# Electrokinetics: charge transfer coefficient

1. Jul 27, 2017

### ussername

I'm trying to understand the concept of Butler-Volmer equation and its kinetic derivation. What I don't know and didn't find it anywhere is related to the charge transfer coefficient.

Let's have a reaction coordinate during electrode reaction with a transfer of electrons:

Can anybody explain why the derivation of free activation energy of oxidation $\Delta G*_{ox}$ with respect to the electrode potential $E$ is:
$$\left( \frac{\partial \Delta G*_{ox}}{\partial E} \right)_{T,p,E_{eq}}=-F\cdot \alpha_{ox}$$
where $\alpha_{ox}$ is the charge transfer coefficient of oxidation - dimensionless number with value from 0 to 1.
Why is there Faraday constant and not any other number?

The explanation could be related to the change of free energy during transport of electrons through the electrode potential - it is $\Delta G_{m}=-F\cdot E$ for reversible case and $\Delta G_{m}>-F\cdot E$ for irreversible case (with heat dissipation). In that case $\alpha_{ox}=1$ would stand for reversible charge transport and $\alpha_{ox}=0$ would stand for totally irreversible charge transport.

Note: I know there are more definitions of charge transfer coefficient but please let's work with this difinition:
$$\alpha_{ox}=-\frac{1}{F}\cdot \left (\frac{\partial \Delta G*_{ox}}{\partial E} \right )_{T,p,E_{eq}}$$ $$\alpha_{red}=\frac{1}{F}\cdot \left (\frac{\partial \Delta G*_{red}}{\partial E} \right )_{T,p,E_{eq}}$$

2. Jul 30, 2017