Question

Which of the following will liberate one gram equivalence of a substance at an electrode?
A.$6.023 \times {10^{23}}$electrons
B.$96500C$
C.1 ampere current for 1 second
D.1 ampere current for $96500\sec$

Answer 1

Hint : Electrolysis is defined as the process which leads to a chemical change on passing electricity through the electrolyte present either in their molten state or in their aqueous state. The cell which converts electrical energy into chemical energy is called an Electrolytic cell.

Complete step by step solution :
Step 1
The process of electrolysis takes place via three steps:
Dissociation – Where the electrolyte dissociates into cations and anions.
Migration – Cations migrate towards cathode and anions migrate towards anode.
Discharge – The cations take electrons from the cathode and undergo reduction at cathode whereas the anions transfer the electrons to the anode and undergo the process of oxidation. As oxidation and reduction take place simultaneously so electrolysis is a redox process.
Step 2
In the year 1832 Michael Faraday, studied the phenomenon of electrolysis and established a relationship between the amount of products liberated at the electrodes and the quantity of electricity passed in the solution during the process of electrolysis. Based on this Faraday gave two laws of electrolysis.
Step 3
Faraday’s first law of electrolysis – The amount of substance liberated or deposited at a particular electrode during electrolysis is directly proportional to the quantity of electricity or total charge passed in the solution. The mathematical expression for the first law is $W = ZIt$, where W is the mass of products deposited, Z is the electrochemical equivalent, I is the current in amperes and t is the time in second.
Faraday’s second law of electrolysis states that when the same quantity of electricity is passed through the solutions of different electrolytes connected in series, the masses of the substances liberated at the respective electrodes are directly proportional to their equivalent masses. The mathematical expression of the second law is $E = F \times Z$where E is the equivalent mass, F is the Faraday’s constant which is 96500 C, and Z is the electrochemical equivalent. The amount of charge carried by one mole of electrons in one second through a conductor is known as one Faraday.
Step 4
From Faraday’s first law we have:
$W = ZIt$,
From Faraday’s second law we have:
$E = F \times Z$
$E = F \times \dfrac{W}{{I \times t}}$
$W = \dfrac{{E \times I \times t}}{F}$
If, $I \times t = 1F$, then $W = E$.
So, on passing one Faraday charge in the solution of an electrolyte the amount of substance liberated is its equivalent mass.
Hence, one gram equivalence of a substance will be liberated by $6.023 \times {10^{23}}$electrons, one Faraday charge which is $96500C$ and 1 ampere current for $96500\sec$ as 1 ampere charge flowing for 1 sec through a conductor is equal to 1C charge. So, correct options are, option a), option b) and option d).

Note : A substance having a mass which is equal to its equivalent mass is said to have one gram equivalent mass.