Faraday's law of electromagnetic induction for beginners. Electrolysis. Faraday's laws

In 1831, the world first learned about the concept of electromagnetic induction. It was then that Michael Faraday discovered this phenomenon, which ultimately became the most important discovery in electrodynamics.

History of development and experiments of Faraday

Until the middle of the 19th century, it was believed that the electric and magnetic fields have no connection, and the nature of their existence is different. But M. Faraday was confident in the unified nature of these fields and their properties. The phenomenon of electromagnetic induction, discovered by him, subsequently became the foundation for the design of generators of all power plants. Thanks to this discovery, humanity's knowledge of electromagnetism has made great strides forward.

Faraday performed the following experiment: he closed a circuit in coil I and the magnetic field around it increased. Further, the induction lines of this magnetic field crossed coil II, in which an induced current arose.

Rice. 1. Scheme of Faraday's experiment

In fact, simultaneously with Faraday, but independently of him, another scientist, Joseph Henry, discovered this phenomenon. However, Faraday published his research earlier. Thus, the author of the law of electromagnetic induction was Michael Faraday.

No matter how many experiments Faraday conducted, one condition remained unchanged: for the formation of an induced current, a change in magnetic flux piercing a closed conducting circuit (coil).

Faraday's law

The phenomenon of electromagnetic induction is determined by the occurrence electric current in a closed electrically conducting circuit when the magnetic flux changes through the area of ​​this circuit.

Faraday's basic law is that electromotive force (EMF) is directly proportional to the rate of change of magnetic flux.

The formula for Faraday's law of electromagnetic induction is as follows:

Rice. 2. Formula for the law of electromagnetic induction

And if the formula itself, based on the above explanations, does not raise questions, then the “-” sign may raise doubts. It turns out that there is a rule by Lenz, a Russian scientist who conducted his research based on Faraday’s postulates. According to Lenz, the “-” sign indicates the direction of the emerging EMF, i.e. the induced current is directed in such a way that the magnetic flux it creates, through the area bounded by the circuit, tends to oppose the change in flux that the current causes.

Faraday-Maxwell law

In 1873, J.C. Maxwell presented the theory in a new way electromagnetic field. The equations he derived formed the basis of modern radio engineering and electrical engineering. They are expressed as follows:

• Edl = -dФ/dt– electromotive force equation
• Hdl = -dN/dt– equation of magnetomotive force.

Where E– electric field strength in the area dl; H– magnetic field strength in the area dl; N– flow of electrical induction, t- time.

The symmetrical nature of these equations establishes a connection between electrical and magnetic phenomena, as well as magnetic and electrical. the physical meaning that defines these equations can be expressed by the following provisions:

• If electric field changes, then this change is always accompanied by a magnetic field.
• if the magnetic field changes, then this change is always accompanied by an electric field.

Rice. 3. Emergence of a vortex magnetic field

Maxwell also established that the propagation of the electromagnetic field is equal to the speed of propagation of light.

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Laws of electrolysis (Faraday's laws)

Since the passage of electric current through electrochemical systems is associated with chemical transformations, there must be a certain relationship between the amount of electricity flowing and the amount of reacted substances. It was discovered by Faraday and was expressed in the first quantitative laws of electrochemistry, later called Faraday's laws.

Faraday's first law . The amounts of substances converted during electrolysis are proportional to the amount of electricity passing through the electrolyte:

Dm = k e q = k uh It ,

Dm is the amount of reacted substance; k e – some coefficient of proportionality; q is the amount of electricity equal to the product of current I and time t. Ifq = It = 1, thenDm = k uh, that is, the coefficient k e represents the amount of substance reacted as a result of the flow of a unit amount of electricity. Coefficient k uhcalled electrochemical equivalent .

Faraday's second law reflects the relationship that exists between the amount of reacted substance and its nature: with a constant amount of electricity passed, masses of various substances undergoing transformation at the electrodes (release from solution, change in valency), are proportional to the chemical equivalents of these substances:

Dm i/A i= const .

Both Faraday's laws can be combined into one general law: to excrete or transform by means of current 1 g-eq any substance (1/zmole of a substance) always requires the same amount of electricity, called Faraday number (or Faraday ):

Dm =It=It .

Precisely measured value of Faraday number

F = 96484,52 ± 0.038 C/g-eq.

This is the charge carried by one gram equivalent of ions of any kind. Multiplying this number byz (the number of elementary charges of the ion), we obtain the amount of electricity carried by 1 g-ion . Dividing the Faraday number by the Avogadro number, we obtain the charge of one monovalent ion equal to the charge of the electron:

e = 96484,52 / (6,022035 × 10 23) = 1,6021913 × 10 –19 Grade.

The laws discovered by Faraday in 1833 are strictly followed for conductors of the second type. Observed deviations from Faraday's laws are apparent. They are often associated with the presence of unaccounted parallel electrochemical reactions. Deviations from Faraday's law in industrial installations are associated with current leaks, loss of substance when spraying a solution, etc. IN technical installations the ratio of the amount of product obtained by electrolysis to the amount calculated on the basis of Faraday's law is less than unity and is called current output :

B T = = .

With careful laboratory measurements for unambiguously occurring electrochemical reactions, the current output is equal to unity (within the limits of experimental errors). Faraday's law is strictly observed, so it underlies the most accurate method of measuring the amount of electricity passing through a circuit by the amount of substance deposited at the electrode. For such measurements use coulometers . Electrochemical systems are used as coulometers, in which there are no parallel electrochemical and side chemical reactions. By methods for determining the amount of substances formed coulometers are divided into electrogravimetric, gas and titration. An example of electrogravimetric coulometers are silver and copper coulometers. The action of the Richardson silver coulometer, which is an electrolyzer

(–) Agï AgNO3× aqï Ag (+) ,

based on weighing the mass of silver deposited on the cathode during electrolysis. When 96500 C (1 faraday) of electricity is passed through the cathode, 1 g-equiv of silver (107 g) will be released. When skippingn F of electricity, an experimentally determined mass is released at the cathode (Dm To). The number of transmitted Faradays of electricity is determined from the relation

n = Dm /107 .

The principle of operation of a copper coulometer is similar.

In gas coulometers, the products of electrolysis are gases, and the amounts of substances released on the electrodes are determined by measuring their volumes. An example of a device of this type is a gas coulometer based on the electrolysis of water. During electrolysis, hydrogen is released at the cathode:

2H 2 O+2 e– =2OH – +H2,

and at the anode - oxygen:

H 2 O=2H + +½ O 2 +2 e – V– total volume of released gas, m3.

In titration coulometers, the amount of substance formed during electrolysis is determined titrimetrically. This type of coulometer includes the Kistyakovsky titration coulometer, which is an electrochemical system

(–) Ptï KNO3, HNO3ï Ag (+) .

During the electrolysis process, the silver anode dissolves, forming silver ions, which are titrated. The number of Faradays of electricity is determined by the formula

n = mVc ,

Where m– mass of solution, g; V– volume of titrant used for titration of 1 g of anode liquid; c – titrant concentration, g-equiv/cm3.

1. Faraday's first law is the fundamental quantitative law of electrochemistry.

2.Electrochemical equivalent.

3.Coulometers.Classification of coulometers.

4. Exit of substance by current.

5. Methods for determining current output when using direct and pulsed current.

6.Faraday's second law.

7. Apparent cases of deviation from Faraday's laws.

1. Faraday's first law

There are three main types of coulometers: gravimetric (gravimetric), volumetric (volumetric) and titration.

In weighing coulometers (these include silver and copper), the amount of electricity passed through them is calculated by the change in the mass of the cathode or anode. In volumetric coulometers, the calculation is made based on measuring the volume of the resulting substances (gas in a hydrogen coulometer, liquid mercury in a mercury coulometer). In titration coulometers, the amount of electricity is determined from titration data of substances formed in solution as a result of an electrode reaction.

Copper coulometer most common in laboratory research practice, because it is easy to manufacture and quite accurate. The accuracy of determining the amount of electricity is 0.1%. The coulometer consists of two copper anodes and a thin copper foil cathode located between them. The electrolyte in the copper coulometer is an aqueous solution of the composition: CuSO 4 ∙ 5H 2 O, H 2 SO 4 and ethanol C 2 H 5 OH. Sulfuric acid increases the electrical conductivity of the electrolyte and, in addition, prevents the formation of basic copper compounds in the cathode space, which can be adsorbed on the cathode, thereby increasing its mass. H 2 SO 4 in the copper coulometer electrolyte is necessary to prevent the accumulation of Cu 1+ compounds that can form as a result of the disproportionation reaction:

Cu 0 + Cu 2+ → 2Cu +

Ethyl alcohol is added to the electrolyte to obtain more finely crystalline, compact cathode deposits and to prevent oxidation of the copper electrodes of the coulometer.

The amount of electricity passed is judged by the change in the mass of the cathode, before and after electrolysis.

cathode, and the anode is made of pure silver.

A neutral or slightly acidic 30% solution of silver nitrate is used as an electrolyte in a silver coulometer.

Gas hydrogen-oxygen coulometer used for approximate measurements of small amounts of electricity. It measures the total volume of hydrogen and oxygen released during the electrolysis of an aqueous solution of H 2 SO 4 or NaOH, and from this value the amount of electricity passed is calculated. These coulometers are used relatively rarely, because Their accuracy is low, and they are less convenient to use than weighing coulometers.

Volumetric coulometers also include mercury coulometer. It is mainly used in industry to measure the amount of electricity. The accuracy of a mercury coulometer is 1%, but it can operate at high current densities. The anode is mercury. Coal is the cathode. The electrolyte is a solution of mercury iodide and potassium iodide. The amount of electricity is calculated from the level of mercury in the tube.

The most common of titration coulometers– iodine

And Kistyakovsky coulometer.

An iodine coulometer is a vessel with platinum-iridium electrodes separated by cathode and anode spaces. A concentrated solution of potassium iodide with the addition of hydrochloric acid is introduced into the anode compartment, and a solution of hydrochloric acid is introduced into the cathode compartment. When a current is passed through the anode, iodine is released, which is then titrated with sodium thiosulfate (Na 2 S 2 O 3). Based on the titration results, the amount of electricity is calculated.

Kistyakovsky coulometer- This is a glass vessel. The anode is a silver wire soldered into a glass tube with mercury to ensure contact. The vessel is filled with a solution of potassium nitrate (15-20%). A platinum-iridium cathode is immersed in this solution. When current is passed, anodic dissolution of silver occurs. And also based on the results of titration of the solution, the amount of electricity is calculated.

4. Current output

Zn 2+ +2ē →Zn

If several parallel electrochemical reactions occur on the electrode, then Faraday’s first law will be valid for each of them.

For practical purposes, in order to take into account what fraction of the current or amount of electricity passing through the electrochemical system is spent on each specific reaction, the concept output of a substance by current.

Thus, VT makes it possible to determine the part of the amount of electricity passed through the electrochemical system, which accounts for the share of this electrochemical reaction.

Knowledge of VT is necessary, as in solving theoretical issues: for example, when constructing partial polarization curves and elucidating the mechanism of an electrochemical reaction, and in the practice of electrodeposition of metals, non-metals, alloys, in order to assess the effectiveness of a technological operation. In practice, VT is most often determined by dividing the practical mass of a substance by the theoretical mass determined by Faraday’s law.

m practical – the mass of a substance practically transformed as a result of the passage of a certain amount of electricity; m theor is the mass of a substance that should theoretically transform when passing the same amount of electricity.

The VT for processes occurring at the cathode, as a rule, do not coincide with the VT of the anodic processes, therefore it is necessary to distinguish between the cathode and anode current output. Until now, we have considered cases of determining VT when a direct electric current flows through the interface between a conductor of the first type and a conductor of the second type.

5. Methods for determining VT using pulsed current

If a pulsed current flows through the phase interface, then great difficulties arise in determining the VT. There is no single method or instrument for determining VT during pulse electrolysis. The difficulty of determining VT under pulsed electrolysis conditions is due to the fact that the current passing through the system is spent not only on the electrochemical reaction, but also on charging the electrical double layer. An electric current passing through an interface and causing an electrochemical transformation is often called Faraday current. The charging current is spent on charging the electrical double layer, reorganizing the solvent, the reagent itself, i.e. everything that creates the conditions for an electrochemical reaction to occur, so the expression for the total current passing through the electrochemical system will be as follows:

I = Iz + Iph, where Iz is the charging current, Iph is the Faraday current.

If it is not necessary to determine the absolute values ​​of VT, then the ratio of the amount of electricity spent on dissolving the precipitate to the amount of electricity spent on its formation can be used as a criterion for assessing the efficiency of pulsed electrolysis.

6. Faraday's second law.

Mathematically, this law is expressed by the equation:

Faraday's second law is a direct consequence of the first law. Faraday's second law reflects the relationship that exists between the amount of reacted substance and its chemical nature.

According to Faraday's second law:

If at the interface between a conductor of the first kind and a conductor of the second kind one and only one electrochemical reaction occurs, in which several substances participate, then the masses of the participants in the reaction that have undergone transformations relate to each other as their chemical equivalents.

7. Apparent cases of deviation from Faraday's laws

Faraday's First Law, based on the atomic nature of matter and electricity, is an exact law of nature. There can be no deviations from it. If in practice deviations from this law are observed during calculations, they are always due to incomplete consideration of the processes accompanying the main electrochemical reaction. For example, during the electrolysis of an aqueous solution of NaCl in a system with platinum electrodes and anode and cathode spaces separated by a porous diaphragm, the following reaction occurs at the cathode:

2H 2 O + 2ē = H 2 + 2OH -

and at the anode: 2Cl - - 2ē = Cl 2

The amount of chlorine gas formed is always less than what follows according to Faraday's law due to the fact that Cl 2 dissolves in the electrolyte and undergoes a hydrolysis reaction:

Cl 2 + H 2 O → HCl+ HClO

If we take into account the mass of chlorine that reacted with water, we obtain a result corresponding to that calculated according to Faraday’s law.

Or, during the anodic dissolution of many metals, two processes occur in parallel - the formation of ions of normal valence and the so-called subions - i.e. ions of lower valence, for example: Cu 0 - 2ē → Cu 2+ and

Cu- 1ē → Cu +. Therefore, the calculation according to Faraday's law under the assumption that only ions of the highest valence are formed turns out to be incorrect.

Often, not one electrochemical reaction occurs at the electrode, but several independent parallel reactions. For example, when separating Zn from an acidic solution of ZnSO 4 along with the discharge of Zn ions:

Zn 2+ +2ē →Zn

the reduction reaction of hydronium ions occurs: 2H 3 O + +2ē → H 2 + 2H 2 O.

If several parallel electrochemical reactions occur on the electrode, then Faraday’s first law will be valid for each of them.

Electrolysis is a physical and chemical process carried out in solutions of various substances using electrodes (cathode and anode). There are many substances that chemically decompose into their components when an electric current passes through their solution or melt. They are called electrolytes. These include many acids, salts and bases. There are strong and weak electrolytes, but this division is arbitrary. In some cases, weak electrolytes exhibit the properties of strong ones and vice versa.

When current is passed through a solution or molten electrolyte, various metals are deposited on the electrodes (in the case of acids, hydrogen is simply released). Using this property, you can calculate the mass of the released substance. For such experiments, a solution of copper sulfate is used. A red copper deposit can easily be seen on the carbon cathode when current is passed through. The difference between the values ​​of its masses before and after the experiment will be the mass of the deposited copper. It depends on the amount of electricity passing through the solution.

Faraday's first law can be formulated as follows: the mass of substance m released at the cathode is directly proportional to the amount of electricity (electric charge q) passing through the solution or melt of the electrolyte. This law is expressed by the formula: m=KI=Kqt, where K is the proportionality coefficient. It is called the electrochemical equivalent of the substance. For each substance he takes different meanings. He is numerically equal to mass substance released on the electrode in 1 second at a current of 1 ampere.

Faraday's second law

In special tables you can see the electrochemical values ​​for various substances. You will notice that these values ​​are significantly different. Faraday gave an explanation for this difference. It turned out that the electrochemical equivalent of a substance is directly proportional to its chemical equivalent. This statement is called Faraday's second law. Its truth has been confirmed experimentally.

The formula expressing Faraday's second law looks like this: K=M/F*n, where M is molar mass, n is valence. The ratio of molar mass to valency is called chemical equivalent.

The quantity 1/F has the same meaning for all substances. F is called Faraday's constant. It is equal to 96.484 C/mol. This value shows the amount of electricity that needs to be passed through a solution or molten electrolyte so that one mole of the substance settles on the cathode. 1/F shows how many moles of a substance will settle on the cathode when a charge of 1 C passes through.

The emergence of the electromotive force of induction was the most important discovery in the field of physics. It was fundamental for the development of the technical application of this phenomenon.

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Michael Faraday

Story

In the 20s of the 19th century, the Dane Oersted observed the deflection of a magnetic needle when it was placed next to a conductor through which an electric current flowed.

Michael Faraday wanted to explore this phenomenon more closely. With great persistence he pursued his goal of converting magnetism into electricity.

Faraday's first experiments brought him a number of failures, since he initially believed that a significant direct current in one circuit could generate a current in a nearby circuit, provided there was no electrical connection between them.

The researcher modified the experiments, and in 1831 they were crowned with success. Faraday's experiments began with winding copper wire around the paper tube and connecting its ends to the galvanometer. The scientist then placed a magnet inside the coil and noticed that the galvanometer needle gave an instantaneous deflection, indicating that a current had been induced in the coil. After removing the magnet, the arrow deflected in the opposite direction. Soon, in the course of other experiments, he noticed that at the moment of applying and removing voltage from one coil, a current appeared in a nearby coil. Both coils had a common magnetic circuit.

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Faraday's experiments

Faraday's numerous experiments with other coils and magnets were continued, and the researcher found that the strength of the induced current depends on:

• number of turns in the coil;
• magnet strength;
• the speed at which the magnet was immersed in the coil.

The term electromagnetic induction (EMF) refers to the phenomenon that an emf is generated in a conductor by an alternating external magnetic field.

Formulation of the law of electromagnetic induction

Verbal formulation of the law of electromagnetic induction: the induced electromotive force in any closed circuit is equal to the negative time rate of change of the magnetic flux enclosed in the circuit.

This definition is expressed mathematically by the formula:

E = - ΔΦ/ Δt,

where Ф = B x S, with magnetic flux density B and area S, which is crossed perpendicularly by the magnetic flux.

Additional Information. There are two different approaches to induction. The first explains induction using the Lorentz force and its action on a moving electric charge. However, in certain situations, such as magnetic shielding or unipolar induction, problems may arise in understanding the physical process. The second theory uses the methods of field theory and explains the process of induction using variable magnetic fluxes and the associated densities of these fluxes.

The physical meaning of the law of electromagnetic induction is formulated in three provisions:

1. A change in the external MF in a wire coil induces a voltage in it. When the conducting electrical circuit is closed, the induced current begins to circulate through the conductor;
2. The magnitude of the induced voltage corresponds to the rate of change of the magnetic flux associated with the coil;
3. The direction of the induced emf is always opposite to the cause that caused it.

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Law of Electromagnetic Induction

Important! The formula for the law of electromagnetic induction applies in the general case. There is no known form of induction that cannot be explained by a change in magnetic flux.

Induction emf in a conductor

To calculate the induction voltage in a conductor that moves in the MF, another formula is used:

E = - B x l x v x sin α, where:

• B – induction;
• l is the length of the conductor;
• v – speed of its movement;
• α is the angle formed by the direction of movement and the vector direction of magnetic induction.

Important! A method of determining where the induction current created in a conductor is directed: by placing right hand palm perpendicular to the entry of the power lines of the MP and, retracted thumb indicating the direction of movement of the conductor, we recognize the direction of the current in it by straightening four fingers.

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Right hand rule

Laws of electrolysis

Faraday's historical experiments in 1833 were also related to electrolysis. He took a test tube with two platinum electrodes immersed in dissolved tin chloride heated with an alcohol lamp. Chlorine was released on the positive electrode, and tin was released on the negative electrode. He then weighed the released tin.

In other experiments, the researcher connected containers with different electrolytes in series and measured the amount of substance deposited.

Based on these experiments, two laws of electrolysis are formulated:

1. The first of them: the mass of the substance released at the electrode is directly proportional to the amount of electricity passed through the electrolyte. Mathematically it is written like this:

m = K x q, where K is a constant of proportionality, called the electrochemical equivalent.

Formulate its definition as the mass of a substance in g released at the electrode when a current of 1 A passes in 1 s or when 1 C of electricity passes;

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First law of electrolysis

1. Faraday's Second Law states that if the same amount of electricity is passed through different electrolytes, then the amount of substances released at the corresponding electrodes is directly proportional to their chemical equivalent (the chemical equivalent of a metal is obtained by dividing its molar mass by its valency - M/z).

For the second law of electrolysis, the following notation is used:

HereF – Faraday's constant, which is determined by the charge of 1 mole of electrons:

F = Na (Avogadro's number) x e (elementary electric charge) = 96485 C/mol.

Write another expression for Faraday's second law:

m1/m2 = K1/K2.

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Second Law of Electrolysis

For example, if you take two electrolytic containers connected in series containing a solution of AgNO 3 and CuSO 4 and pass the same amount of electricity through them, then the ratio of the mass of deposited copper on the cathode of one container to the mass of deposited silver on the cathode of the other container will be equal to the ratio of their chemical equivalents. For copper it is Rate this article: