Subject: Physics
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 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 (NA)
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 NA 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*}
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.
Faraday’s constant is defined as the ratio between chemical equivalents of a substance to its electrochemical equivalent.
Electroplating is the process coating one valuable metal over another common metal by electrolysis.
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.
Electrolysis is used in various field like electroplating, purification of metals, manufacture of chemicals, chemical analysis, medical analysis and so on.
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