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## Nernst equationIn electrochemistry, the It is used in physiology for finding the electric potential of a cell membrane with respect to one type of ion. where is the standard electrode potential*E*^{0}*R*is the universal gas constant (8.314510 J K^{-1}mol^{-1})*T*is the absolute temperature. (*T*_{K}= 273.15 +*T*_{°C}.)*a*are the chemical activities for the reduced and oxidized species respectively.*a*_{X}= γ_{X}[*X*] where γ_{X}is the activity coefficient of species X. (Since activity coefficients tends to unity at low concentrations, activities in the Nernst equation are frequently replaced by simple concentrations.)*F*is the Faraday constant (the magnitude of the charge per mole of electrons), equal to 9.6485309×10^{4}C mol^{-1}*n*is the number of electrons transferred in the cell reaction or half-reaction.
The constant The Nernst equation is frequently expressed in terms of base 10 logarithms rather than natural logarithms, in which case it is written, - .
Note that the Nernst equation is expressed more generally by replacing the ratio of activities with the reaction quotient ## Additional recommended knowledge
## Physiological application: the Nernst potentialFor a cell membrane potential with respect to one (the sign before the logarithm changes to a minus for anions). The potential level across the cell membrane that exactly opposes net diffusion of a particular ion through the membrane is called the ## Derivation
The Nernst Equation may be derived in several different ways. Chemistry textbooks frequently give the derivation in terms of entropy and the Gibbs free energy, but there is a more intuitive method for anyone familiar with Boltzmann factors. ## Using Boltzmann factorsFor simplicity, we will consider a solution of redox-active molecules that undergo a one electron reversible reaction and which have a standard potential of zero. The chemical potential μ The ratio of oxidized to reduced molecules, [Ox]/[Red], is equivalent to the probability of being oxidized (giving electrons) over the probability of being reduced (taking electrons), which we can write in terms of the Boltzmann factors for these processes: Taking the natural logarithm of both sides gives If at [Ox]/[Red] = 1, we need to add in this additional constant: Dividing the equation by ## Using entropy and Gibbs free energyQuantities here are given per molecule, not per mole,
and so Boltzmann's constant The entropy of a molecule is defined as where Ω is the number of states available to the molecule.
The number of states must vary linearly with the volume The change in entropy from some state 1 to another state 2 is therefore so that the entropy of state 1 is If state 1 is at standard conditions, in which where is then given by We define the ratio in the last term as the reaction quotient: In an electrochemical cell, the cell potential and the cell potential, This is the more general form of the Nernst equation.
For the redox reaction
The cell potential at standard conditions ## LimitationsIn dilute solutions, the Nernst equation can be expressed directly in terms of concentrations (since activity coefficients are close to unity). But at higher concentrations, the true activities of the ions must be used. This complicates the use of the Nernst equation, since estimation of non-ideal activities of ions generally requires experimental measurements. The Nernst equation also only applies when there is no net current flow through the electrode. The activity of ions at the electrode surface changes when there is current flow, and there are additional overpotential and resistive loss terms which contribute to the measured potential. ## See also |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Nernst_equation". A list of authors is available in Wikipedia. |