Faraday explained that the decomposition of electrolytes by an electric current is governed by two laws.

First law: The amount of the substance liberated or deposited or dissolved at an electrode during electrolysis of an electrolyte is directly proportional to the quantity of electricity passing through the solution of electrolyte or melt. Mathematically Faraday’s first law is \(m \propto q\) or \(m = eq\) or \(m = ect\), where m is the mass of the substance liberated or deposited or dissolved, q is the quantity of electricity in coulomb, t is the time in seconds, C is the strength of current in amperes and e is the electrochemical equivalent of the ion or metal or molecule deposited or liberated or dissolved at the electrode. Electrochemical equivalent of a substance is the amount deposited or liberated or dissolved or underwent electrode reaction at an electrode by passing one ampere current for 1 s, i.e., 1 C. Chemical equivalent of a substance is the amount of substance deposited or liberated or dissolved or had undergone electrode reaction at an electrode during the passage of one Faraday of electricity during the electrolysis of electrolyte solution or melt.

\(\text{Chemical equivalent of an element or ion = }\frac{\text{Atomic weight}}{\text{Valency or charge of the ion}}\)

The electrochemical equivalent of an element is directly proportional to its chemical equivalent

\[e \propto E \text{ or }E = F.e\]

Unit of electrochemical equivalent is gram C^–1. One Faraday, i.e., 96,500 C is equal to the charge present on mole (6.023×10²³) [Avogadro’s number] of electrons or protons

\[m= \frac{ECt}{96500}\]

Second law of Faraday states that if same quantity of electricity is passed through different electrolyte solutions or melts, the amount of the different substances liberated or deposited or dissolved or had undergone reaction at electrode is directly proportional to their chemical equivalents.

\[\frac{W_1}{E_1} = \frac{W_2}{E_2} = \frac{W_3}{E_3}\]

The chemical equivalents depend on the number of electrons participated at the electrode reaction. The chemical equivalents or equivalent weights of NaCl, KCl, KBr, NaOH, etc., are equal to their molecular weights since only one electron take part in electrode reaction. The equivalent weights of other electrolytes depend on the number of electrons.

\[\text{Equivalent weight} =\frac{\text{Molecular weight}}{\text{Number of electrons involved in electrode reaction}}\]

The amount of an ion discharged during electrolysis is not dependent of

resistance of solution

The correct answer is option 1. resistance of solution.

During electrolysis, the amount of an ion discharged is primarily determined by factors directly related to the electric charge passed through the electrolyte. Let's analyze each option to identify which one is not a determining factor.

Factors affecting the amount of ion discharged:

Time:

This statement is relevant. The amount of ion discharged during electrolysis is proportional to the duration for which the current is applied. According to Faraday’s first law, the mass of the substance deposited or liberated is directly proportional to the charge, which is the product of current and time.

Current strength:

This statement is relevant.The amount of ion discharged is directly proportional to the current. Higher current means more charge passing through the solution in a given time, leading to more ions being discharged.

The electrochemical equivalent of the element :

This statement is relevant. The electrochemical equivalent (Z) is a measure of how much of a particular substance is deposited per unit charge. Different elements have different electrochemical equivalents, affecting how much of each substance is deposited for a given amount of electric charge.

Factor not affecting the amount of ion discharged:

Resistance of solution:

The statement is not directly relevant. While the resistance of the solution can influence the overall efficiency and the voltage required to maintain a certain current, it does not directly determine the amount of ion discharged. The key factors are the current and time, not the resistance. If the current is kept constant, the resistance of the solution does not affect the amount of substance discharged.

The amount of an ion discharged during electrolysis is not dependent on the resistance of the solution.