On the thermodynamic derivation of Nernst relation

TL;DR

This paper revisits the thermodynamic derivation of the Nernst relation, clarifying assumptions and correcting common misconceptions to improve the modeling of electrochemical cells like vanadium redox flow and zinc-air batteries.

Contribution

It provides a rigorous thermodynamic derivation of the Nernst relation, addressing and correcting historical assumptions often overlooked in prior derivations.

Findings

Correct form of Nernst relation derived thermodynamically

Clarification of assumptions behind the Nernst equation

Implications for battery modeling and corrosion effects

Abstract

What is the maximum voltage of a cell with a given electrochemical reaction? The answer to this question has been given more than a century ago by Walther Nernst and bears his name. Unfortunately, the assumptions behind the answer have been forgotten by many authors, which leads to wrong forms of the Nernst relation. Such mistakes can be overcome by applying a correct thermodynamic derivation independently of the form in which the reaction is written. The correct form of Nernst relation is important for instance in modelling of vanadium redox flow batteries or zinc-air batteries. In particular, the presence of corrosion can impact the OCV in the case of zinc-air batteries.