Question

Give the number of (valence) \(d\) electrons associated with the central metal ion in each of the following complexes: (a) \(\mathrm{K}_{3}\left[\mathrm{TiCl}_{6}\right],(\mathbf{b}) \mathrm{Na}_{3}\left[\mathrm{Co}\left(\mathrm{NO}_{2}\right)_{6}\right],(\mathbf{c})\left[\mathrm{Ru}(\mathrm{en})_{3}\right] \mathrm{Br}_{3},\) \((\mathbf{d})[\mathrm{Mo}(\mathrm{EDTA})] \mathrm{ClO}_{4},(\mathbf{e}) \mathrm{K}_{3}\left[\mathrm{ReCl}_{6}\right].\)

Short answer

The number of valence d electrons for each complex is: (a) 1 (b) 6 (c) 5 (d) 5 (e) 4

Step-by-step solution

Identify the central metal ion in each complex

We can identify the central metal ions in each complex as follows: (a) Ti (b) Co (c) Ru (d) Mo (e) Re

Determine the oxidation state of the central metal ion

To find the oxidation state of the central metal ion in each complex, we can analyze the overall charge of the complex. (a) K3[TiCl6]: Charge of Ti + 6 * Charge of Cl = -3 (accounting for the 3 positive charges from K+) Charge of Ti - 6 = -3 Charge of Ti = +3 (b) Na3[Co(NO2)6]: Charge of Co + 6 * Charge of NO2 = -3 (accounting for the 3 positive charges from Na+) Charge of Co - 6 * (-1) = -3 (as NO2 is a monoanionic ligand) Charge of Co = +3 (c) [Ru(en)3]Br3: Charge of Ru + 0 = +3 (as 3 Br- ions neutralize +3 charge) (en = ethylenediamine has no charge) Charge of Ru = +3 (d) [Mo(EDTA)]ClO4: Charge of Mo + Charge of EDTA = -1 (as ClO4 is a monoanionic ligand) Charge of Mo + (-2) = -1 (as EDTA is a bi-anionic ligand) Charge of Mo = +1 (e) K3[ReCl6]: Charge of Re + 6 * Charge of Cl = -3 (accounting for the 3 positive charges from K+) Charge of Re - 6 = -3 Charge of Re = +3

Determine the number of valence d electrons for each central metal ion

Using the oxidation state found in Step 2, we can determine the electron configuration for each central metal ion. The number of valence d electrons will be the number of electrons in the d orbitals in their respective electron configuration. (a) Ti(III) has electron configuration: [Ar] 3d1 Number of valence d electrons = 1 (b) Co(III) has electron configuration: [Ar] 3d6 Number of valence d electrons = 6 (c) Ru(III) has electron configuration: [Kr] 4d5 Number of valence d electrons = 5 (d) Mo(I) has electron configuration: [Kr] 4d5 Number of valence d electrons = 5 (e) Re(III) has electron configuration: [Xe] 5d4 Number of valence d electrons = 4 So, the number of valence d electrons for each complex is: (a) 1 (b) 6 (c) 5 (d) 5 (e) 4

Key concepts

Oxidation State

Understanding the oxidation state of an atom within a compound is essential for predicting its chemical behavior. The oxidation state, also known as oxidation number, is an indicator of the degree of oxidation of an atom. It tells us how many electrons an atom has gained, lost, or shared when forming bonds in a compound.

In coordination complexes, the central metal atom or ion has an oxidation state that balances the overall charge. Ligands, which are molecules or ions surrounding the central atom, can influence the oxidation state. They provide or accept electrons through their interaction with the central metal ion. The oxidation state of the metal is denoted by a Roman numeral in parentheses following the element symbol.

For instance, in the complex \(\mathrm{K}_{3}[\mathrm{TiCl}_{6}]\), the central titanium atom (Ti) has an oxidation state of +3, written as Ti(III). This is figured out by considering the net charge of the coordination complex and the known charges of other ions or ligands in the structure. In this example, it is the negative charges from the six \(\mathrm{Cl}^{-}\) ions and the positive charges from the three \(\mathrm{K}^{+}\) ions that guide us to the +3 oxidation state for titanium.

Electron Configuration

Electron configuration is the arrangement of electrons in an atom's orbitals. It is represented by a sequence of numbers and letters that describe the energy levels, sublevels, and the number of electrons in those sublevels. The valence electrons, especially those in the 'd' sublevel for transition metals, are of prime importance as they are responsible for the chemical properties of the atom.

An understanding of electron configurations allows us to predict how an atom will react chemically. For example, the valence d electrons for a metal in a coordination complex determine its color, magnetic properties, and reactivity. In the provided exercise, the central metal ions like Ti, Co, Ru, Mo, and Re all have distinct d electron counts, which affect the structure and function of their respective complexes.

The step-by-step solution above meticulously establishes the electron configuration by first determining the oxidation state. Upon figuring out the oxidation number, we can deduce the electron configuration for the particular charge state of the metal. For example, in Ti(III), the electron configuration is \[\text{[Ar]} 3d^1\], suggesting one valence d electron, derived from its neutral state by removing three electrons.

Coordination Complexes

Coordination complexes, consisting of a central metal ion surrounded by ligands, are found in many areas of chemistry, including biochemistry, inorganic chemistry, and material science. Ligands, which can be neutral molecules or ions, donate a pair of electrons to form coordinate covalent bonds with the metal ion.

The geometric arrangement of these complexes is influenced by the properties of the metal ion and the ligands. Common geometries include octahedral, tetrahedral, and square planar structures. The nature of ligands also impacts the electronic and structural attributes of the central metal ion. This is indeed evident in the exercise solutions where different ligands of varying charges and types contribute to the overall charge, hence affecting the oxidation state and d electron count of the central metal ion.

Coordination complexes exhibit a vast array of chemical behavior due to the variability in their composition. This can be attributed to factors like the number of available d electrons on the metal and its oxidation state, which were both used in our textbook solution to elucidate the characteristics of the given metal complexes.