0 and with the presence of C,O; at this pH value. (b) at oxalate concentrations > 0.1 M Fe(C,O,)i-

+ lee 4 Fe(C,O,)<-

(5)

which is also in agreement with the experimental results. With theaforementioned pH intervals, we shall now discuss the electrochemical reaction orders, Tafel slopes and the species reduced at the electrode. At pH = 1.8-2.8 and oxalate concentrations of less than 0.1 M, the electrochemical order with respect: to the proton concentration is 2, to the oxalate concentration it is -2 and to the complex ferric ion is 1. Taking into account these results, together with the i-value (coordination number of the snecies that

Fe(C,O,);

+ H4

e

Fe(C,O,)+

+C,O,H-.

As i = 1, under these conditions Fe(C,O,,)’ species that reduces at the electrode Fe(C,O,)’

is the

+ le- 2 F&,0,

and the intensity equation could be written as: -aFA&

i = FkeKBCfe,c,o,,, - Cn. .C&‘O,H..exp RT~

This equation agrees with the overall process, electrochemical orders, Tafel slow and K value. At pH = 3.5, it is found that the overall processes, due to the (p-q) values and number of intervening. protons in the overall reaction, would be (1). (2) and (3). If we study the plot of E, ,2 us pH, however, we observe that the overall process I scarcely takes place, and would only exist to a small extent at oxalatk concentrations of less than 5.10 ‘. Process (2) would only take place at oxalate concentrations greater than 0.1 M. Theelectrochemical order with respect to the proton concentration is 1, and to the oxalate concentration is - 1 and therefore the most favoured reaction is (21. The intensity equation would bc the same as that mentioned before. At pH’s greater than 4 the overall processes taking place are: Fe(C,O,);

+ le- =+ Fe(C,O,):

Fe(C,O,);

- + C,O;

+ le- e Fe(C,O&

(4) (5)

pH

2.2 2.4 2.6 2.8

2.2 2.4 2.6 2.8

2.2 2.4 2.6 2.8

(C,O,=)

4.1o-z

6.WL

0.2

66 67 63 66

62 66 67 66

61 62 62 66

@V)

= dlogi

-1

-2

-2

Table 3. Tafel slopes and electrochemical

E 3:s

0.1

2.8 3.1 3.5

2.8 3.1 3.5

6.10- ’

0.2

2.8 3.1 3.5

pH

2.10-l

(C,O,=)

SE

66 67 66

67 66 67

67 66 67

(mv)

dlogi

-

-1

-1

-1

-1

6.10-’

4.W2

(C204=)

5.7

4 4.2 4.5 4.7 5.1 5.4

5.7

4 4.2 4.5 4.7 5.1 5.4

pH

order with respect to the pH at varying oxalate concentrations

66 68 66 67 66 66 67

66 67 67 68 66 68 67

WI

6E alogi

(Fe+‘) = 10e3 M

0

0

8.10-’ 0.1 0.2 0.28

2.10-z 3.10-f 4.10-l 5.W’ 6.10-’ 7.10-l

GO*‘)

pH 3.5

order with respect to the potassium

oxaiate concentration. pH 4.5

(Fe*‘) = 10m3 M

63 62

:: 63

63 62 62

W)

-1

-2

0.1 0.2 0.28 0.36

0.1

6.W’ S” 2

2.10-= 3.10-Z 4.10-z 5.10~’

IO-*

66 67 66 68 67

WV)

-1

-2

0

0.1 0.15 0.20 0.30 0.35

t:r 1 7.10-a

2.10- 2 3.10-Z 4.10-’

66 68 67 66 67

z 68

70

OW

0

-1

(A$)(6*o~~~~,-,)E,c‘ *, (61,6,1ocp,l., G”4=)(A$) ),,*, Kzo4=)G&i)(6lo::“,“,b,JE,,,.,

pH 1.8-2.8

Table 4. Tafel slope and electrochemical

Electrochemical

kinetic study of the Fe’+-Fe*+

(4) predominates at oxalate concentrations lower than O.lM and (5) is favoured at oxalate concentrations greater than 0.1 hi. The electrochemical order with respect: to the proton concentration is 0, to the oxalate concentration - 1 (when oxalate concentration < O.lM) and 0 (concentration > O.lM). i = 2 when the oxalate concentration is less than O.lM and 3 when the concentration is greater than 0.1 M. Under the conditions in which (4) takes place, the mobile equilibrium would be:

Fe(C,W-

K, * Fe(C,O,);

+C,Os

i + leFe(C,O& and the intensity equation would be expressed by: -*FA4

i = Fk,. K4CFc(C,0,,; ~2;~;; exp ~

RT

which is in agreement with all the experimental data. Under those conditions where (5) takes place, the intensity equation would be: -aFA4

i = Fk,.Cr,(cIo,,;- exp ___

RT

system in oxalate medium

863

where the orders with respect to the oxalate and proton concentrations are 0. Acknowledgernear-This study was supported by the Comisiim Asesora de investigaci6n Cientifica y Tecnica, Madrid.

REFERENCES 1. V. Lbpez and M. J. Peti. An. Quim. to be published. 2. M. V. Stack&erg and H. V. Freyhold, Z. Elektruchrm. 46, I20 (1940). 3. V. F. Toropova, Zh. Obschei Khim. 11, 1211 (1941). 4. KolthofT and Lingane, J. Am. Gem. Sot. 2448 (1946). 5. W. B. Scbaap, H. A. Laltinem and J. C. Bailar, Jr., J. Am. Chem. Sot. 76, 5868 (1954). 6. A. K. Babko and L. 1. Dubovenko. Zh. Obschei Khim. 660 (1956). Ibid. 26, 996 (1956). 7. J. J. Lingane, Chem. Reu. 1, 29 (1941). 8. Matsuda and Ayabe, Z. Elektruchem. 63, 1164 (1959). 9. S. L. Bogans, L. Meites, E. Peters and J. M. Stertevant, J. Am. Chem. Sot. 73,411 (1951). 10. G. A. Gilbert and E. K. Rideal, ~WIS. for&y Sot. 47, 396 (1951). 11. J. Heyrovsky and J. M. Kuta, Principles ojPolarography, pp. 213, 222, Academic Press, Oxford (1966). 12. Adams, R. N.. Electrockemislry at Solid Electrodes, Marcel Dckker, New York (1969).