Langmuir 1998, 14, 1539-1543
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Articles Micellar Effects upon the Reaction between Acetonitrile Pentacyanoferrate(II) and Bis(ethylenediammine)(2-pyrazinecarboxylato)cobalt(III) R. Prado-Gotor, R. Jime´nez, P. Lo´pez, P. Pe´rez, C. Go´mez-Herrera, and F. Sa´nchez* Department of Physical Chemistry, University of Sevilla c/Profesor Garcı´a Gonza´ lez S/N, 41012 Sevilla, Spain Received June 9, 1997. In Final Form: November 20, 1997 The substitution reaction of bis-ethylenediammine(2-pyrazinecarboxylato)cobalt(III) for acetonitrile ligand in acetonitrile pentacyanoferrate(II) was studied in micellar solutions of sodium dodecyl sulfate. The results are interpreted considering the influence of the electric field in the micellar interfacial region on the formation of the encounter complex between the reactants. The influence of the field on the reverse (dissociation) process is also discussed.
Introduction Electric fields influence the rate of the reactions in several ways. When the reactants are charged species, the field can affect the encounter of the reactants. Indeed, the free energy of a charged particle is modified by the existence of a field. Consequently, the free energy of reaction will be different in the presence or absence of the field when the reactants are ions. The adiabaticity of the reaction can also be influenced by the field. For example, in the case of electron-transfer reactions, the adiabaticity depends on the coupling of the intervening orbitals of the donor and the acceptor. As this coupling can be modified by the field, through polarization effects, a change in the adiabaticity will result for applied fields1 that are strong enough. The electric field can also have an indirect influence on solution processes. In fact the field can affect the solvent properties by changing the equilibrium distribution and thus producing a nonhomogeneous state. The dynamics of the solvent can also be changed by the field; for example, diffusion coefficients corresponding to the nonhomogeneous state (in the presence of the field) can be quite different from those of the homogeneous state (without field). The equilibrium correlations, such as the direct correlation functions, in the presence of a field can also be rather different from those in the absence of the field. Finally, some fundamental theorems of statistical mechanics, like the fluctuation-dissipation one, may no longer be valid in the presence of a strong field.2 To produce the above-mentioned effects, the applied electric field must be quite strong, about 107 V/m. Such intense fields exist, for example, in the region close to an electrode surface and also in the vicinity of the surface of the micelles, their effects having been studied from a theoretical as well as experimental point of view on * To whom the correspondence should be sent. (1) Cukier, R. I.; Morillo, M. Chem. Phys. 1990, 183, 375. (2) Bagchi, B.; Chandra, A. Adv. Chem. Phys. 1991, 80, 1.
electron and proton-transfer reactions.1-3 However, as far as we know, the electric field effects on ligand substitution reactions have not been considered previously. In this paper a study of the title reaction in micellar solutions is presented and the effect of the field at the micellar surface on the processes
Fe(CN)5ACN3- + Co(en)2(2-pzCO2)2+ a [(en)2Co(2-pzCO2)Fe(CN)5]- + ACN (I) is considered. Experimental Section Materials. [Fe(CN)5NH3]Na3‚3H2O and [Co(en)2(2-pzCO2)](ClO4)2 were prepared according to the methods in refs 4 and 5, respectively, and characterized by visible absorption spectra and C, H, N microanalysis. The other reagents were all AnalaR grade and used as purchased. Dodecyl sulfate sodium salt (SDS) (Merck, purity >99%) was stored in a vacuum desiccator over P2O5 for several days before use. The water used in the preparation of solutions had a conductivity ∼10-6 S m-1. Methods. Kinetics. Rate measurements were performed by following the absorbance changes produced after mixing solutions A and B, at 630 nm. This wavelength corresponds to the absorbance maximum of the binuclear complex in eq I. Solution A contained the iron complex at concentrations in the range 5 × 10-4 to 2 × 10-3 mol dm-3 and acetonitrile (ACN) at concentration 0.05 mol dm-3. As is known,6 a rapid hydrolysis of the ammonia complex produces the corresponding acuo complex. This complex, in the presence of ACN, produces (3) See for example: Aviram, A. J. Am. Chem. Soc. 1988, 110, 5687. Farazdel, A.; Dupuis, M.; Clementi, E.; Aviram, A. J. Chem. Soc. 1990, 112, 4206 and references therein. (4) Braver, G. Handbook of Preparative Inorganic Chemistry, 2nd ed.; Academic Press: New York, 1965; Vol. 2, p 1511. (5) Soria, D. B.; Hidalgo, V.; Kutz, N. J. Chem. Soc., Dalton Trans. 1976, 1293. (6) Juretic, R.; Paulovic, D.; Asperger, S. J. Chem. Soc., Dalton Trans. 1979, 2029.
S0743-7463(97)00607-0 CCC: $15.00 © 1998 American Chemical Society Published on Web 02/18/1998
1540 Langmuir, Vol. 14, No. 7, 1998
Prado-Gotor et al. ([Fe(CN)5ACN]3- was substituted by [Fe(CN)6]4- in order to avoid reaction) by using a conductimetric method. The results are practically independent of the concentration of the anionic reactant. To perform the calculations in the following sections, a common value of cmc ) 5 × 10-3 mol dm-3 was used.
Results Table 1 gives kobs, the pseudo-first-order rate constant, obtained as previously mentioned. The observed rate constant is a composite magnitude. In fact it contains contributions from the forward and reverse processes corresponding to the formation and dissociation of the binuclear complex in eq I. According to Toma et al.,8 the mechanism of ligand substitution at pentacyanoferrates is the following: k1
Fe(CN)5L′ 3- {\ } L′ + Fe(CN)53k -1
Figure 1. Plot of ln(Ainf - At) versus t/s for the reaction Co(en)2(2-pzCO2)2+ + Fe(CN)5ACN3- (b): [SDS] ) 10-2 mol dm-3; [Fe(CN)5ACN3-] ) 10-3 mol dm-3. Table 1. Observed and Calculated (in Parentheses) Rate Constants (103kobs/s-1) for the Reaction Co(en)2PzCO22+ + Fe(CN)5ACN3- at Different Concentrations of SDS and Fe(CN)5ACN3102[SDS]/
103 [Fe(CN)5ACN3-]/mol dm-3 1 1.5
mol dm-3
0.5
1.00 1.10 1.15 1.20 1.50 2.00 3.00 4.00 5.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 22.00 25.00 30.00
1.92 (1.93) 1.86 (1.80) 1.80 (1.75) 1.58 (1.71) 1.50 (1.54) 1.45 (1.41) 1.38 (1.32) 1.29 (1.28) 1.30 (1.27) 1.24 (1.26) 1.26 (1.26) 1.20 (1.28) 1.32 (1.29) 1.30 (1.31) 1.27 (1.33) 1.35 (1.35) 1.37 (1.37) 1.48 (1.40) 1.40 (1.43) 1.50 (1.49)
3.36 (3.06) 2.78 (2.79) 2.70 (2.68) 2.23 (2.59) 2.15 (2.24) 1.89 (1.98) 1.83 (1.78) 1.72 (1.70) 1.70 (1.67) 1.75 (1.66) 1.70 (1.67) 1.78 (1.69) 1.79 (1.72) 1.78 (1.75) 1.72 (1.78) 1.78 (1.82) 1.76 (1.86) 1.90 (1.90) 1.96 (1.96) 2.10 (2.07)
4.40 (4.34) 4.16 (3.93) 4.00 (3.77) 3.30 (3.64) 2.80 (3.12) 2.60 (2.72) 2.45 (2.42) 2.17 (2.30) 2.32 (2.25) 2.34 (2.23) 2.40 (2.23) 2.12 (2.25) 2.58 (2.28) 2.10 (2.32) 2.42 (2.37) 2.45 (2.41) 2.50 (2.46) 2.60 (2.51) 2.67 (2.59) 2.50 (2.72)
2
6.00 (5.68) 5.50 (5.12) 4.83 (4.91) 4.00 (4.72) 3.83 (4.01) 3.44 (3.46) 3.18 (3.04) 2.78 (2.88) 2.75 (2.81) 2.90 (2.78) 3.20 (2.76) 2.55 (2.79) 2.91 (2.82) 2.70 (2.87) 2.90 (2.92) 3.08 (2.98) 3.16 (3.04) 3.18 (3.10) 3.10 (3.19) 3.26 (3.36)
k2
Fe(CN)5 3- + L2+ {\ } Fe(CN)5Lk -2
(1a) (1b)
In this case
L′ ) ACN;
L2+ ) [Co(en)2(pzCO2)]2+
Using the steady-state approximation for the concentration of Fe(CN)53-, it can be easily shown that
d[Fe(CN)5L′ -] ) dt k2k1[Fe(CN)5L′ 3-][L2+] - k-2k-1[L′][Fe(CN)5L-] k-1[L′] + k2[L2+]
(2)
It has been checked, by performing measurements at different concentrations of cobalt complex, that
k2[L2+] , k-1[L′]
(3)
So, eq 2 can be written as
d[Fe(CN)5L′ -] ) dt k2k1[Fe(CN)5L′ 3-][L2+] - k-2k-1[L′][Fe(CN)5L-] k-1[L′]
(4)
[Fe(CN)5ACN]3-7
instantaneously. So, solutions A are in fact solutions of the ACN complex at the above-mentioned concentrations of the iron complex [Fe(CN)5H2O]3-. The use of the ACN complex was preferred to those of the acuo complex because this complex suffers dimerization processes that complicate the kinetics.6 Solution B contained the cobalt(III) complex at concentration 10-4 mol dm-3. Concentrations of solutions A and B were selected so that first-order kinetics were always followed. These solutions also contained the desired concentration of SDS. All the solutions were prepared after deoxygenation of the solvent and immediately before use. Rate measurements were performed using a Hitachi 150-20 UV-vis spectrophotometer, at the thermostated cell holding. The temperature was mantained at 298.2 ( 0.1 K. The rate constants, kobs, were obtained from the slopes of ln(Ainf - At) vs t plots, Ainf and At being the final absorbance and the absorbance at time t of the binuclear complex. A representative plot of ln(Ainf - At) vs t appears in Figure 1. Measurement of the Critical Micellar Concentration (cmc). cmc was obtained in the presence of the reactants (7) Norris, P. R.; Pratt, J. M. J. Chem. Soc., Dalton Trans. 1995, 3643.
or
d[Fe(CN)5L′ -] ) k1ap[Fe(CN)5L′ 3-][L2+] dt k-2[Fe(CN)5L-] (5) with
k1ap ) k2k1/k-1[L′]
(6)
kobs ) k1ap[Fe(CN)5L′ 3-] + k-2
(7)
According to9
Looking at eq 7, it is easy to see that k1ap and k-2 can be obtained from the slope and intercept, respectively, of a (8) Toma, H. E. Inorg. Nucl. Chem. 1975, 37, 785. (9) Frost, A. A.; Pearson, R. G. Kinetics and Mechanism; John Wiley and Sons: New York, 1953; p 172.
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Langmuir, Vol. 14, No. 7, 1998 1541
Figure 2. Plot of kobs/s-1 versus [Fe(CN)5ACN3-]/mol dm-3 for the reaction Co(en)2(2-pzCO2)2+ + Fe(CN)5ACN3- in [SDS] ) 0.05 mol dm-3.
Figure 3. Plot of k1ap/(mol-1 dm3 s-1) versus [SDS]/mol dm-3 for the reaction Co(en)2(2-pzCO2)2+ + Fe(CN)5ACN3- in SDS micellar systems.
Table 2. k1ap/mol-1 dm3 s-1 and 104k-2/s-1 at Different Concentrations of SDS 102[SDS]/ mol dm-3
k1ap
k-2
102[SDS]/ mol dm-3
k1ap
k-2
1.00 1.15 1.50 3.00 5.00 8.00 12.00 16.00 20.00 25.00
2.50 2.11 1.66 1.09 1.07 1.03 1.05 1.08 1.12 1.18
6.34 6.47 6.59 6.76 6.76 7.01 7.21 7.61 7.86 8.21
1.10 1.20 2.00 4.00 6.00 10.00 14.00 18.00 22.00 30.00
2.21 2.01 1.39 1.10 1.04 1.04 1.06 1.10 1.14 1.23
6.48 6.56 6.63 6.76 6.91 7.06 7.46 7.71 7.96 8.62
plot of kobs vs [Fe(CN)5L′ 3-]. One such plot is given in Figure 2. It is worth pointing out that, when the experimental values of kobs were used directly to obtain k1ap and k-2, the values of both rate constants showed some scattering, due to the experimental error in kobs. So, to minimize the consequences of such errors, the values of kobs were fitted to an equation of the type
kobs )
a + b[SDS] + c[SDS]2 1 + d[SDS]
(8)
Here, a, b, c, and d are adjustable parameters and [SDS] is the micellized surfactant concentration, equal to the total surfactant concentration minus the critical micellar concentration, cmc, of the surfactant under the reaction working conditions. The values of kobs calculated from the fit are given in Table 1 (in parentheses). To obtain k1ap and k-2, these values of kobs have been used. The rate constants obtained in this way are given in Table 2. Also, the plots of these rate constants vs [SDS] are given in Figure 3 and Figure 4. Discussion According to the meaning of k1ap (eq 6), this rate constant is the product of the equilibrium constant of step 1a and k2 (notice that [L′] ) constant). As in step 1a no charges appear or disappear and, indeed, Fe(CN)5L′ 3- and Fe(CN)53- bear charges of the same sign as the micelles, it can be assumed that the corresponding equilibrium constant is independent of [SDS]. So the variations of
Figure 4. Plot of k-2/s-1 versus [SDS]/mol dm-3 for the reaction Co(en)2(2-pzCO2)2+ + Fe(CN)5ACN3- in SDS micellar systems.
k1ap with [SDS] concentration will correspond mainly to the variations of k2. This rate constant corresponds (see eq 1b) to the reaction between ions of opposite sign (3and 2+, respectively). In fact k1ap has a behavior similar to that previously found in other cation-anion processes in micellar solutions of SDS. So, Figure 3 in this paper is nearly identical with Figures 1 and 2 in ref 10, which correspond to the reactions Ru(NH3)5pz2+ + S2O82- and Ru(NH3)5pz2+ + Co(C2O4)33- in SDS micellar solutions. For this reason, the behavior of k1ap can be explained as in ref 10, that is, by using an “extended” pseudophase model or using the Bro¨nsted equation. Alternatively, the decreasing part of the k1ap vs [SDS] plot can be interpreted as a consequence of the adsorption of the cobalt complex in the micellar interfacial region. As the Fe(CN)53- bears a negative charge, this adsorption (10) Lo´pez Cornejo, P.; Jime´nez, R.; Moya´, M. L.; Sa´nchez, F.; Burgess, J. Langmuir 1996, 12, 4981.
1542 Langmuir, Vol. 14, No. 7, 1998
Prado-Gotor et al.
process would imply a decrease in reaction rate, as observed. According to this, the minimun in the curve in Figure 3 would correspond to a situation where the cobalt complex is completely adsorbed at the micellar surface. Once the cobalt complex is completely absorbed at the surface, a constant value of k1ap should be expected according to the pseudophase model
k1ap )
(k1ap)w + (k1ap)mK[SDS] 1 + K[SDS]
(9)
Here (k1ap)w and (k1ap)m are the rate constants for the processes that take place in the bulk phase and micellar pseudophase, respectively, K is the equilibrium constant for the binding of the substrate (the cobalt complex in the present case) to the micelles, and [SDS] is the micellized surfactant concentration. This model predicts, for high [SDS] values, a constant value of k1ap, k1ap ) (k1ap)m, as mentioned above. So, it cannot explain the rise in the curve, after the minimun. However it is important to realize that the pseudophase model operates with the explicit assumption that changes in size as well as in shape of the micelles, caused by the different surfactant concentrations used, and by the presence of reactants in the reaction media, are not important. But, changes in surfactant concentration produce, in fact, variations in the interfacial electric potential, ∆Φ, decreasing its absolute value when the surfactant concentrations increases.12 This decrease in ∆Φ will favor the approach of Fe(CN)5ACN3- to the micellar interfacial region, thus producing an increase in rate, as observed, because (k1ap)m should increase. Considering, according to previous arguments, that the free energy of activation controlling (k1ap)m has two components, an intrinsic one, ∆Gqint, independent of the influence of the interfacial electrical potential, and an electrical component, ∆Gqelec, representing the contribution of the electrical potential, it can be writen
-RT ln(k1ap)m ) ∆Gq ) ∆Gqintr + ∆Gqelec
(10)
∆Gqelec, as mentioned above, is the component of ∆Gq due to the electric repulsion suffered by the reactant of the same charge sign of the micelle, so
∆Gqelec ) zFeRF∆Φ
(11)
where R∆Φ is the fraction of ∆Φ that effectively influences the approach of the iron complex and zFe the charge of this complex (zFe ) -3). According to this ap
zFeRF∆Φ )°m RT
ln(k1 )m ) ln(k1
ap
(12)
Figure 5. Plot of ln k1ap/(mol-1 dm3 s-1) versus ∆Φ/mV according to eq 12. (The plotted values of k1ap correspond to surfactant concentrations >8 × 10-2, that is, to values of surfactant concentrations at which k1ap ) (k1ap)m.)
(k1ap) ) (k1ap)m.) The values of ∆Φ in the figure have been obtained from ref 12b. It is worth pointing out that this interpretation is based, simply, on the application of a Frumkim correction to the approximation of the iron complex to the micellar surface. This correction is an usual one in electrochemical studies. In fact it has also been used in ref 12b. Now the variation of k-2 with [SDS] will be considered. In this regard it is important to realize (see eq 1b) that k-2 is a true unimolecular rate constant, corresponding to the dissociation of the binuclear complex. The variation of this rate constant with [SDS] corresponds to eq 9 with K , 1 and (k1ap)m > (k1ap)w. A small value of K is consistent with the negative charge of the binuclear complex. On the other hand, in this case, (k1ap)m should be greater than (k1ap)w. This point will be considered as follows: For a first-order process in a micellar solution, the rate constant is defined by
k-2 ) -
d[x] 1 dt [x]
(14)
x being the reactant, in this case the binuclear complex. On the other hand, taking into account the distribution of the reactant between the bulk and the micellar interfacial region it can be written
dnx dnxm dnxw ) + dt dt dt
(15)
Considering that [x] ) nx/V and nx ) nxw + nxm (V is the solution volume), the above equation can be written as:
with
(k1ap)°m ) exp(-∆Gqintr/RT)
(13)
1 dnx d[x] d[xm] d[xw] ) ) + V dt dt dt dt
(16)
In line with eq 12 a plot of ln(k1ap)m vs ∆Φ should be linear. Figure 5 gives this plot, that supports this interpretation. (The plotted values of k1ap correspond to [SDS] > 8 × 10-2, that is, to values of surfactant concentrations at which
where [xm] and [xw] represent the concentration of x in the micellar region and in the bulk of the aqueous phase, respectively, referred to the total volume of solution, V. If [x]i is the concentration of x in phase i referred to the volume of phase i, Vi, that is, [x]i ) nxi/Vi, it is easily seen that
(11) Menger, F. M.; Portnoy, C. E. J. Am. Chem. Soc. 1967, 89, 4698. (12) (a) Mysels, K. J.; Dorion, F.; Gaboriand, R. J. J. Phys. Chim. 1984, 81, 187. (b) Grand, D.; Hauetecloque, S. J. Phys. Chem. 1990, 94, 837.
d[x] Vm d[x]m Vw d[x]w ) + dt V dt V dt
(17)
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Langmuir, Vol. 14, No. 7, 1998 1543
k-2 corresponds
and using eq 14
k-2[x] )
Vm Vw k [x] + kw[x]w V m m V
k-2
(18)
Fe(CN)53- + [(en)2Co(2-pzCO2)2+
As [x] ≈ [x]w and Vw/V ≈ 1 it follows that
Vm [x]m k + kw k-2 ) V m [x]
[(en)2Co(2-pzCO2)Fe(CN)5]- 98
(19)
This approximation is supported by the fact that V ≈ Vw. Indeed, given that, in the present case, x bears a negative charge, zx, this species will be located preferentially in the aqueous phase, so nxw ≈ n. The value of [x]m can be obtained considering that, at equilibrium, the electrochemical potential of x must be the same in all the phases of the system, that is
This is the sorting of a negatively charged species (Fe(CN)53-) with a charge zFe. So, it is expected to have some dependence on the value of ∆Φ. In other words, km should be dependent on the potential. If this dependence is written as
km ) km° exp(zFeβF∆Φ/RT)
(25)
(β∆Φ is the fraction of ∆Φ that influences the sorting of the Fe(CN)53- moiety), the slope of k-2 vs [SDS] should be
slope ) K′km° exp((βzFe - Rzx)F∆Φ/RT)
(26)
w
µx ) µx° + RT ln[x]w + zxFRΦw ≈ µx° + RT ln[x] + zxFRΦw ) µx° + RT ln[x]m + zxFRΦm (20) where the approximation [x]w ≈ [x] has been done again. From the above equation results
RT ln
[x]m [x]
) -zxFR(Φm - Φw) ) - zxFR∆Φ (21)
In this way, it is possible to obtain
k-2 )
Vm k exp(-zxFR∆Φ/RT) + kw V m
(22)
The quotient Vm/V is given by
Vm K′ moles of SDS micellized ) V V
(23)
where K′ represents the volume of the micellar interfacial region corresponding to unit concentration of micellized SDS. So
k-2 ) kmK′[SDS] exp(-zxFR∆Φ/RT) + kw (24) This equation predicts a slope of k-2 vs [SDS] dependent on ∆Φ. However, as can be seen in Figure 4, a practically constant slope is obtained. These facts can be rationalized considering the chemical nature of the process to which
Consequently the fact that the slope is practically independent of the potential, implies that βzFe ≈ Rzx. Finally, the value of km° will be estimated, by taking a value of K′ ) 0.14 dm3 mol-1.13 The resulting value for km° is 5 × 10-3 s-1 which, in fact, is an order of magnitude higher than kw ) 6.5 × 10-4 s-1, this being the intercept of the plot of k-2 vs [SDS] in Figure 4. In conclusion, the influence of the micelles on the reactions of formation and dissociation of the binuclear complex in I was studied. The formation is influenced by the adsorption of cobalt complex in the micellar interfacial region. When the adsorption process is complete, the kinetics is controlled by the approximation of the iron complex to the micellar surface, this process being dependent on the electrical potential in the interfacial region. On the other hand, this potential promotes the dissociation of the binuclear complex. However, given the negative charge of this complex, the increase in the field hinders its approximation to the interfacial region. These two effects act oppositely in such a way that they apparently compensate one another, producing a constant apparent value of the rate constant of the reaction at the surface of the micelles. Acknowledgment. The authors wish to thank D.G.I.C.Y.T. (PB95-0535), the Consejerı´a de Educacio´n y Ciencia de la Junta de Andalucı´a, and Fundacio´n Ca´mara for support of this work. LA9706072 (13) Bunton, C. A.; Carruso, N.; Huang, S. K.; Paik, C. A.; Romsted, L. S. J. Am. Chem. Soc. 1978, 100, 5420.
