In the Classroom
Ruthenium(VI)-Catalyzed Oxidation of Alcohols by Hexacyanoferrate(III): An Example of Mixed Order Antonio E. Mucientes* and María A. de la Peña Departamento de Química Física, Facultad de Ciencias Químicas, Universidad de Castilla La Mancha, Avda. Camilo José Cela 10, 13071 Ciudad Real, Spain; *
[email protected] In the chapter dedicated to formal kinetics in physical chemistry texts, the concept of reaction order is defined, and differential and integration methods are described to obtain it (1–2). The integration method involves integrating the corresponding simple rate equation and testing whether the experimental concentration–time data fit the integrated equation. Thus, the calculus for the order with respect to time is normally illustrated in detail for zero, first, and second integral orders (3–5). Although the kinetics of many reactions obeys some of these integrated rate laws for much of the reaction, it is very common to observe deviations from this behavior after the first, second, or third half-lives. These deviations could be due to a change in the environmental conditions, such as shift in pH as the reaction proceeds (3), but for many reactions the cause is of a purely kinetic nature. In such cases the deviations involve complicated rate equations that arise largely for complex reactions. A good example of this behavior is found in the oxidation of primary and secondary alcohols in alkaline media by hexacyanoferrate(III) when catalyzed by Ru(VI) (6). The aim of this article is to demonstrate to students how the reaction rate depends on hexacyanoferrate(III) concentration, using the integration method, and to explain this dependence in terms of the proposed reaction mechanism.
kf. Separation of variables in eq 1 and further integration between the limits (A0, t0) and (A, t) gives the integrated rate
Experimental Results
Discussion
The progress of this reaction can be followed spectrophotometrically by measuring (at 420 nm) the absorbance decay of hexacyanoferrate(III) as a function of time while maintaining an excess alcohol concentration. The shape of the curve for the disappearance of this species for a kinetics run is plotted in Figure 1, and it is evident that the initial linear decay transforms gradually to an exponential decay as the reaction progresses. This variation may follow an experimental rate equation as follows: A dA = − (1) dt kα + kβ A
The mechanism of the RuO42−-catalyzed oxidation of primary and secondary alcohols by hexacyanoferrate(III) involves oxidation of the substrate by the catalyst via the reversible formation of a Ru(VI)–substrate complex. This
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0.8 0.7 0.6
Absorbance
where A is the hexacyanoferrate(III) absorbance at 420 nm and time t and kα and kβ are rate constants. Equation 1 is not a simple rate equation with an integral reaction order but a complicated rate equation that may explain the progressive deviation observed from zero to first order as the hexacyanoferrate(III) decreases. When kβA >> kα or kβA > k3 (k−1 + k2) c + k1 k3 c calc
(4)
R2CO + Ru(IV)
Ru(V) + Fe(CN)64− (5) Ru(VI) + Fe(CN)64 − (6)
Application of the steady-state approximation with respect to the intermediate complex and the reduced form of catalyst, Ru(IV), gives the following theoretical rate equation for the disappearance of hexacyanoferrate(III) 2k1 k2 k3 c calc cRu( VI ) dc − = (7) dt k1 k2 calc + k3 (k−1 + k2 )c + k1 k3 c calc where c is the hexacyanoferrate(III) concentration at time t (c0, at t = 0), and calc and cRu(VI) are the initial concentrations of alcohol and Ru(VI) species, both of which remain constant as the reaction progresses. Students can observe that eq 7 contains a Michaelis–Menten-type dependence on hexacyanoferrate(III) concentration, which explains the absorbance decay of hexacyanoferrate(III) as a function of time. This expression involves a mixed order with respect to Fe(CN)63−. The reaction order changes from zero to one on decreasing the hexacyanoferrate(III) concentration. The reaction order will be zero if
k1 k3 c calc + k3 (k−1 + k 2) c >> k1 k2 calc and in this case eq 7 reduces to 2 k1k2 calc cRu ( VI) dc − = dt (k−1 + k2) + k1 calc
(8)
then eq 7 reduces to dc = 2 k3 c c Ru ( VI) (9) dt Substrate oxidation is now fast with respect to catalyst regeneration and the kinetics will be first order with respect to hexacyanoferrate(III). This situation occurs at low hexacyanoferrate(III) concentrations. Therefore the change in reaction order is due to a change in the relative rate of substrate oxidation with respect to that of catalyst regeneration. The dependence of the rate of this last step on c explains the order change observed as the hexacyanoferrate(III) concentration is varied. Comparison of eq 1 with eq 7 leads to −
k3 =
1 2 kα cRu( VI )
(10)
The value of k3 obtained from this expression is 4.35 ± 0.06 × 10᎑4 L mol᎑1 min᎑1. Conclusion The integration method was used to obtain the dependence of the reaction rate on hexacyanoferrate(III) concentration. The complicated law obtained in this way involves a mixed order and has been explain theoretically. This kinetics represents a good didactic example of mixed order and this example is useful to students to understand this kind of behavior. Acknowledgment The authors acknowledge financial support from the Consejería de Educación y Cultura de la Junta de Comunidades de Castilla La Mancha.
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+ kβ (A0 − A)
This means that the catalyst regeneration is fast with respect to substrate oxidation by the catalyst, which occurs at high hexacyanoferrate(III) concentrations. Equation 8 is identical to the Michaelis–Menten equation for enzyme-catalyzed reactions. On the other hand, if
12
10
Literature Cited 8
kα ln
A0 A
5
4
2
0 0
2
4
6
8
10
12
14
Time / min Figure 2. Plot of eq 2 using the absorbance–time data and the values of kα = 2.87 min and kβ = 6.59 min: (䊏) experimental data; (—) theoretical values.
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1. Laidler, K. J. Chemical Kinetics, 3rd ed.; Harper & Row: New York, 1987; pp 18–38. 2. Atkins, P. W. Physical Chemistry, 7th ed.; Oxford University Press: Oxford, 2002; pp 862–892. 3. Connors, K. A. Chemical Kinetics. The Study of Reaction Rates in Solution; VCH: New York, 1990; pp 17–53. 4. Espenson, J. H. Chemical Kinetics and Reaction Mechanisms; McGraw-Hill: New York, 1981; pp 12–38. 5. Birk, J. P. J. Chem. Educ. 1976, 53, 704–707. 6. Mucientes, A. E.; Gabaldón, R. E.; Poblete, F. J.; Villarreal, S. J. Phys. Org. Chem. 2004, 17, 236–240. 7. Marquardt, D. W. J. Soc. Ind. Appl. Math. 1963, 11, 431.
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