One litre of \(1 \mathrm{M} \mathrm{CuSO}_{4}\) solution is electrolysed. After passing \(2 \mathrm{~F}\) of electricity, molarity of \(\mathrm{CuSO}_{4}\) solution will be: (a) \(\mathrm{M} / 2\) (b) \(\mathrm{M} / 4\) (c) \(\mathrm{M}\) (d) 0

Faraday's laws of electrolysis are essential for understanding the relationship between the amount of electrical charge passed through a substance and the amount of substance that is electrolyzed. According to the first law, the amount of a substance that undergoes oxidation or reduction at each electrode during electrolysis is directly proportional to the amount of electricity that passes through the electrolyte. This is expressed mathematically by the equation:
\( m = (Q / F) \times M \)
where \( m \) is the mass of the substance altered at the electrode, \( Q \) is the total electric charge passed through the substance, \( F \) is Faraday's constant (approximately 96485 coulombs per mole), and \( M \) is the molar mass of the substance.
The second law states that for the same quantity of electric charge, the masses of different substances electrolyzed or deposited are proportional to their equivalent weights (which is the molar mass divided by the valence).
In our exercise, passing 2 Faradays (F) of electricity corresponds to the reduction of 1 mole of copper ions (\( Cu^{2+} \)) because each copper ion requires 2 moles of electrons to turn into copper metal. This is a direct application of Faraday's first law where the amount of copper deposited is proportional to the amount of electricity passed, and this proportionality is given by the Faraday's constant \( F \).

The mole concept is a fundamental principle in chemistry that allows chemists to count particles by weighing them. One mole is defined as the amount of substance that contains the same number of particles (atoms, molecules, ions, or electrons) as there are atoms in 12 grams of carbon-12. This number of particles is known as Avogadro's number, approximately \(6.022 \times 10^{23}\) particles per mole.
When dealing with solutions, molarity is a common unit of concentration, defined as moles of solute per liter of solution (mol/L). This concept helps us understand the changes in concentration when a reaction occurs in a solution, such as during electrolysis. For example, in the given exercise, a 1-liter solution of \(1 M \mathrm{CuSO}_{4}\) signifies that there is 1 mole of \( \mathrm{CuSO}_{4} \) dissolved in 1 liter of water. After electrolysis, we use the mole concept to infer, based on Faraday's laws, that the reduction of 1 mole of \( \mathrm{Cu}^{2+} \) ions to copper metal will alter the molarity of the solution, which in the context of this reaction, results in a molarity of 0.

Reduction and oxidation reactions, often referred to as redox reactions, are processes that involve the transfer of electrons between substances. A reduction reaction is where a substance gains electrons (reduced in charge), and an oxidation reaction is where a substance loses electrons (increased in charge).
These reactions are integral to the process of electrolysis. During electrolysis, at the cathode, a reduction reaction occurs, where positively charged ions gain electrons to form neutral atoms or molecules. Conversely, at the anode, an oxidation reaction takes place, where neutral atoms lose electrons to form positively charged ions.
In our exercise, copper ions \( \mathrm{Cu}^{2+} \) undergo a reduction reaction, gaining two electrons to become pure copper metal (\( \mathrm{Cu} \)). This effectively decreases the concentration of \( \mathrm{CuSO}_{4} \) in the solution, because the copper ions are being removed from the electrolyte. This process exemplifies the practical application of redox reactions, where the reduction of copper ions leads to a change in the molarity of the original copper sulfate solution.