# Nernst Equation

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== References & Notes
== == References & Notes
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+ == External Links  == == External Links  == *[http://www.nernstgoldman.physiology.arizona.edu/ The Nernst/Goldman Equation Simulator] *[http://www.nernstgoldman.physiology.arizona.edu/ The Nernst/Goldman Equation Simulator]

## Revision as of 15:07, 15 November 2010

Nernst Equation is an equation used to calculate the electrical potential of a chemical reaction. In its equilibrium state, the Nernst equation should be zero. It also shows the direct relation between energy or potential of a cell and its participating ions. The equation is proposed by a German chemist, Walther H. Nernst (1864-1941).[1]

## Equation

Nernst equation can be expressed as follows:

where

Ecell is the half-cell potential difference

Eθcell is the standard half-cell potential

R is the universal gas constant; R = 8.314471 J K-1 mol-1

T is the thermodynamics temperature, in Kelvin; 0 K = -273.15oC

z is the number of moles of electrons transferred between cells (defined by the valency of ions)

F is the Faraday's constant; F = 96,485.3415 C mol-1

[red] is the concentration of ion that gained electrons (reduction)

[oxi] is the concentration of ion that lost electrons (oxidation)

## Membrane potential

Main article: Membrane potential

Nernst equation is also can be used to calculate the potential of an ion across the membrane. For potential difference of a membrane, we can manipulate the Nernst Equation as follows:

or

where

Em is the potential difference of an ion between membranes

R is the universal gas constant; R = 8.314471 J mol-1

T is the thermodynamics temperature, in Kelvin; 0 K = -273.15oC

z is the number of moles of electrons transferred between membranes (defined by the valency of ion)

F is the Faraday's constant; F = 96,485.3415 C mol-1

[A-] is the concentration of ion outside the membrane (in this case is anion, negative charge ion)

[A-] is the concentration of ion inside the membrane (in this case is anion, negative charge ion)

## Application

### Ussing study of frog skin

In biochemistry, Nernst equation can be used to calculate the potential difference of ion between membranes. Hans H. Ussing, a Danish scientist, used a frog skin to measure the potential difference of sodium and potassium ions across the membranes with his famous invention, the Ussing chamber.

[2]Ussing model of transepithelial ions absorption.

For example at the standard condition and temperature of 25oC (298K), the above sodium ion membrane potential can be calculated as:

### Goldman equation

Main article: Goldman equation

In presence of more than one ion, the Nernst equation can be modified into Hodgkin-Katz-Goldman equation or is commonly known as Goldman equation. Goldman equation is proposed by David E. Goldman of Columbia University together with Alan L. Hodgkin and Bernard Katz.

## References & Notes

1. http://nobelprize.org/nobel_prizes/chemistry/laureates/1920/nernst-bio.html, The Nobel Prize in Chemistry 1920; Walther Nernst
2. Diagram based on CMB2003: Cell and Membrane Transport lecture note (2010).