Problem 55 - Chemistry: The Central Science

Question

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

Step-by-Step Solution

Answer

The number of valence d electrons for the central metal ions in each complex are: (a) \(\mathrm{K}_{3}\left[\mathrm{TiCl}_{6}\right]\): 1 valence d electron for Ti\(^{3+}\) (b) \(\mathrm{Na}_{3}\left[\mathrm{Co}\left(\mathrm{NO}_{2}\right)_{6}\right]\): 6 valence d electrons for Co\(^{3+}\) (c) \(\left[\mathrm{Ru}(e n)_{3}\right] \mathrm{Br}_{3}\): 5 valence d electrons for Ru\(^{3+}\) (d) \([\mathrm{Mo}(\mathrm{EDTA})] \mathrm{ClO}_{4}\): 3 valence d electrons for Mo\(^{3+}\) (e) \(\mathrm{K}_{3}\left[\mathrm{ReCl}_{6}\right]\): 4 valence d electrons for Re\(^{3+}\)

Step 1: Determine the oxidation state of the central metal ion

For each complex, we need to first determine the oxidation state of the central metal ion. To do this, we can consider the charges of the ligands in the complex and the overall charge of the complex.

Step 2: Find the valence d electrons for the metal ion

Once we have the oxidation state of the metal ion, we can use the periodic table to find the number of valence d electrons for that oxidation state. (a) \(\mathrm{K}_{3}\left[\mathrm{TiCl}_{6}\right]\)

Step 1: Determine the oxidation state of Ti

The overall charge of the complex is \(3^+\) (due to the 3 potassium ions). The 6 chloride ligands have a total charge of \(6^-\), so the oxidation state of Ti must be \(3^+\).

Step 2: Find the valence d electrons for Ti\(^{3+}\)

Ti is in group 4, and in the \(3^+\) oxidation state, it has 1 valence d electron. Therefore, the number of valence d electrons for Ti in this complex is 1. (b) \(\mathrm{Na}_{3}\left[\mathrm{Co}\left(\mathrm{NO}_{2}\right)_{6}\right]\)

Step 1: Determine the oxidation state of Co

The overall charge of the complex is \(3^+\) (due to the 3 sodium ions). The 6 nitrite ligands have a total charge of \(6^-\), so the oxidation state of Co must be \(3^+\).

Step 2: Find the valence d electrons for Co\(^{3+}\)

Co is in group 9, and in the \(3^+\) oxidation state, it has 6 valence d electrons. Therefore, the number of valence d electrons for Co in this complex is 6. (c) \(\left[\mathrm{Ru}(e n)_{3}\right] \mathrm{Br}_{3}\)

Step 1: Determine the oxidation state of Ru

The overall charge of the complex is \(3^+\) (due to the 3 bromide ions). Ethylenediamine (en) is a neutral bidentate ligand, so the oxidation state of Ru must be \(3^+\).

Step 2: Find the valence d electrons for Ru\(^{3+}\)

Ru is in group 8, and in the \(3^+\) oxidation state, it has 5 valence d electrons. Therefore, the number of valence d electrons for Ru in this complex is 5. (d) \([\mathrm{Mo}(\mathrm{EDTA})] \mathrm{ClO}_{4}\)

Step 1: Determine the oxidation state of Mo

The overall charge of the complex is \(1^+\) (due to the perchlorate ion). EDTA is a hexadentate ligand with a total charge of \(4^-\), so the oxidation state of Mo must be \(3^+\).

Step 2: Find the valence d electrons for Mo\(^{3+}\)

Mo is in group 6, and in the \(3^+\) oxidation state, it has 3 valence d electrons. Therefore, the number of valence d electrons for Mo in this complex is 3. (e) \(\mathrm{K}_{3}\left[\mathrm{ReCl}_{6}\right]\)

Step 1: Determine the oxidation state of Re

The overall charge of the complex is \(3^+\) (due to the 3 potassium ions). The 6 chloride ligands have a total charge of \(6^-\), so the oxidation state of Re must be \(3^+\).

Step 2: Find the valence d electrons for Re\(^{3+}\)

Re is in group 7, and in the \(3^+\) oxidation state, it has 4 valence d electrons. Therefore, the number of valence d electrons for Re in this complex is 4.

Key Concepts

Oxidation States

The oxidation state of a metal in a complex is crucial for understanding the electron distribution. It indicates how many electrons have been removed or added from the elemental state.
This concept helps in predicting reactivity and bonding.To determine the oxidation state of the central metal ion:

• Identify the charges on all ligands and the overall charge of the complex.
• Sum up those charges, and subtract from the total charge to find the metal's oxidation state.

For example, in the complex \(\mathrm{K}_{3}\left[\mathrm{TiCl}_{6}\right]\), potassium contributes "+1" each, leading to a charge of \(3^+\). Chloride is "-1" per ligand, totaling \(6^-\), thus titanium must be \(+3\).
Understanding oxidation states allows us to explore how metals interact with ligands in various chemical scenarios.

Valence d Electrons

Valence d electrons are the outer electrons of transition metals that participate in bonding. Their count affects color, magnetism, and reactivity of complexes.
These electrons come from the d-orbital, which is critical for forming coordination bonds.Here's how to find valence d electrons:

• Start with the metal's total d electrons from the periodic table.
• Subtract the oxidation state to discover the remaining valence d electrons.

For example, Cobalt (Co) in a \(3^+\) oxidation state (Group 9) starts with 9 d electrons. After subtracting 3 (from electrons lost), it retains 6 d electrons.
This balance of electrons dictates a complex’s properties, making it a central concept in coordination chemistry.

Ligands

Ligands are molecules or ions that bind to central metal ions, creating complexes through coordinate bonds.
They are essential in defining a complex's structure and properties. Traits of ligands include:

• Charge: Ligands can be neutral (e.g., water, ethylenediamine) or charged (e.g., chloride).
• Denticity: Refers to how many donor atoms a ligand uses to bind. Bidentate ligands, like EDTA, use multiple donor sites.

The interaction between ligands and metal ions influences everything from the geometry to the stability of complexes.
Understanding ligands helps us see how they tailor the electronic environment of the metal, thereby affecting overall complex reactivity.