# Faraday's Laws of Electrolysis: Definition & Equation

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Instructor: Hemnath (Vikash) Seeboo

Taught Science (mainly Chemistry, Physics and Math) at high school level and has a Master's Degree in Education.

This lesson is about the quantitative aspects of electrolysis. During electrolysis, there are substances that are produced at the anode and at the cathode. This lesson, with the help of Faraday's laws of electrolysis, will guide you towards calculating amounts of substances formed during electrolysis.

## Definition of Electrolysis

Electrolysis is the passage of electricity through an electrolyte, with cations moving to the cathode to get reduced, and anions moving towards the anode to get oxidized. An electrolyte is a liquid that conducts electricity.

The table below shows three different constants that we'll use during this lesson. Their details will be dealt with during the lesson.

Let's first go through a few quantitative measures involved in electrolysis. Let's take a look at the relationship between current, charge, and time.

How is a current produced? An electric current arises whenever there is a flow of charges (for example, electrons) and is defined as the rate at which charge flows. The formula is as follows:

Current = Quantity of charge/Time, or I = Q/t, where

I is the current in Ampere (A), which is the flow of 1 Coulomb of charge per second, or C/s,

t is time in seconds, and

Q is quantity of electricity in Coulombs

Do you know how much charge is carried by a single electron?

The answer is 1.6023 x 10 -19 C.

What will then be the total charge carried by one mole of electrons?

1 mole of electrons is represented by the Avogadro's Number, L = 6.022 x 1023 electrons.

Therefore, 6.022 x 1023 electrons carries a charge of 6.022 x 1023 x 1.6023 x 10-19 C/mol = 96,485 C/mol.

96,485 C/mol, or one Faraday, denoted by the symbol F, is the amount of electricity that is carried by one mole of electrons and is known as the Faraday constant.

Equivalent weight or equivalent mass is another quantity which is often used in electrolytic calculations and is given by:

Equivalent weight, or E = Atomic weight/Valency, where atomic weight or atomic mass is in g/mol and the value is usually provided. Valency is an atom's ability to combine with other atoms, and equivalent weight or equivalent mass is measured in grams.

Now let's take a look at some examples.

Example 1 - Find the equivalent weight for silver.

Atomic mass of Ag is given as 108.

Valency = 1, since only 1 mole of electron can be used to combine with another atom.

Equivalent weight = Atomic weight of silver/Valency of silver= 108/1=108g

Example 2 - Find the equivalent weight for aluminum

Atomic mass of Al is given as 27.

Valency = 3, since 3 moles of electrons can be used to combine with another atom.

Equivalent weight = Atomic weight of aluminum/Valency of aluminum = 27/3 = 9g

## Faraday's First Law of Electrolysis

The mass of the substance (m) deposited or liberated at any electrode is directly proportional to the quantity of electricity or charge (Q) passed.

In the mathematical form, this law can be represented as follows:

Removing the proportionality sign gives m = ZQ, where m is the mass in grams (g), Q is measured in Coulombs (C), and Z is the proportionality constant in g/C (in grams per coulomb) and is also known as the electrochemical equivalent, which is the mass of a substance produced at the electrode during electrolysis by one Coulomb of charge.

Faraday further observed that 1 Faraday (96,485C) of charge liberates 1 gram equivalent of the substance at the electrodes.

This means that 1C will liberate one gram equivalent of a substance/96,485, which is the electrochemical equivalent (Z) of the substance.

This goes to a relationship between electrochemical equivalent (Z) and equivalent weight or equivalent mass (E) of a substance, and this can be expressed as:

Z = Equivalent weight/96,485, or Z = E/96,485

Moving back to the equation m = ZQ, it can alternately be written as:

m = Z x I x t (since Q = I x t)

m = E x I x t /96,485 (since Z = E/96,485)

Let's now wrap up all what we've learned so far in two examples:

1. During an electrolysis of molten sodium chloride, a 4A current is passed through electrodes for 1 hour. Calculate the mass of sodium that is produced during this time.

Given I = 4A, t = 1 x 60 x 60 = 3,600s, and E of sodium is 23/1 = 23g

Mass of sodium produced = E x I x t/96,485

= (23 x 4 x 3,600)/96,485

= 3.43g

2. A plant to produce aluminum from molten aluminum oxide will use a current of 200,000A. A simplistic view of the plant is shown below:

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