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Examination of the Eyring Equation under various conditions.PowerPoint Presentation

Examination of the Eyring Equation under various conditions.

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Kinetics of Electron Transfer at the Solid Electrode-Solution Interface

Examination of the Eyring Equation under various conditions.

Case II: At applied potentials E different than Eeq such that we are applying an overpotential, h = E- Eeq

Skipping the derivation (you should be able to do it):

Known as i- h Eqn

NB: Not corrected for DL effects- see page 571

At E = Eeq, Ci(0,t) = Ci*, and so i = i0

High h, MT control

Low h, Exponential control

Kinetics of Electron Transfer at the Solid Electrode-Solution Interface

This expression makes it difficult to extract key information.

Must use approximations resulting from certain limiting conditions:

Approximation A : 1) Well-stirred solution, and 2) i is small

That means that Ci(0,t) = Ci* and E is near Eeq

Butler-Volmer

Eqn.

This is a good approximation of the i-h Eqn. when:

0.9 ≤Ci(0,t)/Ci* ≤ 1.1

Or

i is ≤ 10% of ilim

Kinetics of Electron Transfer at the Solid Electrode-Solution Interface

Because MT is not a component of the measured i, then i is based solely on the activation energy of the process.

So, the observed potentials for oxidation are more positive and those for reduction more negative than E0’.

i0 is merely a measure of a system’s ability to provide a net current w/o a significant energy loss due to activation effects.

Approximation A, with Small h:

For small x, ex≈ 1+x

(be able to derive)

Linearized

Butler-Volmer

Eqn.

jc

Use for Fast ET

Region

of

interest

+h

-h

ja

Kinetics of Electron Transfer at the Solid Electrode-Solution Interface

Approximation A, with Large ±h:

For large -h

Or

Tafel Eqn.

Holds when:

1. ib is < 0.01 if

Or

2. |h| > 118/n mV

Use for Slow ET

(Typically for Totally Irreversible Systems)

Tafel Plots to Obtain Kinetic and Other Information

h large negative

hlarge positive

Kinetics of Electron Transfer at the Solid Electrode-Solution Interface

When h is large, must recognize that MT limitations occur.

When h is small, near 0, must be cognizant of back reactions.

n should be there

Anodic

Branch

Cathodic

Branch

Extrapolate to 0 h and obtain log i0.

Obtain ah from slope.

Read about exchange current plots (pp. 105-107) on your own and learn about methods to obtain a and other parameters independently (see problem 3.11).

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