Faraday's laws of electrolysis explained

Faraday's laws of electrolysis are quantitative relationships based on the electrochemical research published by Michael Faraday in 1833.^{[1] [2]}

First law

Michael Faraday reported that the mass of a substance deposited or liberated at an electrode is directly proportional to the charge (; SI units are ampere seconds or coulombs).^[3]

$$m\; \backslash propto\; Q\; \backslash quad\; \backslash implies\; \backslash quad\; \backslash frac\; =\; Z$$

Here, the constant of proportionality,, 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 . This turns out to be the molar mass divided by the valence

\begin{align} & m \propto E; E = (molarmass)/(valence) = (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}

Derivation

A monovalent ion requires 1 electron for discharge, a divalent ion requires 2 electrons for discharge and so on. Thus, if electrons flow,

\tfrac{x}{v} atoms are discharged.

Thus, the mass discharged is$$m\; =\; \backslash frac\; =\; \backslash frac\; =\; \backslash frac$$where

• is the Avogadro constant;
• is the total charge, equal to the number of electrons times the elementary charge ;
• is the Faraday constant.

Mathematical form

Faraday's laws can be summarized by

Z = (m)/(Q) = (1)/(\left( F) (M)/(v) \right) = (E)/(F)

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

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

For Faraday's second law, are constants; thus, the larger the value of

\tfrac{M}{v} (equivalent weight), the larger will be.

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

m = (ItM)/(Fv)

and then to

n = (It)/(Fv)

where:

• is the amount of substance ("number of moles") liberated:

n = \tfrac m M

• is the total time the constant current was applied.

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

$$m\; =\; \backslash frac$$

where represents the mass fraction of the -th element.

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

Q = \int ^{t} _{0} I(\tau) d\tau

Here is the total electrolysis time.^[4]

See also

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

References

1. Michael . Faraday . Michael Faraday . 1834 . on Electrical Decomposition . Philosophical Transactions of the Royal Society . 10.1098/rstl.1834.0008 . 124 . 77–122. 116224057 .
2. Ehl, Rosemary Gene . Ihde, Aaron . Faraday's Electrochemical Laws and the Determination of Equivalent Weights . Journal of Chemical Education . 1954 . 31 . May . 226 - 232 . 10.1021/ed031p226 . 1954JChEd..31..226E.
3. Web site: Faraday's laws of electrolysis chemistry . 2020-09-01 . Encyclopedia Britannica . en.
4. For a similar treatment, see Strong, F. C. . Faraday's Laws in One Equation . Journal of Chemical Education . 1961 . 38 . 2. 98 . 10.1021/ed038p98 . 1961JChEd..38...98S .

Further reading

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