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.

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

Which of the following statements is wrong?

Faraday’s law of electrolysis fails when temperature is increased

The correct answer is option 2. Faraday’s law of electrolysis fails when the temperature is increased.

Let us analyze each statement to determine which one is incorrect:

1. The unit of electrochemical equivalent is gram/C

The statement is true. The electrochemical equivalent (Z) is defined as the mass of a substance (in grams) deposited or liberated by passing one Coulomb of charge through the electrolyte. Thus, the unit is indeed grams per Coulomb (g/C).

2. Faraday’s law of electrolysis fails when temperature is increased

The statement is false. Faraday's laws of electrolysis are based on the relationship between the amount of electric charge and the amount of substance deposited or liberated at the electrode. These laws hold true regardless of temperature. However, the rate of electrolysis and the overpotentials might be affected by temperature, but this does not mean Faraday's laws fail.

3. During electrolysis of a fused salt, the weight deposited on an electrode will not depend on temperature of both

The statement is true. The weight of the substance deposited during electrolysis primarily depends on the amount of electric charge passed through the electrolyte, not directly on the temperature. While temperature can influence the efficiency and rate of the reaction, the theoretical relationship described by Faraday's laws does not change with temperature.

4. The electric charge for electrode deposition of 1g equivalent of a substance is charge on one mole of electrons

The statement is true. One Faraday of electricity (96,485.3 Coulombs) is the charge carried by one mole of electrons. According to Faraday's laws, this amount of charge will deposit or liberate one gram equivalent of a substance.

The incorrect statement is: Faraday’s law of electrolysis fails when temperature is increased.

Faraday's laws of electrolysis are not invalidated by temperature changes, even though temperature can affect the kinetics and overpotentials of the electrochemical reactions.