Английская Википедия:Faraday's laws of electrolysis

Содержание

Текст

Текст

Текст

Текст

Текст

Текст

Текст

Текст

Текст

Файл:M Faraday Th Phillips oil 1842.jpg

Michael Faraday.

Faraday's laws of electrolysis are quantitative relationships based on the electrochemical research published by Michael Faraday in 1833.

First law

Michael Faraday reported that the mass (Шаблон:Mvar) of a substance deposited or liberated at an electrode is directly proportional to the charge (Шаблон:Mvar; SI units are ampere seconds or coulombs).

<math display="block">m \propto Q \quad \implies \quad \frac{m}{Q} = Z</math>

Here, the constant of proportionality, Шаблон:Mvar, is called the electro-chemical equivalent (ECE) of the substance. Thus, the ECE can be defined as the mass of the substance deposited or liberated per unit charge.

Second law

Faraday discovered that when the same amount of electric current is passed through different electrolytes connected in series, the masses of the substances deposited or liberated at the electrodes are directly proportional to their respective chemical equivalent/equivalent weight (Шаблон:Mvar). This turns out to be the molar mass (Шаблон:Mvar) divided by the valence (Шаблон:Mvar)

<math>\begin{align}

& m \propto E; \quad E = \frac{\text{molar mass}}{\text{valence}} = \frac{M}{v} \\ & \implies m_1 : m_2 : m_3 : \ldots = E_1 : E_2 : E_3 : \ldots \\ & \implies Z_1 Q : Z_2 Q : Z_3 Q : \ldots = E_1 : E_2 : E_3 : \ldots \\ & \implies Z_1 : Z_2 : Z_3 : \ldots = E_1 : E_2 : E_3 : \ldots \end{align}</math>

Derivation

A monovalent ion requires 1 electron for discharge, a divalent ion requires 2 electrons for discharge and so on. Thus, if Шаблон:Mvar electrons flow, <math> \tfrac{x}{v} </math> atoms are discharged.

Thus, the mass Шаблон:Mvar discharged is <math display="block"> m = \frac{x M}{v N_{\rm A}} = \frac{Q M}{e N_{\rm A} v} = \frac{Q M}{vF}</math> where

• Шаблон:Math is the Avogadro constant;
• Шаблон:Math is the total charge, equal to the number of electrons (Шаблон:Mvar) times the elementary charge Шаблон:Mvar;
• Шаблон:Mvar is the Faraday constant.

Mathematical form

Faraday's laws can be summarized by

<math>Z = \frac{m}{Q} = \frac{1}{F}\left(\frac{M}{v}\right) = \frac{E}{F}</math>

where Шаблон:Mvar is the molar mass of the substance (usually given in SI units of grams per mole) and Шаблон:Mvar is the valency of the ions .

For Faraday's first law, Шаблон:Mvar are constants; thus, the larger the value of Шаблон:Mvar, the larger Шаблон:Mvar will be.

For Faraday's second law, Шаблон:Mvar are constants; thus, the larger the value of <math>\tfrac{M}{v}</math> (equivalent weight), the larger Шаблон:Mvar will be.

In the simple case of constant-current electrolysis, Шаблон:Math, leading to

<math>m =\frac{ItM}{Fv}</math>

and then to

<math>n =\frac{It}{Fv}</math>

where:

• Шаблон:Mvar is the amount of substance ("number of moles") liberated: <math>n = \tfrac m M</math>
• Шаблон:Mvar is the total time the constant current was applied.

For the case of an alloy whose constituents have different valencies, we have

<math display="block">m = \frac{It}{F \times \sum_{i} \frac{w_i v_i}{M_i}}</math>

where Шаблон:Mvar represents the mass fraction of the Шаблон:Mvar-th element.

In the more complicated case of a variable electric current, the total charge Шаблон:Mvar is the electric current Шаблон:Math integrated over time Шаблон:Mvar:

<math> Q = \int_0^t I(\tau) \, d\tau </math>

Here Шаблон:Mvar is the total electrolysis time.

See also

• Electrolysis
• Faraday's law of induction
• Tafel equation

Further reading

• Serway, Moses, and Moyer, Modern Physics, third edition (2005), principles of physics.
• Experiment with Faraday's laws