# Nernst Equation

**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

### 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 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).