Problem 10 - Chemistry and Chemical Reactivity

Question

Give the oxidation number of the metal ion in each of the following complexes. (a) \(\left[\mathrm{Fe}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\) (c) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5}\left(\mathrm{NO}_{2}\right)\right]^{+}\) (b) \(\left[\mathrm{Zn}(\mathrm{CN})_{4}\right]^{2-}\) (d) \(\left[\mathrm{Cu}(\mathrm{en})_{2}\right]^{2+}\)

Step-by-Step Solution

Answer

(a) +2, (b) +3, (c) +2, (d) +2

Step 1: Determine Oxidation Number for (a)

In the complex \([\mathrm{Fe}(\mathrm{NH}_{3})_{6}]^{2+}\), ammonia \((\mathrm{NH}_{3})\) is a neutral ligand, contributing 0 to the overall charge. So, the oxidation state of iron must be +2 to match the charge on the ion: \[\text{Charge of complex} = +2 = \text{Oxidation state of Fe} + 6 \times 0 \] Thus, Iron (Fe) has an oxidation number of +2.

Step 2: Determine Oxidation Number for (b)

In the complex \([\mathrm{Co}(\mathrm{NH}_{3})_{5}(\mathrm{NO}_{2})]^{+}\), ammonia \((\mathrm{NH}_{3})\) contributes 0, and \(\mathrm{NO}_{2}\) as a unidentate ligand is considered as \(\mathrm{NO}_{2}^{-}\) contributing -1. With overall charge being +1, we get: \[\text{Charge of complex} = +1 = \text{Oxidation state of Co} + 5 \times 0 - 1\] Solving gives \(\text{Oxidation state of Co} = +3.\) Co has an oxidation number of +3.

Step 3: Determine Oxidation Number for (c)

For the complex \([\mathrm{Zn}(\mathrm{CN})_{4}]^{2-}\), each cyanide \((\mathrm{CN}^{-})\) contributes -1. Therefore, the equation is:\[\text{Charge of complex} = -2 = \text{Oxidation state of Zn} + 4 \times (-1)\]Solving gives: \(\text{Oxidation state of Zn} = +2.\) Hence, Zn has an oxidation number of +2.

Step 4: Determine Oxidation Number for (d)

In the complex \([\mathrm{Cu}(\mathrm{en})_{2}]^{2+}\), each \(\mathrm{en}\) (ethylene diamine) is a neutral ligand, contributing 0. The overall charge is +2, giving:\[\text{Charge of complex} = +2 = \text{Oxidation state of Cu} + 2 \times 0\]Thus, the oxidation state of Copper (Cu) is +2.

Key Concepts

Oxidation State

The concept of oxidation state, or oxidation number, is essential in the realm of coordination chemistry. It refers to the formal charge of an atom if all the bonds it forms with other atoms are assumed to be completely ionic. In coordination complexes, oxidation states help us ascertain the distribution of electrons between the metal center and the surrounding ligands. To determine the oxidation state of a metal in a complex, you can use the following general steps:

• Identify all ligands attached to the metal and their respective charges.
• Sum up the total known charges of these ligands.
• Subtract this total from the overall charge of the complex.
• The remaining value is the oxidation state of the metal ion.

This calculation aids chemists in understanding the electronic structure and reactivity of metal complexes.

Metal Complexes

Metal complexes, also known as coordination compounds, consist of a central metal atom or ion surrounded by molecules or anions, termed ligands. These complexes are ubiquitous in nature and technology, playing critical roles in processes like catalysis, biological systems, and material science. In these complexes:

• The metal serves as the Lewis acid, accepting electron pairs from the ligands.
• Ligands are the Lewis bases, donating pairs of electrons.
• Complexes can have a variety of coordination numbers, depending on the number of ligand atoms directly bonded to the central metal atom.

Understanding metal complexes is crucial as it provides insights into their bonding, geometry, and reactivity which influences their chemical and physical properties.

Neutral Ligand

In coordination chemistry, ligands are classified based on their charge:

• Neutral ligands carry no charge and do not contribute to the overall charge of the metal complex. Common examples include molecules like ammonia (\(\mathrm{NH}_3\)).
• Anionic ligands are negatively charged, therefore contributing negative charges to the complex.
• Cationic ligands are positively charged, contributing positive charges to the complex—though less common.

When neutral ligands coordinate with a metal center, they don't alter the charge of the metal ion. Therefore, their inclusion in charge calculations focuses solely on the metal's oxidation state and the charge contributions of any anionic or cationic ligands present.

Charge Calculation

Charge calculations in metal complexes are vital for determining the oxidation state of the central metal. This process involves:

• Recognizing the overall charge presented on the complex given its chemical formula (e.g., \([\mathrm{Cu}(\mathrm{en})_2]^{2+}\)).
• Identifying each ligand's charge, particularly anionic ones, and tallying up their collective charges.
• The calculation involves setting up an equation where the oxidation state of the metal, summed with the total ligand charges, equals the complex's net charge.

By solving this equation, chemists establish the oxidation state of metals within complex structures, providing essential insight into their valency and chemical behavior. This calculus is crucial in predicting chemical reactions and properties of coordination compounds.