The **key difference** between Nernst equation and Goldman equation is that **the Nernst equation describes the relation between reduction potential and standard electrode potential, whereas Goldman equation is a derivative of the Nernst equation and describes the reversal potential across a cell membrane.**

An electrochemical cell is an electrical device that can generate electricity using the chemical energy of chemical reactions. Or else we can use these devices to aid chemical reactions via providing the required energy from electricity. The reduction potential of an electrochemical cell determines the ability of the cell to produce electricity.

### CONTENTS

1. Overview and Key Difference

2. What is Nernst Equation

3. What is Goldman Equation

4. Side by Side Comparison – Nernst Equation vs. Goldman Equation in Tabular Form

5. Summary

## What is Nernst Equation?

Nernst equation is a mathematical expression that gives the relationship between reduction potential and the standard reduction potential of an electrochemical cell. The equation is named after the scientist Walther Nernst. And, it was developed using the other factors affecting the electrochemical oxidation and reduction reactions, such as temperature and chemical activity of chemical species that undergo oxidation and reduction.

When deriving the Nernst equation, we have to consider the standard changes in Gibbs free energy that is associated with electrochemical transformations that occur in the cell. The reduction reaction of an electrochemical cell can be given as follows:

Ox + z e^{–} ⟶ Red

According to thermodynamics, the actual free energy change of the reaction is,

E = E_{reduction} – E_{oxidation}

However, Gibbs free energy(ΔG) is related to the E (potential difference) as follows:

ΔG = -nFE

Where n is the number of electrons transferred between chemical species when the reaction is progressing, F is the Faraday constant. If we consider the standard conditions, then the equation is as follows:

ΔG^{0} = -nFE^{0}

We can relate the Gibbs free energy of non-standard conditions with the Gibbs energy of standard conditions via the following equation.

ΔG = ΔG^{0} + RTlnQ

Then, we can substitute the above equations into this standard equation to get the Nernst equation as follows:

-nFE = -nFE^{0} + RTlnQ

However, we can rewrite the above equation using the values for Faraday constant and R (universal gas constant).

E = E^{0} – (0.0592VlnQ/n)

## What is Goldman Equation?

Goldman equation is useful in determining the reverse potential across a cell membrane in cell membrane physiology. This equation was named after the scientist David E. Goldman, who developed the equation. And, it was derived from the Nernst equation. Goldman equation takes the uneven distribution of ions across the cell membrane and differences in membrane permeability into account when determining this reverse potential. The equation is as follows:

Where

- Em is the potential difference across the cell membrane,
- R is the universal gas constant,
- T is the thermodynamic temperature,
- Z is the number of moles of electrons that are being transferred between chemical species,
- F is the Faraday constant,
- P
_{A or B}is the permeability of the membrane towards A or B ion, and - [A or B]
_{i}is the concentration of A or B ion inside the cell membrane.

## What is the Difference Between Nernst Equation and Goldman Equation?

Nernst equation and the Goldman equation are mathematical expressions that can be used as measurements of the potential of electrochemical cells. The key difference between Nernst equation and Goldman equation is that the Nernst equation describes the relation between reduction potential and the standard electrode potential, whereas the Goldman equation is a derivative of the Nernst equation and describes the reversal potential across a cell membrane.

The below infographic summarizes the difference between Nernst equation and Goldman equation.

## Summary – Nernst Equation vs Goldman Equation

Nernst equation and the Goldman equation are mathematical expressions that can be used as measurements of the potential of electrochemical cells. The key difference between Nernst equation and Goldman equation is that the Nernst equation describes the relation between reduction potential and the standard electrode potential, but the Goldman equation is a derivative of the Nernst equation and describes the reversal potential across a cell membrane.

##### Reference:

1. “Nernst Equation.” Chemistry LibreTexts, Libretexts, 5 June 2019, Available here.

##### Image Courtesy:

1. “ElectrochemCell” By Alksub at the English Wikipedia (CC BY-SA 3.0) via Commons Wikimedia

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