# Nernst Equation

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− | '''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 [[Ion|ions]]. The equation is proposed by a German chemist, Walther H. Nernst (1864-1941).<ref>http://nobelprize.org/nobel_prizes/chemistry/laureates/1920/nernst-bio.html, The Nobel Prize in Chemistry 1920; Walther Nernst</ref><br> | + | '''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 [[Ion|ions]]. The equation is proposed by a German chemist, Walther H. Nernst (1864-1941).<ref>http://nobelprize.org/nobel_prizes/chemistry/laureates/1920/nernst-bio.html, The Nobel Prize in Chemistry 1920; Walther Nernst</ref><br> |

== Equation == | == Equation == | ||

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Nernst equation can be expressed as follows: | Nernst equation can be expressed as follows: | ||

− | [[Image:Nernst equation1.png|354x85px]]<br> | + | [[Image:Nernst equation1.png|354x85px|Nernst equation1.png]]<br> |

− | where<br> | + | where<br> |

E<sub>cell </sub>is the half-cell potential difference | E<sub>cell </sub>is the half-cell potential difference | ||

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R is the [[Universal gas constant|universal gas constant]]; R = 8.314471 J K<sup>-1</sup> mol<sup>-1</sup> | R is the [[Universal gas constant|universal gas constant]]; R = 8.314471 J K<sup>-1</sup> mol<sup>-1</sup> | ||

− | T is the thermodynamics temperature, in ''[[Kelvin|Kelvin]]''; 0 K = -273.15<sup>o</sup>C<br> | + | T is the thermodynamics temperature, in ''[[Kelvin|Kelvin]]''; 0 K = -273.15<sup>o</sup>C<br> |

− | z is the number of [[Moles|moles]] of [[Electrons|electrons]] transferred between cells (defined by the valency of [[Ion|ions]])<br> | + | z is the number of [[Moles|moles]] of [[Electrons|electrons]] transferred between cells (defined by the valency of [[Ion|ions]])<br> |

− | F is the [[Faraday's constant|Faraday's constant]]; F = 96,485.3415 C mol<sup>-1</sup><br> | + | F is the [[Faraday's constant|Faraday's constant]]; F = 96,485.3415 C mol<sup>-1</sup><br> |

− | [red] is the concentration of [[Ion|ion]] that gained [[Electrons|electrons]] ([[Reduction|reduction]])<br> | + | [red] is the concentration of [[Ion|ion]] that gained [[Electrons|electrons]] ([[Reduction|reduction]])<br> |

− | [oxi] is the concentration of [[Ion|ion]] that lost [[Electrons|electrons]] ([[Oxidation|oxidation]])<br> | + | [oxi] is the concentration of [[Ion|ion]] that lost [[Electrons|electrons]] ([[Oxidation|oxidation]])<br> |

− | == Membrane potential<br> | + | == Membrane potential<br> == |

''Main article: ''[[Membrane Potential|Membrane potential]] | ''Main article: ''[[Membrane Potential|Membrane potential]] | ||

− | Nernst equation is also can be used to calculate the potential of an [[Ion|ion]] across the membrane. For potential difference of a membrane, we can manipulate the Nernst Equation as follows:<br> | + | Nernst equation is also can be used to calculate the potential of an [[Ion|ion]] across the membrane. For potential difference of a membrane, we can manipulate the Nernst Equation as follows:<br> |

− | [[Image:Nernst equation2.png|278x98px]]<br> | + | [[Image:Nernst equation2.png|278x98px|Nernst equation2.png]]<br> |

− | or<br> | + | or<br> |

− | [[Image:Nernst equation3.png|371x97px]]<br> | + | [[Image:Nernst equation3.png|371x97px|Nernst equation3.png]]<br> |

− | where<br> | + | where<br> |

E<sub>m</sub> is the potential difference of an ion between membranes<sub></sub> | E<sub>m</sub> is the potential difference of an ion between membranes<sub></sub> | ||

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F is the Faraday's constant; F = 96,485.3415 C mol<sup>-1</sup> | F is the Faraday's constant; F = 96,485.3415 C mol<sup>-1</sup> | ||

− | [A<sup>-</sup>]<sub>o</sub> is the concentration of ion outside the membrane (in this case is anion, negative charge ion)<br> | + | [A<sup>-</sup>]<sub>o</sub> is the concentration of ion outside the membrane (in this case is anion, negative charge ion)<br> |

− | [A<sup>-</sup>]<sub>i</sub> is the concentration of ion inside the membrane (in this case is anion, negative charge ion) | + | [A<sup>-</sup>]<sub>i</sub> is the concentration of ion inside the membrane (in this case is anion, negative charge ion) |

== Application == | == Application == | ||

− | === | + | === Using 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.<br> | + | 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.<br> |

[[Image:Ussing model.png|629x322px|Ussing model of transepithelial ions absorption.]] | [[Image:Ussing model.png|629x322px|Ussing model of transepithelial ions absorption.]] | ||

− | <ref>Diagram based on CMB2003: Cell and Membrane Transport lecture note (2010).</ref>Ussing model of transepithelial ions absorption.<br> | + | <ref>Diagram based on CMB2003: Cell and Membrane Transport lecture note (2010).</ref>Ussing model of transepithelial ions absorption.<br> |

− | For example at the standard condition and temperature of 25<sup>o</sup>C (298K), the above sodium ion membrane potential can be calculated as:<br> | + | For example at the standard condition and temperature of 25<sup>o</sup>C (298K), the above sodium ion membrane potential can be calculated as:<br> |

[[Image:Nernst equation4.png]] | [[Image:Nernst equation4.png]] | ||

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== See also == | == See also == | ||

− | *[[Membrane potential]]<br> | + | *[[Membrane potential]]<br> |

*[[Goldman equation]]<br> | *[[Goldman equation]]<br> | ||

− | == References & Notes<br> | + | == References & Notes<br> == |

− | <references /><br> | + | <references /><br> |

== 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 13:57, 24 October 2012

**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]}

## Contents |

## Equation

Nernst equation can be expressed as follows:

where

E_{cell }is the half-cell potential difference

E^{θ}_{cell }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 = -273.15^{o}C

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

E_{m} 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 = -273.15^{o}C

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^{-}]_{o} is the concentration of ion outside the membrane (in this case is anion, negative charge ion)

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

## Application

### Using 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 25^{o}C (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.

## See also

## References & Notes

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