Understanding the Electrolysis Deposition Statement

The question asks us to identify the scientific law associated with the given statement about the mass deposited or liberated at an electrode during electrolysis. The statement specifically says that the mass of the substance (\(m\)) is directly proportional to the quantity of electricity or charge (\(Q\)) passed through the electrolytic solution.

Let's break down the statement:

• Mass of the substance (\(m\)): This refers to the amount of material (like metal) that gets deposited on an electrode or gas that is liberated at an electrode during electrolysis.
• Electrode: This is a conductor through which electric current enters or leaves an electrolytic cell.
• Quantity of electricity or charge (\(Q\)): This is the total amount of electrical charge that passes through the solution. It is measured in Coulombs (C). The quantity of charge is related to the current (\(I\)) and the time (\(t\)) for which the current flows by the formula \(Q = I \times t\).
• Directly proportional: This means if you double the charge passed, you double the mass deposited (assuming other conditions are constant). Mathematically, this relationship can be written as \(m \propto Q\).

Analyzing the Options and Related Laws

Now, let's look at the given options and see which law best matches this description of electrolysis:

1. Ohm's Law

Ohm's Law describes the relationship between voltage (\(V\)), current (\(I\)), and resistance (\(R\)) in an electrical circuit. It is given by the formula \(V = I \times R\). This law deals with how current flows through a conductor under a potential difference and resistance, not the chemical effects of current like deposition during electrolysis.

2. Faraday's Laws Of Electrolysis

Michael Faraday formulated laws that describe the quantitative aspects of electrolysis. There are two main laws:

• Faraday's First Law of Electrolysis: This law states that the mass (\(m\)) of a substance deposited or liberated at any electrode is directly proportional to the quantity of charge (\(Q\)) passed through the electrolyte. This is exactly the statement provided in the question. Mathematically, it is expressed as \(m \propto Q\), or \(m = ZQ\), where \(Z\) is the electrochemical equivalent of the substance.
• Faraday's Second Law of Electrolysis: This law deals with what happens when the same quantity of electricity is passed through different electrolytes connected in series. It states that the masses of different substances deposited or liberated at the electrodes are proportional to their equivalent weights.

The statement in the question perfectly aligns with Faraday's First Law of Electrolysis, which is part of Faraday's Laws of Electrolysis.

3. Kirchhoff's Current Law

Kirchhoff's Current Law (KCL) is a fundamental principle used in circuit analysis. It states that the total current entering a junction or a node in an electrical circuit is equal to the total current leaving the junction. This law is based on the conservation of charge in a circuit and is not related to the deposition of substances during electrolysis.

4. Faraday's Law Of Electromagnetic Induction

Faraday's Law of Electromagnetic Induction describes how a voltage (electromotive force) is induced in a conductor when it is exposed to a changing magnetic field. This law is fundamental to the operation of generators, transformers, and motors. It deals with the relationship between changing magnetic fields and induced electric fields, not the chemical processes occurring during electrolysis.

Conclusion

Comparing the statement with the descriptions of the laws, it is clear that the statement "The mass of the substance (m) deposited or liberated at any electrode is directly proportional to the quantity of electricity or charge (Q) passed" is directly associated with Faraday's First Law of Electrolysis, which is encompassed within the broader term "Faraday's Law Of Electrolysis".

Therefore, the statement is associated with Faraday's Law Of Electrolysis.

Revision Table: Key Laws in Physics

Additional Information: Understanding Faraday's Laws in Detail

Faraday's Laws of Electrolysis are crucial for understanding how electrolysis works quantitatively. The first law, as discussed, gives us \(m = ZQ\). The constant \(Z\) is called the electrochemical equivalent (ECE). It represents the mass of a substance deposited or liberated by one Coulomb of charge. The ECE of a substance can be calculated using the formula:

\(\( Z = \frac{\text{Molar Mass (M)}}{\text{Faraday Constant (F)} \times \text{Valency (n)}} \)\)

Where:

• Molar Mass (M) is the mass of one mole of the substance.
• Faraday Constant (F) is the charge carried by one mole of electrons, approximately \(96485 \text{ C/mol}\).
• Valency (n) is the number of electrons gained or lost by one atom or ion of the substance during the electrode reaction.

So, the first law can also be written as:

\(\( m = \frac{M}{nF} Q = \frac{M}{nF} It \)\)

This expanded form explicitly shows the dependence of the mass deposited on the current (\(I\)), time (\(t\)), and the properties of the substance (\(M\), \(n\)).

Faraday's Second Law connects the amount of different substances deposited when the same charge passes. If two different electrolytic cells are connected in series (so the same charge passes through both), and substances 1 and 2 are deposited, then according to the second law:

\(\( \frac{m_1}{m_2} = \frac{\text{Equivalent Weight}_1}{\text{Equivalent Weight}_2} \)\)

The equivalent weight is the molar mass divided by the valency (\(\text{Equivalent Weight} = M/n\)). Thus, the second law is consistent with the first law and the definition of ECE.