Problem 41 - Chemistry: The Central Science

Question

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

Step-by-Step Solution

Answer

The number of \(d\) electrons associated with the central metal ions in the given complexes are: (a) \(\mathrm{K}_{3}\left[\mathrm{TiCl}_{6}\right]\): 1 \(d\) electron, (b) \(\mathrm{Na}_{3}\left[\mathrm{Co}\left(\mathrm{NO}_{2}\right)_{6}\right]\): 6 \(d\) electrons, (c) \(\left[\operatorname{Ru}(\mathrm{en})_{3}\right] \mathrm{Br}_{3}\): 5 \(d\) electrons, (d) \([\mathrm{Mo}(\mathrm{EDTA})] \mathrm{ClO}_{4}\): 2 \(d\) electrons, and (e) \(\mathrm{K}_{3}\left[\mathrm{ReCl}_{6}\right]\): 4 \(d\) electrons.

Step 1: Identify the central metal ion and its ligands

The central metal ion is \(\mathrm{Ti}\) (titanium) and its ligands are six \(\mathrm{Cl}\) (chloride ions).

Step 2: Determine the charge on the central metal ion

We know that the overall complex charge must be equal to the sum of the charges on the central metal ion and the ligands. Here, each \(\mathrm{Cl}\) ion has a charge of -1 and there are 3 \(\mathrm{K}\)+ ions with a charge of +1 each in the complex. Therefore, the metal ion's charge can be determined as: \(3 - 6 \times 1 = +3\) Thus, \(\mathrm{Ti}\) is in the +3 oxidation state.

Step 3: Calculate the number of \(d\) electrons associated with the central metal ion

In its ground state, Titanium has the electron configuration \(\mathrm{[Ar]3d^24s^2}\). When it forms a +3 oxidation state, it loses three electrons: two from \(\mathrm{4s}\) and one from \(\mathrm{3d}\). Therefore, the number of \(d\) electrons associated with the central metal ion is 1. (b) \(\mathrm{Na}_{3}\left[\mathrm{Co}\left(\mathrm{NO}_{2}\right)_{6}\right]\):

Step 1: Identify the central metal ion and its ligands

The central metal ion is \(\mathrm{Co}\) (cobalt) and its ligands are six \(\mathrm{NO}_{2}\) (nitro) groups.

Step 2: Determine the charge on the central metal ion

We know that each \(\mathrm{NO}_{2}\) ligand has a charge of -1 and there is a total of 3 \(\mathrm{Na}$$+\) ions with a charge of +1 each present in the complex. Therefore, the charge on the cobalt ion can be determined as: \(3 - 6 \times 1 = +3\) Thus, Cobalt is in the +3 oxidation state.

Step 3: Calculate the number of \(d\) electrons associated with the central metal ion

In its ground state, Cobalt has the electron configuration \(\mathrm{[Ar]3d^74s^2}\). When it forms a +3 oxidation state, it loses 3 electrons: two from \(\mathrm{4s}\) and one from \(\mathrm{3d}\). Therefore, the number of \(d\) electrons associated with the central metal ion is 6. (c) \(\left[\operatorname{Ru}(\mathrm{en})_{3}\right] \mathrm{Br}_{3}\):

Step 1: Identify the central metal ion and its ligands

The central metal ion is \(\mathrm{Ru}\) (ruthenium) and its ligands are three \(\mathrm{en}\) (ethylenediamine) groups.

Step 2: Determine the charge on the central metal ion

We know that each \(\mathrm{en}\) ligand has a charge of 0 (because it is a neutral ligand), and overall, the charge on the complex is +3 due to three \(\mathrm{Br}\)- ions with charge -1. Therefore, the charge on the ruthenium ion is: \(3 - 3 \times 0 = +3\) Thus, Ruthenium is in the +3 oxidation state.

Step 3: Calculate the number of \(d\) electrons associated with the central metal ion

In its ground state, Ruthenium has the electron configuration \(\mathrm{[Kr]4d^75s^1}\). When it forms a +3 oxidation state, it loses three electrons: one from \(\mathrm{5s}\) and two from \(\mathrm{4d}\). Therefore, the number of \(d\) electrons associated with the central metal ion is 5. (d) \([\mathrm{Mo}(\mathrm{EDTA})] \mathrm{ClO}_{4}\):

Step 1: Identify the central metal ion and its- ligands

The central metal ion is \(\mathrm{Mo}\) (molybdenum) and its ligand is one \(\mathrm{EDTA}\) (ethylenediaminetetraacetic acid) group.

Step 2: Determine the charge on the central metal ion

We know that \(\mathrm{EDTA}\) has a charge of -4 and that the overall charge on the complex is neutral. Therefore, the charge on the molybdenum ion can be determined as: \(0 + 4 = +4\) Thus, Molybdenum is in the +4 oxidation state.

Step 3: Calculate the number of \(d\) electrons associated with the central metal ion

In its ground state, Molybdenum has the electron configuration \(\mathrm{[Kr]4d^55s^1}\). When it forms a +4 oxidation state, it loses 4 electrons: one from \(\mathrm{5s}\) and three from \(\mathrm{4d}\). Therefore, the number of \(d\) electrons associated with the central metal ion is 2. (e) \(\mathrm{K}_{3}\left[\mathrm{ReCl}_{6}\right]\):

Step 1: Identify the central metal ion and its ligands

The central metal ion is \(\mathrm{Re}\) (rhenium) and its ligands are six \(\mathrm{Cl}\) (chloride) ions.

Step 2: Determine the charge on the central metal ion

We know that each \(\mathrm{Cl}\) ion has a charge of -1 and that there are 3 \(\mathrm{K}\)+ ions with a charge of +1 each present in the complex. Therefore, the charge on the rhenium ion can be determined as: \(3 - 6 \times 1 = +3\) Thus, Rhenium is in the +3 oxidation state.

Step 3: Calculate the number of \(d\) electrons associated with the central metal ion

In its ground state, Rhenium has the electron configuration \(\mathrm{[Xe]4f^{14} 5d^56s^2}\). When it forms a +3 oxidation state, it loses 3 electrons: two from \(\mathrm{6s}\) and one from \(\mathrm{5d}\). Therefore, the number of \(d\) electrons associated with the central metal ion is 4.

Key Concepts

d Electron Count

The 'd electron count' is a crucial factor in understanding the behavior of transition metal complexes. It determines the electronic structure of the central metal ion, which directly influences the properties of the complex, such as color, magnetism, and reactivity. The d electron count is determined by first establishing the oxidation state of the metal ion and then subtracting the number of electrons it loses upon ionization from its ground state d electron configuration.

Importance of Correct d Electron Count

Understanding the d electron count allows chemists to predict the geometric and electronic configuration of complexes, which is essential for designing new materials and catalysts.

Oxidation States of Transition Metals

Transition metals can exhibit a variety of oxidation states, which are integral to the reactivity and stability of their complexes. The oxidation state is the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100% ionic. It is represented conventionally by a Roman numeral and can be positive, negative, or zero. Transition metals are known for their ability to have multiple oxidation states due to the close energy levels of their d and s orbitals.

Role of Oxidation States

Oxidation states influence the color, magnetic behavior, and reactivity of transition metal complexes. High oxidation states are usually associated with oxidizing behavior, while lower oxidation states may render metals more reducing.

Ligand Field Theory

Ligand Field Theory (LFT) is an essential concept in coordination chemistry that explains the electronic structure of complexes. LFT extends the ideas of crystal field theory by considering the metal-ligand bonds as being more covalent than ionic. It helps to describe the splitting of d orbitals in a transition metal ion under the influence of the electric field created by surrounding ligands.

Simplified Explanation of Ligand Field Splitting

According to LFT, ligands approach the central metal ion, and depending on their geometry, d orbitals experience different extents of energy splitting. This splitting can significantly affect the physical and chemical properties of the complex.

Coordination Chemistry

Coordination chemistry is the study of compounds formed between metal ions and one or more ligands. These compounds are characterized by the coordinate covalent bonds between the central metal ion and the ligands. Ligands can be ions or molecules and may donate one or more pairs of electrons to the metal ion.

Significance of Coordination Compounds

Coordination compounds have diverse applications, ranging from industrial catalysts to biological systems. They are also crucial in biochemical processes such as oxygen transport and enzyme functions. A deep understanding of coordination chemistry is not only valuable for chemistry students but also for professionals in research and industry.