Write a net ionic equation for the reaction with ammonia by which (a) \(\mathrm{Cu}(\mathrm{OH})_{2}\) dissolves. (b) \(\mathrm{Cd}^{2+}\) forms a complex ion. (c) \(\mathrm{Pb}^{2+}\) forms a precipitate.

Chemical reactions are essential transformations within chemistry where substances, known as reactants, change into new substances called products. The hallmark of a chemical reaction is the formation of new chemical bonds and the breaking of old ones. This can be caused by various types of changes, such as temperature, pressure, presence of catalysts, or interaction with other chemical substances.

Demonstrated through the exercise, when copper(II) hydroxide reacts with ammonia, the reactants (copper(II) hydroxide and ammonia) transform into products (tetraamminecopper(II) complex ion and hydroxide ions). Chemical equations represent these reactions, balancing the number of atoms on each side to obey the Law of Conservation of Mass. The net ionic equation further simplifies this by focusing only on the ions that undergo a change during the reaction, which are directly involved in the process of forming the products.

Complex ions consist of a metal ion at the center surrounded by molecules or anions called ligands. These ligands are bonded to the central ion by coordinate covalent bonds. In the exercise, both copper(II) and cadmium(II) ions react with ammonia to form complex ions, namely tetraamminecopper(II) and tetraamminecadmium(II), respectively.

In these reactions, the lone pairs of electrons on the ammonia molecules donate to the empty d-orbitals of the metal ions, creating a bond and resulting in a charged entity known as a complex ion. Such processes are critical in areas like biochemistry and material science, as they directly impact the properties and behavior of substances.

Precipitation reactions occur when two soluble reactants produce an insoluble product, known as a precipitate. This transformation is signified by the formation of a solid from a solution and is used extensively in various analytical and synthetic chemistry techniques. In the provided exercise, lead(II) ions react with hydroxide ions to form an insoluble substance, lead(II) hydroxide, which appears as a precipitate.

The net ionic equation for a precipitation reaction includes only the species that participate in forming the precipitate, leaving out the spectator ions—ions that do not change their physical state or oxidation number. The net ionic equation thus vividly illustrates the fundamental chemistry taking place, making it a valuable tool for understanding chemical processes.

Ammonia, a compound with the formula NH3, is a common reactant in chemistry that can act as a base or a ligand. It readily donates a pair of electrons, which enables it to neutralize acids or bind to metal ions to form complex ions. For instance, in the context of this exercise, we see ammonia reacting in two different ways: neutralizing the hydroxide ions from copper(II) hydroxide and forming a complex ion with cadmium and lead ions.

Ammonia’s reactivity stems from the nitrogen atom's ability to share its lone pair of electrons, which explains its role in these reactions. Understanding ammonia reactions is fundamental in understanding a wide range of chemical systems, from industrial synthesis to biochemical pathways.