The Faraday 's laws , named after their discoverer Michael Faraday , describe the relationship between electrical charge and metabolism in electrochemical reactions, e.g. B. in electrolysis . They are therefore the basic laws of electrochemistry and electrolysis. Traditionally the laws are called Faraday's laws of electrolysis, but they are also applicable to the metabolism in galvanic cells , i.e. H. Batteries , accumulators and fuel cells , valid. To separate them is the Faraday's law of induction, which refers to the electromagnetic induction relates; see disambiguation note at the beginning of the article.

## Basic concepts of electrolysis

The electrolysis , a method of electrochemistry , allowed in the 19th century for the first time, some newly discovered metals represent in elemental form. An electric current is passed through a melt made of compounds of these metals. Faraday called this method electrolysis (from a Greek expression for "liberate with electricity").

Faraday called a liquid or solution that had electrical conductivity an electrolyte . He called the metal rods that were immersed in the liquid or solution electrodes (from the Greek word for "the street of electricity"). He called the electrode into which the external current flows an anode (ἄνοδος “ascent”). Accordingly, he called the electrode from which the current flows out as the cathode (κάϑοδος "downward path").

Faraday compared the flow of electricity to water flowing from above (in the case of electricity, from the anode) downwards (to the cathode). He followed the example of Franklin , who had defined a flow of electricity from positive to negative. This is also the direction of transport of positively charged charge carriers; the definition of the current direction says nothing about the sign of the charge on the charge carriers. In electrolytes there are positive and negative charge carriers called ions , while in metallic conductors the charge carriers are negatively charged electrons . Positively charged ions are called cations and negatively charged anions . The name is derived from the name of the electrode with the opposite sign on which these ions are deposited.

Michael Faraday on an oil painting created around 1841/42

In 1834 Faraday published the basic laws of electrolysis, now known as Faraday's laws :

The amount of substance that is deposited on an electrode during electrolysis is proportional to the electrical charge that is sent through the electrolyte. (n ~ Q)
The mass of an element deposited by a certain amount of charge is proportional to the atomic mass of the deposited element and inversely proportional to its valency (i.e. the number of monovalent atoms that can combine with this element).

## Today's wording

In order to electrolytically deposit one mole of a monovalent ion, the amount of charge or charge Q 1 is required:

${\ displaystyle {\ frac {Q_ {1}} {\ text {1 mol}}} = e \ cdot N _ {\ mathrm {A}} = F}$

Here e is the elementary charge and N A is Avogadro's constant , which says how many particles are contained in a mole. F is the Faraday constant of 96485 C / mol and it is equal to the charge required to deposit one mole of a monovalent substance. It is also equal to the amount of charge of one mole of electrons that is required or released for deposition.

In order to electrolytically deposit any amount of substance of a z-valent ion, it needs the charge:

${\ displaystyle Q = n \ cdot z \ cdot F}$

with the charge number for the ion used, the amount of substance n and the Faraday constant F .

Because of the definition of the molar mass M, the following can be written for the mass m of a substance:

${\ displaystyle m = M \ cdot n}$

with mass m of the substance, the molar mass M and the amount of substance n of the substance. If the second equation is now converted to n and inserted into the equation for the mass m , it follows:

${\ displaystyle m = {M \ cdot Q \ over z \ cdot F}}$

Here, the mass m is the mass of the substance deposited by electrolysis.

This equation sums up the two Faraday laws in a relationship. Therefore, such equations can also be referred to with the singular term “Faraday's law” .

If one defines the electrochemical equivalent Ä e

${\ displaystyle {\ ddot {A}} _ {e} = {\ frac {M} {z \ cdot F}}}$

so we get the equation

${\ displaystyle m = {\ ddot {A}} _ {e} Q}$.

This equation follows from Faraday's first law, but it expresses the proportionality of the charge to the mass of the substance.

By rearranging the equation above, the charge Q is obtained , which is necessary to deposit a certain mass m of the substance by electrolysis:

${\ displaystyle Q = {m \ cdot z \ cdot F \ over M}}$

With a constant current I , the charge Q is proportional to the electrolysis time t :

${\ displaystyle Q = I \ cdot t}$

If this is inserted into the equation for the mass m of the electrodeposited substance, it follows:

${\ displaystyle m = {M \ cdot I \ cdot t \ over z \ cdot F}}$

This equation states how large the deposited mass m of the substance is, depending on the (constant) current strength and the electrolysis time. Where M and F are constants. By rearranging this equation one obtains for the electrolysis time t :

${\ displaystyle t = {m \ cdot z \ cdot F \ over M \ cdot I}}$

This equation states how long the electrolysis time has to be in order to electrolytically deposit a certain mass of a deposited material at a given constant current strength.

## Applications

Faraday's laws serve as a support for atomic theory , i.e. as a strong indication that there are atoms and ions: As is known from the Millikan experiment , the electrical charge is quantized, i.e. H. there is a smallest electrical charge, the elementary charge. Since, according to Faraday's laws, the amount of substance is proportional to the charge, it immediately follows that the substances are converted in the smallest portions during electrolysis, precisely the atoms or the ions that carry a charge that corresponds either to the elementary charge or a multiple thereof.

Other historically important applications are the determination of relative molar masses M and of charge numbers z . For this purpose, for example, two electrolysis cells connected in series were used, with two silver electrodes in one of them being immersed in a silver salt solution. Since the cells are connected in series, the same charge flows through both cells, and if one mole of silver is converted in one, 1 mol / z is converted in the other .

Faraday's laws are also used in electroplating , where they are e.g. B. with a known geometric surface A of a workpiece allow the estimation of the layer thickness d . According to the definition of density ( ) we have ${\ displaystyle \ varrho}$

${\ displaystyle \ varrho = {m \ over V} = {m \ over d \ cdot A}}$.

So you get

${\ displaystyle d = {M \ cdot Q \ over z \ cdot A \ cdot \ varrho \ cdot F} = {M \ cdot I \ cdot t \ over z \ cdot A \ cdot \ varrho \ cdot F}.}$

## Historical

In 1833 Michael Faraday reported that the amount of substance converted was not proportional to the current strength, but to the charge (“When electro-chemical decomposition takes place, there is great reason to believe that the quantity of matter decomposed is not proportionate to the intensity, but to the quantity of electricity passed ”). In his summarizing work of 1834 he made the laws clear. Although some scientists soon recognized the meaning and correctness of the Faraday laws, they were largely disregarded between 1834 and 1880, especially since the recognized chemist Jöns Jakob Berzelius considered them wrong because he had not correctly differentiated current strength and charge.

The Faraday Laws may have been discovered independently by Carlo Matteucci . Matteucci himself wrote in 1839 that he had discovered it on his own. However, since his work was published in October 1834 or 1835, so that it cannot be ruled out that he knew Faraday's published results before that, Faraday is considered a discoverer, so that the laws only bear his name.

From 1881 on, Faraday's laws were widely used in science and technology, in particular electrolysis was also used to determine charges and currents in a direct current circuit. The devices used for this purpose were called voltameters in the 19th century , later coulometers. From 1938 onwards, the charge measurement was used for quantitative analysis, the method is called coulometry .

## Individual evidence

1. ^ A b c Michael Faraday: Experimental Researches in Electricity. Seventh Series . In: Philosophical Transactions of the Royal Society of London . tape 124 , January 1834, p. 77-122 , doi : 10.1098 / rstl.1834.0008 .
2. Frederick C. Strong: Faraday's laws in one equation . In: Journal of Chemical Education . tape 38 , no. 2 , 1961, p. 98 , doi : 10.1021 / ed038p98 .
3. ^ William B. Jensen: Faraday's Laws or Faraday's Law? In: Journal of Chemical Education . tape 89 , no. 9 , May 2012, p. 1208-1209 , doi : 10.1021 / ed101193q .
4. Michael Faraday: Experimental Researches in Electricity. Third Series . In: Philosophical Transactions of the Royal Society of London . tape 123 , January 1833, §7 Identity of Electricities derived from different sources. II Ordinary Electricity. 329., pp. 23-54 , doi : 10.1098 / rstl.1833.0006 .
5. a b c d Rosemary Gene Ehl, Aaron J. Ihde: Faraday's Electrochemical Laws and the Determination of Equivalent Weights . In: Journal of Chemical Education . tape 31 , no. 5 , May 1954, p. 226–232 , doi : 10.1021 / ed031p226 .
6. ^ Charles Matteucci: Sur la Force eléctro-chimique de la pile . In: Annales de chimie et de physique . tape 58 , 1835, pp. 75–88 (owner of the original: Bayerische Staatsbibliothek).