Question

What current is required to pass $1$ mole of electrons per hour through an electrolytic bath? How many grams of $Al$ and $Cd$ will be liberated by $1$ mole of electrons?

Answer 1

An electrolytic bath refers to the set-up of an electrolytic cell in which the cathode is the negative electrode and anode is the positive electrode. Electropositive metals like aluminum and cadmium get deposited on the cathode.

Complete answer:
Electrons are negatively charged species that contain a very minute amount of charge on them. But one mole of electrons consists of a number of electrons equal to the Avogadro’s number, therefore such a large population of electrons carry a significant amount of charge on them.
The charge carried by one mole electrons is $1{\text{ faraday}} = 96500coulomb$
The current is a physical quantity that is measured as rate of flow of charge. Thus a ration of charge and the time (in seconds) would give the current.
$current = \dfrac{{ch\arg e}}{{time}}$
The time given in the question is one hours which is equal to $3600$ seconds.
${\text{current carried by one mole of electrons}} = \dfrac{{96500coulomb}}{{3600s}} = 26.80A$
For calculating the mass deposited by the reduction of metal ions in an electrolytic bath, the electrochemical equivalents $(z)$ of aluminium and cadmium must be calculated by finding the ratio of their molar mass and charge. The electrochemical equivalent gives the measure of the mass deposited by one ampere current in one second and should therefore be divided by one faraday.
${z_{Al}} = \dfrac{{27}}{{3 \times 96500}}$
${z_{Cd}} = \dfrac{{112.4}}{{2 \times 96500}}$
Since one mole of electrons has one faraday charge, the mass deposited can be calculated by multiplying the electrochemical equivalent with one faraday charge.
${\text{Mass of Al deposited}} = \dfrac{{27}}{{3 \times 96500}} \times 96500 = 9g$
${\text{Mass of Cd deposited}} = \dfrac{{112.4}}{{2 \times 96500}} \times 96500 = 56.2g$
Hence, the current required is $26.80A$ and the mass of aluminium and cadmium deposited by one mole of electrons is $9g$ and $56.2g$ respectively.

Note:
An electrolytic cell has the opposite signs of electrodes as compared to a galvanic cells and therefore the charges on electrodes are never fixed but the process associated with an electron remains the same i.e. oxidation reaction is always carried out at the anode and the reduction process is always carried out at the cathode.