Does reduction occur well above the reduction potential?

Question

I was reading the voltammetry section of Analytical Chemistry 2.1 (Harvey), and it says that for the reduction of $\ce{[Fe(CN)^{III}6]^3-}$ to $\ce{[Fe^{II}(CN)6]^4-}$, which has a standard reduction potential of +0.356 V, if a potential of +0.530 V is applied to a solution of 0.100 mM $\ce{[Fe(CN)^{III}6]^3-}$ and no $\ce{[Fe^{II}(CN)6]^4-}$, there will be no faradaic current or change of concentrations at the surface of the electrode.

Using the Nernst equation, I would expect the concentration of $\ce{[Fe^{II}(CN)6]^4-}$ at the electrode surface to be 0.00114 mM. Is the textbook rounding this down to zero, or is there truly no reduction well above the reduction potential?

Answer 1

You're right, the textbook statement is not entirely accurate. While applying a potential of +0.530 V, significantly higher than the standard reduction potential (+0.356 V), would thermodynamically drive the reduction of [Fe(CN)6]3 to [Fe(CN)6]4, some reduction will indeed occur. It's just that the rate of reduction might be very slow under those conditions.

Here's why:

Nernst Equation and Concentration: The Nernst equation tells us the equilibrium concentration of [Fe(CN)6]4 at the electrode surface for a given potential. In your case, calculating it using the Nernst equation gives 0.00114 mM. However, this value represents the equilibrium concentration, not the actual concentration at any given time.

Kinetics and Current: The actual rate of reduction depends on the kinetics of the electron transfer reaction. Even though the applied potential is thermodynamically favorable for reduction, the reaction might be kinetically slow. This means that the reduction will happen, but at a very slow rate, leading to a negligible faradaic current and a very slow change in the concentration of [Fe(CN)6]4.

Therefore, while the book took it zero might be a simplification for practical purposes, it's important to understand that some reduction will occur in reality, even if the rate is very slow and the change in concentration is negligible.