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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.

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  • $\begingroup$ 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 $\endgroup$ – CuriousOne Dec 31 '14 at 5:08
  • $\begingroup$ For the potential alone, you won't get much. In batteries you need to know about the materials and the type. $\endgroup$ – Steeven Dec 31 '14 at 9:47
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Something that is very relevant to your question is to consider the difference between thermodynamics and kinetics.

The potential difference across a battery depends on thermodynamics... or to put it another way.... the potential difference depends on the energies of the initial and final states.

Rates of reaction or kinetics depend on the pathway from initial to final states.

For example see the image below shows two reaction pathways schematically - one with an enzyme and one without. The energies of the initial and final states are the same with and without the enzyme, but the rates of reaction will be very different. The rate with the enzyme will be faster because the potential energy barrier is lower.

enter image description here

Thus, the answer to your question is that you need more information than just potential difference to calculate rates of reaction. More specifically if you could measure the energy of activation (see diagram) then you could estimate the rate and the dependence of rate on temperature.

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