Explain faraday's second law of electrolysis in details.

Faraday's second law of electrolysis

• Michael Faraday established the second law of electrolysis.
• It states, "The masses of different ions liberated at the electrodes, when the same amount of electricity is passed through different electrolytes are directly proportional to their chemical equivalent weight."
• The amount of electricity needed to release one gram-equivalent of any material at any electrode is called a faraday, and it passes through an electrolyte.
• Faraday's constant is equal to $96485\mathrm{C}{\mathrm{mol}}^{-1}$.

Formula of Faraday's second law

• It follows that the electrochemical equivalent of an element is directly proportional to its equivalent weight.

$\begin{array}{rcl}\frac{W_1}{W_2}& =& \frac{E_1}{E_2}\\ Z& \propto & E\end{array}$

• $W_1,W_2$ are the deposited amount of any substance.
• $E_1,E_2$ are the equivalent weights of that substance.
• $Z$ is the electrochemical equivalent.
• $E$ is the equivalent weight.

Example

• The same current is passed through the solutions of sulfuric acid $\left({\mathrm{H}}_2{\mathrm{SO}}_4\right)$, copper sulfate $\left({\mathrm{CuSO}}_4\right)$, and silver nitrate $\left({\mathrm{AgNO}}_3\right)$ for the same period of time.
• Then,

$\begin{array}{rcl}\frac{\mathrm{Mass}\mathrm{of}\mathrm{copper}\mathrm{deposited}}{\mathrm{Mass}\mathrm{of}\mathrm{silver}\mathrm{deposited}}& =& \frac{\mathrm{Equivalent}\mathrm{mass}\mathrm{of}\mathrm{copper}}{\mathrm{Equivalent}\mathrm{mass}\mathrm{of}\mathrm{silver}}\\ \frac{\mathrm{Mass}\mathrm{of}\mathrm{copper}\mathrm{deposited}}{\mathrm{Mass}\mathrm{of}\mathrm{hydrogen}\mathrm{gas}\mathrm{liberated}}& =& \frac{\mathrm{Equivalent}\mathrm{mass}\mathrm{of}\mathrm{copper}}{\mathrm{Equivalent}\mathrm{mass}\mathrm{of}\mathrm{hydrogen}\mathrm{gas}}\end{array}$