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Electrode kinetics of the acetylacetonate complexes of nickel(II) at the dropping mercury electrode
ELECTROANALYTICALCHEMISTRYAND INTERFACIALELECTROCHEMISTRY Elsevier Sequoia S.A., Lausanne Printedin The Netherlands
17
E L E C T R O D E K I N E T I C S OF T H E A C E T Y L A C E T O N A T E C O M P L E X E S OF NICKEL(II) A T T H E D R O P P I N G M E R C U R Y E L E C T R O D E
CHIZUKO NISHIHARA ANDHIROAKI MATSUDA* Government ChemicalIndustrial Research blstitute, Tokyo, Hon-machi, Shibuva-ku, Tokyo (Japan)
(Received May 18th, 1970)
INTRODUCTION In a series of previous investigations 1- 6 in our laboratory, it has been shown that the polarographic current-voltage curves can be analysed to evaluate the kinetic parameters related to the electrode reactions of metal ion complexes. As examples, the hydroxo, ammine, tartrate and acetate complexes of zinc(II) were experimentally examined and the reaction mechanisms of their electrode processes were elucidated. The metal-acetylacetone systems have recently been attracting our attention due to their complicated and interesting polarographic behavior v- a2. The present paper deals with the polarographic and chronopotentiometric behavior of the nickel(II)-acetylacetone system in a wide range of pH-values (3-10), resulting in the elucidation of its reaction mechanism and in the evaluation of the relevant kinetic parameters. EXPERIMENTAL Reagents
A standard solution of nickel(II) was prepared by dissolving a known amount of pure nickel metal (Johnson Matthey, purity 99.99%o) in dilute HNO3, evaporating to paste and diluting to 5 x 10-3 M. Stock solutions were prepared of 1 M KC1 (supporting electrolyte), 0.5 ~ carboxymethyl cellulose (CMC) (maximum suppressor), 2.5 x 10-1 M acetylacetone (HAcac) and 2.5 x 10-1 M buffer, from analytical reagent grade chemicals and distilled water. For buffer solutions the systems HAc-NaAc was used for the pH-range 3.2-5.1, K H z P O 4 - N a z H P O 4 for 5.2-7.6 and H3BO3N a O H for 8.1-9.8. Apparatus
The d.c. polarograph used was of a conventional type, which contained a recorder (San'ei Sokki Galvanograph HR-101) with a suitable damping circuit and a potentiometer drum with 20 turns of 10 f~ resistance. The instrument was operated at a rate of change of applied potential of ca. 20 mV m i n - 1. The dropping mercury electrode (DME) employed had a drop time t of 5.2 s and a flow rate of mercury m * Present address : Department of Electrochemistry,Faculty of Engineering, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo.
J. Electroanal. Chem., 28 (1970) 17-32
18
c . NISHIHARA, H. MATSUDA
of 1.46 mg s- 1 when measured in an air-free sample solution at - 1.2 V vs. SCE and at 49 cm of height of the mercury head. An H-type electrolysis cell was connected to a saturated calomel electrode of surface area ca. 8 cm 2, which was used as a counter electrode, through an agar agar bridge containing 0.1 M KC1 solution. The chronopotentiometric apparatus used was of conventional design, in which a memory-oscilloscope (Iwasaki Tsushinki Memoriscope MS-5013) was used for tracing the potential-time curves. A balanced head, stationary, hanging mercury drop electrode (HMDE) a3 (working electrode), a platinum wire electrode (counter electrode) and a saturated calomel electrode (SCE) (reference electrode) were arranged with an H-type electrolysis cell. The characteristics of H M D E used were : t = 5.8 min, m=4.0 mg min ~ and t = 10.5 min, m = 1.9 mg m i n - ~ in distilled water at 49 cm of height of the mercury head with no applied potential. The mercury run-off time, at which the growth of the mercury drop was ended by lowering the mercury reservoir, was chosen as 3.0 min and 5.0 min. Procedure
The composition of sample solutions was 0.5 m M Ni(II), 0,1 M KC114, 0.005,o,/o CMC, 2.5 x 10 .2 M HAcac and 2.5 x 10 -2 M buffer, unless otherwise stated. For chronopotentiometry, CMC was omitted. The sample solutions were left at room temperature for one night after preparation, and before measurements they were left in a thermostat for more than 30 min and then deaerated for 20 rain with nitrogen gas which had passed through distilled water. All measurements were carried out in the thermostat at 30.0 +_0.1 °C. In d.c. polarography the ~hrrent was measured as the difference between the total current and the residual current at the same potential axis. In chronopotentiometry the transition time was determined graphically after Gierst and Juliard 15. Most of the numerical calculations were performed by a digital computer (FACOM 270-30). RESULTS AND DISCUSSION
D.c. polarograms at three typical pH-values are shown in Fig. 1. Below pH 4.5, only one wave which is assumed to be a composite of two independent waves is observed at about - 1.0 V vs. SCE. At higher pH values, the height of the first wave decreases, and a second wave appears at about - 1 . 5 V vs. SCE, the height of which increases with pH. In the basic medium, the first wave has almost vanished and the height of the second wave decreases with increasing pH-value. In order to analyse the complicated polarographic behavior mentioned above, it is necessary at first to know the equilibrium distribution between various species of the acetylacetonate complexes of nickel(II) in the bulk of the solution. In Fig. 2, solid curves show such an equilibrium distribution in dependence on pH. In the construction of this diagram, the activity coefficients of all species in the solution were assumed to be equal to unity, and for the acid dissociation constant of acetylacetone and for the total stability constants of Ni (Acac) ÷ and Ni (Acac)2 the following values were used: p K n A c a c = 8.8, log/~1 = 5.5 and log/~2 = 9.8 at 30°C 16. The total stability constant of Ni(Acac)~, was assumed as log/~3 = 12.8 at 30°C for reasons mentioned later. J. Electroanal. Chem.,
28 (1970) 1%32
19
ACETYLACETONATE COMPLEXES OF NICKEL(IX)
::?:
-0.8
--1,0
::: :: :,-~:
-12
-1.4
-1,6
E/V vs.SC E
~
t
t'l2*~~Acac)~i(Acac)j
3
4
5
6
7
8
9
10
pH
Fig. 1. D.c. polarograms of acetylacetonate complexes of nickel(II) for three different pH-values. Composition of solutions: 0.5 mM Ni(II), 0.1 M KC1, 2.5 x 10 z M HAcac, 2.5 x 10 -e M buffer and 0.00500 CMC, (a) pH 4.2, (b) pH 6.3, (c) pH 7.8. Fig. 2, Equilibrium distribution of nickel(II)-acetylacetonate complexes vs. pH-value for total concn, of nickel(II)=5 x 10 -4 M, total concn, of acetylacetone=2.5 x 10 .2 M and ionic strength=0.1 at 30°C. ~ ) Calcd. using pKHA~a¢= 8.8, log/31 = 5.5, log f12 = 9.8 and log f13 = 12.8; ( x ) distribution of Ni 2+ and Ni(Acac) + determined by d.c. polarography; (O) distribution of Ni(Acac) + and Ni(Acac)2 obtained by chronopotentiometry.
Analysis of the first wave At pH-values from 3.5 to 4.5, one wave is observed at about - 1.0 V vs. SCE, which is here called the first wave, and its limiting current is diffusion-controlled. The shapes of the d.c. and a.c. polarograms (see Figs. 1 and 3) suggest that the first wave is a composite of two independent irreversible reduction waves. These two waves are assumed to be due to the reduction of two complex species, Ni(Acac)g + and Ni (Acac) +, which are prevailing species in equilibrium in the bulk of the solution (see Fig. 2). The current-voltage curve for the s u m o f two independent irreversible reduction waves can be expressed by
i = iNi(Acac)o-}- iNi(Acac) ll,Ni(Aca¢)o = l -~-exp { (2F/RT) ~Ni(Acac)o (E -- g½,Ni(Acac)o) } -~ ll,Ni(Acac) 1 + exp {(2F/R T) ~Ni(Acac)(E -- E½,Ni(Acac)) }
(1) J. Electroanal. Chem., 28 (1970) 17-32
20
C. NISHIHARA, H. MATSUDA
~O~8
.... ;:1.O
Fig. 3. Typical a.c. polarogram ofnickel(II) acetylacetonate complexes at pH 4.5 (drop time = 3.3 s).
where i is the average polarographic current, il the average limiting current, E the electrode potential of DME, E~ the irreversible half-wave potential, ~ the cathodic transfer coefficient, and F, R, T have their usual significance. Thus, it follows that an observed current-voltage curve should be expressed by eqn. (1) with appropriate parameters. In order to separate the observed wave into two waves, the six parameters, il,Ni(Acac)o, ~Ni(Acac)o, E~-,Ni(Acac)o, ll,Ni(Acac), ~Ni(Acac) and E½,Ni(Acac), a r e chosen as unknown constants and determined by the non-linear least squares method (see Appendix). The results are given in Tables 1 and 2. Differences in currents between observed and calculated points at the same potentials were within experimental error, i.e. within 1,5o of the limiting current (see Table 3 in Appendix). In Fig. 4, two separated TABLE 1 •
7+
LIMITING CURRENTS~ HALF-WAVE POTENTIALS AND TRANSFER COEFFICIENTS OF N1 (Acac)~ AND N i (Acac) + SEPARATED BY THE METHOD OF LEAST SQUARES FOR THREE DIFFERENT DROP TIMES AT p n 3.9
(Sensitivity: 2.5 x 10 8 A m m -1) t/s
Ni(Acac)~ +
Ni(Acac) +
h.Ni~A.,~>o
lI,Ni(Acac)
3.4 5.1 7.4
ijmm
-- E~/ (V vs. SCE)
~
i Its~ mms ~
124.7 102.7 85.4
1.009 1.005 0.997
0.41 228 0.39 232 0.38 232
J. Electroanal. Chem., 28 (1970) 17-32
~jmm
-- E4_/ (V vs. SCE)
~
il t}/ mms ~
22.0 19.2 14.5
0.899 0.899 0.896
0.54 40 0.50 43 0.58 39
5.7 5.3 5.9
ACETYLACETONATE COMPLEXES OF NICKEL(II)
21
TABLE 2 LIMITINOCURRENTS,HALF-WAVEPOTENTIALSANDTRANSFERCOEFFICIENTSOF Ni (Acac)2+ ANDNi(Acac) + DETERMINEDBY THEMETHODOF LEASTSQUARESFOR V A R I O U S pH-VALUESAT t = 5.1 S (Sensitivity: 2.5 x 10 -8 A ram-i) N i (A cac )~ + iz/mm - E ~ / ( V vs. SCE)
ct
N i( Acac) + ijmm - E ~ / ( V vs. SCE)
ct
it.uitacad~o il,Nitac~)
a
3.6 3.7 3.9 4.2 4.5
104.4 105.6 102.7 94.4 83.1
1.010 1.007 1.005 0.987 0.968
0.41 0.40 0.39 0.38 0.38
16.8 16.3 19.2 28.9 35.5
0.49 0.44 0.50 0.53 0.63
6.2 6.5 5.3 3.3 2.3
b
3.6 3.7 3.9 4.2 4.5
• 121.8 115.5 119.1 119.8 120.8
0.997 0.988 0.985 0.968 0.949
0.39 0.38 0.39 0.37 0.35
3.5 4.0 4.5 4.8
121.4 120.2 122.3 123.9
0.999 0.973 0.941 0.913
0.41 0.38 0.36 0.36
pH
c
0.897 0.895 0.899 0.894 0.890
a: in 0.1 M KC1 solutions with HAcac and acetate buffer; b: in 0.1 M KCI solutions with acetate buffer: c: in 0.1 M KC1 solutions. waves, which can be c a l c u l a t e d b y using the six p a r a m e t e r s d e t e r m i n e d above, are s h o w n t o g e t h e r with the o r i g i n a l c o m p o s i t e wave. D u r i n g the p r o g r e s s of the p r e s e n t investigation, Cosovi6 e t al. 17 have s h o w n t h a t the c o m p o s i t e wave c a n be s e p a r a t e d into two i n d e p e n d e n t curves by derivative pulse p o l a r o g r a p h y . F u r t h e r m o r e , Ru~id a n d B r a n i c a 18 have p r o p o s e d a m e t h o d of l o g a r i t h m i c analysis of two o v e r l a p p i n g d,c. p o l a r o g r a p h i c waves. H o w e v e r , the p r e s e n t m e t h o d seems to be m o r e reliable, b e c a u s e the values of p a r a m e t e r s a r e chosen b y the m e t h o d of least squares. T a b l e 1 indicates t h a t /1,Ni(Acac)o, /l,Ni(Acac) a n d also the s u m of these two are diffusion-controlled, so t h a t the r a t i o o f two limiting currents, ll.Ni(Acac)o//l,Ni(Acac), is i n d e p e n d e n t of the d r o p time. This r a t i o c o r r e s p o n d s to the e q u i l i b r i u m d i s t r i b u tion of N i ( A c a c ) g+ a n d N i ( A c a c ) + in the b u l k of the solution, if the diffusion coefficients a n d the activity coefficients of these two c o m p l e x e s are a s s u m e d to be e q u a l to each other. T h e results o b t a i n e d for v a r i o u s p H - v a l u e s at t = 5.1 s are given in T a b l e 2. In Fig. 2 the e q u i l i b r i u m d i s t r i b u t i o n of c o m p l e x e s thus o b t a i n e d is shown b y crosses. T h e e x p e r i m e n t a l p o i n t s are a l m o s t in a g r e e m e n t with the t h e o r e t i c a l curve. T h e r e l a t i o n b e t w e e n the values of the half-wave poteritial of N i ( A c a c ) 2 + a n d the p H - v a l u e is given b y the o p e n circles in Fig. 5, which indicates t h a t the half-wave p o t e n t i a l varies with the p H - v a l u e s . Thus, it m a y be s u p p o s e d t h a t h y d r o x y l ion o r acetate ion (which is a c o n s t i t u e n t of the buffer in the p H - r a n g e considered) p a r t i c i p a t e s in the r e d u c t i o n of nickel(II). F o r this reason, the r e d u c t i o n of nickel(II) in 0.1 M K C l - s o l u t i o n s with a n d w i t h o u t acetate buffer has been examined. F o r this case the c u r r e n t - v o l t a g e curve m a y simply be expressed by J. Electroanal. Chem., 28 (1970) 17-32
22
C. NISHIHARA~ H. M A T S U D A
150
-1.00~~m\
jj, j,
E 100 E ,.'b_ 50
S cQ 2-
I
-0.9
rn\ .\\
ua
\
\
\
-090 I
-1.0
I
-1.1
E / V vs SCE
-u
0 u
•
I -1.2
i
3.5
i
4,0
i
pH
45
Fig. 4. Composite wave and two waves separated by method of least squares at p H 3.9 (drop t i m e = 5 . 1 s). ( ) Original composite wave, ( - - ) separated wave due to the reduction of Ni(Acac)20 +, @ . . . . ) separated wave due to the reduction of Ni(Acac) +. Fig. 5. Dependence of the half-wave potentials of Ni(Acac)g + and Ni(Acac) ÷ on pH-value. Half-wave potential of: (O) Ni(Acac)g ÷ in 0.1 M KC1 solution with HAcac and acetate buffer, (A) Ni 2 + in 0.1 M KC1 solution with acetate buffer, ([~) Ni z+ in 0.1 M KC1 solution, (O) Ni(Acac) + in 0.1 M KC1 solution with HAcac and acetate buffer.
J = i1[1 +exp
\
[3 \
// -0.8
\ \'~X
-0.95
{(2F/RT)c~(E-E¢)}]-I
(2)
The analysis of the observed current-voltage curves with the aid of eqn. (2) has also been performed by the non-linear least squares method similar to the case of composite wave. The results are given in Table 2 and shown in Fig. 5 by open triangles and squares. Table 2 indicates that the transfer coefficient of Ni(Acac) 2 ~ is, independently of the composition of solutions, equal to 0.38, which is in agreement with the value reported by Morinaga 19 (0.41 in 0.1 M KNO3 with 0.01°Jo gelatin). As seen from Fig. 5, the values of the half-wave potential for the three kinds of solutions (with HAcac and buffer, without HAcac and with buffer, and without HAcac and buffer) show the same dependence on the pH-value ; nevertheless those of the composite wave are somewhat more negative, this being supposed to arise from the difference in composition of the solutions. Accordingly, we may conclude that in these three kinds of solution, nickel(II) is reduced in the same mechanism, so that the reacting species are nickel(II)aquo and -hydroxo complexes 14. According to Matsuda and Ayabe 2'5, when nickel(II) is reduced as a series of successive hydroxo complexes, between which the dissociation and association reactions proceed reversibly, the following relation between the irreversible half-wave potential and the concentration of hydroxyl ion holds: J. Electroanal. Chem., 28 (1970) 17 32
ACETYLACETONATE
H o = 1.13
COMPLEXES OF
NICKEL(II)
23
t-}( Z fl'~C~on)exp {(2F/RT)a(E_~-E°i)} v--O
=D-~
~,
o
(3)
, 1-
p-0
where it is assumed that all relevant electrode processes have the c o m m o n value of transfer coefficients and that the activity coefficients of all species are equal to unity and the diffusion coefficients of all species in the solution and of Ni (in amalgam) are equal to each other. In eqn. (3), new notations are: D the c o m m o n value of the diffusion coefficients; Con the concentration of hydroxyl ion, which is assumed to be constant everywhere in the solution; fl'o the total stability constant of the p-th nickel(II) hydroxo complex, Ni(OH)~2-m+ ; E ° i the standard potential of Ni (amalgam)/ Ni(II); k~i~omp the electrode reaction rate constant of Ni(OH)(p2- P)+ at the standard potential of Ni (amalgam)/Ni(OH)(pz-p)+, E°iton)p. Since the stability constant of the nickel(II)-hydroxo complex 16 is log fit = pKyi(OH )= 4.6 at 30°C, eqn. (3) can be simplified into H o - 1.13 t -~ exp { ( 2 F / R T ) a ( E ~ - E ° i ) } = D-~{koi
o , ) 1 - ~ COHq-...} q- kNi~Otl)(fil
(4)
in the pH-range considered. The function Ho in eqn. (4) contains four parameters, E+, c~, t and E°i. The first three can be determined from experiment. For E°~ we shall here use the value of the standard potential of Ni(metal)/Ni(II), i.e., E°i = - 0 . 4 9 6 V vs. SCE 2° at 30°C, because the value of the standard potential of Ni (amalgam)/Ni(II) " 0 is not available in the literature. Then, if kNi(o.), is read as the value at the standard potential of Ni(metal)/Ni(OH)~2-p)+, eqn. (4) holds in its original form*. In Fig. 6, the values of H o are plotted against the concentration of hydroxyl ion. This figure shows a linear relationship. Therefore, it can be concluded that the nickel( I I ~ a q u o and m o n o h y d r o x o complexes are the reacting species. The intersection with the ordinate and the slope give the values of two reaction rate constants, as seen from eqn. (4). The results obtained are: k°i = 2.9 x 10- lO cm s - ~ (at E ° i = - 0.496 V vs. SCE) k°i{on) = 5.7 x 10 - 3 (cm s-1)/(mol 1-1)
(at ENi(On) o = -- 0.634 V vs. SCE)**,
where the value (8.6 x 10 -6 cm 2 s - l ) calculated from the experimental value of limiting diffusion current by the Ilkovic equation was used for D. As seen from the above discussions, the current iNi(acac)o is composed of two parts, one being the current iNi due to the reduction of the prevailing nickel(II)-aquo complex and the other the current iNilom which comes from the reduction ofnickel(II)m o n o h y d r o x o complex produced from the aquo complex at the surface of DME. * If the standard potential of Ni(amalgam)/Ni(II) became available, the standard rate constant of the electrode reaction Ni(amalgam)/Ni(OHyp2 P~+can be calculated by multiplyingby the factor exp {(2F/RT) 0 0 c~[Esi(metal) - ENi(amalgam)] }. ** For the reduction of nickel (II) in 0.1 M KC1 solutions without acetylacetone,we obtain k0Ni(OH) = 1.2
x 10 2 (cm s- 1)/(mol 1-1),
as seen from Fig. 6. J. Electroanal. Chem., 28 (1970) 17 32
24
C. NISHIHARA H. MATSUDA
/
/
/
/
/
/
/ /A /A
/ 1oo (%)
///
-:
~
tNi(OH)
5
711]
#
t Ni
A
/
/
A
~
I "-"-----x-
I
00
1
I
2
I
3
L
0
xlO -10
2,0
3,0
40
COH /M
5.0
60
pH
Fig. 6. Dependence of the values of function H 0 on the concn, of hydroxyl ion COH.((2)) Ni(Acac) 2 + in 0.1 M KC1 solution with HAcac and acetate buffer, (A) Ni 2 ÷ in 0.1 M KC1 solution with acetate buffer, (D) Ni 2 + in 0.1 M KC1 solution. Fig. 7. Dependence of the currents due to the reduction of Ni 2 ÷ and Ni(OH) + on pH-value.
The ratios, lNi/INi(Acac)o and iNi(OH)/1Ni(Acac)o, indicate the degrees with which the two reacting species participate in the electrode processes, and can be expressed by z iNi/iNi(Acac)o
0 + kN,(O.)(#,) 0 1 = k 0. ; [kNi 0
INi(OH)/INi(Acac)o = kNi(OH) (ill)
1 --a
0
Co.l 0
COH/[kNi+ kNi(Om(fll)
1 -a
Co.].
Figure 7 shows the dependence of these ratios in per cent on the pH-values. For the wave concerning Ni(Acac)+, on the other hand, Table 2 gives eNi(aca¢)= 0.51 and Fig. 5 shows that the values of E},Ni(Acac} are constant ( - 0 . 8 9 6 V vs. SCE), independently of pH-value. This confirms that the reacting species is Ni(Acac) +, which is the prevailing species in the bulk of the solution. The electrode reaction rate constant can be calculated by 1'5 o = ( 2 F / 2 . 3 R T ) O ~ N i ( A c a ~ ) ( E 7. ~ Ni(Acac) --ENi(Acac) 0 l o g kNi(Acac) )1
log(t/D) +0.053 (5)
o
o where ENi(A¢.¢) is the standard potential of Ni(metal)/Ni(Acac) + and kN~(aca¢) the o standard rate constant at ENI(Acac). The result obtained is:
kOi(Aca¢) = 1.5 x 10 -7 c m s -1
(at EOi(Acac)---= - 0 . 6 6 1 V vs. S C E ) .
Analysis of the second wave
In the basic medium, the second wave is observed at about - 1.5 V vs. SCE, while the first wave is almost diminished, especially for small values of the drop time. Thus, in order to avoid the complexity caused by the first wave, the polarograms at t = 2.8 s in the basic medium were used for analysis of the second wave. The second wave shows the nature of a kinetic current, which seems to be due to the preceding chemical reaction, Ni(Acac)2 ~ N i ( A c a c ) 2 + A c a c - . As shown in the previous J. Electroanal. Chem., 28 (1970) 17-32
ACETYLACETONATECOMPLEXESOF NICKEL(II)
25
papers 4'6, even when the overall electrode reaction involves the preceding reactions, the irreversible current-voltage curves can also be expressed by eqn. (2), if only one species participates in the electrode process. Thus analysis of the second wave with the aid of eqn. (2) can be carried out similarly to that of the wave of nickel(II), yielding c~=0.51 and E ~ = - 1.46~ - 1.47 V vs. SCE (see Fig. 8) for pH 7.0-8.5. With
m ÷
~22.0 -1.47
-21.0
kd
>
-20.0 LU
c~
u.i
~k)
-19.0
-18.( -2.0
~-.o- . . . . . . i -2.5
t - 3.0
~ - -1.46 i -35
Log(oA~oc/tool i-~)
Fig. 8. Variation of the half-wave potentials, E+, of the second wave (Vq)and of the function {(2F/2.3 RT) 3
~E~+log Z fl~ c~,~a~+l°g (i,/id)} (O)with log CA¢,~. v=0
the assumption that the reacting species is Ni(Acac)~ ~--p)+, p can be given by 4,6 p = A
2F/2.3RT)c~E~+log
flvC~ac
+log(ilfid) /Alog CAcao.
(6)
AS seen from Fig. 8, in which the dependence of the numerator on the denominator on the right-hand side of eqn. (6) is shown, p is equal to 2, i.e., the reacting species is o Ni(Acac)2. The electrode reaction rate constant, kNi~g~a~)2, at the standard potential of Ni(metal)/Ni(Acac),, ENi~Ac,~) o 2, can be calculated by 4'6 _
log kNi(Acac) 2 0 =
(2FOCNi(AcaC)E/2.3R T)(E½,Ni(Acac)2-- EOi(Acac)z)q-- log { flzC2cac/( v~=OflvCVAcac) } -t- ½ log (t/O) + 0.053 + log (i,/id) •
(7)
The values of kinetic parameters obtained are : •
~Ni(mcac)2
=
0.51
k°i(Acae)2= 8.7× 10 15 cm s 1 (at ENitAca~ o = - 0 . 7 9 1 V v s . SCE). Preceding chemical reactions The first and the second waves involve the kinetic currents at pH-range 5 7
J. Electroanal.Chem.,28 (1970) 17-32
26
c. NISHIHARA,H. MATSUDA
and 7 10, respectively. As shown from the analyses of the d.c. polarograms, the reaction mechanism can be expressed by k 12 -- k 2 1 " K 2
Ni(Acac) + -7-
(first wave)
k23 = k32 •K3
' Ni(Acac)2 ,
' Ni(Acac)~
(8)
(second wave)
where k12, k21, k23 and k32 are the corresponding rate constants of the preceding chemical reactions and K2 and K3 the successive stability constants of Ni(Acac)2 and Ni(Acac);-, respectively. As is well known, chronopotentiometry is of great advantage in evaluating the kinetic parameters of preceding chemical reactions, because a wide range of transition times, i.e., from several thousandths to several tens of seconds, can easily be determined experimentally and the theoretical expressions of transition time are available for complicated reaction mechanisms and without limitation of the magnitude of rate constants. Furthermore, in some cases information about the equilibrium composition in the bulk of the solution can be obtained from the plateau of the I r ~ - I diagram, (where I is the applied current and r the transition time). In the following, we shall therefore determine the rate and stability constants of preceding chemical reactions by analysing the chronopotentiometric behavior. In order to avoid the complexity caused by the reduction of Ni(Acac)~ +, the pH-value of the solution should be chosen higher than 6.3, in which the reduction of Nl(Acac)~ does not occur. For pH > 6.3 the prevailing species in the solution are Ni(Acac) +, Ni(Acac)2 and Ni(Acac)3. Now, we should consider the two step-wise preceding chemical reactions, which are characterized by two kinetic parameters and two stability constants. Generally speaking, there may be large ambiguities for determining four parameters from one experimental I ~ - I curve. Fortunately, in the solution of pH-value above 8.4, the species Ni(Acac) + is practically absent in the bulk of the solution and the first wave has almost vanished. Then, we have only the second wave, which is accompanied with a single preceding reaction. Accordingly, it may be desirable that, at first, one determines the values of k23 (= k32"K3) and k32 from the second wave in the pH-range 8.4-9.5 and thereafter the values of k12 (= k 21" K2) and k21 from the first wave in the pH-range 6.3-7.4 by using the values of k23 and ka2 determined previously. For the second wave with a single preceding reaction, the relation between the applied constant current I and the transition time z is given by 21 I' z ~ = 1--½l'~½ K3CAcac.~.3
1 ~
erf([23z] ~)
(9)
with I' = I/(Tz ~ q F D ~ c °)
23 = k32 +k23cacac = k32(l + K3caca~)
(10) (11)
where q is the surface area of H M D E and c o the total concentration of Ni(II). In eqn. (9), the pseudo first-order reaction mechanism is assumed, because the total concentration of acetylacetone is sufficiently high, although that of acetylacetonate ion is not high enough. J. Electroanal. Chem., 28 (1970) 17-32
A CETYLACETONATE cOMPLEXES OF NICKEL (II)
27
For small values of z, which one can obtain for sufficiently large values of I, eqn. (9) is reduced to I' z ~ = (1 + K3 CAcac)-I = CNi(Acac)2 (CNi(Acac) 2 _~_CNi(Acae)3 ) - 1
(12)
as erf([2az]~)~2(23~/70~. Therefore, for sufficiently large values of I, the I'z ~ 1' curve shows a plateau, which corresponds to the concentration of Ni(Acac)z in equilibrium in the bulk of the solution (see Fig. 9). Thus, one can calculate the value of K 3 ( = k23/k32 ) from the value of I ' z ~ at the plateau. The average value obtained for pH-values from 8.4 to 9.8 is: K 3-- 1.0 × 103, which is about ten times too large in comparison with the value (1.3 × 10 z) given by Ringbom 16. 1.C
Q
0.5
~lcJ
0.0 0.0
1
I
05
10
_!
I
I
15
2.0
I~/s 2 Fig. 9. Typical example of the chronopotentiometric I' z{-I ' curves for the reduction of Ni(Acac)2 at pH 8.4. ( 0 ) O b s e r v e d ; ( - - ) calcd, by eqn. (9) for various values of 23: (a) 104, (b) 103, (c) 102, (d) 30, (e) 10, (f) 1, (g) lO i s I
In Fig. 9, the theoretical 1' z ~ - I ' curves calculated by eqn. (9) with K 3 = 1.0 x 103 for various values of the kinetic parameter 23 are shown by solid curves, together with the experimental points for pH 8.4. The correct value of 23 has been chosen so as to fit the theoretical curve by eqn. (9) to the experimental points as close as possible. In Fig. 10, the values of 23 determined in this way for pH-values from 8.4 to 9.5 are 80-
4O
20
0~ 0
I
I
I
I
0.5
1
1.5
2
I x l O -2
cAcoc/M Fig. 10. Dependence of the kinetic parameter 2 3 on Cac.c. J. Electroanal. Chem., 28 (1970) 17 32
28
C. NISHIHARA, H. MATSUDA
plotted against CAcao.This plot shows a linear relationship, as expected from eqn. (11), yielding k32 = 3.5 s- ~ and
k23 = 3.5 x 103 1 m o l - 1 s- 1
for the rate constants of the preceding reaction: Ni(Acac)~-~Ni(Acac)z+Acac-. For the first wave, which is observed in the pH-range 6.3 7.3, one should consider the two step-wise preceding chemical reactions, given by eqn. (8). Theoretical treatment of chronopotentiometry for two step-wise first-order preceding reactions has recently been given by Galus 22. The transition time of the first wave, which is due to the reduction of Ni(Acac) ÷, can then be expressed by I' r ~ = 1 - ¼I' ~z½( 1 + K3 CAcac)Ke CAcacJ - 1 X
{ erf([k+, z]4) id -- (2 3-t- 1--g2CAcac 1~2) kg
1 q- K 2 CAcao
g3CAcac
23--2"]
1 "-t-K 3 CAcac
1 -+-K 3 Cacac
1 -- K2CAcae ]~2~ K3CAcac + erf([k-z]~)IJ+(23+k~ 1 q- K2CA . . . . ) 1 + K3CAcac
23--22
]
+ I+K- o.oj } (13)
with 22 = k21 + k,2cgc,¢ = k21(1 + K2CAeae) J
=
(14)
K3CAca c ~½ (~3-22)2q-a~2J[3 (I@K3CAcac)2J
k+ = (23+22+J)/2 k_ = ( 2 3 + 2 2 - S ) / 2 , where I' is defined by eqn. (10). For sufficiently small values of v, eqn. (13) can be simplified into
I'r ~ = (1 + K2 CAcac-I- K2K3C2ea¢) - 1 = CNi(Acac) (CNi(Acac)_}_CNi(Acac}2_}_CNi(Acac)3)- 1
(15)
as eft( [k +z] ~)-+ 2 (k +"c/lr)~ and eft( [k_ r] ~) --+2 (k z/~) ~. Accordingly, the I'z}-I ' curve gives a plateau for sufficiently large values of I (see Fig. 11). As seen from eqn. (15), the value of I'z ~ at the plateau corresponds to the equilibrium composition of Ni(Acac) + in the' bulk of the solution, which is shown by open circles in Fig. 2 for various values of pH. These experimental points are in good agreement with the theoretical curve calculated by the values of stability constants by Ringbom a6. The theoretical I'z}-I ' curves have been calculated with the aid of eqn. (13) for various values of 22 by using the values of 23, which were calculated by eqn. (11) from the values of k32 and k23 previously determined. As an example, the theoretical curves for pH 6.7 are shown by solid curves in Fig. 11, in which the experimental points are also given. The correct value of 22 has been determined by the method of curve fitting similar to that used for the second wave. The values of 22 obtained in this way are plotted against CAcacin Fig. 12, in which one has a linear relationship, as ex-
J. Electroanal. Chem., 28 (1970) 1232
ACETYLACETONATE COMPLEXES OF NICKEL(II)
29
1.O (1
b
~
O5 f
~
d
~
0 o.o
I
0.0
C)
I
0.5
1.0
I
I
1.5
z/;½
20
Fig. 11. Typical example of the chronopotentiometric I' ~ - I ' curves for the reduction of Ni(Acac) + at pH 6.7. (O) Observed; ( - - ) calcd, by eqn. (13) with 23=(3.5+3.5 x 103 CAcao) S I for various values of 22: (a) 10'*.(b) 103, (c) 102, (d) 10, (e) 2, (f) 1, (g) 1 0 - 1 S 1. 8
O
~to
• 0
I
I
I
I
2
4
6
8
I
10×10 -4
CAcoc/M Fig. 12. Dependence of the kinetic parameter 22 on CAcao. p e c t e d f r o m eqn. (14). Therefore, the rate c o n s t a n t s of the p r e c e d i n g r e a c t i o n , N i ( A c a c ) z ~ N i ( A c a c ) + + A c a c - , c a n be c a l c u l a t e d as: k21=0.4s -1
and
k12=8.0x1031mol-Xs
-1.
F r o m the results o b t a i n e d in the p r e s e n t i n v e s t i g a t i o n b y a n a l y s i n g the d.c. p o l a r o g r a p h i c a n d c h r o n o p o t e n t i o m e t r i c b e h a v i o r , it m a y be c o n c l u d e d t h a t the e l e c t r o d e r e a c t i o n of n i c k e l ( I I ) - a c e t y l a c e t o n a t e c o m p l e x e s c a n be expressed b y the r e a c t i o n s c h e m e g i v e n i n Fig. 13. Ni(OH)*9
FO.St
2 Slow R12 k23 L Ni * . " Ni(Acac)* . P Ni(Acac) 2 4 k21 R32
• 2e °~'Ni(OH) kONi(OH) Ni
~e Ni
1
kONi
Ni
First wave
*2e °~'Ni (Acoc) kONi(A¢oc) Ni
Ni(Acac) 3
+2ei(Acac)2N o~
l"°
Ni(Acoc) 2
Ni
Second w a v e
Fig. 13. Reaction scheme of the reduction of nickei(II) acetyiacetonate complexes. The term "fast" means that the reaction proceeds so fast that the equilibrium between the relevant species is practically established, even when the current is flowing. The term "slow'" means that the reaction proceeds so slowly that the reaction practically does not occur in the vicinity of the electrode surface during electrolysis, although in the bulk of the solution the equilibrium between the relevant species is established.
J. Electroanal.Chem.,28 (1970) 17
32
30
C, N I S H I H A R A , H . M A T S U D A
APPENDIX
The current-voltage curve for the sum of two independent irreversible waves can be expressed by i = i, + i2 = i,,1/(1 + ~Pl) + il,2/(1 -}-~02)
(16)
with gos = exp
{(nsF/RT)~j(E-E~,j)}
(j= 1, 2).
Since eqn. (16) contains the six unknown parameters, il,s, ~j, E}o (J= 1, 2), in nonlinear fashion, one cannot here apply the usual method of least squares, in which the equations of condition are linear. However, if a reasonable approximation of the values of six parameters is available, an approximate linearization of the problem can be achieved in the following way: TABLE 3 EXAMPLE OF OUTPUT DATA OF A DIGITAL COMPUTER M1
INITIAL
M2
IL
E1/2
ALPHA
IL
100.0 78.8 78.3 78.0 78.1
- 1.0000 -0.9918 -0.9901 -0.9902 -0.9902
0,40 0,40 0.41 0,42 0.42
20.0 41.3 41.7 42.0 42.0
E
I OBS.
I CAL.
I DIF.
-- 0.7503 - 0.7728 -0.7953 --0.8178 --0.8403 -0.8629 -0.8854 -- 0.9079 -- 0.9304 - 0.9529 - 0.9754 0.9979 - 1.0204 -- 1.0429 - 1.0654 1.0880 1.1105 - 1.1330 - 1.1555 -- 1.1780 - 1.2005
0.0 0.l 1.1 2.6 5.0 9,6 17.8 28.6 41.1 54,4 69,1 84.5 97,9 107.5 113.2 116,6 118.5 119,5 119,6 119.8 119.8
0.2 0.5 1.1 2.3 4.9 9.8 17.8 28.6 41.0 54.4 69.2 84.5 97.8 107.5 113.4 116.7 118.4 119.2 119.6 119.8 120.0
- 0.2 - 0.4 0.0 0.3 0.1 -0.2 0.0 - 0.0 0.1 - 0.0 - 0.1 0.0 0.1 0.0 --0.2 -0.1 0.1 0.3 -0.0 -0.0 - 0.2
-
-
-
J. Electroanal, Chem., 28 (1970) 17-32
El~ z - 0.9000 -0.9031 -0.9013 -0.9017 .-0.9017
ALPHA
IL(M1/M2)
0.50 0.43 0.47 0.47 0.47
1.91 1.88 1.86 1.86
ACETYLACETONATE COMPLEXES OF NICKEL (II)
31
Suppose that (i~d)o, (aj)0 (E+,j)o (J = 1, 2) are known, by inspection or otherwise, to be reasonably approximate values. Then one can expand eqn. (16) in a Taylor series about these preliminary values. After omitting the second- and higher-order terms with respect to the small quantities, Aiz.j= il.j - (iLj)o, Aaj=ej--(aj)o and AE~,i= E~,j-(E~o)o (j= 1, 2), one has i = ~ (ij)o{1 +
j=l
(i,,j)o*Ai,,j- njV[E-(E~,j)o] (qOj)o ko~j+ RT 1 + (~oj)0 njV(aj)o (q~j)o AE+,j} RT 1 + (q~j)o
(17)
with (q~j)o = exp
{(njF/RT)(aj)o [ E - (E~,j)o] }
(ij) o = (i, ,j)o/ {1 + (~Pj)o} which is linear in the unknown corrections, Ai1,j, Aa2, AE~,j (j = 1, 2). The method of least squares can now be applied to system (17) in a straightforward manner, following which the initial estimate can be appropriately corrected. A second application, based upon expanding eqn. (16) around the corrected values, yields the improved values. Of course, one can repeat the process, until the correct values to be desired can be obtained. In the present investigation, the conditions: A~/a< 10 -2,
Ail/il< 10 -3
and
AErIEs< 10 4
were used as a criterion of correctness. An example of the output data of the digital computer is illustrated in Table 3, from which one can see the circumstances of convergence and the differences between the observed values and the calculated values obtained from eqn. (16) with the appropriate values of six parameters. ACKNOWLEDGEMENTS
The authors express their sincere thanks to Dr. Y. Takemori for his help in the chronopotentiometric measurements and to Mr. Y. Yamazaki for his useful advice in the construction of HMDE. SUMMARY
The polarographic and chronopotentiometric behavior of nickel(II)-acetylacetonate complexes is examined in the pH-range 3.6~9.8. By analysing the dependence of the d.c. polarographic current-voltage curves on the pH-value, the mechanism of the electrode reaction is elucidated and the relevant kinetic parameters, i.e., the transfer coefficients and the electrode reaction rate constants, are evaluated. For the preceding chemical reactions involved, the rate and equilibrium constants are determined by analysing the chronopotentiometric Iz~-I curves. The results obtained are summarized by the reaction scheme illustrated in Fig. 13. J. Electroanal. Chem., 28 (1970) 17-32
32
c . NISHIHARA, H. MATSUDA
REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
H. MATSUDA AND Y. AYABE,Z. Elektrochem., 63 (1959) 1164. H. MATSUDA AND Y. AYABE, Z. Elektrochem., 66 (1962) 469. H. MATSUDA, Y. AYABE AND K. ADACHI, Ber. Bunsenges. Physik. Chem., 67 (1963) 593. H. MATSUDAAND Y. AYABE,Bull. Chem. Soc. Japan, 29 (1956) 134. H. MATSUDA, Tokyo Kogyo Shikensho Hokoku, 61 (1966) 315. H. MATSUDA, Tokyo Kogyo Shikensho Hokoku, 62 (1967) 107. M. PETEK AND M. BRANICA, J. Polarog. Soc., 9 (1963) l. M. PI~TEK, LJ. JEFTI6 AND M. BRANICA in G. J. HILLS (Ed.), Pola?ography 1964, Proc. 3rd Intern. Conf., Southampton, Vol. 1, Macmillan, L o n d o n and Melbourne, 1966, p. 491. M. PEa'EK, J. KOTA AYD M. BRANICA, Collection Czech. Chem. Commun., 32 (1967) 3510. LJ. JEFTId AND M. BRANICA, Croat. Chem. Aeta, 35 (1963) 203, 211. M. BRANICA AND J. KISTA, Collection Czech. Chem. Connnun., 31 (1966) 2833. B. CoSOVld AND M. BRANICA, J. Polarog. Soc., 12 (1966) 5, 97. Y. YAMAZAKI, Rev. Polarog. Kyoto, 13 (1965) 26. J. DANDOY AND L. GIERST, J. Electroaual. Chem., 2 (1961) 116. L. GIERST AND A. L. JULIARD, J. Phys. Chem., 57 (1953) 701. A. RINGBOM, Complexation in AnaO, tical Chemistry, John Wiley and Sons Inc., New York, 1963. B. CoSOVld, M. VER:~I AND M. BRANtCA, J. Electroanal. Chem.. 22 (1969) 325. I. Ru~t(~ AND M. BRANICA, J. Electroanal. Chem., 22 (1969) 243. K. MORINAGA, Nippon Kagaku Zasshi, 76 (1955) 133. A. J. BETHUNE AND N. A. SWENDEMAN LOUD, Standard Aqueous Electrode Potentials. A. Hampel. Skokie, Ill., 1964. P. DELAHAY, New Instrumental Methods in Electrochemistry, Interscience Pub. Inc., New York, 1954, p. 179. Z. GaLus, Soviet Electrochem., 4 (1968) 491.
J. Electroanal. Chem., 28 (1970) 17 32
17
E L E C T R O D E K I N E T I C S OF T H E A C E T Y L A C E T O N A T E C O M P L E X E S OF NICKEL(II) A T T H E D R O P P I N G M E R C U R Y E L E C T R O D E
CHIZUKO NISHIHARA ANDHIROAKI MATSUDA* Government ChemicalIndustrial Research blstitute, Tokyo, Hon-machi, Shibuva-ku, Tokyo (Japan)
(Received May 18th, 1970)
INTRODUCTION In a series of previous investigations 1- 6 in our laboratory, it has been shown that the polarographic current-voltage curves can be analysed to evaluate the kinetic parameters related to the electrode reactions of metal ion complexes. As examples, the hydroxo, ammine, tartrate and acetate complexes of zinc(II) were experimentally examined and the reaction mechanisms of their electrode processes were elucidated. The metal-acetylacetone systems have recently been attracting our attention due to their complicated and interesting polarographic behavior v- a2. The present paper deals with the polarographic and chronopotentiometric behavior of the nickel(II)-acetylacetone system in a wide range of pH-values (3-10), resulting in the elucidation of its reaction mechanism and in the evaluation of the relevant kinetic parameters. EXPERIMENTAL Reagents
A standard solution of nickel(II) was prepared by dissolving a known amount of pure nickel metal (Johnson Matthey, purity 99.99%o) in dilute HNO3, evaporating to paste and diluting to 5 x 10-3 M. Stock solutions were prepared of 1 M KC1 (supporting electrolyte), 0.5 ~ carboxymethyl cellulose (CMC) (maximum suppressor), 2.5 x 10-1 M acetylacetone (HAcac) and 2.5 x 10-1 M buffer, from analytical reagent grade chemicals and distilled water. For buffer solutions the systems HAc-NaAc was used for the pH-range 3.2-5.1, K H z P O 4 - N a z H P O 4 for 5.2-7.6 and H3BO3N a O H for 8.1-9.8. Apparatus
The d.c. polarograph used was of a conventional type, which contained a recorder (San'ei Sokki Galvanograph HR-101) with a suitable damping circuit and a potentiometer drum with 20 turns of 10 f~ resistance. The instrument was operated at a rate of change of applied potential of ca. 20 mV m i n - 1. The dropping mercury electrode (DME) employed had a drop time t of 5.2 s and a flow rate of mercury m * Present address : Department of Electrochemistry,Faculty of Engineering, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo.
J. Electroanal. Chem., 28 (1970) 17-32
18
c . NISHIHARA, H. MATSUDA
of 1.46 mg s- 1 when measured in an air-free sample solution at - 1.2 V vs. SCE and at 49 cm of height of the mercury head. An H-type electrolysis cell was connected to a saturated calomel electrode of surface area ca. 8 cm 2, which was used as a counter electrode, through an agar agar bridge containing 0.1 M KC1 solution. The chronopotentiometric apparatus used was of conventional design, in which a memory-oscilloscope (Iwasaki Tsushinki Memoriscope MS-5013) was used for tracing the potential-time curves. A balanced head, stationary, hanging mercury drop electrode (HMDE) a3 (working electrode), a platinum wire electrode (counter electrode) and a saturated calomel electrode (SCE) (reference electrode) were arranged with an H-type electrolysis cell. The characteristics of H M D E used were : t = 5.8 min, m=4.0 mg min ~ and t = 10.5 min, m = 1.9 mg m i n - ~ in distilled water at 49 cm of height of the mercury head with no applied potential. The mercury run-off time, at which the growth of the mercury drop was ended by lowering the mercury reservoir, was chosen as 3.0 min and 5.0 min. Procedure
The composition of sample solutions was 0.5 m M Ni(II), 0,1 M KC114, 0.005,o,/o CMC, 2.5 x 10 .2 M HAcac and 2.5 x 10 -2 M buffer, unless otherwise stated. For chronopotentiometry, CMC was omitted. The sample solutions were left at room temperature for one night after preparation, and before measurements they were left in a thermostat for more than 30 min and then deaerated for 20 rain with nitrogen gas which had passed through distilled water. All measurements were carried out in the thermostat at 30.0 +_0.1 °C. In d.c. polarography the ~hrrent was measured as the difference between the total current and the residual current at the same potential axis. In chronopotentiometry the transition time was determined graphically after Gierst and Juliard 15. Most of the numerical calculations were performed by a digital computer (FACOM 270-30). RESULTS AND DISCUSSION
D.c. polarograms at three typical pH-values are shown in Fig. 1. Below pH 4.5, only one wave which is assumed to be a composite of two independent waves is observed at about - 1.0 V vs. SCE. At higher pH values, the height of the first wave decreases, and a second wave appears at about - 1 . 5 V vs. SCE, the height of which increases with pH. In the basic medium, the first wave has almost vanished and the height of the second wave decreases with increasing pH-value. In order to analyse the complicated polarographic behavior mentioned above, it is necessary at first to know the equilibrium distribution between various species of the acetylacetonate complexes of nickel(II) in the bulk of the solution. In Fig. 2, solid curves show such an equilibrium distribution in dependence on pH. In the construction of this diagram, the activity coefficients of all species in the solution were assumed to be equal to unity, and for the acid dissociation constant of acetylacetone and for the total stability constants of Ni (Acac) ÷ and Ni (Acac)2 the following values were used: p K n A c a c = 8.8, log/~1 = 5.5 and log/~2 = 9.8 at 30°C 16. The total stability constant of Ni(Acac)~, was assumed as log/~3 = 12.8 at 30°C for reasons mentioned later. J. Electroanal. Chem.,
28 (1970) 1%32
19
ACETYLACETONATE COMPLEXES OF NICKEL(IX)
::?:
-0.8
--1,0
::: :: :,-~:
-12
-1.4
-1,6
E/V vs.SC E
~
t
t'l2*~~Acac)~i(Acac)j
3
4
5
6
7
8
9
10
pH
Fig. 1. D.c. polarograms of acetylacetonate complexes of nickel(II) for three different pH-values. Composition of solutions: 0.5 mM Ni(II), 0.1 M KC1, 2.5 x 10 z M HAcac, 2.5 x 10 -e M buffer and 0.00500 CMC, (a) pH 4.2, (b) pH 6.3, (c) pH 7.8. Fig. 2, Equilibrium distribution of nickel(II)-acetylacetonate complexes vs. pH-value for total concn, of nickel(II)=5 x 10 -4 M, total concn, of acetylacetone=2.5 x 10 .2 M and ionic strength=0.1 at 30°C. ~ ) Calcd. using pKHA~a¢= 8.8, log/31 = 5.5, log f12 = 9.8 and log f13 = 12.8; ( x ) distribution of Ni 2+ and Ni(Acac) + determined by d.c. polarography; (O) distribution of Ni(Acac) + and Ni(Acac)2 obtained by chronopotentiometry.
Analysis of the first wave At pH-values from 3.5 to 4.5, one wave is observed at about - 1.0 V vs. SCE, which is here called the first wave, and its limiting current is diffusion-controlled. The shapes of the d.c. and a.c. polarograms (see Figs. 1 and 3) suggest that the first wave is a composite of two independent irreversible reduction waves. These two waves are assumed to be due to the reduction of two complex species, Ni(Acac)g + and Ni (Acac) +, which are prevailing species in equilibrium in the bulk of the solution (see Fig. 2). The current-voltage curve for the s u m o f two independent irreversible reduction waves can be expressed by
i = iNi(Acac)o-}- iNi(Acac) ll,Ni(Aca¢)o = l -~-exp { (2F/RT) ~Ni(Acac)o (E -- g½,Ni(Acac)o) } -~ ll,Ni(Acac) 1 + exp {(2F/R T) ~Ni(Acac)(E -- E½,Ni(Acac)) }
(1) J. Electroanal. Chem., 28 (1970) 17-32
20
C. NISHIHARA, H. MATSUDA
~O~8
.... ;:1.O
Fig. 3. Typical a.c. polarogram ofnickel(II) acetylacetonate complexes at pH 4.5 (drop time = 3.3 s).
where i is the average polarographic current, il the average limiting current, E the electrode potential of DME, E~ the irreversible half-wave potential, ~ the cathodic transfer coefficient, and F, R, T have their usual significance. Thus, it follows that an observed current-voltage curve should be expressed by eqn. (1) with appropriate parameters. In order to separate the observed wave into two waves, the six parameters, il,Ni(Acac)o, ~Ni(Acac)o, E~-,Ni(Acac)o, ll,Ni(Acac), ~Ni(Acac) and E½,Ni(Acac), a r e chosen as unknown constants and determined by the non-linear least squares method (see Appendix). The results are given in Tables 1 and 2. Differences in currents between observed and calculated points at the same potentials were within experimental error, i.e. within 1,5o of the limiting current (see Table 3 in Appendix). In Fig. 4, two separated TABLE 1 •
7+
LIMITING CURRENTS~ HALF-WAVE POTENTIALS AND TRANSFER COEFFICIENTS OF N1 (Acac)~ AND N i (Acac) + SEPARATED BY THE METHOD OF LEAST SQUARES FOR THREE DIFFERENT DROP TIMES AT p n 3.9
(Sensitivity: 2.5 x 10 8 A m m -1) t/s
Ni(Acac)~ +
Ni(Acac) +
h.Ni~A.,~>o
lI,Ni(Acac)
3.4 5.1 7.4
ijmm
-- E~/ (V vs. SCE)
~
i Its~ mms ~
124.7 102.7 85.4
1.009 1.005 0.997
0.41 228 0.39 232 0.38 232
J. Electroanal. Chem., 28 (1970) 17-32
~jmm
-- E4_/ (V vs. SCE)
~
il t}/ mms ~
22.0 19.2 14.5
0.899 0.899 0.896
0.54 40 0.50 43 0.58 39
5.7 5.3 5.9
ACETYLACETONATE COMPLEXES OF NICKEL(II)
21
TABLE 2 LIMITINOCURRENTS,HALF-WAVEPOTENTIALSANDTRANSFERCOEFFICIENTSOF Ni (Acac)2+ ANDNi(Acac) + DETERMINEDBY THEMETHODOF LEASTSQUARESFOR V A R I O U S pH-VALUESAT t = 5.1 S (Sensitivity: 2.5 x 10 -8 A ram-i) N i (A cac )~ + iz/mm - E ~ / ( V vs. SCE)
ct
N i( Acac) + ijmm - E ~ / ( V vs. SCE)
ct
it.uitacad~o il,Nitac~)
a
3.6 3.7 3.9 4.2 4.5
104.4 105.6 102.7 94.4 83.1
1.010 1.007 1.005 0.987 0.968
0.41 0.40 0.39 0.38 0.38
16.8 16.3 19.2 28.9 35.5
0.49 0.44 0.50 0.53 0.63
6.2 6.5 5.3 3.3 2.3
b
3.6 3.7 3.9 4.2 4.5
• 121.8 115.5 119.1 119.8 120.8
0.997 0.988 0.985 0.968 0.949
0.39 0.38 0.39 0.37 0.35
3.5 4.0 4.5 4.8
121.4 120.2 122.3 123.9
0.999 0.973 0.941 0.913
0.41 0.38 0.36 0.36
pH
c
0.897 0.895 0.899 0.894 0.890
a: in 0.1 M KC1 solutions with HAcac and acetate buffer; b: in 0.1 M KCI solutions with acetate buffer: c: in 0.1 M KC1 solutions. waves, which can be c a l c u l a t e d b y using the six p a r a m e t e r s d e t e r m i n e d above, are s h o w n t o g e t h e r with the o r i g i n a l c o m p o s i t e wave. D u r i n g the p r o g r e s s of the p r e s e n t investigation, Cosovi6 e t al. 17 have s h o w n t h a t the c o m p o s i t e wave c a n be s e p a r a t e d into two i n d e p e n d e n t curves by derivative pulse p o l a r o g r a p h y . F u r t h e r m o r e , Ru~id a n d B r a n i c a 18 have p r o p o s e d a m e t h o d of l o g a r i t h m i c analysis of two o v e r l a p p i n g d,c. p o l a r o g r a p h i c waves. H o w e v e r , the p r e s e n t m e t h o d seems to be m o r e reliable, b e c a u s e the values of p a r a m e t e r s a r e chosen b y the m e t h o d of least squares. T a b l e 1 indicates t h a t /1,Ni(Acac)o, /l,Ni(Acac) a n d also the s u m of these two are diffusion-controlled, so t h a t the r a t i o o f two limiting currents, ll.Ni(Acac)o//l,Ni(Acac), is i n d e p e n d e n t of the d r o p time. This r a t i o c o r r e s p o n d s to the e q u i l i b r i u m d i s t r i b u tion of N i ( A c a c ) g+ a n d N i ( A c a c ) + in the b u l k of the solution, if the diffusion coefficients a n d the activity coefficients of these two c o m p l e x e s are a s s u m e d to be e q u a l to each other. T h e results o b t a i n e d for v a r i o u s p H - v a l u e s at t = 5.1 s are given in T a b l e 2. In Fig. 2 the e q u i l i b r i u m d i s t r i b u t i o n of c o m p l e x e s thus o b t a i n e d is shown b y crosses. T h e e x p e r i m e n t a l p o i n t s are a l m o s t in a g r e e m e n t with the t h e o r e t i c a l curve. T h e r e l a t i o n b e t w e e n the values of the half-wave poteritial of N i ( A c a c ) 2 + a n d the p H - v a l u e is given b y the o p e n circles in Fig. 5, which indicates t h a t the half-wave p o t e n t i a l varies with the p H - v a l u e s . Thus, it m a y be s u p p o s e d t h a t h y d r o x y l ion o r acetate ion (which is a c o n s t i t u e n t of the buffer in the p H - r a n g e considered) p a r t i c i p a t e s in the r e d u c t i o n of nickel(II). F o r this reason, the r e d u c t i o n of nickel(II) in 0.1 M K C l - s o l u t i o n s with a n d w i t h o u t acetate buffer has been examined. F o r this case the c u r r e n t - v o l t a g e curve m a y simply be expressed by J. Electroanal. Chem., 28 (1970) 17-32
22
C. NISHIHARA~ H. M A T S U D A
150
-1.00~~m\
jj, j,
E 100 E ,.'b_ 50
S cQ 2-
I
-0.9
rn\ .\\
ua
\
\
\
-090 I
-1.0
I
-1.1
E / V vs SCE
-u
0 u
•
I -1.2
i
3.5
i
4,0
i
pH
45
Fig. 4. Composite wave and two waves separated by method of least squares at p H 3.9 (drop t i m e = 5 . 1 s). ( ) Original composite wave, ( - - ) separated wave due to the reduction of Ni(Acac)20 +, @ . . . . ) separated wave due to the reduction of Ni(Acac) +. Fig. 5. Dependence of the half-wave potentials of Ni(Acac)g + and Ni(Acac) ÷ on pH-value. Half-wave potential of: (O) Ni(Acac)g ÷ in 0.1 M KC1 solution with HAcac and acetate buffer, (A) Ni 2 + in 0.1 M KC1 solution with acetate buffer, ([~) Ni z+ in 0.1 M KC1 solution, (O) Ni(Acac) + in 0.1 M KC1 solution with HAcac and acetate buffer.
J = i1[1 +exp
\
[3 \
// -0.8
\ \'~X
-0.95
{(2F/RT)c~(E-E¢)}]-I
(2)
The analysis of the observed current-voltage curves with the aid of eqn. (2) has also been performed by the non-linear least squares method similar to the case of composite wave. The results are given in Table 2 and shown in Fig. 5 by open triangles and squares. Table 2 indicates that the transfer coefficient of Ni(Acac) 2 ~ is, independently of the composition of solutions, equal to 0.38, which is in agreement with the value reported by Morinaga 19 (0.41 in 0.1 M KNO3 with 0.01°Jo gelatin). As seen from Fig. 5, the values of the half-wave potential for the three kinds of solutions (with HAcac and buffer, without HAcac and with buffer, and without HAcac and buffer) show the same dependence on the pH-value ; nevertheless those of the composite wave are somewhat more negative, this being supposed to arise from the difference in composition of the solutions. Accordingly, we may conclude that in these three kinds of solution, nickel(II) is reduced in the same mechanism, so that the reacting species are nickel(II)aquo and -hydroxo complexes 14. According to Matsuda and Ayabe 2'5, when nickel(II) is reduced as a series of successive hydroxo complexes, between which the dissociation and association reactions proceed reversibly, the following relation between the irreversible half-wave potential and the concentration of hydroxyl ion holds: J. Electroanal. Chem., 28 (1970) 17 32
ACETYLACETONATE
H o = 1.13
COMPLEXES OF
NICKEL(II)
23
t-}( Z fl'~C~on)exp {(2F/RT)a(E_~-E°i)} v--O
=D-~
~,
o
(3)
, 1-
p-0
where it is assumed that all relevant electrode processes have the c o m m o n value of transfer coefficients and that the activity coefficients of all species are equal to unity and the diffusion coefficients of all species in the solution and of Ni (in amalgam) are equal to each other. In eqn. (3), new notations are: D the c o m m o n value of the diffusion coefficients; Con the concentration of hydroxyl ion, which is assumed to be constant everywhere in the solution; fl'o the total stability constant of the p-th nickel(II) hydroxo complex, Ni(OH)~2-m+ ; E ° i the standard potential of Ni (amalgam)/ Ni(II); k~i~omp the electrode reaction rate constant of Ni(OH)(p2- P)+ at the standard potential of Ni (amalgam)/Ni(OH)(pz-p)+, E°iton)p. Since the stability constant of the nickel(II)-hydroxo complex 16 is log fit = pKyi(OH )= 4.6 at 30°C, eqn. (3) can be simplified into H o - 1.13 t -~ exp { ( 2 F / R T ) a ( E ~ - E ° i ) } = D-~{koi
o , ) 1 - ~ COHq-...} q- kNi~Otl)(fil
(4)
in the pH-range considered. The function Ho in eqn. (4) contains four parameters, E+, c~, t and E°i. The first three can be determined from experiment. For E°~ we shall here use the value of the standard potential of Ni(metal)/Ni(II), i.e., E°i = - 0 . 4 9 6 V vs. SCE 2° at 30°C, because the value of the standard potential of Ni (amalgam)/Ni(II) " 0 is not available in the literature. Then, if kNi(o.), is read as the value at the standard potential of Ni(metal)/Ni(OH)~2-p)+, eqn. (4) holds in its original form*. In Fig. 6, the values of H o are plotted against the concentration of hydroxyl ion. This figure shows a linear relationship. Therefore, it can be concluded that the nickel( I I ~ a q u o and m o n o h y d r o x o complexes are the reacting species. The intersection with the ordinate and the slope give the values of two reaction rate constants, as seen from eqn. (4). The results obtained are: k°i = 2.9 x 10- lO cm s - ~ (at E ° i = - 0.496 V vs. SCE) k°i{on) = 5.7 x 10 - 3 (cm s-1)/(mol 1-1)
(at ENi(On) o = -- 0.634 V vs. SCE)**,
where the value (8.6 x 10 -6 cm 2 s - l ) calculated from the experimental value of limiting diffusion current by the Ilkovic equation was used for D. As seen from the above discussions, the current iNi(acac)o is composed of two parts, one being the current iNi due to the reduction of the prevailing nickel(II)-aquo complex and the other the current iNilom which comes from the reduction ofnickel(II)m o n o h y d r o x o complex produced from the aquo complex at the surface of DME. * If the standard potential of Ni(amalgam)/Ni(II) became available, the standard rate constant of the electrode reaction Ni(amalgam)/Ni(OHyp2 P~+can be calculated by multiplyingby the factor exp {(2F/RT) 0 0 c~[Esi(metal) - ENi(amalgam)] }. ** For the reduction of nickel (II) in 0.1 M KC1 solutions without acetylacetone,we obtain k0Ni(OH) = 1.2
x 10 2 (cm s- 1)/(mol 1-1),
as seen from Fig. 6. J. Electroanal. Chem., 28 (1970) 17 32
24
C. NISHIHARA H. MATSUDA
/
/
/
/
/
/
/ /A /A
/ 1oo (%)
///
-:
~
tNi(OH)
5
711]
#
t Ni
A
/
/
A
~
I "-"-----x-
I
00
1
I
2
I
3
L
0
xlO -10
2,0
3,0
40
COH /M
5.0
60
pH
Fig. 6. Dependence of the values of function H 0 on the concn, of hydroxyl ion COH.((2)) Ni(Acac) 2 + in 0.1 M KC1 solution with HAcac and acetate buffer, (A) Ni 2 ÷ in 0.1 M KC1 solution with acetate buffer, (D) Ni 2 + in 0.1 M KC1 solution. Fig. 7. Dependence of the currents due to the reduction of Ni 2 ÷ and Ni(OH) + on pH-value.
The ratios, lNi/INi(Acac)o and iNi(OH)/1Ni(Acac)o, indicate the degrees with which the two reacting species participate in the electrode processes, and can be expressed by z iNi/iNi(Acac)o
0 + kN,(O.)(#,) 0 1 = k 0. ; [kNi 0
INi(OH)/INi(Acac)o = kNi(OH) (ill)
1 --a
0
Co.l 0
COH/[kNi+ kNi(Om(fll)
1 -a
Co.].
Figure 7 shows the dependence of these ratios in per cent on the pH-values. For the wave concerning Ni(Acac)+, on the other hand, Table 2 gives eNi(aca¢)= 0.51 and Fig. 5 shows that the values of E},Ni(Acac} are constant ( - 0 . 8 9 6 V vs. SCE), independently of pH-value. This confirms that the reacting species is Ni(Acac) +, which is the prevailing species in the bulk of the solution. The electrode reaction rate constant can be calculated by 1'5 o = ( 2 F / 2 . 3 R T ) O ~ N i ( A c a ~ ) ( E 7. ~ Ni(Acac) --ENi(Acac) 0 l o g kNi(Acac) )1
log(t/D) +0.053 (5)
o
o where ENi(A¢.¢) is the standard potential of Ni(metal)/Ni(Acac) + and kN~(aca¢) the o standard rate constant at ENI(Acac). The result obtained is:
kOi(Aca¢) = 1.5 x 10 -7 c m s -1
(at EOi(Acac)---= - 0 . 6 6 1 V vs. S C E ) .
Analysis of the second wave
In the basic medium, the second wave is observed at about - 1.5 V vs. SCE, while the first wave is almost diminished, especially for small values of the drop time. Thus, in order to avoid the complexity caused by the first wave, the polarograms at t = 2.8 s in the basic medium were used for analysis of the second wave. The second wave shows the nature of a kinetic current, which seems to be due to the preceding chemical reaction, Ni(Acac)2 ~ N i ( A c a c ) 2 + A c a c - . As shown in the previous J. Electroanal. Chem., 28 (1970) 17-32
ACETYLACETONATECOMPLEXESOF NICKEL(II)
25
papers 4'6, even when the overall electrode reaction involves the preceding reactions, the irreversible current-voltage curves can also be expressed by eqn. (2), if only one species participates in the electrode process. Thus analysis of the second wave with the aid of eqn. (2) can be carried out similarly to that of the wave of nickel(II), yielding c~=0.51 and E ~ = - 1.46~ - 1.47 V vs. SCE (see Fig. 8) for pH 7.0-8.5. With
m ÷
~22.0 -1.47
-21.0
kd
>
-20.0 LU
c~
u.i
~k)
-19.0
-18.( -2.0
~-.o- . . . . . . i -2.5
t - 3.0
~ - -1.46 i -35
Log(oA~oc/tool i-~)
Fig. 8. Variation of the half-wave potentials, E+, of the second wave (Vq)and of the function {(2F/2.3 RT) 3
~E~+log Z fl~ c~,~a~+l°g (i,/id)} (O)with log CA¢,~. v=0
the assumption that the reacting species is Ni(Acac)~ ~--p)+, p can be given by 4,6 p = A
2F/2.3RT)c~E~+log
flvC~ac
+log(ilfid) /Alog CAcao.
(6)
AS seen from Fig. 8, in which the dependence of the numerator on the denominator on the right-hand side of eqn. (6) is shown, p is equal to 2, i.e., the reacting species is o Ni(Acac)2. The electrode reaction rate constant, kNi~g~a~)2, at the standard potential of Ni(metal)/Ni(Acac),, ENi~Ac,~) o 2, can be calculated by 4'6 _
log kNi(Acac) 2 0 =
(2FOCNi(AcaC)E/2.3R T)(E½,Ni(Acac)2-- EOi(Acac)z)q-- log { flzC2cac/( v~=OflvCVAcac) } -t- ½ log (t/O) + 0.053 + log (i,/id) •
(7)
The values of kinetic parameters obtained are : •
~Ni(mcac)2
=
0.51
k°i(Acae)2= 8.7× 10 15 cm s 1 (at ENitAca~ o = - 0 . 7 9 1 V v s . SCE). Preceding chemical reactions The first and the second waves involve the kinetic currents at pH-range 5 7
J. Electroanal.Chem.,28 (1970) 17-32
26
c. NISHIHARA,H. MATSUDA
and 7 10, respectively. As shown from the analyses of the d.c. polarograms, the reaction mechanism can be expressed by k 12 -- k 2 1 " K 2
Ni(Acac) + -7-
(first wave)
k23 = k32 •K3
' Ni(Acac)2 ,
' Ni(Acac)~
(8)
(second wave)
where k12, k21, k23 and k32 are the corresponding rate constants of the preceding chemical reactions and K2 and K3 the successive stability constants of Ni(Acac)2 and Ni(Acac);-, respectively. As is well known, chronopotentiometry is of great advantage in evaluating the kinetic parameters of preceding chemical reactions, because a wide range of transition times, i.e., from several thousandths to several tens of seconds, can easily be determined experimentally and the theoretical expressions of transition time are available for complicated reaction mechanisms and without limitation of the magnitude of rate constants. Furthermore, in some cases information about the equilibrium composition in the bulk of the solution can be obtained from the plateau of the I r ~ - I diagram, (where I is the applied current and r the transition time). In the following, we shall therefore determine the rate and stability constants of preceding chemical reactions by analysing the chronopotentiometric behavior. In order to avoid the complexity caused by the reduction of Ni(Acac)~ +, the pH-value of the solution should be chosen higher than 6.3, in which the reduction of Nl(Acac)~ does not occur. For pH > 6.3 the prevailing species in the solution are Ni(Acac) +, Ni(Acac)2 and Ni(Acac)3. Now, we should consider the two step-wise preceding chemical reactions, which are characterized by two kinetic parameters and two stability constants. Generally speaking, there may be large ambiguities for determining four parameters from one experimental I ~ - I curve. Fortunately, in the solution of pH-value above 8.4, the species Ni(Acac) + is practically absent in the bulk of the solution and the first wave has almost vanished. Then, we have only the second wave, which is accompanied with a single preceding reaction. Accordingly, it may be desirable that, at first, one determines the values of k23 (= k32"K3) and k32 from the second wave in the pH-range 8.4-9.5 and thereafter the values of k12 (= k 21" K2) and k21 from the first wave in the pH-range 6.3-7.4 by using the values of k23 and ka2 determined previously. For the second wave with a single preceding reaction, the relation between the applied constant current I and the transition time z is given by 21 I' z ~ = 1--½l'~½ K3CAcac.~.3
1 ~
erf([23z] ~)
(9)
with I' = I/(Tz ~ q F D ~ c °)
23 = k32 +k23cacac = k32(l + K3caca~)
(10) (11)
where q is the surface area of H M D E and c o the total concentration of Ni(II). In eqn. (9), the pseudo first-order reaction mechanism is assumed, because the total concentration of acetylacetone is sufficiently high, although that of acetylacetonate ion is not high enough. J. Electroanal. Chem., 28 (1970) 17-32
A CETYLACETONATE cOMPLEXES OF NICKEL (II)
27
For small values of z, which one can obtain for sufficiently large values of I, eqn. (9) is reduced to I' z ~ = (1 + K3 CAcac)-I = CNi(Acac)2 (CNi(Acac) 2 _~_CNi(Acae)3 ) - 1
(12)
as erf([2az]~)~2(23~/70~. Therefore, for sufficiently large values of I, the I'z ~ 1' curve shows a plateau, which corresponds to the concentration of Ni(Acac)z in equilibrium in the bulk of the solution (see Fig. 9). Thus, one can calculate the value of K 3 ( = k23/k32 ) from the value of I ' z ~ at the plateau. The average value obtained for pH-values from 8.4 to 9.8 is: K 3-- 1.0 × 103, which is about ten times too large in comparison with the value (1.3 × 10 z) given by Ringbom 16. 1.C
Q
0.5
~lcJ
0.0 0.0
1
I
05
10
_!
I
I
15
2.0
I~/s 2 Fig. 9. Typical example of the chronopotentiometric I' z{-I ' curves for the reduction of Ni(Acac)2 at pH 8.4. ( 0 ) O b s e r v e d ; ( - - ) calcd, by eqn. (9) for various values of 23: (a) 104, (b) 103, (c) 102, (d) 30, (e) 10, (f) 1, (g) lO i s I
In Fig. 9, the theoretical 1' z ~ - I ' curves calculated by eqn. (9) with K 3 = 1.0 x 103 for various values of the kinetic parameter 23 are shown by solid curves, together with the experimental points for pH 8.4. The correct value of 23 has been chosen so as to fit the theoretical curve by eqn. (9) to the experimental points as close as possible. In Fig. 10, the values of 23 determined in this way for pH-values from 8.4 to 9.5 are 80-
4O
20
0~ 0
I
I
I
I
0.5
1
1.5
2
I x l O -2
cAcoc/M Fig. 10. Dependence of the kinetic parameter 2 3 on Cac.c. J. Electroanal. Chem., 28 (1970) 17 32
28
C. NISHIHARA, H. MATSUDA
plotted against CAcao.This plot shows a linear relationship, as expected from eqn. (11), yielding k32 = 3.5 s- ~ and
k23 = 3.5 x 103 1 m o l - 1 s- 1
for the rate constants of the preceding reaction: Ni(Acac)~-~Ni(Acac)z+Acac-. For the first wave, which is observed in the pH-range 6.3 7.3, one should consider the two step-wise preceding chemical reactions, given by eqn. (8). Theoretical treatment of chronopotentiometry for two step-wise first-order preceding reactions has recently been given by Galus 22. The transition time of the first wave, which is due to the reduction of Ni(Acac) ÷, can then be expressed by I' r ~ = 1 - ¼I' ~z½( 1 + K3 CAcac)Ke CAcacJ - 1 X
{ erf([k+, z]4) id -- (2 3-t- 1--g2CAcac 1~2) kg
1 q- K 2 CAcao
g3CAcac
23--2"]
1 "-t-K 3 CAcac
1 -+-K 3 Cacac
1 -- K2CAcae ]~2~ K3CAcac + erf([k-z]~)IJ+(23+k~ 1 q- K2CA . . . . ) 1 + K3CAcac
23--22
]
+ I+K- o.oj } (13)
with 22 = k21 + k,2cgc,¢ = k21(1 + K2CAeae) J
=
(14)
K3CAca c ~½ (~3-22)2q-a~2J[3 (I@K3CAcac)2J
k+ = (23+22+J)/2 k_ = ( 2 3 + 2 2 - S ) / 2 , where I' is defined by eqn. (10). For sufficiently small values of v, eqn. (13) can be simplified into
I'r ~ = (1 + K2 CAcac-I- K2K3C2ea¢) - 1 = CNi(Acac) (CNi(Acac)_}_CNi(Acac}2_}_CNi(Acac)3)- 1
(15)
as eft( [k +z] ~)-+ 2 (k +"c/lr)~ and eft( [k_ r] ~) --+2 (k z/~) ~. Accordingly, the I'z}-I ' curve gives a plateau for sufficiently large values of I (see Fig. 11). As seen from eqn. (15), the value of I'z ~ at the plateau corresponds to the equilibrium composition of Ni(Acac) + in the' bulk of the solution, which is shown by open circles in Fig. 2 for various values of pH. These experimental points are in good agreement with the theoretical curve calculated by the values of stability constants by Ringbom a6. The theoretical I'z}-I ' curves have been calculated with the aid of eqn. (13) for various values of 22 by using the values of 23, which were calculated by eqn. (11) from the values of k32 and k23 previously determined. As an example, the theoretical curves for pH 6.7 are shown by solid curves in Fig. 11, in which the experimental points are also given. The correct value of 22 has been determined by the method of curve fitting similar to that used for the second wave. The values of 22 obtained in this way are plotted against CAcacin Fig. 12, in which one has a linear relationship, as ex-
J. Electroanal. Chem., 28 (1970) 1232
ACETYLACETONATE COMPLEXES OF NICKEL(II)
29
1.O (1
b
~
O5 f
~
d
~
0 o.o
I
0.0
C)
I
0.5
1.0
I
I
1.5
z/;½
20
Fig. 11. Typical example of the chronopotentiometric I' ~ - I ' curves for the reduction of Ni(Acac) + at pH 6.7. (O) Observed; ( - - ) calcd, by eqn. (13) with 23=(3.5+3.5 x 103 CAcao) S I for various values of 22: (a) 10'*.(b) 103, (c) 102, (d) 10, (e) 2, (f) 1, (g) 1 0 - 1 S 1. 8
O
~to
• 0
I
I
I
I
2
4
6
8
I
10×10 -4
CAcoc/M Fig. 12. Dependence of the kinetic parameter 22 on CAcao. p e c t e d f r o m eqn. (14). Therefore, the rate c o n s t a n t s of the p r e c e d i n g r e a c t i o n , N i ( A c a c ) z ~ N i ( A c a c ) + + A c a c - , c a n be c a l c u l a t e d as: k21=0.4s -1
and
k12=8.0x1031mol-Xs
-1.
F r o m the results o b t a i n e d in the p r e s e n t i n v e s t i g a t i o n b y a n a l y s i n g the d.c. p o l a r o g r a p h i c a n d c h r o n o p o t e n t i o m e t r i c b e h a v i o r , it m a y be c o n c l u d e d t h a t the e l e c t r o d e r e a c t i o n of n i c k e l ( I I ) - a c e t y l a c e t o n a t e c o m p l e x e s c a n be expressed b y the r e a c t i o n s c h e m e g i v e n i n Fig. 13. Ni(OH)*9
FO.St
2 Slow R12 k23 L Ni * . " Ni(Acac)* . P Ni(Acac) 2 4 k21 R32
• 2e °~'Ni(OH) kONi(OH) Ni
~e Ni
1
kONi
Ni
First wave
*2e °~'Ni (Acoc) kONi(A¢oc) Ni
Ni(Acac) 3
+2ei(Acac)2N o~
l"°
Ni(Acoc) 2
Ni
Second w a v e
Fig. 13. Reaction scheme of the reduction of nickei(II) acetyiacetonate complexes. The term "fast" means that the reaction proceeds so fast that the equilibrium between the relevant species is practically established, even when the current is flowing. The term "slow'" means that the reaction proceeds so slowly that the reaction practically does not occur in the vicinity of the electrode surface during electrolysis, although in the bulk of the solution the equilibrium between the relevant species is established.
J. Electroanal.Chem.,28 (1970) 17
32
30
C, N I S H I H A R A , H . M A T S U D A
APPENDIX
The current-voltage curve for the sum of two independent irreversible waves can be expressed by i = i, + i2 = i,,1/(1 + ~Pl) + il,2/(1 -}-~02)
(16)
with gos = exp
{(nsF/RT)~j(E-E~,j)}
(j= 1, 2).
Since eqn. (16) contains the six unknown parameters, il,s, ~j, E}o (J= 1, 2), in nonlinear fashion, one cannot here apply the usual method of least squares, in which the equations of condition are linear. However, if a reasonable approximation of the values of six parameters is available, an approximate linearization of the problem can be achieved in the following way: TABLE 3 EXAMPLE OF OUTPUT DATA OF A DIGITAL COMPUTER M1
INITIAL
M2
IL
E1/2
ALPHA
IL
100.0 78.8 78.3 78.0 78.1
- 1.0000 -0.9918 -0.9901 -0.9902 -0.9902
0,40 0,40 0.41 0,42 0.42
20.0 41.3 41.7 42.0 42.0
E
I OBS.
I CAL.
I DIF.
-- 0.7503 - 0.7728 -0.7953 --0.8178 --0.8403 -0.8629 -0.8854 -- 0.9079 -- 0.9304 - 0.9529 - 0.9754 0.9979 - 1.0204 -- 1.0429 - 1.0654 1.0880 1.1105 - 1.1330 - 1.1555 -- 1.1780 - 1.2005
0.0 0.l 1.1 2.6 5.0 9,6 17.8 28.6 41.1 54,4 69,1 84.5 97,9 107.5 113.2 116,6 118.5 119,5 119,6 119.8 119.8
0.2 0.5 1.1 2.3 4.9 9.8 17.8 28.6 41.0 54.4 69.2 84.5 97.8 107.5 113.4 116.7 118.4 119.2 119.6 119.8 120.0
- 0.2 - 0.4 0.0 0.3 0.1 -0.2 0.0 - 0.0 0.1 - 0.0 - 0.1 0.0 0.1 0.0 --0.2 -0.1 0.1 0.3 -0.0 -0.0 - 0.2
-
-
-
J. Electroanal, Chem., 28 (1970) 17-32
El~ z - 0.9000 -0.9031 -0.9013 -0.9017 .-0.9017
ALPHA
IL(M1/M2)
0.50 0.43 0.47 0.47 0.47
1.91 1.88 1.86 1.86
ACETYLACETONATE COMPLEXES OF NICKEL (II)
31
Suppose that (i~d)o, (aj)0 (E+,j)o (J = 1, 2) are known, by inspection or otherwise, to be reasonably approximate values. Then one can expand eqn. (16) in a Taylor series about these preliminary values. After omitting the second- and higher-order terms with respect to the small quantities, Aiz.j= il.j - (iLj)o, Aaj=ej--(aj)o and AE~,i= E~,j-(E~o)o (j= 1, 2), one has i = ~ (ij)o{1 +
j=l
(i,,j)o*Ai,,j- njV[E-(E~,j)o] (qOj)o ko~j+ RT 1 + (~oj)0 njV(aj)o (q~j)o AE+,j} RT 1 + (q~j)o
(17)
with (q~j)o = exp
{(njF/RT)(aj)o [ E - (E~,j)o] }
(ij) o = (i, ,j)o/ {1 + (~Pj)o} which is linear in the unknown corrections, Ai1,j, Aa2, AE~,j (j = 1, 2). The method of least squares can now be applied to system (17) in a straightforward manner, following which the initial estimate can be appropriately corrected. A second application, based upon expanding eqn. (16) around the corrected values, yields the improved values. Of course, one can repeat the process, until the correct values to be desired can be obtained. In the present investigation, the conditions: A~/a< 10 -2,
Ail/il< 10 -3
and
AErIEs< 10 4
were used as a criterion of correctness. An example of the output data of the digital computer is illustrated in Table 3, from which one can see the circumstances of convergence and the differences between the observed values and the calculated values obtained from eqn. (16) with the appropriate values of six parameters. ACKNOWLEDGEMENTS
The authors express their sincere thanks to Dr. Y. Takemori for his help in the chronopotentiometric measurements and to Mr. Y. Yamazaki for his useful advice in the construction of HMDE. SUMMARY
The polarographic and chronopotentiometric behavior of nickel(II)-acetylacetonate complexes is examined in the pH-range 3.6~9.8. By analysing the dependence of the d.c. polarographic current-voltage curves on the pH-value, the mechanism of the electrode reaction is elucidated and the relevant kinetic parameters, i.e., the transfer coefficients and the electrode reaction rate constants, are evaluated. For the preceding chemical reactions involved, the rate and equilibrium constants are determined by analysing the chronopotentiometric Iz~-I curves. The results obtained are summarized by the reaction scheme illustrated in Fig. 13. J. Electroanal. Chem., 28 (1970) 17-32
32
c . NISHIHARA, H. MATSUDA
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J. Electroanal. Chem., 28 (1970) 17 32