When \(\mathrm{Zn}\) metal is added to \(\mathrm{CuSO}_{4}\) solution, \(\mathrm{Cu}\) is precipitated it is due to: (a) Ionization of \(\mathrm{CuSO}_{4}\) (b) Hydrolysis of \(\mathrm{CuSO}_{4}\) (c) Reduction of \(\mathrm{Cu}^{2+}\) (d) Oxidation of \(\mathrm{Cu}^{2+}\)

In the realm of chemistry, particularly in aqueous solutions, chemical precipitation is a process where a solid, referred to as a precipitate, forms and separates from a liquid solution. This phenomenon occurs when the concentration of a certain solute exceeds its solubility limit in the solution, often due to a reaction between chemical species. In the context of our exercise, copper (Cu) is precipitated when zinc (Zn) is introduced to a solution of copper sulfate (CuSO₄).

Crucial to understanding chemical precipitation is the concept of solubility product (K_sp). This represents the extent to which a compound can dissolve in water and varies for different substances. When a solution's ion product for a solute exceeds the K_sp, precipitation will likely occur. This underlies the importance of understanding the conditions, such as temperature and presence of other ions, which may affect solubility and thus the likelihood of precipitation.

The terms oxidation and reduction are essential aspects of a broader concept known as redox reactions. In simple terms, oxidation refers to the process wherein an atom, ion, or molecule loses electrons; conversely, reduction means gaining electrons. It's crucial to remember the mnemonic 'OIL RIG': Oxidation Is Loss, Reduction Is Gain.

In our exercise, Zn gets oxidized as it donates electrons and changes into Zn²⁺. On the other side of this redox equation, Cu²⁺, an ion in solution, is reduced because it accepts the electrons that Zn releases. This electron transfer is fundamental to redox reactions and drives many processes in both nature and industry, from the rusting of iron to the generation of energy in batteries. Understanding which species gets oxidized and which gets reduced is key in balancing redox reactions and predicting the outcomes of chemical processes.

A metal displacement reaction is a type of redox reaction where a metal in a compound is replaced by another metal. The displacement occurs because of differences in the reactivity of the two metals; the more reactive metal displaces the less reactive metal from its compound.

In the case of the exercise where Zn displaces Cu from copper sulfate, the chemical principles dictate that zinc, which is more reactive, can replace copper in the solution, leading to the formation of copper metal as a precipitate. The zinc becomes oxidized to Zn²⁺ ions while the copper ions in solution are reduced to metallic copper. These types of reactions are also referred to as 'single replacement reactions' and are commonly encountered in galvanic cells, corrosion, and metallurgical processes.