Understanding Faraday's First Law of Electrolysis

Faraday's first law of Electrolysis describes the quantitative relationship between the amount of substance deposited or liberated during electrolysis and the quantity of electricity passed through the electrolyte. Simply put, the more electricity you pass, the more substance is deposited or liberated.

The law states that the mass (m) of any substance deposited or liberated at any electrode during electrolysis is directly proportional to the quantity of electricity (Q) passed through the electrolyte.

Mathematically, this direct proportionality can be written as:

\(m \propto Q\)

To turn this proportionality into an equation, we introduce a constant of proportionality. This constant is known as the electrochemical equivalent (Z) of the substance. So, the mathematical form becomes:

\(m = ZQ\)

Let's break down the terms in this equation:

• m: Represents the mass of the substance deposited or liberated at an electrode (usually in grams).
• Q: Represents the total quantity of electricity passed through the electrolyte (usually in Coulombs). The quantity of electricity is calculated as the product of the current (I) and the time (t) for which the current flows (\(Q = I \times t\)).
• Z: Represents the electrochemical equivalent of the substance. It is the mass of the substance deposited or liberated when one Coulomb of electricity is passed through the electrolyte. Z is a characteristic constant for each substance.

Analyzing the Options for Faraday's First Law

We are looking for the mathematical form of Faraday's first law of Electrolysis, which we established is \(m = ZQ\).

Let's look at the given options:

1. \(m = ZQ\)
2. \(m = Z/Q\)
3. \(z = Q/m\)
4. \(m = -Z/Q\)

Comparing our derived mathematical form \(m = ZQ\) with the given options, we can see that the first option matches the correct relationship where mass (m) is directly proportional to the quantity of electricity (Q), with Z being the constant of proportionality (electrochemical equivalent).

The other options represent different or incorrect relationships:

• \(m = Z/Q\) implies mass is inversely proportional to charge, which contradicts the law.
• \(z = Q/m\) is a rearrangement, but the question asks for the mathematical form starting with 'm', and it's not the standard way the law is stated. The standard form directly relates m and Q.
• \(m = -Z/Q\) introduces a negative sign and inverse proportionality, which is incorrect for this law. Mass deposited is a positive quantity.

Therefore, the correct mathematical form of Faraday's first law of Electrolysis is \(m = ZQ\).