Законы электролиза Фарадея — это… Что такое Законы электролиза Фарадея? Майкл Фарадей, портрет Томаса Филипса, 1841-1842

Зако́ны электро́лиза Фараде́я являются количественными соотношениями, основанными на электрохимических исследованиях, опубликованных Майклом Фарадеем в 1836 году.^[1]

Формулировка законов

В учебниках и научной литературе можно найти несколько версий формулировки законов. В наиболее общем виде законы формулируются следующим образом:

• Первый закон электролиза Фарадея: масса вещества, осаждённого на электроде при электролизе, прямо пропорциональна количеству электричества, переданного на этот электрод. Под количеством электричества имеется в виду электрический заряд, измеряемый, как правило, в кулонах.

• Второй закон электролиза Фарадея: для данного количества электричества (электрического заряда) масса химического элемента, осаждённого на электроде, прямо пропорциональна эквивалентной массе элемента. Эквивалентной массой вещества является его молярная масса, делённая на целое число, зависящее от химической реакции, в которой участвует вещество.

Математический вид

Законы Фарадея можно записать в виде следующей формулы:

где:

• m — масса осаждённого на электроде вещества в граммах
• Q — полный электрический заряд, прошедший через вещество
• F = 96 485,3383(83) Кл·моль⁻¹ — постоянная Фарадея
• M — молярная масса вещества
• z — валентное число ионов вещества (число электронов на один ион).

Заметим, что M/z — это эквивалентная масса осаждённого вещества.

Для первого закона Фарадея M, F и z являются константами, так что чем больше величина Q, тем больше будет величина m.

Для второго закона Фарадея Q, F и z являются константами, так что чем больше величина M/z (эквивалентная масса), тем больше будет величина m.

В простейшем случае постоянного тока электролиза приводит к:

и тогда

где:

В более сложном случае переменного электрического тока полный заряд Q тока I() суммируется за время :

Здесь t — полное время электролиза. Обратите внимание, что тау используется в качестве переменной, ток I является функцией от тау.^[2]

Примечания

1. ↑ Ehl, Rosemary Gene; Ihde, Aaron (1954). «Faraday’s Electrochemical Laws and the Determination of Equivalent Weights». Journal of Chemical Education 31 (May): 226–232. DOI:10.1021/ed031p226. Bibcode: 1954JChEd..31..226E.
2. ↑ For a similar treatment, see Strong, F. C. (1961). «Faraday’s Laws in One Equation». Journal of Chemical Education 38 (2): 98. DOI:10.1021/ed038p98.

Ссылки

• Serway, Moses, and Moyer, Modern Physics, third edition (2005).

См. также

Формула — Объединенный закон Фарадея

\(M\) — масса выделившегося вещества \((кг)\)

\(\mu\) — молярная масса \((\frac{кг}{моль})\)

\(Q\) — электрический заряд \((Кл)\)

\(Z\) — валентность

\(F\) — постоянная Фарадея \(\approx 9.65 * 10^{4}\) \(\frac{Кл}{моль}\)

\(K_x\) — химический эквивалент вещества \((\frac{кг}{моль})\)

90000 Faraday’s law of induction for Dummies 90001 90002 90003 Faraday’s law of induction was discovered through experiments carried out by Micheal Faraday in England In 1831 and by Joseph Henry in the United States at about the same time. 90004 Even though Faraday published his results first, which gives him priority of discovery, the SI unit of inductance is called the 90005 henry (abbreviation H) 90006. On the other hand, the SI unit of capacitance is, as we have seen, called the 90005 farad (abbreviation F) 90006.90004 In the chapter, we discuss oscillations in capacitative-inductive circuits, we see how appropriate it is to link the names of these two talented contemporaries in a single context. 90010 90002 * In addition to their independent simultaneous discovery of the law of induction, Faraday and Henry have several other similarities in their lives. Both were apprentices at an early age. Faraday, at age 14, was apprenticed to a London bookbinder. Henry at age 13, was apprenticed to a watchmaker in Albany, New York.In later years Faraday was appointed a director of the royal institution in London, whose founding was due in large part on an American, Benjamin Thomson (Count Rumford). Henry, on the other hand, because the secretary of the Smithsonian Institution in Washington, DC, which was found by an endowment from an Englishman, James Smithson. 90010 90002 Faraday observed that if a magnet is moved towards a coil of wire (solenoid) connected in series with a galvanometer, an electric current is produced in the current.When the magnet is moved towards the solenoid, the galvanometer shows deflection in one direction and when the magnet is moved away from the solenoid, the galvanometer shows deflection in the opposite direction. When the magnet is stationary there is no deflection in the galvanometer. Similar results are obtained when the magnet is kept stationary and the coil is moved. When the magnet is moved if the deflection in the galvanometer is large and when it is moved slowly the deflection is small. It was also found that if there are two closed circuits in close proximity, one containing a battery and the other a galvanometer, and the battery circuit is closed by pressing the tapping key K, and then broken, the galvanometer in the secondary circuit shows a deflection first in one direction and then in the other.90010 90002 It is observed that no deflection is produced in the galvanometer if the current in the primary circuit flows continuously. The deflection is produced in the galvanometer only at make or break of the current in the primary circuit. Faraday summed up these experimental results in the form of the following laws: 90010 90017 90018 1: Whenever there is a change in the magnetic lines of force or magnetic flux, an induced current is produced in the circuit. 90019 90018 2: The induced current or EMF lasts only for the time for which lines of force or magnetic flux is actually changing.90019 90018 3: The magnitude of the induced EMF depends upon the rate at which the magnetic lines of force or magnetic flux changes. 90019 90024 90002 Figure (1) shows a coil of wire as a part of a circuit containing an ammeter. Normally, we would expect the ammeter to show no current in the circuit because there seems to be no electromotive force. However, if we push a bar magnet toward the coil, with its north pole facing the coil, a remarkable thing happens. While the magnet is moving, the ammeter deflects, showing that the current has been set up in the coil.If we hold the magnet stationary with respect to the coil, the ammeter does not deflect. If we move the magnet away from the coil, the meter again deflects, but in the opposite direction, which means that the current in the coil is in the opposite direction. If we use the north pole end of a magnet instead of the north pole end, the experiment works as described but the deflections are reversed. The faster the magnet is moved, the greater is the reading of the meter. Further experimentation shows that what matters is the relative motion of the magnet and the coil.It marks no differences whether we move the magnet toward the coil or the coil toward the magnet. 90010 90027 Faraday’s law of induction formula 90028 90002 «The induced emf in the circuit is equal to the negative of the rate at which the magnetic flux through the circuit is changing with time.» Mathematically it is written as: 90010 90002 90032 90010 90002 90035 Explanation: 90036 90010 90002 Faraday’s experiment showed, and as Faraday’s technique of field lines helps us visualize, it is the change in the number of field lines passing through a circuit loop that induces the emf in the loop.Especially, it is the rate of change in the number of field lines passing through the loop that determines the induced emf. 90010 90002 To make this statement quantitative, we introduce the magnetic flux Φ 90041 B 90042, which is stated as «The number of magnetic lines of force passing normally through the certain area is called magnetic flux.» It is denoted as Φ 90041 B. 90042 It is a scalar quantity and its SI unit is Weber (Wb). It is measured by the product of magnetic field strength and the component of the vector area parallel to the magnetic field.Mathematically it is represented as: 90010 90002 90035 Φ 90041 B 90042 = BA 90036 90010 90002 Φ 90041 B 90042 = BA cosθ 90010 90002 Where A is a vector whose magnitude is the area of ​​the element and whose direction is along the normal to the surface of the element, θ is the angle between the directions of the vectors 90035 B 90036 and 90035 A. 90036 90010 90002 90063 90010 90002 When a magnet is moved toward the loop, the ammeter needle deflects in one direction, as shown in figure (a ).When the magnet is brought to rest and held stationary relative to the loop figure (b), no deflection is observed. When the magnet is moved away from the loop, the needle deflects in the opposite direction, as shown in figure (c). Finally, if the magnet is held stationary and the loop is moved either toward or away from it, the needle deflects. From these observations, we conclude that the loop detects that the magnet is moving relative to it and we relate this detection to a change in the magnetic field.Thus, it seems that a relationship exists between the current and changing magnetic fields. 90010 90002 These results are quite remarkable in view of the fact that a current is set up even though no batteries are present in the circuit. We call such a current induced current which is produced by induced emf. This phenomenon is called electromagnetic induction. 90010 90002 90070 90071 90004 There are other related topics on our website are: 90004 1: Lenz’s law 90004 2: Electromagnetic induction 90004 3: Transformer 90004 4: Magnetism 90004 External sources 90010 90017 90018 https: // en.wikipedia.org/wiki/Faraday%27s_law_of_induction 90019 90018 https://www.daenotes.com/electronics/basic-electronics/faraday-laws-of-electromagnetic-induction 90019 90024.90000 What Is Faraday’s Law of Induction? 90001 90002 Faraday’s Law of Induction describes how an electric current produces a magnetic field and, conversely, how a changing magnetic field generates an electric current in a conductor. English physicist Michael Faraday gets the credit for discovering magnetic induction in 1830; however, an American physicist, Joseph Henry, independently made the same discovery about the same time, according to the University of Texas. 90003 90002 It is impossible to overstate the significance of Faraday’s discovery.Magnetic induction makes possible the electric motors, generators and transformers that form the foundation of modern technology. By understanding and using induction, we have an electric power grid and many of the things we plug into it. 90003 90002 Faraday’s law was later incorporated into the more comprehensive Maxwell’s equations, according to Michael Dubson, a professor of physics at the University of Colorado Boulder. Maxwell’s equations were developed by Scottish physicist James Clerk Maxwell to explain the relationship between electricity and magnetism, essentially uniting them into a single electromagnet force and describing electromagnetic waves that make up radio waves, visible light, and X-rays.90003 90008 Electricity 90009 90002 Electric charge is a fundamental property of matter, according to the Rochester Institute of Technology. Although it is difficult to describe what it actually is, we are quite familiar with how it behaves and interacts with other charges and fields. The electric field from a localized point charge is relatively simple, according to Serif Uran, a professor of physics at Pittsburg State University. He describes it as radiating out equally in all directions, like light from a bare light bulb, and decreasing in strength as the inverse square of the distance (1/90011 r 90012 90013 2 90014), in accordance with Coulomb’s Law.When you move twice as far away, the field strength decreases to one-fourth, and when you move three times farther away, it decreases to one-ninth. 90003 90002 Protons have positive charge, while electrons have negative charge. However, protons are mostly immobilized inside atomic nuclei, so the job of carrying charge from one place to another is handled by electrons. Electrons in a conducting material such as a metal are largely free to move from one atom to another along their conduction bands, which are the highest electron orbits.A sufficient electromotive force (emf), or voltage, produces a charge imbalance that can cause electrons move through a conductor from a region of more negative charge to a region of more positive charge. This movement is what we recognize as an electric current. 90003 90008 Magnetism 90009 90002 In order to understand Faraday’s Law of Induction, it is important to have a basic understanding of magnetic fields. Compared to the electric field, the magnetic field is more complex. While positive and negative electric charges can exist separately, magnetic poles always come in pairs — one north and one south, according to San Jose State University.Typically, magnets of all sizes — from sub-atomic particles to industrial-size magnets to planets and stars — are dipoles, meaning they each have two poles. We call these poles north and south after the direction in which compass needles point. Interestingly, since opposite poles attract, and like poles repel, the magnetic north pole of the Earth is actually a south magnetic pole because it attracts the north poles of compass needles. 90003 90002 A magnetic field is often depicted as lines of magnetic flux.In the case of a bar magnet, the flux lines exit from the north pole and curve around to reenter at the south pole. In this model, the number of flux lines passing through a given surface in space represents the flux density, or the strength of the field. However, it should be noted that this is only a model. A magnetic field is smooth and continuous and does not actually consist of discrete lines. 90003 90002 90003 Magnetic field lines from a bar magnet. (Image credit: snapgalleria Shutterstock) 90002 Earth’s magnetic field produces a tremendous amount of magnetic flux, but it is dispersed over a huge volume of space.Therefore, only a small amount of flux passes through a given area, resulting in a relatively weak field. By comparison, the flux from a refrigerator magnet is tiny compared to that of the Earth, but its field strength is many times stronger at close range where its flux lines are much more densely packed. However, the field quickly becomes much weaker as you move away. 90003 90008 Induction 90009 90002 If we run an electric current through a wire, it will produce a magnetic field around the wire.The direction of this magnetic field can be determined by the right-hand rule. According to the physics department at Buffalo State University of New York, if you extend your thumb and curl the fingers of your right hand, your thumb points in the positive direction of the current, and your fingers curl in the north direction of the magnetic field . 90003 90002 90003 Left-hand and right-hand rule for a magnetic field due to a current in a straight wire. (Image credit: Fouad A. Saad Shutterstock) 90002 If you bend the wire into a loop, the magnetic field lines will bend with it, forming a toroid, or doughnut shape.In this case, your thumb points in the north direction of the magnetic field coming out of the center of the loop, while your fingers will point in the positive direction of the current in the loop. 90003 90002 90003 In a current-carrying circular loop, (a) the right-hand rule gives the direction of the magnetic field inside and outside the loop. (B) More detailed mapping of the field, which is similar to that of a bar magnet. (Image credit: OpenStax) 90002 If we run a current through a wire loop in a magnetic field, the interaction of these magnetic fields will exert a twisting force, or torque, on the loop causing it to rotate, according to the Rochester Institute of Technology.However, it will only rotate so far until the magnetic fields are aligned. If we want the loop to continue rotating, we have to reverse the direction of the current, which will reverse the direction of the magnetic field from the loop. The loop will then rotate 180 degrees until its field is aligned in the other direction. This is the basis for the electric motor. 90003 90002 Conversely, if we rotate a wire loop in a magnetic field, the field will induce an electric current in the wire. The direction of the current will reverse every half turn, producing an alternating current.This is the basis for the electric generator. It should be noted here that it is not the motion of the wire but rather the opening and closing of the loop with respect to the direction of the field that induces the current. When the loop is face-on to the field, the maximum amount of flux passes through the loop. However, when the loop is turned edge-on to the field, no flux lines pass through the loop. It is this change in the amount of flux passing through the loop that induces the current. 90003 90002 Another experiment we can perform is to form a wire into a loop and connect the ends to a sensitive current meter, or galvanometer.If we then push a bar magnet through the loop, the needle in the galvanometer will move, indicating an induced current. However, once we stop the motion of the magnet, the current returns to zero. The field from the magnet will only induce a current when it is increasing or decreasing. If we pull the magnet back out, it will again induce a current in the wire, but this time it will be in the opposite direction. 90003 90002 90003 Magnet in a wire loop connected to a galvanometer. (Image credit: Fouad A.Saad Shutterstock) 90002 If we were to put a light bulb in the circuit, it would dissipate electrical energy in the form of light and heat, and we would feel resistance to the motion of the magnet as we moved it in and out of the loop . In order to move the magnet, we have to do work that is equivalent to the energy being used by the light bulb. 90003 90002 In yet another experiment, we might construct two wire loops, connect the ends of one to a battery with a switch, and connect the ends of the other loop to a galvanometer.If we place the two loops close to each other in a face-to-face orientation, and we turn on the power to the first loop, the galvanometer connected to the second loop will indicate an induced current and then quickly return to zero. 90003 90002 What is happening here is that the current in the first loop produces a magnetic field, which in turn induces a current in the second loop, but only for an instant when the magnetic field is changing. When you turn off the switch, the meter will deflect momentarily in the opposite direction.This is further indication that it is the change in the intensity of the magnetic field, and not its strength or motion that induces the current. 90003 90002 The explanation for this is that a magnetic field causes electrons in a conductor to move. This motion is what we know as electric current. Eventually, though, the electrons reach a point where they are in equilibrium with the field, at which point they will stop moving. Then when the field is removed or turned off, the electrons will flow back to their original location, producing a current in the opposite direction.90003 90002 Unlike a gravitational or electric field, a magnetic dipole field is a more complex 3-dimensional structure that varies in strength and direction according to the location where it is measured, so it requires calculus to describe it fully. However, we can describe a simplified case of a uniform magnetic field — for example, a very small section of a very large field — as Φ 90011 B 90012 = 90011 BA 90012, where Φ 90011 B 90012 is the absolute value of the magnetic flux , 90011 B 90012 is the strength of the field, and 90011 A 90012 is a defined area through which the field passes.Conversely, in this case the strength of a magnetic field is the flux per unit area, or 90011 B 90012 = Φ 90011 B 90012/90011 A 90012. 90003 90008 Faraday’s Law 90009 90002 Now that we have a basic understanding of the magnetic field, we are ready to define Faraday’s Law of Induction. It states that the induced voltage in a circuit is proportional to the rate of change over time of the magnetic flux through that circuit. In other words, the faster the magnetic field changes, the greater will be the voltage in the circuit.The direction of the change in the magnetic field determines the direction of the current. 90003 90002 We can increase the voltage by increasing the number of loops in the circuit. The induced voltage in a coil with two loops will be twice that with one loop, and with three loops it will be triple. This is why real motors and generators typically have large numbers of coils. 90003 90002 In theory, motors and generators are the same. If you turn a motor, it will generate electricity, and applying voltage to a generator, it will cause it to turn.However, most real motors and generators are optimized for only one function. 90003 90008 Transformers 90009 90002 Another important application of Faraday’s Law of Induction is the transformer, invented by Nikola Tesla. In this device, alternating current, which changes direction many times per second, is sent through a coil wrapped around a magnetic core. This produces a changing magnetic field in the core, which in turn induces a current in second coil wrapped around a different part of the same magnetic core.90003 90002 90003 Transformer diagram (Image credit: photoiconix Shutterstock) 90002 The ratio of the number of turns in the coils determines the ratio of the voltage between the input and output current. For instance, if we take a transformer with 100 turns on the input side and 50 turns on the output side, and we input an alternating current at 220 volts, the output will be 110 volts. According to Hyperphysics, a transformer can not increase power, which is the product of voltage and current, so if the voltage is raised, the current is proportionally lowered and vice versa.In our example, an input of 220 volts at 10 amps, or 2,200 watts, would produce an output of 110 volts at 20 amps, again, 2,200 watts. In practice, transformers are never perfectly efficient, but a well-designed transformer typically has a power loss of only a few percent, according to the University of Texas. 90003 90002 Transformers make possible the electric grid we depend on for our industrial and technological society. Cross-country transmission lines operate at hundreds of thousands of volts in order to transmit more power within the current-carrying limits of the wires.This voltage is stepped down repeatedly using transformers at distribution substations until it reaches your house, where it is finally stepped down to 220 and 110 volts that can run your electric stove and computer. 90003 90002 90091 Additional resources 90092 90003 .90000 Faraday’s law of induction | physics 90001 90002 90003 Faraday’s law of induction 90004, in physics, a quantitative relationship between a changing magnetic field and the electric field created by the change, developed on the basis of experimental observations made in тисячі вісімсот тридцять одна by the English scientist Michael Faraday. 90005 90002 Read More on This Topic 90005 90002 electromagnetism: Faraday’s law of induction 90005 90002 Faraday’s discovery in тисячу вісімсот тридцять одна of the phenomenon of magnetic induction is one of the great milestones in the quest toward understanding and… 90005 90002 The phenomenon called electromagnetic induction was first noticed and investigated by Faraday; the law of induction is its quantitative expression. Faraday discovered that, whenever the magnetic field about an electromagnet was made to grow and collapse by closing and opening the electric circuit of which it was a part, an electric current could be detected in a separate conductor nearby. Moving a permanent magnet into and out of a coil of wire also induced a current in the wire while the magnet was in motion.Moving a conductor near a stationary permanent magnet caused a current to flow in the wire, too, as long as it was moving. 90005 90002 Faraday visualized a magnetic field as composed of many lines of induction, along which a small magnetic compass would point. The aggregate of the lines intersecting a given area is called the magnetic flux. The electrical effects were thus attributed by Faraday to a changing magnetic flux. Some years later the Scottish physicist James Clerk Maxwell proposed that the fundamental effect of changing magnetic flux was the production of an electric field, not only in a conductor (where it could drive an electric charge) but also in space even in the absence of electric charges.Maxwell formulated the mathematical expression relating the change in magnetic flux to the induced electromotive force (90015 E, 90016 or 90015 emf 90016). This relationship, known as Faraday’s law of induction (to distinguish it from his laws of electrolysis), states that the magnitude of the 90015 emf 90016 induced in a circuit is proportional to the rate of change of the magnetic flux that cuts across the circuit. If the rate of change of magnetic flux is expressed in units of webers per second, the induced 90015 emf 90016 has units of volts.Faraday’s law is one of the four Maxwell equations that define electromagnetic theory. 90005.90000 Faraday’s law of induction — Simple English Wikipedia, the free encyclopedia 90001 90002 90003 Faraday’s law of induction 90004 is a law of physics proposed by English physicist Michael Faraday in 1831. 90005 [1] 90006 It is one of the basic laws of electromagnetism. The law explains why generators, transformers and electrical motors work. 90007 90002 Faraday’s law of induction says that when a magnetic field changes, it causes a voltage, a difference in the electric potential that can make electric currents flow.90005 [2] 90006 That phenomenon was also found by Joseph Henry in 1831. 90005 [3] 90006 90007 90002 Imagine we have a closed loop of wire. To figure out how much current will be «induced» (i.e. produced by the magnetic field), we need to define the magnetic flux, a number describing how much of the magnetic field is actually going through the loop. Magnetic fields are vector fields, so they have both a strength and a direction. This leads to the following surface integral: 90007 90016 90017 Φ B = ∬ Σ ( t ) B ( r , t ) ⋅ d A {\ Displaystyle \ Phi _ {B} = \ iint \ limits _ {\ Sigma (t)} \ mathbf {B} (\ mathbf {r}, t) \ cdot d \ mathbf {A}} 90018 90019 90002 where 90007 90022 90023 Φ 90024 90025 B 90026 90027 is the magnetic flux 90028 90023 Σ ( t ) {\ Displaystyle \ Sigma (t)} is the (possibly moving) surface whose boundary is the wire loop 90028 90023 90003 B 90004 is the magnetic field 90028 90023 90025 d 90026 90003 A 90004 is a small part of the surface.90028 90041 90002 That is, we could imagine filling in the wire loop with a thin surface, like a soap film. This formula tells us to look at every point on that surface, measure how much the magnetic field is pointing straight through the loop at that point, and add up all those measurements to get a single number. That number is the magnetic flux. When the flux changes, it produces electromotive force. The flux changes when 90003 B 90004 changes or when the wire loop is moved or bent, or when both happen.The electromotive force can then be calculated with the following equation: 90007 90016 90017 E = — N d Φ B d t {\ Displaystyle {\ mathcal {E}} = — N {{d \ Phi _ {B}} \ over dt}} 90018 90019 90022 90023 E {\ Displaystyle {\ mathcal {E}}} is the electromotive force 90028 90023 90003 N 90004 is the number of loops the wire makes 90028 90023 Φ 90024 90025 B 90026 90027 is the magnetic flux of one loop 90028 90023 — is representative of Lenz’s law and indicates direction of the electromotive force 90028 90041 90002 This equation says that how much current is induced in the wire loop depends directly on how fast the magnetic flux is changing in time, whether due to the loop moving or the magnetic field changing.90007 .