Faraday’s Constant and Application of Electrolysis

Relation between Electrochemical Equivalent Z and Chemical Equivalent (E) of a Substance

Let m₁ and m₂ be the mass of the substance liberated when the same quantity of charge Q is passed. If Z₁ and Z₂ be their respective electrochemical equivalent, then from Faraday’s first law of electrolysis,

$$ \frac {m_1}{m_1} = \frac {Z_1}{Z_2} \dots (i) $$

If E­₁­ and E₂ be their respective chemical equivalents, then from Faraday’s second law,

\begin{align*} \frac {m_1}{E_1} &= \frac {m_2}{E_2} \\ \text {or,} \: \frac {m_1}{m_2} &= \frac {E_1}{E_2} \dots (ii)\\ \text {From} \: (i) \: \text {and} \: (ii),\: \text {we get} \\ \frac {E_1}{E_2} &= \frac {Z_1}{Z_2} \dots (iii) \\ \therefore E \propto Z \\ \text {or,} \: E &= FZ \dots (iv) \\\end{align*}

where F is constant and is called Faraday’s constant This is the relation between Z and E.

Faraday’s Constant

Faraday’s constant is defined as the ratio between chemical equivalents of a substance to its electrochemical equivalent.

Faraday’s Constant In terms of Gram Equivalent of a substance

From Faraday’s first law, we have,

\begin{align*} m &= ZQ \\ \text {or,} \: Z &= \frac mQ \\ \text {But} \: F = \frac EZ \\ \therefore F &= \frac {E}{m/Q} \\ \text {or,} \: F&= \frac {EQ}{m} \\ \text {If} \: m = E, \: \text {then} , F = Q \\ \end{align*}

Thus Faraday’s constant is defined as the amount of charge required to liberate a gram equivalent of a substance during the process of electrolysis.

\begin{align*} \text {For copper} \: E = 31.5 g \text {and} \: Z = 0.000329 \: g/C \\ \text {Then,} \: F = \frac EZ = \frac {31.5}{0.000329}C = 96500 \: C \\ \text {Thus} \: 1F = 96500\: C\: mol^{-1} \\ \end{align*}

Faraday’s Constant In terms of Avogadro’s number (N_A)

Let x be the valancy of a substance. Then x electrons have to pass through the electrolyte to liberate one atom.

Charge required to liberate one mole of substance or N_A atoms of the substance Q is given by

\begin{align*} Q = N_A \times e \\ \text {But} \: \frac Mx = E \\ \therefore E &= ZN_Ae \\ \text {or,} \: \frac EZ &= N_Ae \\ \text {But} \: \frac EZ &= F \\ \therefore F &= N_A e \\ \end{align*} Thus Faraday’s constant is the product of Avogadro’s number and electronic charge\begin{align*} \\ \text {Putting} \: N_A = 6.023 \times 10^{23} \: \text {and} \: e = 1.6 \times 10^{-19} C. \\ \text {So, we get} \: \\ F = 6.023 \times 6.023 \times 10^{23} \times 1.6 \times 1o^{-19} \equiv 96500 \: C\: mol^{-1}. \\ \end{align*}

Important Practical Applications of Electrolysis

1. Electroplating:
   The process coating one valuable metal over another common metal by electrolysis. The conducting material to be electroplated is used as the cathode. The metal to be coated as anode. The electrolyte is the soluble salt of the anode material.
2. Purification of metals:
   This method is used in the refining of metals like copper, zinc, tin etc. the anode is made of pure metal. The electrolyte used is a soluble salt of the pure metal.
3. Manufacture of chemicals:
   By electrolysis chemical, like sodium hydroxide, sodium chloride, pure sodium etc. can be manufactured.
4. Chemical analysis:
   The chemical composition of salts can be found out by electrolysis.
5. Production of gases for commercial use:
   Oxygen and hydrogen are obtained by the electrolysis of acidulated water, on commercial scales.
6. Medical application:
   Electrolysis is used for stimulating nerves especially for treating polio and for removal of unwanted hair from any part of the body.
7. Printing industry:
   The metal copies of types used in printing books, gramophones, records, block etc. can be made by using the process of electrolysis.
8. Electrolytic capacitors:
   Electrolytic capacitors are prepared by depositing a thin film of aluminium oxide and aluminium anode during electrolysis which acts as the dielectric between the two electrodes. The electrolyte is a mixture of boric acid, glycerin and ammonium hydroxide due to oxide deposit, capacitors have very large capacitance.

Reference

Manu Kumar Khatry, Manoj Kumar Thapa, Bhesha Raj Adhikari, Arjun Kumar Gautam, Parashu Ram Poudel.Principle of Physics. Kathmandu: Ayam publication PVT LTD, 2010.

S.K. Gautam, J.M. Pradhan. A text Book of Physics. Kathmandu: Surya Publication, 2003.