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Kinetic effects in the polarographic behaviour of Co(II) chloride complexes in acetonitrile
.I. inorg,nucl. Chem.. 197I, Vol. 33. pp. 503 to 514. PergamonPress. Printed in Great Britain
KINETIC BEHAV1OUR
EFFECTS IN THE POLAROGRAPH1C OF Co(ll) CHLORIDE COMPLEXES ACETONITRILE L U 1 S A S E S T I L ! and C L A U D I O
IN
FURLANI
Instituto di C h i m i c a G e n e r a l e ed Inorganica delFUniversith, 06100 Perugia, Italy (Received 8 M a y 1970)
Abstract-Polarographic reduction of pseudotetrahedral cobalt(ll)-halide c o m p l e x e s in acetonitrile occurs in several alternative w a v e s assigned to successive complex species [COL6] ~+ and [CoL,,X~_,,] ~-" (L = acetonitrile). Kinetic currents due to fast dissociation of the C o ( l l ) - h a l i d e (particularly chloride) complex species has been o b s e r v e d in solutions at various degrees of complex formation. Rate constants ['or the dissociation: [COX4] = ~
[CoLX:~] + X-
(X = CI-, Br-), and: [CoL.,X~] ~
[COL,] ~+ + 2X .
(X- = CI-) were evaluated from polarographic m e a s u r e m e n t s in the temperature range 2 5 - 4 5 ° C by m e a n s of the model of the reaction layer. Evidence is presented for competition of different reaction m e c h a n i s m s , possibly involving dissociation stages.
INTRODUCTION THE INCREASINGLY wide use of acetonitrile as a convenient polarographic solvent
[1-4], and the recent availability of the constants of the equilibria between the complex species [CoL6] 2+, [CoL2X.~], [CoLX:~]- and [COX4] -z (X = CI, Br) in acetonitrile[5], prompted us to an investigation of the polarographic behaviour of the complex systems C o ( I I ) - X - in that solvent. We have obtained evidence for separate reduction steps corresponding to discharge of all successive complexes at the D.M.E. As the same time the relative intensity of the steps of the more halogenated species turned to be systematically somewhat lower than corresponding to the equilibrium distribution curves of the species, the steps becoming partially kinetic in character. This was a clear indication of fast dissociation rate, respectively slow formation of the halogenated species, and we attempted a preliminary evaluation of the corresponding rate constants. Although the model employed for the treatment of chemical dissociation occurring in the reaction I. 1. N e l s o n and R. l w a m o t o , J. electroanal. Chem. 6 , 2 3 4 (1963). 2. 1. M. Kolthoff and F. G. T h o m a s , J. electrochem. Soc. 11 I, 1065 (1964). 3. C. Furlani, L. Sestili, A. C i a n a and F. G a r b a s s i , Electrochim. Acta 12, 1393 (1967): L. Sestili, C. Furland, A. Ciana and F. Garbassi, Electrochim. ,4 cta 15,225 (1970). 4. V. G u t m a n n and F. Mairinger, Mh. Chem. 8 9 , 7 2 4 (1958). 5. L. Sestili and C. Furlani, J. inorg, nucl. C h e m . 32, 1997 (1970). 503
504
L. SEST1LI and C. FURLAN1
layer is a rather crude one, we feel that the present kinetic study can be of some interest, in view of the rather scarce knowledge of the kinetics of tetrahedral complexes. EXPERIMENTAL Preparation of the complexes, treatment of solvents, composition of solution, and conditions of temperature and ionic strength control were the same as in our previous work on spectrophotometric determination of stability constants of Co(II)/X- in acetonitrile[5]. Polarographic measurements were performed at three controlled temperatures in the range 25-45°C with an Ame1462 polarograph, in three-electrode cells. The employed D.M.E. had m213t'/~ = 1.52 mg2~3sec -j/2, in acetonitrile with 0.1 M supporting electrolyte (C2H5)4 NCIO4 at 25°C and open circuit. Reference electrode Ag/0.01 M AgNO3 in acetonitrile[6]. RESULTS
Figures 1 and 2 show how the shape of the polarograms varies with the ratio x
= [X-]tot/[Co(IJ)]tot(X--
Y
CI, Br) in acetonitrile. It is to be noted that the depen-
b
d
J
J 1
2~A
0-8 V
Fig. 1. Polarograms of AN solutions containing Co(ll)-chloride complexes at various [Cl]tot/[Co2+]tot ratios. 25.0__+0.1°C; /z = 0.1 (TEACIO4); [Co~+]tot= 1.1. 10-3M; other conditions as specified in text. (a) [C1-]tot = 0; (b) 1-50.10-aM; (c) 3"00. 10-3M; (d) 3"50.10-3M; (e) 4.50./0-aM; (f) 22-00.10-aM. 6. W. Forsling, H. Hietanen and L. Sillen, A c t a chem. scand. 6, 901 (1952).
Co(l 1) chloride complexes in acetonitrile
/
505
/
c
/
o e ,,
/
f
/ f
i2p. A O,2V 0.8V
Fig, 2. Polarograms of AN solutions containing CoO D-bromide complexes at various [Br-]tot/[Co2+]tot ratios. 25.0°_+0-1°C; tz = 0.1 (TEAC10,); [Co~+]u,t = I-0.10-:~M; other conditions as specified in text. (a) [Br-]tot = 0; (b) 0.97.10-3M; (c) 2.00. 10-3M: (d) 4-00.10-3M: (e) 10.00.10-3M; (f) 80.00. 10-:~M.
dence of wave heights on x varies to some extent with temperature; critical values of x quoted below are an average o v e r the e m p l o y e d t e m p e r a t u r e range. At x = 0 there is a single rather sharp two-electron-step with E,/~ = - 0 . 9 5 V vs. Ag/0.01 M AgNO3. With increasing x, the intensity of limiting current of the first wave decreases and eventually disappears around x >~ 3.0 with CI, and 3.5 with Br, while two more negative waves appear. T h e height of the first wave is always larger than corresponding to the equilibrium distribution of [COL,] 2+, and contains therefore a substantial kinetic contribution. T h e second and the third w a v e a p p e a r evidently at x >~ 0.4, with E~,, = -- 1.63 respectively - - 2 - 0 5 V for C1, and - - 1 . 4 5 V , r e s p e c t i v e l y - - 1 - 7 5 V for Br. T h e second w a v e increases in height until x - 3-0 for the chloro system, then decreases rapidly and disappears for x > 4; in the b r o m o s y s t e m the variation with x is similar but slower, the m a x i m u m height being ri~ached in the x range 4 - 6 and a
506
L. SESTILI and C. F U R L A N I
small residual height lasting till x - 60. Comparison of the trend of intensity of the second wave with equilibrium percent of [CoL2X2] shows a rough parallelism, except for the shift of the maximum to higher x, with negative kinetic contribution for x lower than maximum, and positive kinetic contribution at higher x values. For the third wave, ia increases or remains approximately constant until x - 30 for CI, and - 8 0 for Br, then decreases slightly; it does however not disappear at higher x, except in the most concentrated chloride solutions. Comparison with the distribution curves of [CoLX3]- shows systematically a strong positive kinetic contribution to ia(lll) in the high x range; kinetic contributions tend to be negative at lower x, when the second wave exhibits a positive kinetic contribution. At still higher values of x (3.6 for C1, 7 for Br), a fourth wave appears (E1/2 = --2.35 V for C1, or -2.20 V for Br), whose height increases steadily with x but does never reach completion except in the presence of high excess of chloride (at least 200 fold). Its height is in any case, except at the highest C1 concentrations, lower than the equilibrium percent of [CoXj 2-, that is kinetic contributions are negative. In the extreme case where it remains alone, the fourth wave is purely diffusive in character. A general comparison of behaviour of the chloro and bromo systems confirms qualitative similarity, but changes in the Br system occur at higher x values, in agreement with the lower stability of the bromocomplexes[5] and the range of existence of wave II is much larger with Br (at expenses of wave Ili). The effect of temperature results in slight quantitative changes of the ratios of wave heights, particularly for the lowest x values; such changes are in qualitative agreement with the known variation of the equilibrium constants with temperature[5], although also kinetic effect are undoubtedly of importance. General consideration of the system of successive waves, and comparison with distribution curves calculated from equilibrium constants suggest that the four waves are due, in order, to reduction of [COL6]2÷, [CoL2X2], [CoLX3]and [COX4]2-. This assignment can be directly proved for wave 1, since its height and position coincide with those of Co(CIO4)2 in AN (reducible species [CoLG]Z÷), and for wave IV, since solutions containing very high excess of CI- (x - 180) show wave IV alone, with purely diffusive character; since [COC14]2- is then the only species present in solution, it is likely that it is also the species being discharged, unless improbably rapid dissociation occur. Assignment of wave II to [CoX2L2] and of wave II1 to [CoLX3]- is only indirect and based mainly on the gross parallelism between distribution curves calculated from equilibrium constants and from polarographic limiting curves as shown particularly in Fig. 3 ; distribution curves from polarographic data were calculated assuming an average diffusion coefficient in the llkovic equation. Of course, full parallelism could be expected only if interconversion rates between different complex species were extremely low or at least negligible with respect to the rate-determining step of the electrode reactions (diffusion for wave I which is not far from reversibility, electron transfer for subsequent waves). Such an assumption can therefore be considered only as a preliminary approximation, particularly in view of the expected lability of tetrahedral complexes. Indeed, as we have already noted, there are some considerable differences in the two types of distribution curves, which show increase of the wave height above the equilibrium values for waves I
507
Co(l 1) chloride complexes in acetonitrile
/ Ivz_._ '
,oo
! i
50
q .,"
\.~Q
/,
. . . .
i
!'
\,% ........
2
,'o --< ' [ct-],o , /[co
30
q,
Fig. 3. Distribution curves for C o ( l l l ) - c h l o r i d e complexes in AN 35.0°+0.1°C: ~ = 0-1 (TEAC100. ( - - ) from equilibrium constants: (----) from polarographic limiting currents.
and I 1I, the latter only for x >~ 3-5 with CI or x >F 8 with Br, while a more complicated behaviour, with alternance of positive and negative kinetic contributions, is shown by wave I1, and wave IV is systematically lower than equilibrium concentration (see Figs. 3 and 4). Such deviations clearly point to rapid dissociation of [CoX2L,,] to [COL6]2+, respectively of [COX4]"- to [ C o L X J - . Of course it would not be realistic to assume that the opposite reactions are infinitely slow, rather data simply indicate that dissociation of these two species are considerably faster than their formation; there are also indications that [CoL2X2] might undergo at low x (x ~< 2) rapid association to [CoLXJ-, while the reverse reaction (rapid dissociation of [CoLX:c] to [CoL2X2]) is predominant from x - 2-5 till disappearance of wave I1, and is particularly evident in the Br system. It appears therefore that the simplest transformation scheme is that involving species [ C o L X J - and [COX4]2- in waves Ill and IV, and it is on this part of the system that we felt it reasonable to attempt an approximate kinetic treatment on the base V
.
.
.
.
.
.
.
]
IOO
~,,.,
.f,l}v .......
', \ \
" ..~/;-"
,/ j/.. . . . . . . . . . . . . . . . . .
Ill
Jl
_ _°
i
--~
.... L ....................
\
60
[8,~,0,/[Co'+],o, Fig. 4. Distribution curves for Co(l~)-bromide complexes in AN 35.0°+_0.1°C: tz = 0-1 (TEACIO4). ( - - ) from equilibrium constants: (.... ) from polarographic limiting currents.
¸
~00
508
L. SESTILI and C. FURLAN1
of the model of the reaction layer, which is appropriate for treatment of rapid kinetic processes perturbing a fundamentally non-interconvertible system, as we shall report in more detail below. An opposite point of view would be the assumption of complexation equilibria rapid in comparison with the rate of electrode processes, in which alternance of successive waves corresponds to progressive variation of ao resulting from diffusion of equilibrium species in the electrode region, as has been applied, e.g. by Koryta et al.[7] for essentially reversible polarographic processes, e.g. cadmium cyanide and similar systems. According to this treatment, the dependence of the limiting current on the concentration of the free ligand at the electrode surface [X]o is given by [7]:
1 IDz\aJ~
1+a o
X-lo-
(1)
In (1) the index o refers to quantities at the electrode surface, and symbols without the same index refer to equilibrium values in the bulk of the solution; Ta represents the total diffusion current for the sum of all metal species. The shape of the current-voltage curve for reversible processes is given by [6]:
RTga_--~. E = Eve+ n F
t
(2)
4
1 "~ E k l ' ' " kj[X-]o j j=l
where
[MXJ kj = [ M X j _ I ] [ X ] "
Formulas (1) and (2), when applied to our systems with the known values of complexation constants in acetonitrile[5], yield in the calculated c.v. curves a succession of four waves, whose distribution path is again in rough correspondance with the experimental polarographic distribution curves of Figs. 3 and 4, except for potential values being obviously much less negative than the experimental ones, and for ia(IV) turning systematically somewhat larger than experimental. The latter circumstance is again a qualitative indication that formation of [COX4]z- is significantly slower than its dissociation to [CoLX,]-, again in qualitative agreement with the trend suggested by the other extreme point of view (Figs. 5 and 6). In an attempt to bring the calculated curve in better agreement with the experimental potential values, we have considered the effect of slow electron transfer by superimposing a transfer overvoltage according to the relations [8]. ~a=~
(1--r)+(l+r)tanh-
~b(H)
(3)
7. J. Koryta, Z. Elektrochem. 61, 423 (1957); N. Tanaka, R. Tamamushi and M. Kodama, Z. phys. Chem. 14, 141 (1958). 8. G. W. C. Milner, The Principles andApplications ofPolarography p. 47. Longmans (1957).
Co(I !) chloride c o m p l e x e s in acetonitrile
509
I0
1 ....£ . . . . . . . . . . . . .
f
06
02
I -I.00
I
I
-150
-200
Fig. 5. C.V. c u r v e s for C o ( l l ) - c h l o r i d e c o m p l e x e s in A N [Co~+]tot = [CI ]tol = 1.1. 10-3M; t = 35.0°±0-1°C. (----) experimental polarographic curves: ( . . . . . ) calculated c.v. curves according Ref. [7]; ( ) calculated c.v. curves according Ref. [8]. (KD-~/2tlJ~ = 5"10 7).
.t
I°i •
/
I .~"~ 0 6
t~
02
i..,,, I 30
[cL-],o,/[co~1,o, Fig. 6. Distribution curves of alternating w a v e s in the C o ( i l ) - c h l o r i d e s y s t e m s in A N as calculated according to Refs. [7, 8]. t = 35.0 ± 0- I°C: p. = 0.1 ( T E A C 1 0 0 .
510
L. SESTILI and C. F U R L A N I
(4)
(KD-1/2t 1/~) e (1/2 - ")~. 2 cos h --
H =
where: v= V--Vo
nF fl=RT
assuming r = td°n = 1, (4) takes the form: Idcat
L=_l[1 ,a
(5)
2[
We took tentative values of ( K D - ' Z t 1/2) in order to calculate H, taking for oS(H) the values tabulated in [8]: a was given the value 0.5 as a first approximation. C.v. curves thus obtained take now a form a little more resembling that of the actual experimental curves (Fig. 5), but can never be brought to a satisfactory quantitative reproduction, not only because extremely low values of K ( - 1 0 -1°) would be required, but also because it would not be possible to reproduce correctly the potential spacings between subsequent steps with only one value of K for each polarogram. Formally, values of K becoming of smaller and smaller order of magnitude would be required; this situation may actually be due to overwhelming importance of electrostatic double layer effects in the region of more negative potentials, or to direct reduction with individual electrode rate constants of each complex species. An attempt at a quantitative evaluation of kinetic data was made by means of the model of the reaction layer[9, I0]. As we have already remarked, this model is likely to give only a lower limit for the rate constants of the rapid processes, so we shall use it to obtain only a semiquantitative picture of the relative inertness in formation, respectively dissociation reactions of the involved complex species. According to the assumption of the reaction layer treatment for the kinetic effects involving waves III and IV, we have followed the equilibrium: k ~ - [CoX3L]- + X- Kforn~= [CoX3L]-[X-] = [COX4]2- ~--~
"
(6)
Pseudo-first order conditions occur in the presence of excess X - (at the electrode surface even better than in the bulk of solution), so we put: = ~'l[X-]o ) . [CoX4]2- S . ~ [CoX3L]-~_~e = Kc = Kforrn[X]o-; k2 ~ = kl;'k2 ~
(7)
The average kinetic current is given by: ~k = zFlO-3ql~k~[CoX4Z-]o
(8)
9. R. Brdi~ka,Advances in Polarography Wol. 2. p. 655. Longmuir (1960). 10. R. Brdi~ka and K. Wiesner, Coll. Czech. chem. Commun. 12, 138 (1947); J. Koutecky and R. Brdi6ka, ColL Czech. chem. Commun. 12,337 (1947).
511
Co(l 1) chloride complexes in acetonitrile
where q is the average electrode area, Ix the effective reaction layer thickness, and [CoX4]o '~- is the concentration of the electroinactive (I 11 wave) species at the electrode surface [CoX42-]o = (Ta--~k)/k, k being the llkovic c u r r e n t - c o n c e n t r a tion proportionality factor for the average diffusion coefficient. Putting ( 10 -:~ zFq)/ k = 0.81 X/t/D, we obtain f r o m (8): ~a" -- 0.81
k2tzX/t/D
with
/z = ~
= X/D[,~2
(9)
By inserting ~~ as a function of the formation constant of [ C o X d 2- we obtain the final relation: ~k = td -- tk
0"81
k~'21/2tl/2
(10
Kform[X ],'"2
which we have used for the numerical evaluation ofk~ = k2 (Tables 1 and 2). It ,s to be noted that the ligand concentration [X]o at the electrode surface can be considerably higher than the bulk equilibrium value, so we tried a correction; disregarding the e x t r e m e choice [X]o = [Xhot we assumed: [X]o=
[X]tot-4(\ ~a~• la h'][coX,2-]eq /
(1])
which we feel is a more realistic approximation. In any case calculated values of p r o v e d rather insensitive to the e m p l o y e d type of correction, especially for high x. Equation (10) predicts a slope 0.5 for a plot of log Tdbl--~a- vs. log IX],,, which is actually verified at 25°C, and less well verified at 35°C, where the slope decreases; at 45°C the slope tends to 0, or log (Tk/~,~--ik)tends to b e c o m e independent of [X]o. T h a t is, at higher t e m p e r a t u r e "k=,= 7,1[X]o holds no longer, and the association reaction b e c o m e s governed by a rate-determining step independent of [X]-, according to the overall scheme:
[CoX3L]- ~ [CoXa]- + L
slow
[CoX3]-+X- ~
fast.
(12) [COX4] ~-
Kinetic effects on the first wave were considered according to the scheme: [CoX2L2] ~ implyingX2
=
[CoLr] 2+ + 2X
(13)
in:
[CoX2L2] ~
[COL6]~+.
14)
~.2 = £, would then obey:
7
15)
512
L. S E S T I L I and C. F U R L A N I
×
? r
o~
c~
~+ 7-~
7-~
[...
<
Co(ll) chloride complexes in acetonitrile
513
Table 2. Rate constants (sec-U of fast dissociation of Co(ll)-halide complexes in acetonitrile from polarographic data (reaction layer treatment); for experimental conditions, see text 25.0o +_0.1oc 0.14. I0:' 0.36. 10~ 0, 15. 10e*
~([CoCI2L._,] ~-~ [CoL6]2J k~t([CoCId2 ~- [CoLCI:,] ) ~([CoBh]'-'- ~- [CoLBh] )
35.0o_+0.1oc 45.0o+0.1oc 0.22. 10:' 0.68. 10~ 0.59. 10'-',E
0-66. 10:' 1.32. 10=':+ 0-76. 10e~
*Slope of the log plot not constant: quoted values are taken from the section of the log plot with slope 0.5. w i t h s l o p e 1 in t h e l o g a r i t h m i c plot in t h e r a n g e 2 5 - 4 5 ° C (see Fig. 7). H o w e v e r , o n e c o u l d a l s o c o n s i d e r a d i f f e r e n t p a t h f o r f o r m a t i o n o f [CoL~X=,]: [COL6] 2+ + X - ~
[CoXL~] + + L
slow (16)
[CoXLd + + X- ~
[CoX.,L,] + 3L
fast
w i t h ~2 = ?<,[X]o. T h e s l o p e o f the log ik/(~d--tk) VS. log [X]o plot w o u l d be 1"5 if [ C o L , ] 2+ = 1/[X] 2, o r 0.5 a s s u m i n g [CoL6] 2+ i n d e p e n d e n t o f [X], as is p l a u s i b l e at v e r y l o w x, w h e r e s u b s t a n t i a l e x c e s s o f [ C o L J 2+ is p r e s e n t , or 1 if [CoL~;] 2+ -- I/ [ X ] , as is a p p r o x i m a t e l y t r u e for x = 0.5 -- I. Still a n o t h e r m e c h a n i s m w o u l d o c c u r if t h e rate d e t e r m i n a t i n g s t e p o f f o r m a t i o n o f [CoX2L2] w o u l d b e a d i s s o c i a tive s t a g e i n d e p e n d e n t o f [ X ] , in w h i c h c a s e t h e log plot s l o p e w o u l d t e n d to 0 in
Io
to4 _~
o-
~
-o~
-< --
\ _
•
NN~
-5
-I
'Og
[CLIo
Fig. 7. Log plot for Co(I|)/CI- systems in AN according to Equations (IO) and (15): ( . . . . )111 wave at 25°C; (A A h A)I wave at 45°C.
514
L. SESTILI and C. F U R L A N I
the region of smallest h. Experimentally, data at 25, 35 and 45°C show a slope of the log plot between 0.5 and 1, but closer to 1. This suggests second order for the association reaction with "k2---"~[X], and [COL6]2÷ approximately decr.easing as 1/[X]. However, large uncertainty arises from the estimate of IX]o; here too we have tried different criteria, as in the case of the kinetic effects on the third wave, and here we found it more reasonable to adopt the approximation:
.
_/ial~,,p.\
[X]o -~- [ X ] t o t - - • 1 . - - - - - - - ~ / [ C o X 2 L 2 ] e q . \ld II theor.,]
3(iam~,,p.~ .
.
.
kid 11i theor./
[CoLX3]eq.
(17)
Of course the adopted criterion for evaluation of [X]o is here more critical, and uncertainty of values of calculated rate constants is much larger. In any case, evaluation of constants could be attempted only for chlorocomplexes, the behaviour of bromocomplexes being more complicated with nonlinear log plots pointing to competition between several alternative reaction mechanisms.
KINETIC BEHAV1OUR
EFFECTS IN THE POLAROGRAPH1C OF Co(ll) CHLORIDE COMPLEXES ACETONITRILE L U 1 S A S E S T I L ! and C L A U D I O
IN
FURLANI
Instituto di C h i m i c a G e n e r a l e ed Inorganica delFUniversith, 06100 Perugia, Italy (Received 8 M a y 1970)
Abstract-Polarographic reduction of pseudotetrahedral cobalt(ll)-halide c o m p l e x e s in acetonitrile occurs in several alternative w a v e s assigned to successive complex species [COL6] ~+ and [CoL,,X~_,,] ~-" (L = acetonitrile). Kinetic currents due to fast dissociation of the C o ( l l ) - h a l i d e (particularly chloride) complex species has been o b s e r v e d in solutions at various degrees of complex formation. Rate constants ['or the dissociation: [COX4] = ~
[CoLX:~] + X-
(X = CI-, Br-), and: [CoL.,X~] ~
[COL,] ~+ + 2X .
(X- = CI-) were evaluated from polarographic m e a s u r e m e n t s in the temperature range 2 5 - 4 5 ° C by m e a n s of the model of the reaction layer. Evidence is presented for competition of different reaction m e c h a n i s m s , possibly involving dissociation stages.
INTRODUCTION THE INCREASINGLY wide use of acetonitrile as a convenient polarographic solvent
[1-4], and the recent availability of the constants of the equilibria between the complex species [CoL6] 2+, [CoL2X.~], [CoLX:~]- and [COX4] -z (X = CI, Br) in acetonitrile[5], prompted us to an investigation of the polarographic behaviour of the complex systems C o ( I I ) - X - in that solvent. We have obtained evidence for separate reduction steps corresponding to discharge of all successive complexes at the D.M.E. As the same time the relative intensity of the steps of the more halogenated species turned to be systematically somewhat lower than corresponding to the equilibrium distribution curves of the species, the steps becoming partially kinetic in character. This was a clear indication of fast dissociation rate, respectively slow formation of the halogenated species, and we attempted a preliminary evaluation of the corresponding rate constants. Although the model employed for the treatment of chemical dissociation occurring in the reaction I. 1. N e l s o n and R. l w a m o t o , J. electroanal. Chem. 6 , 2 3 4 (1963). 2. 1. M. Kolthoff and F. G. T h o m a s , J. electrochem. Soc. 11 I, 1065 (1964). 3. C. Furlani, L. Sestili, A. C i a n a and F. G a r b a s s i , Electrochim. Acta 12, 1393 (1967): L. Sestili, C. Furland, A. Ciana and F. Garbassi, Electrochim. ,4 cta 15,225 (1970). 4. V. G u t m a n n and F. Mairinger, Mh. Chem. 8 9 , 7 2 4 (1958). 5. L. Sestili and C. Furlani, J. inorg, nucl. C h e m . 32, 1997 (1970). 503
504
L. SEST1LI and C. FURLAN1
layer is a rather crude one, we feel that the present kinetic study can be of some interest, in view of the rather scarce knowledge of the kinetics of tetrahedral complexes. EXPERIMENTAL Preparation of the complexes, treatment of solvents, composition of solution, and conditions of temperature and ionic strength control were the same as in our previous work on spectrophotometric determination of stability constants of Co(II)/X- in acetonitrile[5]. Polarographic measurements were performed at three controlled temperatures in the range 25-45°C with an Ame1462 polarograph, in three-electrode cells. The employed D.M.E. had m213t'/~ = 1.52 mg2~3sec -j/2, in acetonitrile with 0.1 M supporting electrolyte (C2H5)4 NCIO4 at 25°C and open circuit. Reference electrode Ag/0.01 M AgNO3 in acetonitrile[6]. RESULTS
Figures 1 and 2 show how the shape of the polarograms varies with the ratio x
= [X-]tot/[Co(IJ)]tot(X--
Y
CI, Br) in acetonitrile. It is to be noted that the depen-
b
d
J
J 1
2~A
0-8 V
Fig. 1. Polarograms of AN solutions containing Co(ll)-chloride complexes at various [Cl]tot/[Co2+]tot ratios. 25.0__+0.1°C; /z = 0.1 (TEACIO4); [Co~+]tot= 1.1. 10-3M; other conditions as specified in text. (a) [C1-]tot = 0; (b) 1-50.10-aM; (c) 3"00. 10-3M; (d) 3"50.10-3M; (e) 4.50./0-aM; (f) 22-00.10-aM. 6. W. Forsling, H. Hietanen and L. Sillen, A c t a chem. scand. 6, 901 (1952).
Co(l 1) chloride complexes in acetonitrile
/
505
/
c
/
o e ,,
/
f
/ f
i2p. A O,2V 0.8V
Fig, 2. Polarograms of AN solutions containing CoO D-bromide complexes at various [Br-]tot/[Co2+]tot ratios. 25.0°_+0-1°C; tz = 0.1 (TEAC10,); [Co~+]u,t = I-0.10-:~M; other conditions as specified in text. (a) [Br-]tot = 0; (b) 0.97.10-3M; (c) 2.00. 10-3M: (d) 4-00.10-3M: (e) 10.00.10-3M; (f) 80.00. 10-:~M.
dence of wave heights on x varies to some extent with temperature; critical values of x quoted below are an average o v e r the e m p l o y e d t e m p e r a t u r e range. At x = 0 there is a single rather sharp two-electron-step with E,/~ = - 0 . 9 5 V vs. Ag/0.01 M AgNO3. With increasing x, the intensity of limiting current of the first wave decreases and eventually disappears around x >~ 3.0 with CI, and 3.5 with Br, while two more negative waves appear. T h e height of the first wave is always larger than corresponding to the equilibrium distribution of [COL,] 2+, and contains therefore a substantial kinetic contribution. T h e second and the third w a v e a p p e a r evidently at x >~ 0.4, with E~,, = -- 1.63 respectively - - 2 - 0 5 V for C1, and - - 1 . 4 5 V , r e s p e c t i v e l y - - 1 - 7 5 V for Br. T h e second w a v e increases in height until x - 3-0 for the chloro system, then decreases rapidly and disappears for x > 4; in the b r o m o s y s t e m the variation with x is similar but slower, the m a x i m u m height being ri~ached in the x range 4 - 6 and a
506
L. SESTILI and C. F U R L A N I
small residual height lasting till x - 60. Comparison of the trend of intensity of the second wave with equilibrium percent of [CoL2X2] shows a rough parallelism, except for the shift of the maximum to higher x, with negative kinetic contribution for x lower than maximum, and positive kinetic contribution at higher x values. For the third wave, ia increases or remains approximately constant until x - 30 for CI, and - 8 0 for Br, then decreases slightly; it does however not disappear at higher x, except in the most concentrated chloride solutions. Comparison with the distribution curves of [CoLX3]- shows systematically a strong positive kinetic contribution to ia(lll) in the high x range; kinetic contributions tend to be negative at lower x, when the second wave exhibits a positive kinetic contribution. At still higher values of x (3.6 for C1, 7 for Br), a fourth wave appears (E1/2 = --2.35 V for C1, or -2.20 V for Br), whose height increases steadily with x but does never reach completion except in the presence of high excess of chloride (at least 200 fold). Its height is in any case, except at the highest C1 concentrations, lower than the equilibrium percent of [CoXj 2-, that is kinetic contributions are negative. In the extreme case where it remains alone, the fourth wave is purely diffusive in character. A general comparison of behaviour of the chloro and bromo systems confirms qualitative similarity, but changes in the Br system occur at higher x values, in agreement with the lower stability of the bromocomplexes[5] and the range of existence of wave II is much larger with Br (at expenses of wave Ili). The effect of temperature results in slight quantitative changes of the ratios of wave heights, particularly for the lowest x values; such changes are in qualitative agreement with the known variation of the equilibrium constants with temperature[5], although also kinetic effect are undoubtedly of importance. General consideration of the system of successive waves, and comparison with distribution curves calculated from equilibrium constants suggest that the four waves are due, in order, to reduction of [COL6]2÷, [CoL2X2], [CoLX3]and [COX4]2-. This assignment can be directly proved for wave 1, since its height and position coincide with those of Co(CIO4)2 in AN (reducible species [CoLG]Z÷), and for wave IV, since solutions containing very high excess of CI- (x - 180) show wave IV alone, with purely diffusive character; since [COC14]2- is then the only species present in solution, it is likely that it is also the species being discharged, unless improbably rapid dissociation occur. Assignment of wave II to [CoX2L2] and of wave II1 to [CoLX3]- is only indirect and based mainly on the gross parallelism between distribution curves calculated from equilibrium constants and from polarographic limiting curves as shown particularly in Fig. 3 ; distribution curves from polarographic data were calculated assuming an average diffusion coefficient in the llkovic equation. Of course, full parallelism could be expected only if interconversion rates between different complex species were extremely low or at least negligible with respect to the rate-determining step of the electrode reactions (diffusion for wave I which is not far from reversibility, electron transfer for subsequent waves). Such an assumption can therefore be considered only as a preliminary approximation, particularly in view of the expected lability of tetrahedral complexes. Indeed, as we have already noted, there are some considerable differences in the two types of distribution curves, which show increase of the wave height above the equilibrium values for waves I
507
Co(l 1) chloride complexes in acetonitrile
/ Ivz_._ '
,oo
! i
50
q .,"
\.~Q
/,
. . . .
i
!'
\,% ........
2
,'o --< ' [ct-],o , /[co
30
q,
Fig. 3. Distribution curves for C o ( l l l ) - c h l o r i d e complexes in AN 35.0°+0.1°C: ~ = 0-1 (TEAC100. ( - - ) from equilibrium constants: (----) from polarographic limiting currents.
and I 1I, the latter only for x >~ 3-5 with CI or x >F 8 with Br, while a more complicated behaviour, with alternance of positive and negative kinetic contributions, is shown by wave I1, and wave IV is systematically lower than equilibrium concentration (see Figs. 3 and 4). Such deviations clearly point to rapid dissociation of [CoX2L,,] to [COL6]2+, respectively of [COX4]"- to [ C o L X J - . Of course it would not be realistic to assume that the opposite reactions are infinitely slow, rather data simply indicate that dissociation of these two species are considerably faster than their formation; there are also indications that [CoL2X2] might undergo at low x (x ~< 2) rapid association to [CoLXJ-, while the reverse reaction (rapid dissociation of [CoLX:c] to [CoL2X2]) is predominant from x - 2-5 till disappearance of wave I1, and is particularly evident in the Br system. It appears therefore that the simplest transformation scheme is that involving species [ C o L X J - and [COX4]2- in waves Ill and IV, and it is on this part of the system that we felt it reasonable to attempt an approximate kinetic treatment on the base V
.
.
.
.
.
.
.
]
IOO
~,,.,
.f,l}v .......
', \ \
" ..~/;-"
,/ j/.. . . . . . . . . . . . . . . . . .
Ill
Jl
_ _°
i
--~
.... L ....................
\
60
[8,~,0,/[Co'+],o, Fig. 4. Distribution curves for Co(l~)-bromide complexes in AN 35.0°+_0.1°C: tz = 0-1 (TEACIO4). ( - - ) from equilibrium constants: (.... ) from polarographic limiting currents.
¸
~00
508
L. SESTILI and C. FURLAN1
of the model of the reaction layer, which is appropriate for treatment of rapid kinetic processes perturbing a fundamentally non-interconvertible system, as we shall report in more detail below. An opposite point of view would be the assumption of complexation equilibria rapid in comparison with the rate of electrode processes, in which alternance of successive waves corresponds to progressive variation of ao resulting from diffusion of equilibrium species in the electrode region, as has been applied, e.g. by Koryta et al.[7] for essentially reversible polarographic processes, e.g. cadmium cyanide and similar systems. According to this treatment, the dependence of the limiting current on the concentration of the free ligand at the electrode surface [X]o is given by [7]:
1 IDz\aJ~
1+a o
X-lo-
(1)
In (1) the index o refers to quantities at the electrode surface, and symbols without the same index refer to equilibrium values in the bulk of the solution; Ta represents the total diffusion current for the sum of all metal species. The shape of the current-voltage curve for reversible processes is given by [6]:
RTga_--~. E = Eve+ n F
t
(2)
4
1 "~ E k l ' ' " kj[X-]o j j=l
where
[MXJ kj = [ M X j _ I ] [ X ] "
Formulas (1) and (2), when applied to our systems with the known values of complexation constants in acetonitrile[5], yield in the calculated c.v. curves a succession of four waves, whose distribution path is again in rough correspondance with the experimental polarographic distribution curves of Figs. 3 and 4, except for potential values being obviously much less negative than the experimental ones, and for ia(IV) turning systematically somewhat larger than experimental. The latter circumstance is again a qualitative indication that formation of [COX4]z- is significantly slower than its dissociation to [CoLX,]-, again in qualitative agreement with the trend suggested by the other extreme point of view (Figs. 5 and 6). In an attempt to bring the calculated curve in better agreement with the experimental potential values, we have considered the effect of slow electron transfer by superimposing a transfer overvoltage according to the relations [8]. ~a=~
(1--r)+(l+r)tanh-
~b(H)
(3)
7. J. Koryta, Z. Elektrochem. 61, 423 (1957); N. Tanaka, R. Tamamushi and M. Kodama, Z. phys. Chem. 14, 141 (1958). 8. G. W. C. Milner, The Principles andApplications ofPolarography p. 47. Longmans (1957).
Co(I !) chloride c o m p l e x e s in acetonitrile
509
I0
1 ....£ . . . . . . . . . . . . .
f
06
02
I -I.00
I
I
-150
-200
Fig. 5. C.V. c u r v e s for C o ( l l ) - c h l o r i d e c o m p l e x e s in A N [Co~+]tot = [CI ]tol = 1.1. 10-3M; t = 35.0°±0-1°C. (----) experimental polarographic curves: ( . . . . . ) calculated c.v. curves according Ref. [7]; ( ) calculated c.v. curves according Ref. [8]. (KD-~/2tlJ~ = 5"10 7).
.t
I°i •
/
I .~"~ 0 6
t~
02
i..,,, I 30
[cL-],o,/[co~1,o, Fig. 6. Distribution curves of alternating w a v e s in the C o ( i l ) - c h l o r i d e s y s t e m s in A N as calculated according to Refs. [7, 8]. t = 35.0 ± 0- I°C: p. = 0.1 ( T E A C 1 0 0 .
510
L. SESTILI and C. F U R L A N I
(4)
(KD-1/2t 1/~) e (1/2 - ")~. 2 cos h --
H =
where: v= V--Vo
nF fl=RT
assuming r = td°n = 1, (4) takes the form: Idcat
L=_l[1 ,a
(5)
2[
We took tentative values of ( K D - ' Z t 1/2) in order to calculate H, taking for oS(H) the values tabulated in [8]: a was given the value 0.5 as a first approximation. C.v. curves thus obtained take now a form a little more resembling that of the actual experimental curves (Fig. 5), but can never be brought to a satisfactory quantitative reproduction, not only because extremely low values of K ( - 1 0 -1°) would be required, but also because it would not be possible to reproduce correctly the potential spacings between subsequent steps with only one value of K for each polarogram. Formally, values of K becoming of smaller and smaller order of magnitude would be required; this situation may actually be due to overwhelming importance of electrostatic double layer effects in the region of more negative potentials, or to direct reduction with individual electrode rate constants of each complex species. An attempt at a quantitative evaluation of kinetic data was made by means of the model of the reaction layer[9, I0]. As we have already remarked, this model is likely to give only a lower limit for the rate constants of the rapid processes, so we shall use it to obtain only a semiquantitative picture of the relative inertness in formation, respectively dissociation reactions of the involved complex species. According to the assumption of the reaction layer treatment for the kinetic effects involving waves III and IV, we have followed the equilibrium: k ~ - [CoX3L]- + X- Kforn~= [CoX3L]-[X-] = [COX4]2- ~--~
"
(6)
Pseudo-first order conditions occur in the presence of excess X - (at the electrode surface even better than in the bulk of solution), so we put: = ~'l[X-]o ) . [CoX4]2- S . ~ [CoX3L]-~_~e = Kc = Kforrn[X]o-; k2 ~ = kl;'k2 ~
(7)
The average kinetic current is given by: ~k = zFlO-3ql~k~[CoX4Z-]o
(8)
9. R. Brdi~ka,Advances in Polarography Wol. 2. p. 655. Longmuir (1960). 10. R. Brdi~ka and K. Wiesner, Coll. Czech. chem. Commun. 12, 138 (1947); J. Koutecky and R. Brdi6ka, ColL Czech. chem. Commun. 12,337 (1947).
511
Co(l 1) chloride complexes in acetonitrile
where q is the average electrode area, Ix the effective reaction layer thickness, and [CoX4]o '~- is the concentration of the electroinactive (I 11 wave) species at the electrode surface [CoX42-]o = (Ta--~k)/k, k being the llkovic c u r r e n t - c o n c e n t r a tion proportionality factor for the average diffusion coefficient. Putting ( 10 -:~ zFq)/ k = 0.81 X/t/D, we obtain f r o m (8): ~a" -- 0.81
k2tzX/t/D
with
/z = ~
= X/D[,~2
(9)
By inserting ~~ as a function of the formation constant of [ C o X d 2- we obtain the final relation: ~k = td -- tk
0"81
k~'21/2tl/2
(10
Kform[X ],'"2
which we have used for the numerical evaluation ofk~ = k2 (Tables 1 and 2). It ,s to be noted that the ligand concentration [X]o at the electrode surface can be considerably higher than the bulk equilibrium value, so we tried a correction; disregarding the e x t r e m e choice [X]o = [Xhot we assumed: [X]o=
[X]tot-4(\ ~a~• la h'][coX,2-]eq /
(1])
which we feel is a more realistic approximation. In any case calculated values of p r o v e d rather insensitive to the e m p l o y e d type of correction, especially for high x. Equation (10) predicts a slope 0.5 for a plot of log Tdbl--~a- vs. log IX],,, which is actually verified at 25°C, and less well verified at 35°C, where the slope decreases; at 45°C the slope tends to 0, or log (Tk/~,~--ik)tends to b e c o m e independent of [X]o. T h a t is, at higher t e m p e r a t u r e "k=,= 7,1[X]o holds no longer, and the association reaction b e c o m e s governed by a rate-determining step independent of [X]-, according to the overall scheme:
[CoX3L]- ~ [CoXa]- + L
slow
[CoX3]-+X- ~
fast.
(12) [COX4] ~-
Kinetic effects on the first wave were considered according to the scheme: [CoX2L2] ~ implyingX2
=
[CoLr] 2+ + 2X
(13)
in:
[CoX2L2] ~
[COL6]~+.
14)
~.2 = £, would then obey:
7
15)
512
L. S E S T I L I and C. F U R L A N I
×
? r
o~
c~
~+ 7-~
7-~
[...
<
Co(ll) chloride complexes in acetonitrile
513
Table 2. Rate constants (sec-U of fast dissociation of Co(ll)-halide complexes in acetonitrile from polarographic data (reaction layer treatment); for experimental conditions, see text 25.0o +_0.1oc 0.14. I0:' 0.36. 10~ 0, 15. 10e*
~([CoCI2L._,] ~-~ [CoL6]2J k~t([CoCId2 ~- [CoLCI:,] ) ~([CoBh]'-'- ~- [CoLBh] )
35.0o_+0.1oc 45.0o+0.1oc 0.22. 10:' 0.68. 10~ 0.59. 10'-',E
0-66. 10:' 1.32. 10=':+ 0-76. 10e~
*Slope of the log plot not constant: quoted values are taken from the section of the log plot with slope 0.5. w i t h s l o p e 1 in t h e l o g a r i t h m i c plot in t h e r a n g e 2 5 - 4 5 ° C (see Fig. 7). H o w e v e r , o n e c o u l d a l s o c o n s i d e r a d i f f e r e n t p a t h f o r f o r m a t i o n o f [CoL~X=,]: [COL6] 2+ + X - ~
[CoXL~] + + L
slow (16)
[CoXLd + + X- ~
[CoX.,L,] + 3L
fast
w i t h ~2 = ?<,[X]o. T h e s l o p e o f the log ik/(~d--tk) VS. log [X]o plot w o u l d be 1"5 if [ C o L , ] 2+ = 1/[X] 2, o r 0.5 a s s u m i n g [CoL6] 2+ i n d e p e n d e n t o f [X], as is p l a u s i b l e at v e r y l o w x, w h e r e s u b s t a n t i a l e x c e s s o f [ C o L J 2+ is p r e s e n t , or 1 if [CoL~;] 2+ -- I/ [ X ] , as is a p p r o x i m a t e l y t r u e for x = 0.5 -- I. Still a n o t h e r m e c h a n i s m w o u l d o c c u r if t h e rate d e t e r m i n a t i n g s t e p o f f o r m a t i o n o f [CoX2L2] w o u l d b e a d i s s o c i a tive s t a g e i n d e p e n d e n t o f [ X ] , in w h i c h c a s e t h e log plot s l o p e w o u l d t e n d to 0 in
Io
to4 _~
o-
~
-o~
-< --
\ _
•
NN~
-5
-I
'Og
[CLIo
Fig. 7. Log plot for Co(I|)/CI- systems in AN according to Equations (IO) and (15): ( . . . . )111 wave at 25°C; (A A h A)I wave at 45°C.
514
L. SESTILI and C. F U R L A N I
the region of smallest h. Experimentally, data at 25, 35 and 45°C show a slope of the log plot between 0.5 and 1, but closer to 1. This suggests second order for the association reaction with "k2---"~[X], and [COL6]2÷ approximately decr.easing as 1/[X]. However, large uncertainty arises from the estimate of IX]o; here too we have tried different criteria, as in the case of the kinetic effects on the third wave, and here we found it more reasonable to adopt the approximation:
.
_/ial~,,p.\
[X]o -~- [ X ] t o t - - • 1 . - - - - - - - ~ / [ C o X 2 L 2 ] e q . \ld II theor.,]
3(iam~,,p.~ .
.
.
kid 11i theor./
[CoLX3]eq.
(17)
Of course the adopted criterion for evaluation of [X]o is here more critical, and uncertainty of values of calculated rate constants is much larger. In any case, evaluation of constants could be attempted only for chlorocomplexes, the behaviour of bromocomplexes being more complicated with nonlinear log plots pointing to competition between several alternative reaction mechanisms.