Steady-State Electrolysis

Calculate the transport-limited current at a microdisc electrode of radius 10 /rm due to the one-electron oxidation of ImM ferrocene in acetonitrile/0.1 M tetrabutylammonium perchlorate at 25°C, where the ferrocene has a diffusion coefficient of 2.3 x 10 cm s . If the electrode radius were halved, how would the limiting current change, and why If the cell contained 100 mL of solution, what duration of electrolysis would be required to oxidise 10% of the ferrocene in the cell  

The transport-limited current to a microdisc electrode of radius is given for a 

If the electrode radius is halved then the limiting current is also halved, since the current scales with the electrode radius and not with the electrode area. The reason for this lies in the non-uniform current density across the disc electrode surface with a much greater current density at the circumference of the disc than near the disc centre. 

To evaluate the time taken for 10% electrolysis of the cell contents, we first note that 100 mL of a 1 mM solution contains 10 moles of ferrocene. For 10% oxidation we need to calculate the time to electrolyse 10 moles. The required quantity of charge is 

This corresponds to 3.5 years Of course this negiects convection effects, but it is nonetheiess true that aithough diffusionai rates and current densities are iarge at microeiectrodes, absoiute currents are smaii and the eiectroiysis essentiaiiy does not perturb the ceii contents. If electrosynthesis is to be attempted, a large electrode (and probably large concentrations) are essential. 

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Ferry, G. V. Gill, S. (1962). Transference studies of sodium polyacrylate under steady state electrolysis. Journal of Physical Chemistry, 66, 999-1003. 

As the electrolysis proceeds, there is a progressive depletion of the Ox species at the interface of the test electrode (cathode). The depletion extends farther and farther away into the solution as the electrolysis proceeds. Thus, during this non-steady-state electrolysis, the concentration of the reactant Ox is a function of the distance x from the electrode (cathode) and the time f, [Ox] = Concurrently, concentration of the reaction product Red increases with time. For simplicity, the concentrations will be used instead of activities. Weber (19) and Sand (20) solved the differential equation expressing Pick s diffusion law (see Chapter 18) and obtained a function expressing the variation of the concentration of reactant Ox and product Red on switching on a constant current. Figure 6.10 shows this variation for the reactant. 

Figure 6.10. Variation of concentration of reactant during non-steady-state electrolysis. The number on each curve is the time elapsed since the beginning of electrolysis, t5>t4>...tj. (From Ref 23, with permission from Elsevier.)...

Figure 6.11. Variation of concentration of reactant during non-steady-state electrolysis Cq...

For steady-state electrolysis conditions, i.e., [dci (x, t)/dx] = 0, when the solution is well stirred, and both the reactant and product molecules are soluble, in the case of planar diffusion in x direction, the following relationship is valid ... 

In electrochemical kinetics under steady-state electrolysis conditions often a simplified form of Eq. (1) is used ... 

The mathematical methods and the derivation can be found in several electrochemistry books [1 ] and reviews [5]. Herein, we present the most important considerations and formulae for steady-state electrolysis conditions. It is assumed that the solution is well stirred (the concentration gradient at the electrode surface is constant) and that both the reactant and product molecules are soluble. By combining Eqs. (1.3.28), (1.3.29), and (1.3.30) and considering the respective initial and boundary conditions [Eqs. (1.3.31), (1.3.32), and (1.3.36)], we obtain... 

Oldham, K.B. (1997) Limiting currents for steady-state electrolysis of an equilibrium mixture, with and without supporting inert electrolyte. Analytical Chemistry, 69,446-453. 

The concentration of a species undergoing steady-state electrolysis at an electrode is often approximated as changing linearly between the concentration at the electrode surface (x = 0, c = c ) and the bulk concentration value at the edge of a diffusion layer (x = 5, c = c ) so that... 

Juliard,A. Non-steady state electrolysis under constant current J. Phys. Chem. 57, 701 (1953). 

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