Which of the following statement is incorrect? (a) In \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\), the ligand has satisfied both primary and secondary valencies of ferric ion (b) In \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) the ligand has satisfied only the secondary valency of ferric ion (c) In \(\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) the ligand has satisfied both primary and secondary valencies of ferrous ion (d) In \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right] \mathrm{SO}_{4}\), the ligand has satisfied only the secondary valency of copper

Understanding the distinction between primary and secondary valencies in coordination compounds is key to grasping the complex nature of these molecules.

Primary valency corresponds to the oxidation state of the central metal ion. In simpler terms, it reflects the positive charge of the metal ion and is often satisfied by negatively charged ions called anions. For example, in potassium ferricyanide (K_3[Fe(CN)_6]), the ferric ion (Fe^{3+}) has a primary valency of 3, which is balanced by three potassium ions (K^+).

Secondary valency, on the other hand, is related to the number of ligands the metal ion can coordinate or bind to. This valency is directional and non-ionizable, which explains the geometries of coordination compounds. Ligands, whether anions or neutral molecules, fulfill the metal's coordination capacity. For instance, in the same compound, the iron's secondary valency is 6 due to six cyanide ligands attaching to it.

In essence, the primary valency is indicative of ionic interactions, while secondary valency deals with covalent bond formation between the metal and the ligands.

The coordination number is a fundamental concept in coordination chemistry that indicates the number of ligand atoms directly bonded to the central metal ion.

This number can vary, typically ranging from 2 to 12, depending on the size, charge, and electronic configuration of the metal ion, as well as the nature of the ligands. It's essential for predicting the geometry of the complex; for example, a coordination number of 4 could lead to a square-planar or tetrahedral geometry, while 6 could form an octahedral complex.

Returning to the example of (K_3[Fe(CN)_6]), the coordination number of the ferric ion (Fe^{3+}) is 6, due to its six cyanide ligands. This is a common coordination number for many transition metals and results in an octahedral shape of the complex.

Ligands are atoms or molecules that can donate a pair of electrons to form a covalent bond with a metal ion in a coordination compound. These can be categorized into various types such as monodentate, bidentate, or polydentate, depending on how many points of attachment they have to the metal ion.

Ligands such as water, ammonia, or chloride ions are monodentate, connecting to the metal at a single bonding site. However, there are more complex ligands like ethylenediamine (en) or oxalate, which can attach at multiple points; these are called polydentate ligands and form chelate complexes. Ligands are crucial in determining the properties of the coordination compound, as they influence factors like color, magnetic behavior, and stability.

The oxidation state in a complex indicates the degree of electron loss or gain of the central metal ion. Determining the oxidation state is essential as it affects the compound's reactivity, stability, and magnetism.

It's commonly represented by a Roman numeral and can be deduced by considering the overall charge of the complex and the charges of the ligands or counterions. For example, in copper sulfate ([Cu(NH_3)_4]SO_4), the ammonium ligands are neutral, which means the oxidation state of copper is +2, corresponding to the metal ion itself. This oxidation state is vital in predicting how the metal will interact with external agents, like ligands or reducing and oxidizing agents.