Give the oxidation numbers of the metals in these species: (a) \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) (b) \(\mathrm{K}_{3}\left[\mathrm{Cr}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]\) (c) \(\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]^{2-}\)

Understanding the oxidation state, or oxidation number, of an element in a compound is fundamental in chemistry, especially in examining redox reactions and coordination compounds. An oxidation state is a number assigned to an element in a chemical form which represents the number of electrons lost or gained by an atom of that element in the compound.

In the context of coordination compounds, determining the oxidation state can be slightly more complex due to the nature of the bonds between the central metal and the ligands. However, by using simple rules and algebraic calculations, one can deduce the oxidation numbers efficiently.

General Approach for Oxidation State Determination

• Identify the known oxidation states of ligands and counter ions.
• Consider the overall charge of the compound.
• Apply the concept that the sum of the oxidation states in a molecule equals the overall charge.
• Solve for the unknown oxidation state, usually that of the central metal atom.

Following these steps allows us to figure out that metals like iron (Fe), chromium (Cr), and nickel (Ni), in their respective coordination complexes, have oxidation states of +3, +3, and +2 respectively.

Coordination chemistry is a branch of inorganic chemistry dealing with the study of coordination compounds. These are complex molecules that consist of a central metal atom or ion bonded to surrounding molecules or ions, known as ligands. Coordination compounds are unique due to their properties and the variety of structures they can form.

Understanding Complex Ions

• Central Metal Ion/Atom: Typically a transition metal with vacant orbitals ready to accept electron pairs from ligands.
• Ligands: Molecules or ions that donate pairs of electrons to the metal, forming coordinate covalent bonds. Examples include water, ammonia, cyanide, and oxalate.
• Coordination Number: Represents the number of ligand electron pairs bonded to the central metal.
• Charge Considerations: The sum of the central metal's oxidation state and the charges of the ligands must equal the charge of the entire coordination complex.

In our exercise example, potassium acts as a counter ion to the complex ions, balancing the overall charge. Ligands like cyanide and oxalate form specific and identifiable charge patterns that assist in the determination of the central metal's oxidation state.

Redox chemistry, which stands for reduction-oxidation chemistry, involves the transfer of electrons between two species. It's the driving force behind a breadth of chemical processes, from biological systems to industrial applications. In redox reactions, one species undergoes oxidation (loss of electrons) while another undergoes reduction (gain of electrons).

Role of Oxidation States in Redox Reactions

• Identify Redox Couples: Analyzing the changes in oxidation states helps in identifying the species that get oxidized and reduced.
• Determine the Direction of Electron Transfer: Electrons move from the species being oxidized to the one being reduced.
• Balance Equations: Knowing the oxidation states can facilitate the balancing of redox equations through techniques like the half-reaction method.

In coordination chemistry, redox processes can involve the central metal undergoing changes in oxidation state. Ligands can influence these redox processes by stabilizing certain oxidation states of the metal. With our textbook exercise examples, it is essential to understand the oxidation states to analyze any redox behavior within coordination complexes.