Faraday Constant

The Faraday constant, symbol $F$, is the electric charge per mole of elementary charges. Equivalently, it is the magnitude of the charge carried by one mole of electrons. It connects electrical quantities with amount of substance and is central to electrochemistry. Its exact value in the International System of Units (SI) is $96\,485.332\,123\,310\,0184\ \mathrm{C\,mol^{-1}}$, obtained from the product of two exactly defined constants. (goldbook.iupac.org)

Definition and exact value

The defining relationship is

where $N_{\mathrm A}$ is the Avogadro constant and $e$ is the positive elementary charge. Their exact SI values are

Multiplication gives the exact value above. For ordinary calculations, $F\approx96\,485.33\ \mathrm{C\,mol^{-1}}$, or $9.6485\times10^4\ \mathrm{C\,mol^{-1}}$, is usually sufficient. The unit is the coulomb per mole, equivalently $\mathrm{A\,s\,mol^{-1}}$. (bipm.org)

The revised SI took effect on 20 May 2019, fixing the numerical values of both $e$ and $N_{\mathrm A}$. Consequently, $F$ has no definitional uncertainty in SI units. It is not itself one of the seven SI defining constants: its exactness follows from their fixed values. Earlier determinations carried experimental uncertainty, and older reference tables may therefore contain slightly different values. (bipm.org)

The constant is positive. An electron has charge $-e$, so one mole of electrons has total charge $-F$. In reaction calculations, $F$ normally supplies the magnitude, while signs follow the chosen reaction and current conventions. This interpretation follows directly from its definition as molar elementary charge. (goldbook.iupac.org)

Electrolysis and reaction stoichiometry

The constant appears in Faraday’s laws of electrolysis. The first law states that the mass of electrochemically transformed material is proportional to the charge passed. The second relates the masses transformed by equal charges to their chemical equivalent molar masses. Together they give

where $m$ is the transformed mass, $M$ its molar mass, $Q$ the charge associated with the reaction, and $z$ the number of electrons transferred per specified formula unit. Thus stoichiometry determines how electrical charge translates into chemical production or consumption. (goldbook.iupac.org)

For a reaction involving $z$ electrons per reacting entity, the corresponding amount is

One mole of a species undergoing a one-electron transformation requires a charge magnitude $F$; a two-electron transformation requires $2F$. The relevant electron number belongs to the balanced oxidation–reduction reaction, not necessarily to the charge of an individual ion. These are direct consequences of Faraday’s laws. (goldbook.iupac.org)

For example, the idealized electrode reaction

requires two moles of electrons per mole of copper deposited. A charge of $F$ would therefore deposit $0.5$ mole of copper if all the charge served this reaction. This is a stoichiometric illustration of the law, rather than a prediction independent of experimental conditions. (goldbook.iupac.org)

Coulometry and practical limitations

In coulometry, the charge required to carry out a known electrochemical reaction is measured and converted into an amount of substance using $F$. Experiments may operate at controlled current or controlled potential. Under suitable conditions, coulometry is a primary reference measurement procedure: it does not require calibration against an amount-of-substance standard of the same kind. (goldbook.iupac.org)

A related application is coulometric titration, in which an electrochemically generated reagent reacts stoichiometrically with an analyte. The charge needed to reach the endpoint determines the reagent amount and hence the analyte amount. Quantitative reagent generation requires the appropriate current efficiency. (iupac.org)

Measured total charge need not all contribute to the desired product. When several electrode reactions occur, current efficiency expresses the selected reaction’s share of the electrode current. For a deposition process with effective efficiency $\eta$, the ideal relation becomes

provided subsequent chemical reactions do not independently produce or consume the measured product. Such corrections describe the experiment; they do not change $F$. (goldbook.iupac.org)

Electrochemical thermodynamics

The constant also connects electrical potential with molar Gibbs free energy. For a reversible cell reaction transferring $z$ electrons per reaction as written,

where $E$ is the corresponding cell potential. This expresses the conversion between electrical driving force and chemical free-energy change. (list.iupac.org)

In the Nernst equation, the same conversion gives

where $R$ is the gas constant, $T$ is absolute temperature, and $Q_{\mathrm r}$ is the dimensionless reaction quotient formed from chemical activities. Here $Q_{\mathrm r}$ must be distinguished from the electrical charge $Q$ used in electrolysis calculations. The factor $RT/F$ converts a molar thermal-energy scale into a potential scale. (media.iupac.org)

Historical basis

The constant is named after Michael Faraday, whose electrolysis investigations in the early 1830s established quantitative relations between electricity and chemical transformation. Those laws preceded the modern description of electron transfer. Their contemporary formulation expresses the common charge scale through $F=N_{\mathrm A}e$, allowing macroscopic electrical measurements to quantify chemical transformations. (rigb.org)