Faraday's Laws of Electrolysis
Faraday's Laws of Electrolysis
Electrolysis is the process by which ionic substances are decomposed into simpler substances when an electric current is passed through them. Michael Faraday, an English scientist, formulated two laws which describe the quantitative aspects of electrolysis. These laws are known as Faraday's First and Second Law of Electrolysis.
Faraday's First Law of Electrolysis
Faraday's First Law states that the amount of chemical change (or the mass of the substance deposited or dissolved at an electrode) is directly proportional to the quantity of electricity that passes through the electrolyte.
Mathematically, it can be expressed as:
[ m = ZIt ]
Where:
- ( m ) is the mass of the substance altered at an electrode (in grams),
- ( Z ) is the electrochemical equivalent of the substance (in grams per coulomb),
- ( I ) is the current (in amperes),
- ( t ) is the time for which the current flows (in seconds).
The electrochemical equivalent ( Z ) is a constant for each substance and can be calculated using the equation:
[ Z = \frac{M}{nF} ]
Where:
- ( M ) is the molar mass of the substance (in grams per mole),
- ( n ) is the number of moles of electrons required to deposit or dissolve 1 mole of the substance,
- ( F ) is Faraday's constant, approximately ( 96485 ) coulombs per mole of electrons.
Faraday's Second Law of Electrolysis
Faraday's Second Law states that when the same quantity of electricity is passed through different electrolytes, the mass of substances deposited or dissolved at the respective electrodes is directly proportional to their chemical equivalents (equivalent weights).
Mathematically, the second law can be expressed as:
[ \frac{m_1}{m_2} = \frac{E_1}{E_2} ]
Where:
- ( m_1 ) and ( m_2 ) are the masses of substances deposited or dissolved at the electrodes,
- ( E_1 ) and ( E_2 ) are the equivalent weights of the substances.
The equivalent weight of a substance is defined as the molar mass divided by the valency (number of electrons exchanged per atom or ion of the substance).
Differences and Important Points
Here is a table summarizing the differences and important points of Faraday's Laws of Electrolysis:
| Aspect | Faraday's First Law | Faraday's Second Law |
|---|---|---|
| Basic Principle | Relates mass of substance to quantity of electricity | Relates masses of different substances to their equivalents |
| Mathematical Expression | ( m = ZIt ) | ( \frac{m_1}{m_2} = \frac{E_1}{E_2} ) |
| Proportionality | Mass is directly proportional to current and time | Mass is directly proportional to chemical equivalent |
| Electrochemical Constant | Electrochemical equivalent ( Z ) | Equivalent weight ( E ) |
| Dependency | Depends on the current and duration of electrolysis | Depends on the chemical nature of the substances involved |
| Application | Used to calculate the mass of a single substance | Used to compare the masses of different substances |
Examples to Explain Important Points
Example for Faraday's First Law
Suppose we are electrolyzing a solution of copper(II) sulfate using copper electrodes. The molar mass of copper is ( 63.546 ) g/mol, and the valency of copper in this case is 2.
To find the mass of copper deposited when a current of 2 amperes is passed for 1 hour (3600 seconds), we first calculate the electrochemical equivalent ( Z ):
[ Z = \frac{M}{nF} = \frac{63.546 \text{ g/mol}}{2 \times 96485 \text{ C/mol}} \approx 0.000329 \text{ g/C} ]
Now, using Faraday's First Law:
[ m = ZIt = 0.000329 \text{ g/C} \times 2 \text{ A} \times 3600 \text{ s} \approx 2.37 \text{ g} ]
Thus, approximately 2.37 grams of copper will be deposited on the cathode.
Example for Faraday's Second Law
Let's consider the simultaneous electrolysis of copper(II) sulfate and silver nitrate solutions with the same quantity of electricity. The equivalent weight of copper (Cu) is ( 31.773 ) g/eq (since its valency is 2), and the equivalent weight of silver (Ag) is ( 107.868 ) g/eq (since its valency is 1).
If 2.37 grams of copper are deposited, how much silver will be deposited?
Using Faraday's Second Law:
[ \frac{m_{\text{Cu}}}{m_{\text{Ag}}} = \frac{E_{\text{Cu}}}{E_{\text{Ag}}} ]
[ m_{\text{Ag}} = m_{\text{Cu}} \times \frac{E_{\text{Ag}}}{E_{\text{Cu}}} = 2.37 \text{ g} \times \frac{107.868 \text{ g/eq}}{31.773 \text{ g/eq}} \approx 7.96 \text{ g} ]
Therefore, approximately 7.96 grams of silver will be deposited.
Faraday's Laws of Electrolysis are fundamental to understanding the relationship between electric current and chemical reactions in electrochemistry. They are widely used in industries for electroplating, electrorefining, and the production of chemicals through electrolytic processes.