Faraday's laws of electrolysis

Michael Faraday, by Thomas Phillips c1841-1842

Faraday's laws of electrolysis are quantitative relationships based on the electrochemical researches published by Michael Faraday in 1834.[1]

Statements of the laws

Several versions of the laws can be found in textbooks and the scientific pieces of literature. The most common statements resemble the following:

For an element the equivalent weight is the quantity that combines with or replaces 1.00797 grams (g) of hydrogen or 7.9997 g of oxygen; or, the weight of an element that is liberated in an electrolysis (chemical reaction caused by an electric current) by the passage of 9.64853399(24) x 104 coulombs of electricity. The equivalent weight of an element is its gram atomic weight divided by its valence (combining power). Some equivalent weights are: silver (Ag), 107.868 g; magnesium (Mg), 24.312/2 g; aluminum (Al), 26.9815/3 g; sulfur (S, in forming a sulfide), 32.064/2 g. For compounds that function as oxidizing or reducing agents (compounds that act as acceptors or donors of electrons), the equivalent weight is the gram molecular weight divided by the number of electrons lost or gained by each molecule; e.g., potassium permanganate (KMnO4) in acid solution, 158.038/5 g; potassium dichromate (K2Cr2O7), 294.192/6 g; and sodium thiosulfate (Na2S2O3·5H2O), 248.1828/1 g. For all oxidizing and reducing agents (elements or compounds) the equivalent weight is the weight of the substance that is associated with the loss or gain of 6.023 × 1023 electrons. The equivalent weight of an acid or base for neutralization reactions or of any other compound that acts by double decomposition is the quantity of the compound that will furnish or react with or be equivalent to 1.00797 g of hydrogen ion or 17.0074 g of hydroxide ion; e.g., hydrochloric acid (HCl), 36.461 g; sulfuric acid (H2SO4), 98.078/2 g; sodium hydroxide (NaOH), 40 g; sodium carbonate (Na2CO3), 105.9892/ 2 g. The equivalent weight of a substance may vary with the type of reaction it undergoes. Thus, potassium permanganate reacting by double decomposition has an equivalent weight equal to its gram molecular weight, 158.038/1 g; as an oxidizing agent under different circumstances it may be reduced to the manganate ion (MnO42−), to manganese dioxide (MnO2), or to the manganous ion (Mn2+), with the equivalent weights of 158.038/1 g, 158.038/3 g, and 158.038/5 g, respectively. The number of equivalent weights of any substance dissolved in one liter of solution is called the normality of that solution.

Mathematical form

Faraday's laws can be summarized by

m \ = \ \left({ Q \over F }\right)\left({ M \over z }\right)

where:

Note that M/z is the same as the equivalent weight of the substance altered.

For Faraday's first law, M, F, and z are constants, so that the larger the value of Q the larger m will be.

For Faraday's second law, Q, F, and z are constants, so that the larger the value of M/z (equivalent weight) the larger m will be.

In the simple case of constant-current electrolysis, Q = I t leading to

m \ = \ \left({ I t\over F }\right)\left({ M \over z }\right)

and then to

n \ = \ \left({ I t\over F }\right)\left({ 1 \over z }\right)

where:

In the more complicated case of a variable electrical current, the total charge Q is the electric current I(\tau) integrated over time \tau:

Q = \int_0^t I(\tau) \ d \tau

Here t is the total electrolysis time.[2]

References

  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. Bibcode:1954JChEd..31..226E. doi:10.1021/ed031p226.
  2. ↑ For a similar treatment, see Strong, F. C. (1961). "Faraday's Laws in One Equation". Journal of Chemical Education 38 (2): 98. Bibcode:1961JChEd..38...98S. doi:10.1021/ed038p98.

Further reading

See also