Give reason for the higher values of experimental magnetic moment than expected in case of \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) and \(\left(\mathrm{NiCl}_{4}\right)^{2-}\) complexes.

Transition metal chemistry is an essential area of study in inorganic chemistry, focusing on the properties and behavior of elements in the d-block of the periodic table. Students often encounter transition metals when dealing with coordination complexes, which consist of a central metal atom or ion surrounded by molecules or ions known as ligands.

Transition metals exhibit a range of oxidation states, which is a result of the involvement of their d electrons in bonding. A classic example of this can be seen in the exercise given, where cobalt (Co) and nickel (Ni) ions form complexes with water and chloride ions, showcasing their +2 oxidation states.

These metals are known for their ability to form colorful compounds due to d-d electronic transitions influenced by surrounding ligands. Additionally, their magnetic properties, like the magnetic moments in question, are attributed to the presence of unpaired electrons in the d-orbitals.

Ligand Field Theory (LFT) is an extension of Crystal Field Theory and provides a more nuanced explanation of how ligands influence the energies of d-orbital electrons in transition metal complexes. In the given exercise, understanding LFT is critical to explain the unexpected experimental magnetic moments.

LFT describes that ligands create an electrostatic field that affects the energy levels of the metal's d-orbitals, leading to splitting of these orbitals into different energy sublevels. The energy gap between these levels can dictate whether electrons will pair up or remain unpaired. Ligands can be categorized as 'strong field' or 'weak field' based on their ability to cause this electron pairing or lack thereof. Water (\( \text{H}_2\text{O} \)) and chloride ions (Cl-) are both considered weak field ligands, which means they have a lesser tendency to cause pairing, contributing to the higher magnetic moment observed.

Electron configuration refers to the distribution of electrons in an atom or ion among its available orbitals. It follows the Pauli exclusion principle and Hund's rule to optimize the arrangement for the lowest energy state. In transition metal ions, the filling of d-orbitals is particularly relevant as it determines many properties, including magnetic moments due to the presence of unpaired electrons.

In the context of the provided textbook solutions, the cobalt and nickel ions within the complexes exhibit electronic configurations of [Ar] 3d7 and [Ar] 3d8, respectively. These configurations are key to predicting magnetic behavior. The exercise illustrates that the unexpected higher magnetic moments are because of the retention of unpaired electrons, which is in accordance with the electron configurations seen after considering the oxidation state of the metal and the nature of the ligands.