Faraday’s Laws (VCE SSCE Chemistry): Revision Notes

Faraday's Laws

Introduction

Industrial chemists working with electrolytic cells need to understand the relationships between the amount of product formed, the electric current used, and the operating time. In 1834, Michael Faraday discovered fundamental laws that explain these relationships in electrochemical processes. These laws apply to both electrolytic cells (which use electrical energy to drive chemical reactions) and galvanic cells (which produce electrical energy from chemical reactions).

Electroplating

Electroplating is a commercially important application of electrolysis where a thin coating of metal (only a fraction of a millimetre thick) is applied to the surface of another object. This process has many practical uses in industry.

Applications of electroplating

A common example is the tin coating applied to steel food cans. Although these are called 'tin' cans, they are primarily made of steel (an alloy of iron and carbon). Only a thin layer of tin is plated over the steel surface. This tin coating serves an important purpose: tin corrodes very slowly and prevents contact between the iron, moisture, and air. This effectively stops the steel from rusting and protects the food inside.

Electroplating cells: how they work

Electroplating occurs in electrolytic cells. Understanding the setup and reactions in these cells is essential for applying Faraday's laws.

In an electroplating cell:

• The object to be plated is connected to the negative terminal of a power supply, making it the cathode (negative electrode)
• The object is immersed in an electrolyte solution containing ions of the metal to be plated (for example, $\text{Sn}^{2+}$ ions in tin(II) nitrate solution for tin plating)
• A rod of the plating metal is connected to the positive terminal, making it the anode (positive electrode)
• When the cell operates, the power supply acts as an 'electron pump', pushing electrons onto the cathode and removing them from the anode

Reaction at the cathode (negative electrode)

At the cathode, metal ions from the solution are attracted to the negative electrode. Here they accept electrons and undergo reduction to form metal atoms:

$\text{Sn}^{2+}(aq) + 2e^- \rightarrow \text{Sn}(s)$

This creates a coating of tin metal on the object being plated. Because reduction occurs here (gain of electrons), this electrode is called the cathode.

Reaction at the anode (positive electrode)

At the anode, the power supply withdraws electrons from the metal electrode, causing an oxidation reaction. The tin metal slowly dissolves as $\text{Sn}^{2+}$ ions are formed:

$\text{Sn}(s) \rightarrow \text{Sn}^{2+}(aq) + 2e^-$

This reaction replaces the $\text{Sn}^{2+}$ ions that were consumed at the cathode, keeping the concentration of metal ions in the electrolyte constant. Because oxidation occurs here (loss of electrons), this electrode is called the anode.

Summary of electroplating cell setup

Factors affecting product formation

Several key factors determine how much product forms in an electrolytic cell:

• The charge on the ion involved in the electrode reaction
• The current flowing through the cell
• The length of time the current flows

Faraday's laws describe the mathematical relationships between these factors.

Faraday's first law of electrolysis

Understanding electric charge

Before examining Faraday's first law, we need to understand how electric charge is measured and calculated.

Electric charge (symbol $Q$) is measured in coulombs (C). The charge passing through a cell can be calculated from:

• The current ($I$) through the cell, measured in amperes (A)
• The time ($t$) the current flows, measured in seconds (s)

The relationship is:

$Q = I \times t$

where:

• $Q$ = charge in coulombs (C)
• $I$ = current in amperes (A)
• $t$ = time in seconds (s)

Experimental investigation

An experiment was conducted using a silver-plating cell to investigate the relationship between charge and mass of metal deposited. The apparatus included an ammeter to measure current and a variable resistor to keep the current constant.

The experimental data from the silver-plating cell is shown below:

Current (A)	Time (s)	Charge (C) $Q = I \times t$	Mass of silver formed (g)
2.0	200	400	0.45
2.0	400	800	0.91
2.0	600	1200	1.34
2.0	800	1600	1.79
2.0	1000	2000	2.24

The relationship between charge and mass

When this data is plotted on a graph, it shows a straight line through the origin. This demonstrates that the mass of silver produced at the cathode is directly proportional to the electrical charge passed through the cell.

This observation led to Faraday's first law of electrolysis:

Faraday's second law of electrolysis

Comparing different metals

When the electroplating experiment is repeated using different metals (copper, tin, lead, chromium, and silver), each metal shows a different relationship between charge and mass deposited.

While each metal obeys Faraday's first law (showing a straight line), the slopes of the lines differ. However, when we plot the amount of metal in moles (rather than mass in grams) against charge, an interesting pattern emerges.

All the data now falls onto just three lines! This reveals the underlying principle:

• One mole of silver requires about 96,500 C of charge
• One mole of copper, tin, or lead requires about 193,000 C (which is $2 \times 96,500$ C)
• One mole of chromium requires about 289,500 C (which is $3 \times 96,500$ C)

The Faraday constant

The charge on one mole of electrons is 96,500 C. This quantity is called a faraday and has the symbol $F$. Therefore:

$F = 96,\!500 \text{ C mol}^{-1}$

This is known as the Faraday constant.

The charge on any number of moles of electrons can be calculated using:

$Q = n(e^-) \times F$

or

$Q = n(e^-) \times 96,\!500$

where:

• $Q$ = charge in coulombs (C)
• $n(e^-)$ = number of moles of electrons
• $F$ = Faraday's constant (96,500 C mol⁻¹)

Understanding the pattern

The different lines on the graph arise because different metal ions have different charges, requiring different numbers of electrons:

For silver: $\text{Ag}^+(aq) + e^- \rightarrow \text{Ag}(s)$ 1 mole of electrons produces 1 mole of silver

For copper, tin, and lead: $\text{Cu}^{2+}(aq) + 2e^- \rightarrow \text{Cu}(s)$ $\text{Sn}^{2+}(aq) + 2e^- \rightarrow \text{Sn}(s)$ $\text{Pb}^{2+}(aq) + 2e^- \rightarrow \text{Pb}(s)$ 2 moles of electrons produce 1 mole of metal

For chromium: $\text{Cr}^{3+}(aq) + 3e^- \rightarrow \text{Cr}(s)$ 3 moles of electrons produce 1 mole of chromium

This leads to Faraday's second law of electrolysis:

General statement of Faraday's laws

Faraday's laws can be stated more generally:

• The mass of any substance deposited, evolved or dissolved at an electrode is directly proportional to the electrical charge passed through the cell
• For 1 mole of a substance to be deposited, evolved or dissolved at an electrode, the passage of 1, 2, 3 or another whole number of moles of electrons is required

These laws apply to all electrochemical processes, including both electrolytic cells and galvanic cells (such as fuel cells).

Calculations using Faraday's laws

Faraday's laws enable us to perform quantitative calculations about electrochemical cells. These calculations are based on two key relationships:

$Q = I \times t$ $Q = n(e^-) \times F$

Calculating the mass of product formed

Calculating the time required

Application to fuel cells

Faraday's laws also apply to galvanic cells such as fuel cells. Here, chemical reactions produce electrical energy, and we can calculate how long a given mass of fuel will last.

Exam tips

Historical context

Michael Faraday (1791-1867) was an English scientist who made significant contributions to electrochemistry and electromagnetism. His experiments on the decomposition of tin(II) chloride revealed that the amounts of tin and chlorine gas produced were always proportional to the amount of electric charge passed through the cell. Faraday also played a key role in popularising the terms 'anode', 'cathode', 'electrode' and 'electrolyte' that we still use today.

Remember!