State Faraday’s first law of electrolysis. How is it verified experimentally?

Hint: Faraday’s first law of electrolysis gives a relation between the amount of mass deposited or eroded at an electrode with the charge passing through the electrolytic cell. It is verified by a simple experiment involving a battery, electrolytic cell, ammeter, resistor and key.

Formula used:
$q=It$

Complete step by step answer:
Faraday’s first law of electrolysis states that the mass of material deposited on or eroded from an electrode is directly proportional to the amount of charge passing through the electrolytic cell.
$m\propto q$ --(1)
Where $m$ is the mass of the matter deposited on or eroded from the electrode and $q$ is the charge passing through the electrolytic cell.
Now, the charge $q$ passing through a cross section of a conductor is related to the current $I$ passing through it in time $t$ by
$q=It$ --(2)
Putting (2) in (1), we get,
$m\propto It$
$\therefore m=ZIt$
Where $Z$ is a constant known as the electrochemical equivalent of the substance.
We can experimentally verify Faraday’s first law of electrolysis by a simple experiment.
We will take an electrolytic cell and connect it to a battery, a rheostat, and an ammeter in a series circuit. The circuit has a key in it.
We will observe the change in mass of the cathode. In an electrolytic cell, the cathode dissolves into the electrolyte and hence, its mass goes down.
Case 1) Checking the proportionality of the mass change with the current passing through it.
We will first weight the dry clean cathode and obtain its mass ${{m}_{0}}$.
Then we place it in the electrolytic cell and pass a current ${{I}_{1}}$ through the cell for a time $t$.
Then we will take out the cathode and then weigh it again after cleaning and drying it. Suppose the mass is now ${{m}_{1}}$. Therefore, the change in mass of the cathode will be
$\Delta {{m}_{1}}={{m}_{0}}-{{m}_{1}}$
We will repeat the process for a similar cathode but with current ${{I}_{2}}$.
Then the change in mass will be $\Delta {{m}_{2}}$.
We can then check and verify,
$\dfrac{\Delta {{m}_{1}}}{\Delta {{m}_{2}}}=\dfrac{{{I}_{1}}}{{{I}_{2}}}$ --(3)
Hence, we can conclude that the mass of the matter eroded from the cathode is directly proportional to the current passing through it.

Case 2) Checking the proportionality of the mass change with the time for which current is passed through it.
We will first weight the dry clean cathode and obtain its mass ${{m}_{0}}$.
Then we place it in the electrolytic cell and pass a current $I$ through the cell for a time ${{t}_{1}}$.
Then we will take out the cathode and then weigh it again after cleaning and drying it. Suppose the mass is now ${{m}_{1}}$. Therefore, the change in mass of the cathode will be
$\Delta {{m}_{1}}={{m}_{0}}-{{m}_{1}}$
We will repeat the process for a similar cathode but with the time for which the current is passed being ${{t}_{2}}$.
Then the change in mass will be $\Delta {{m}_{2}}$.
We can then check and verify,
$\dfrac{\Delta {{m}_{1}}}{\Delta {{m}_{2}}}=\dfrac{{{t}_{1}}}{{{t}_{2}}}$ --(4)
Hence, we can conclude that the mass of the matter eroded from the cathode is directly proportional to the current passing through it.
From (3) and (4), we can conclude that the change in mass of the electrode is directly proportional to the product of the current through the cell and the time passed.
$\therefore m\propto It$
Again using (2), we get,
$m\propto q$
Hence, Faraday’s first law of electrolysis is verified experimentally.

Note: Students must remember that in an electrolytic cell, the mass of the cathode reduces while the anode decreases. This is because ions from the cathode dissolve into the electrolyte and are deposited upon the anode. This concept can be kept in mind by the statement “In the cathode, the ions can’t hold” where the words ‘cathode’ and ‘can’t hold’ are similar sounding implying that the ions can’t hold on to the cathode and get dissolved in the electrolyte.