# Can you derive reaction rates from the potential difference across a battery?

There were several cases where I was able to (relatively easily) derive potentials for interactions in my statistical mechanics course. I know that there is no real way to derive the kinetics of a reaction give just the potential difference between the two reactants. However, let's take a look at a specific version of this problem (while leaving it still relatively abstract) with batteries. Construct a simple electrochemical battery starting out with a potential $\varepsilon_0$ at $t_0$ and $\varepsilon_1$at $t_1$.

I was wondering if there was any relationship about the rate of the reactions that you could derive from the ratio of $\varepsilon_0$ to $\varepsilon_1$? (maybe some kind of relative rate)

If not then is there some kind of useful relationship you can define from multiple measurements of $\varepsilon_n$ at $t_n$?

Essentially I'm curious to see if you can make meaningful conclusions about kinetics by combining theoretical models for the potential with experimental data, theoreticla justifications if you will.

• Did you look into impedance spectroscopy and electrochemical relaxation techniques? I think those are being used to learn about details of electrochemical reactions at that level. See e.g. en.wikipedia.org/wiki/Dielectric_spectroscopy – CuriousOne Dec 31 '14 at 5:08
• For the potential alone, you won't get much. In batteries you need to know about the materials and the type. – Steeven Dec 31 '14 at 9:47 