Evaluation of stability constants of complexes based on irreversible polarographic waves with variable electrode mechanism

J. Electroanal. Chem., 130 (1981) 123-140 Elsevier Sequoia S.A., Lausanne--Printed in The Netherlands

123

EVALUATION OF STABILITY CONSTANTS OF COMPLEXES BASED ON IRREVERSIBLE POLAROGRAPHIC WAVES WITH VARIABLE ELECTRODE MECHANISM PART I. THE Co 2+ -C2042- SYSTEM

JADWIGA URBAiqSKA and JAN BIERNAT

Institute of Chemistry, University of Wroclaw, Joliot Curie 14, 50-383 Wroclaw (Poland) (Received 10th June 1980; in revised form 22nd June 1981)

ABSTRACT

Reduction of Co(II) in the presence of oxalate ions was found to proceed with the contribution of two electrode reactions, i.e. the direct reduction of cobalt aquo-ion and the direct reduction of the COC204 complex. The electrode reaction rate constants k ° and k °, as well as the electron-transfer coefficients a 0 and a I have been determined. With oxalate ions, Co(II) was found to form the labile chelate complexes COC204, C0(C204)z2- and the less labile, binuclear C02(C204) 6- complex, producing kinetic waves. Stability constants of complexes under investigation were calculated from the shifts of potential, expressed by log tim =3,51, log fll.2 =6,38 and log f12,~= 18,40.

INTRODUCTION

Very few attempts to utilize the completely irreversible polarographic waves in the calculation of stability constants of labile complexes have been reported. Such a situation is caused by difficulties in the experiments and in interpretation of the data. The problem is relatively simple if the irreversible reduction of labile complexes proceeds through an aquo-ion. The relation and calculations are close to those at the reversible reactions. The measurements allow the calculation of the average ligand number (LN) of complexes. However, if more species are involved in the electrode reaction, the measurements yield only the value of the difference of the average LNs of complexes in a solution and those directly reduced on the electrode. Sometimes on the curves A E1/2 vs log[L] discontinuities appear (e.g. Verdier Piro [1]), and these have not yet been completely explained. Transition elements, known to give irreversible waves, usually form the .not quite labile complexes. In addition, some substances, considered as inactive, also have an influence on the electrode process. Moreover, it is difficult to obtain the half-wave potential of the labile, electrode-active complex. These obstacles are a limiting factor 0022-0728/81/0000-0000)$02.75 © 1981 Elsevier Sequoia S.A.

124

in the investigations. On the other hand, the possibility arises of investigating the effects on the electrode process. Recently, we have undertaken studies on complexes of metals which exhibit high overpotential and give aquo-ion waves, which greatly facilitates the resolution of the electrode mechanism and determination of the stability constants of complexes. EXPERIMENTAL

The measurements were made on a Radelkis OH-105 polarograph (Hungary). The dropping mercury electrode (DME) employed had a drop time t 1 of 3.5 s and a flow rate of mercury m of 2.36 mg s-1 when measured at open circuit and at a height of the mercury head of 0.45 m. The saturated calomel electrode (SCE) connected by the electrolytic bridge with the test solution was used as the reference electrode. The electrolytic bridge was filled with saturated sodium perchlorate. Argon gas was used for removing oxygen from a solution. Measurements were made at 20 ~ 0.1°C. A constant Co(II) ion concentration 1 × 10 -4 mol dm -3 was used. Oxalate ion concentration varied within the range 0.0001-0.1670 mol dm -3. Constant ionic strength, 0.5 mol dm -3 was maintained by adding sodium perchlorate. The measurements for determination of the average ligand number in solution were made by the Ringbom-Eriksson method, using Cu(II) ions of 1 × 10-4 mol dm -3 concentration as an indicator. R E S U L T S A N D DISCUSSION

For the solution of oxalate ions (concentration given in Table 1) only a single, irreversible polarographic wave was obtained. Initially, the waves were quite well shaped, but with increasing oxalate ion concentration they were less developed. The limiting current decreases stepwise with increasing concentration of oxalate ions to the value of 42.4%. Some selected polarographic waves of Co(II) oxalate complexes are given in Fig. 1. A logarithmic analysis for all the waves was performed and half-wave potentials as well as their slopes were determined. The values for the. subsequent concentrations are summarized in Table 1, The diagrams shown in Fig. 2 exhibit two groups of straight lines with different slopes (2.3 RT/anF), as well as an intermediate group of bent lines. One of the straight-line groups with the slope coefficient 0.105 V consists of the aquo-ion wave together with those corresponding to lowest oxalate concentrations ( < 0.0004 mol dm-3). Within the concentration range 0.0004-0.0015 mol dm -3 (intermediate group) the slope coefficient changed from 0.105 to 0.118 V. Above these concentrations the coefficient remains constant, as demonstrated by the second straight-line group. Earlier it was shown [2] that the slope of the plot A Ell 2 vs. log[L] for irreversible waves of complexes gives the difference of the average ligand numbers of the complexes in solution and those which are directly reduced at the electrode. In the case of cobalt oxalate complexes this value changes from zero to 1.38 (at highest

125 TABLE 1 Dependence of limiting current (/]), half-wave potential (El~2), the slope of logarithmic analysis (2.3 R TJanF) and log of complexation ( F 0) on ligand concentration No.

[CzO42-]t/mol d m 3

[] × 108/A

-E,/z/V

(2.3RT/anF)/V

log Fo

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

-0.0001 0.0002 0.0004 0.0006 0.0010 0.0015 0.0020 0.0025 0.0030 0.0040 0.0050 0.0060 0.0070 0.0080 0.0100 0.0200 0.0400 0.0600 0.1000 0.1670

79.2 80.8 78.4 76.8 74.8 74.4 73.2 68.8 68.8 68.4 64.4 66.4 65.6 61.6 67.6 60.8 59.6 52.4 50.4 42.4 33.6

1.283 1.289 1.298 1.314 1.325 1.343 1.357 1.371 1.385 1.391 1.407 1.421 1.431 1.443 1.453 1.470 1.514 1.561 1.589 1.621 1.663

0.105 0.105 0.105 0.107 0.108 0.110 0.118 0.118 0.118 0.118 0.118 0.118 " 0. I 18 0.118 0.118 0.118 0.118 0.118 0.118 0.118 0.118

-0.0484 0.1472 0.2952 0.3998 0.5628 0.6613 0.8069 0.9255 0.9788 1.1408 1.2460 1.3360 1.4650 1.5010 1.6910 2.0811 2.5353 2.7895 3.1357 3.5927

I/,A

'.~ 1t

16

~ 2 1 ,18

0.5

0.0

1.0

1.2 I

1.4. o

1.6 I

111 I

E/V

ZO

Fig. 1. Polarographic waves of Co(II)-oxalate complexes. N u m b e r s of waves correspond to position in Table 1.

126

ua

0

0

0

z

I

o ! o

e~

e~ 0

r"

127 oxalate concentration)(Fig. 3). The last value, corrected for decrease of the limiting currents (log(il/id)), increases to 1.5. Assuming that the reduction proceeds through the aquo-ion, the highest ligand number of the complexes in solution is also calculated to be 1.5. If the reduction proceeds through the complex COC204, the average LN of complexes in solution should be 2.5. The fractional value of the ligand number can be due to the mixture of complexes with different ligand numbers (e.g. 2 and 3) or to the dimeric form of the single complex [e.g. dominating

Co2(C2O,)56-]. Agreement of the wave slope for reduction of the free Co(II) ion in perchlorate solution with that of reduction of Co(II) oxalate complexes at low oxalate ion concentration (the first group of lines) indicates the common character of the electrode reaction, i.e. reduction by the metal aquo-ion [3,4]. Following the BrOnsted theory, the perchlorate ion is a very weak base, weaker than water; for this reason perchlorate Co(II) complexes cannot exist in aqueous solutions of perchlorates. The highest value found for the difference of average ligand numbers is too low, since at the strong chelate complexation it should be close to 3 for an octahedral complex or close to 2 for tetrahedral and square planar complexes (if the aquo-ion were reduced). The change of the wave slope (2.3 RT/anF) indicates a change of the process mechanism, first of all the change of a species being directly reduced at the electrode and with the assumption that the complex with ligand number 1 (i.e. COC204) is reduced at the oxalate ion concentration range over 0.0015 mol dm -3. At the difference of average ligand value 1.5 and with the assumption that the complex with

-0.400

T

0.300- ~

0.200-

0.100-

o-

Log [C202-] ' ~ I

i

I

I

- &-.O

- 3.0

- 2.0

- 1.0

Fig. 3. Dependence of the shift of half-wave potentials AEI/2 o n log[C202 ]: (©) calculated; (O) experimental.

128 ligand number 1 (i.e. COC204) is reduced directly at the oxalate ion concentration range over 0.0015 mol dm -3, the complex of 2.5 LN should predominate in the solution. The oxalate ion is a bidentate ligand, for this reason the Co(II) coordination number should be 5. Such a coordination number is found in some Co(II) complexes [5-8]. Thus, in Co(II) oxalate solution, besides the mononuclear COC204, Co(C204)22- complexes, there also exists the binuclear C02(C204) 6- complex. Approximate stability constant values fl~,l and ill.2 for mononuclear complexes were determined from the diagram of overall complexation function log F 0 vs. log[C2042- ], by the graphical method reported by Yatsimirskii [9], for average ligand numbers 0.5 and 1.0 [10]. However, this method does not apply for the determination of the fl2.s stability constant of the binuclear complex. The occurrence of the binuclear oxalate Co(II) complex has not been reported in the literature. In the binuclear complexes the average ligand number is dependent upon the total metal concentration (i.e. upon the free metal ion concentration), while for mononuclear complexes, that value is concentration independent. For the system investigated the average ligand number will be described by the expression: H=

ill., [L] + 2fl,.2 [L] 2 q- 5fl2.5 [M] [L] 5

(1)

1 + ill., [L] +/~1.2 ILl 2 + 2fl2.5 [M] [L] 5 The value of ill. J for the COC204 complex, determined from the diagram of log F 0 vs. log[C2 O2- ] is quite precise, since the contribution of the COC204 species to the electrode reaction is rather small, owing to its lower rate constant of electrode reaction; in the determination of ill.2 the concentration of COC204 involved in the reaction is higher. The polarographic wave equation for the totally irreversible reduction of complexes was given by ref. 3, if only the mononuclear complexes are formed in a solution:

/q rev _ _

--O.886 d/2 __

4 - '~....

~/2

Ek°/ o

j[LlJexp

----g-r--(E--

)

(2)

~ flJ [L] j o

where fi.... is the average current of irreversible reduction, fa the average limiting diffusion current,/~c the average diffusion coefficient of complexes expressed as n

E Djflj [L] j

o

(3)

~ flj[L] j 0 t 1 the drop time and k ° the electrode reaction rate constant at potential E °. In the case of electrode reduction through two species, i.e. through the free metal ion and through the complex ML (indicated by two different wave slopes) the equation will

129

be written:

aonF l:irrev /Td - - i i ....

o

+

tl/2

0.886

1

D; /

t~

E / 3 j [L] j o

k 1°/31.,[Llexp ( --~--(Ea'nF _EO) } +

.

(4)

E/3j[L] j o

For the calculation of the stability constants of the particular complexes, the value of free metal ion concentration and the electrode reaction rate constants k ° and k ° for the species reduced directly at the electrode are required. The total metal ion concentration in solution, whether or not they were complexed, will be expressed by the equation: [M] t = [M] + [ML] + [ML2] + 2[MaLs]

(5)

Concentration of particular complexes results from the complexation equilibria, hence the total metal ion concentration [M]t will be [M]t = [M] +/3,.,[M][L] +/3,.2[M][L] 2 + 2/32.5[M]Z[L]5

(6)

From eqn. (6), the free metal ion concentration can be calculated if the stability constant for particular complexes are known. Resolution of the quadratic equation (eqn. 6) gives the required value of the metal ion concentration expressed as [M] =

- ( 1 +/3i'l[Ll +/3, 2[L] 2) ~,/31.5[L] 5

•

(7)

4/325[L] 5 The unknown-value fla.5 was estimated roughly and introduced into eqn. (7), togethe r with other data. The reduction rate depends not only on the concentration of the electrode reacting species (q) but also upon the rate constant of their electrode reaction (kj): vj = kjcj

(8)

Next, the electrode reaction rate constant depends upon the applied potential E, according to the relation: kj = k°exp { - - ( a j n F / R T ) ( E -

E°)}

(9)

130

where k ° is the electrode reaction rate constant at the reference potential E °. After consideration of the potential dependence of the electrode reaction rate constant (eqn. 9), the electrode reaction rate will be vj = k°cjexp ( - ( ajnF/RT)( E - E °) )

(10)

In our case the initially predominant electrode reaction mechanism slowly transforms into another mechanism (Fig. 4). That fact depends upon the ligand concentration. Hence, at a given ligand concentration, [Lz], the rate of electrode

0.500

E~/2/V

/

0.400

/

/

/

//

~300

a2oo

0.100"

I

-4.0

,

I,

I

-3.0

-2.0

~'

- -

-t0

Fig. 4. Possible changes of the half-wave potentials, if the reduction of complexes proceeded: (×) by aquo-ion only; (C)) by COC204 complex only; (O) by total reduction by both electroactive forms (aquo-ion and COC204 complex).

131 reduction of complexes by the aquo-ion is equal to the reduction rate of complexes by the ML complex: v0 = v I

(11)

Consideration of eqn. (10) will give:

k°coexp(--(aonF/RT)(Ez-E°))=k°Clexp(-(a~nF/RT)(~-E°))

(12)

where: ko° is the electrode reduction rate constant of complexes at the reference potential E ° = - 1.283 V, k ° the electrode reduction rate constant of complexes by the ML complex at the reference potential E °, %, a| the electron-transfer coefficients in the reaction through the free ion and the ML complex respectively, %, c~ the concentration of the electroactive forms expressed by [M] _ 1 c° = [M]t 1 + fl,.,[L l + fll.2[Ll2 + 2fl2.s[M][L] 5

Cl =

[MLz] fl,.l[Lz] [M], = 1 + B,.,[L] + B,.2[t] 2 + 2B2.5[Ml[L] 5

(13)

(14)

and [Lz] the ligand concentration, where

(15)

~=~(,~o +,~,) After consideration of eqns. (13) and (14), eqn. (12) will be written: kO exp( -

--R-T -~Eza°nF" _ E O ) } = kOfl,.l [Lz ] exp { - --R-T ~Ez°qnF" _ E°)]l

(16i

Hence, the electrode reduction rate constant of complexes by ML complex (k °) is k° ~°- ~,~z] -

a,nF (e~_ EO)) --~-tez- .e°)+--~

exp{-a°nF"

(17)

Thus, the polarographic wave equation for the totally irreversible reduction of complexes (eqn. 4), considering the relation for k 0 given by eqn. (17), will be

zi. . . . .

/:-d -- ii ....

0.886

k °-tl/2

exp -

R---T

0 ~clc/2 [ 1 -~- ~|.1 [t] + ~1.2 [g] 2 nt- 2~2.5 [M] [g] 5

[g] exp { - - -°/1/if [Lz] - - R - ~ ( E - E ° ) } exp(

---(Ez °t°nFeT -E°) -I-aT-{Ez °llnfl --E°)}

1 +/3,., [L] + t3,.2 [L] 2 + 2/32.5[M] [L] 5

(18)

132

,q o~

o

I

]

I

I I I I

I

I

I

I~1

I

0

c~8

O~

I~-

o~

0 o£

~

t

~o~

~

ooo

o

I

6.

~

~

~

~ ~

_.~

0

o

d

odd~--

0

I

0

0

~ Q

o~

~.~

I d

133

This equation could be simplified by introduction of the notation:

{ a[°enzF- E( e°z)-RE-°- )- +- -~T -alnF"

}

B = ~[L] exp -

(19)

Hence, from eqn. (18):

[

r /11/2 ] exp li .... = 0.886 k ° / /:-d --l:'i .... ~c/2 [

(-- a°nF " - - E ° ) } + B exp ( - ~alnF RT (E (E--

Eo)}

1 + ~l.1 [L] + fl, .2 [L] 2 + 2fl2.5 [M] [L] 5

(20) The k ° value could be calculated from the irreversible wave equation for the reduction of the free metal metal ion:

-

qrrev ld __ /Tirrev

=0.866k °

_t~/2 _

[ _ ~aonF" (E--E

exp[

o-)J~

(21)

O 1/2

At the half-wave potential:

k o -_ 1/0.886(t~/2/D2/2)

(22)

Hence, the irreversible wave equation for the reduction of complexes, considering the change of electrode process mechanism, will be as follows:

7

7

t d -- ti=~v

(23) 1 + fiLl[L] + fli.2[L] 2 + 2f12.5[Ml[L] s

assuming that Dc = Ds, in which [M] is the free metal ion concentration described by eqn. (7). The above expressions were applied to the calculations using as [Lz] the value 0.00125 mol dm -3. The approximate values of stability constants were made precise by the calculation of the free metal ion concentration from eqn. (7). Then, its concentration and stability constants were put into eqn. (23) and the increase of the half-wave potential against the aquo-ion AE~/2 was recalculated. Very good agreement between the calculated and experimentally found AE1/~ values was obtained. The course of the electrode reaction in dependence on ligand concentration following the above-mentioned mechanism is plotted in Fig. 4. Stability conslants for Co(II) oxalate complexes determined by that method are: log fill = 3.51, log/~1.2 = 6.38, log J~2.5 = 18.40. Stability constants reported by other authors, using other methods, are summarized in Table 2. The values of/31A, determined by all methods at low ionic strength (0.1-0.2) or at ionic strength extrapolated to zero, exceed the value determined by us. The value of ill.2 was almost identical, but decreased somewhat with increase of the ionic

134

strength. No data concerning the existence of Co(II) binuclear oxalate complex of the formula Co2(C204) 6- have been found in the literature. The log f13 values given by two authors [18,26] are 8.13 and 9.7. They are in satisfactory agreement with our result (log fl2.5 -- 18.40) if the free metal ion concentration is taken into account. Such a model of the electrode reduction of complexes is in good agreement with the experimental data. Let us now examine the plot of the AE1/2 vs. log[C20~- ] (Fig. 3). Over the oxalate ion concentration range 0.0002-0.0020 mol dm -3, some discrepancy between the calculated and experimental values of AE~/2is observed. Experimental values somewhat exceed the calculated ones (by 2-3 mV). This could indicate some adsorption of the electroactive form on a surface of a DME. The problem of the reactant adsorption does not concern the Co(II) aquo-ion adsorption, since the phenomenon of adsorption of such cations on a mercury electrode has rarely been observed. Comparison of that phenomenon with the

t

blzLs//,

11.5¸

(10

~

.

t

-4~)

.

.

.

.

.

I

-.3.0

.

.

.

"+

* *"~'-

!

- 2J]

*

~

-

I

~1.0

Fig. 5. Distribution of complex species as a function of ]iga_qd concentration in the Co(]I)-oxalate system.

135

distribution of Co(II) over the different complex forms dependent on oxalate ion concentration (Fig. 5) reveals that the discrepancy corresponds to the maximal concentration of the complex COC204. Drop time curves taken for solutions of composition corresponding to the appropriate concentrations (Fig. 6) exhibit the essential decay of the surface tension, compared to that observed in the absence of the CoCzO4 complex. Adsorption of the electroactive form is responsible not only for the shift of the waves towards more negative potentials but also has some influence on the shape of the observed polarographic waves [27,28]. We have also performed studies on the determination of the average LN of oxalate Co(II) complexes, using the Ringbom-Eriksson method [29]. The Cu(II) ion, which undergoes the reversible reduction and forms the complexes of stability constants log fl] --5.8 and log fiE = 8.08, was used as indicator. Here, log fll and log fiE were previously determined polarographically by the De Ford- Hume method in 0.5 tool NaCIO 4 solution at 20°C. On the basis of the Cu(II) half-wave potential shifts in the presence and in the

~1/$

3.5

3.0

2.5

2.0

• E/¥ I

I

I

O~

1.0

1.5

Fig. 6. Electrocapillary curves in solution of 0.0001 mo] Co 2+ in 0.5 mol NaC104. Oxalate ion concentration: (O) 0; ( × ) 0.0004; (O) 0.0010 mol. (For pure 0.5 tool N aC104 the curve is identical to that Co2+ in 0.5 mol NaC104. )

136

absence of Co(II) ions (Fig. 7), we have calculated the free ligand concentration at the electrode surface from the formula:

A E,/2 = - R T / n F l n ( 1

+/3,[L]

+/32[L] 2)

(24)

where AE1/2 is the difference in half-wave potential in the presence and in the absence of ligand. The average LN per Co(II) ion at the electrode surface was calculated from the formula:

[L]t- [L] ~co =

~CuCC~ 2

(25)

¢Co

where [L]t is the total oxalate ligand concentration in a solution, [L] the free oxalate concentration at the electrode surface, ffcu the average LN bound by one Cu(II) ion, Ccu the total copper ion concentration and Cco the total cobalt ion concentration. Values of the average LN calculated~ for Co(II) ions dependent on free oxalate concentration are summarized in Table 3. These values are precisely the same as those previously obtained from the shifts of half-wave potentials for the irreversible reduction of Co(II)-oxalate complexes (Fig. 8). As mentioned above, the increase in oxalate ion concentration is accompanied by decay of the limiting current of particular waves. At a concentration of 0.167 mol

i /v E1/z

0.150

0.1¢0

0.130-

0.120"

0.110"

0.100"

=~ 1 0 3 c t / m o l dm -3 O

I 5

I 10

Fig. 7. Plot AE1/2for the Cu(II)-oxalate system in the absence (O) and the presence (0) of 0.0030 mol Co 2+, by the Ringbom-Eriksson method [Cu(II) concentration= 1 × 10 -4 mol, 0.5 mol NaC104 as supporting electrolyte].

137 TABLE3 The dependence of average ligand number on oxalate ion concentration found by the Ringbom-Eriksson method

[CzO42-]t/mol

dm -3

0.005 0.006 0.007 0.008 0.010

logiC2 O2 ] / m o l dm 3

ffco

- 2.96 - 2.81 - 2.67 - 2.55 -2.36

1.27 1.45 1.59 1.70 1.85

dm -3 its value was only 42.4% of the limiting current for reduction of free metal ion. In the solution there exists an equilibrium of the electroactive complexes and the complexes which do not undergo direct reduction on the electrode. If all equilibria in the solution were labile (considering the drop time), the current value would be determined by diffusion of complexes to the electrode only. Decrease of the limiting current indicates the concentration decay of the active form at the electrode surface. Two effects may be the cause here: (1) diffusion rate decrease of depolarizer to the electrode surface, because of the shifts of equilibrium in a solution towards the higher complexes of the lower diffusion coefficients; (2) incomplete dissociation of the electro-nonactive species into the electroactive species.

3.0

2.0

1.0

;

I

I

I

-68

-].0

-1.0

-1.0

Fig. 8. Formation curves

of

the Co(II)-oxalate system.

138

The dependence of the limiting current on the height of a mercury column, found experimentally, is of intermediate character at high ligand concentrations. This indicates that the limiting current is the mixed, diffusion-kinetic current. The composition of the form of dissociation which would determine the electrode process was found from diagram l o g ( i k / i d - i k ) vs. log[C2042- ] (Fig. 9) from the relation [30]: O 1 o g ( i k / i d -- ik)

Olog[C2042- ]

=k-N-0.5

(26)

where k is the LN of complex subjected to the reduction in kinetic waves, and N the LN of complex with the highest coordination number. Since the left-hand term of this equation amounts to -0.63, then k is 2.37 (this value is very close to maximal LN 2.5 found previously). Thus, the equilibrium state between the binuclear Co2(C204) 6- complex and the mononuclear complexes in a solution is slowly established. The observed decay of the limiting current with increase of ligand concentration is due not only to the kinetic effect caused by the slow dissociation of the binuclear complex Co2(C204) 6- but also to the diffusion effect resulting from the slower diffusion of the large and very elongated complex molecule. It was impossible to specify dearly the contribution of each of those effects. The pure kinetic currents are normally much weaker with respect to the diffusion current and independent of the height of the mercury column. In our case the lowering of the limiting current exceeds that of the diffusion current of Co(II) aquo-ion by only 50%. This is probably due to the quite considerable change of the diffusion coefficient because of the formation of the binuclear complex (diffusion effect), and because of the only partial dissociation of that complex into the electroactive species (kinetic current). Because of the kinetic effect, the half-wave potential was corrected in the present

.1 i

ik

0'

-3.0

!

-2.0

I

-1.0

Fig. 9. Dependence of the l o g ( i k / i d - - i k )

on

log[C2042- ]; (O) calculated and (Q) experimental.

139

paper by the same formula as for the diffusion effect (AE1/2 = 1ogid/il) , which would be entirely correct with the condition that the dissociation and formation of the binuclear (kinetic) complex C02(C204) 6- are the first-order reactions (MLj =

MLj_ + L). The stoichiometric reaction of the formation of the binuclear complex C02(C204) 6- is the trimolecular reaction: 2C0(C204) ~- + C2O2- ~:~ C02(C204)65which would be rather indicative of the reaction order > 1. Such a reaction with simultaneous collision of three molecules is improbable and normally consists of simple steps, i.e. C0(C204) ~- + C202- ~=~C0(C204) ~-

(slow, rate-determining)

C0(C204) ~- + C0(C204) ~- ~:~ C02(C204) ~-

(fast)

(I) (IX)

which seems to be the most probable path. The first step is a second-order reaction, but with the excess of ligand becomes first order. The following reaction (II) does not change the total order if its rate is not lower than that of the first. If the second reaction were slower than the first one, the accumulation of the species C0(C204) 4- could be detected, e.g. by increase of the ligand number over 2.5, which is contradictory with the ligand number found. The rectilinearity of logarithmic analysis represented in Fig. 2 (1-19) shows the symmetric form of waves obtained which confirms the first-order dependence. The effects which would contradict the assumption about the first order of the formation reaction of a binuclear complex have not been established experimentally. However, assumption of such a mechanism may contain some simplifications, because it was based upon the theory of quasi-stationary states. In our opinion, the solution of the kinetic problem of a binuclear complex may be entirely correct or, even in the case of somewhat wrong determination of the influence of the kinetic effect, the error in calculation of the stability constants of complexes (and that is the most important for us) would not greatly exceed the accuracy observed in polarographic studies (A log F0 would be < 0.3 because of the correct improvement of the diffusion effect). The contribution of the diffusion effect in the overall limiting current cannot be determined, since the diffusion coefficients of particular complexes are unknown. Consequently, this makes the calculation of the dissociation rate constant of the complex C02(C204) 6- difficult. The total reduction mechanism of Co(II)-oxalate complexes may be described by the scheme: fast fast 2 slow 6 Co 2+ ~ COC204 ~ C0(C204) 2 - ~ C02(C204) 5ao,k °

~, a,,k °

Co(Hg) Co(Hg)

(27)

140

In the system examined the change of electrode mechanism (direct reduction of aquo-ion transforms to reduction of COC204 complex) occurs although the reduction rate constant of aquo-ion exceeds the electrode reaction rate constant k ° of the complex (k ° = 3.40 k ° at a potential of - 1.283 V vs. SCE as reference potential). In our case the electron-transfer coefficient a I is also lower for a complex than for an aquo-ion (2.3RT/aonF----0.105 V, 2.3RT/alnF= 0.118 V). Both these factors prevent the change in the electrode process mechanism. However, this change occurs because of the predominating influence of concentration changes of the electroactive forms. The relation between the COC204 complex concentration and that of a free ion was found to be fl~ L. Predominance of the complex concentration increases with increase of the ligand concentration. ACKNOWLEDGEMENT

This work was performed within the framework of the MR.I.11 plan. REFERENCES 1 2 3 4 5 6

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