# Tafel equation

﻿
Tafel equation

The Tafel equation relates the rate of an electrochemical reaction to the overpotential. [Bard, A. J.; Faulkner, L. R. “Electrochemical Methods. Fundamentals and Applications” 2nd Ed. Wiley, New York. 2001. ISBN 0-471-04372-9] The Tafel equation was first deduced experimentally and was later shown to have a theoretical justification. The equation is named after German chemist Julius Tafel (1862-1918).

On a single electrode the Tafel equation can be stated as

$Delta V=A imes lnleft\left(frac\left\{i\right\}\left\{i_0\right\} ight\right)$

where: $Delta V$ is the overpotential, V : $A$ is the so called "Tafel slope", V: $i$ is the current density, A/m2 and : $i_0$ is the so called "exchange current density", A/m2.

Overview of the terms

The exchange current is the current at equilibrium, i.e. the rate at which oxidized and reduced species transfer electrons with the electrode.In other words, the exchange current density is the rate of reaction at the reversible potential (when the overpotential is zero by definition). At the reversible potential, the reaction is in equilibrium meaning that the forward and reverse reactions progress at the same rates. This rate is the exchange current density.

The Tafel slope is measured experimentally; however, it can be shown theoretically when the dominant reaction mechanism involves the transfer of a single electron that

:$frac\left\{kT\right\}\left\{e\right\} < A$

where A is defined as

:$A = frac\left\{kT\right\}\left\{ealpha\right\}$

where:$k$ is Boltzmann's constant,:$T$ is the absolute temperature, :$e$ is the electron charge, and :$alpha$ is the so called "charge transfer coefficient", the value of which must be between 0 and 1.

An alternative form

The Tafel equation can be also written as:

$i=nFk exp left\left( pm alpha F frac \left\{Delta V\right\} \left\{RT\right\} ight\right)$

where:the plus sign under the exponent refers to an anodic reaction, and a minus sign to a cathodic reaction,:n is the number of electrons involved in the electrode reaction:k is the rate constant for the electrode reaction,:R is the universal gas constant,:F is the Faraday constant.

Applicability

Where an electrochemical reaction occurs in two "half reactions" on separate electrodes, the Tafel equation is applied to each electrode separately.

The Tafel equation assumes that the reverse reaction rate is negligible compared to the forward reaction rate.

The Tafel equation is applicable to the region where the values of polarization are high. At low values of polarization, the dependence of current on polarization is usually linear (not logarithmic):

:$i=i_0 frac \left\{nF\right\} \left\{RT\right\} Delta E$.

This linear region is called "polarization resistance" due to its formal similarity to the Ohm's law.

ee also

*Overpotential
*Butler-Volmer equation

References

*cite journal
title = A Century of Tafel’s Equation: 1905–2005 A Commemorative Issue of Corrosion Science
author = G.T. Burstein
journal = Corrosion Science
volume = 47
issue = 12
pages = 2858–2870
year = 2005
url =
doi = 10.1016/j.corsci.2005.07.002

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Tafel equation — Tafelio lygtis statusas T sritis chemija apibrėžtis Lygtis, išreiškianti tiesinę priklausomybę tarp viršįtampio ir srovės tankio logaritmo. atitikmenys: angl. Tafel equation rus. уравнение Тафеля …   Chemijos terminų aiškinamasis žodynas

• Julius Tafel — Infobox Scientist name = Julius Tafel image width = caption = Julius Tafel birth date = birth date|1862|6|2 birth place = Courrendlin,Switzerland residence = nationality = Swiss death date = death date and age|1918|9|2|1862|6|2 death place =… …   Wikipedia

• Butler-Volmer equation — The Butler Volmer equation is one of the most fundamental relationships in electrochemistry. It describes how the electrical current on an electrode depends on the electrode potential, considering that both a cathodic and an anodic reaction occur …   Wikipedia

• Loi de Tafel — La loi de Tafel en électrochimie relie la surtension entre les électrodes à la densité de courant. L équation de Tafel fut tout d abord une loi empirique, déterminée expérimentalement, et qui a fait l objet, plus tardivement, de justifications… …   Wikipédia en Français

• Glossary of fuel cell terms — The Glossary of fuel cell terms lists the definitions of many terms used within the fuel cell industry. The terms in this glossary may be used by fuel cell industry associations, in education material and fuel cell codes and standards to name but …   Wikipedia

• Overpotential — This article is about a concept in electrochemical use in electrical engineering. For overvoltage, see Overpotential (disambiguation). Overpotential is an electrochemical term which refers to the potential (voltage) difference between a half… …   Wikipedia

• Electrode — For other uses, see Electrode (disambiguation). Electrodes used in arc welding An electrode is an electrical conductor used to make contact with a nonmetallic part of a circuit (e.g. a semiconductor, an electrolyte or a …   Wikipedia

• Tafelio lygtis — statusas T sritis chemija apibrėžtis Lygtis, išreiškianti tiesinę priklausomybę tarp viršįtampio ir srovės tankio logaritmo. atitikmenys: angl. Tafel equation rus. уравнение Тафеля …   Chemijos terminų aiškinamasis žodynas

• уравнение Тафеля — Tafelio lygtis statusas T sritis chemija apibrėžtis Lygtis, išreiškianti tiesinę priklausomybę tarp viršįtampio ir srovės tankio logaritmo. atitikmenys: angl. Tafel equation rus. уравнение Тафеля …   Chemijos terminų aiškinamasis žodynas

• electrochemical reaction — ▪ chemistry Introduction       any process either caused or accompanied by the passage of an electric current and involving in most cases the transfer of electrons between two substances one a solid and the other a liquid.       Under ordinary… …   Universalium