Problem 24 - Chemistry and Chemical Reactivity

Question

Give the oxidation number of the metal ion in each of the following compounds. (a) \(\left[\mathrm{Mn}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{SO}_{4}\) (c) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl}\) (b) \(\mathrm{K}_{3}\left[\mathrm{Co}(\mathrm{CN})_{6}\right]\) (d) \(\mathrm{Cr}(\mathrm{en})_{2} \mathrm{Cl}_{2}\)

Step-by-Step Solution

Answer

(a) Mn = +2; (b) Co = +3; (c) Co = +3; (d) Cr = +2.

Step 1: Understanding Coordination Compounds

Coordination compounds consist of a central metal ion bonded to ligands. The oxidation number of the metal ion can be determined by considering the charges of the ligands and the overall charge of the compound.

Step 2: Calculate oxidation number for Mn in [Mn(NH3)6]SO4

The complex ion is \([\mathrm{Mn(NH_3)_6}]^{2+}\) since \(\mathrm{SO_4}^{2-}\) has a charge of \(-2\). Ammonia (\(\mathrm{NH_3}\)) carries no charge. The oxidation number of \(\mathrm{Mn}\) must balance the \(+2\) charge of the ion: \(\text{Oxidation number of Mn} = +2\).

Step 3: Calculate oxidation number for Co in K3[Co(CN)6]

The complex ion is \([\mathrm{Co(CN)_6}]^{3-}\) because each \(\mathrm{K}^+\) has a \(+1\) charge and there are three \(\mathrm{K}\) ions. Cyanide (\(\mathrm{CN}^{-}\)) has a charge of \(-1\) each. The \(\mathrm{Co}\) oxidation number must balance the \(-6\) total from the cyanides to result in \(-3\): \(\text{Oxidation number of Co} = +3\).

Step 4: Calculate oxidation number for Co in [Co(NH3)4Cl2]Cl

The complex ion is \([\mathrm{Co(NH_3)_4Cl_2}]^{+}\) since \(\mathrm{Cl}^{-}\) has a charge of \(-1\). Ammonia (\(\mathrm{NH_3}\)) is neutral while chloride (\(\mathrm{Cl}^{-}\)) has a \(-1\) charge, contributing \(-2\) total. The oxidation number of \(\mathrm{Co}\) must balance to result in \(+1\): \(\text{Oxidation number of Co} = +3\).

Step 5: Calculate oxidation number for Cr in Cr(en)2Cl2

The compound has no net charge. Ethylenediamine (en) is neutral, contributing no charge, while each chloride (\(\mathrm{Cl}^{-}\)) contributes \(-1\), totaling \(-2\). The oxidation number of \(\mathrm{Cr}\) must balance the \(-2\) to zero: \(\text{Oxidation number of Cr} = +2\).

Key Concepts

Oxidation Number Calculation

In coordination chemistry, calculating the oxidation number of a metal ion is crucial for understanding the nature of the compound. The oxidation number represents the total charge the metal would have if all ligands were removed along with the pairs of electrons they share with the metal. To determine this number, consider the following steps:

• Identify the overall charge of the complex, if provided; this charge is often indicated at the end of the chemical formula inside square brackets.
• Determine the charges on the ligands attached to the metal. Each ligand can either be neutral or charged. Common ligands include ammonia (\(\mathrm{NH_3}\)), which is neutral, and chloride (\(\mathrm{Cl^-}\)), which carries a \(-1\) charge.
• Calculate the total charge contribution by the ligands. This is done by multiplying the individual ligand's charge by its quantity in the complex.
• Use the formula: \[\text{Total Charge} = \text{Metal Oxidation Number} + \text{Total Ligand Charges}\] to find the oxidation number of the metal.

Understanding this process allows one to predict the chemical behavior of the compound and its possible reactions.

Transition Metal Complexes

Transition metal complexes play a vital role in coordination chemistry. These are compounds where a central metal ion binds to surrounding molecules or ions, termed ligands. The transition metals, found in the middle of the periodic table, possess partially filled d orbitals, which allow them to form various structures and participate in unique reactions.
Transition metal complexes can exhibit different coordination numbers which refer to the number of ligand bonds that the central metal can accommodate. For example, a coordination number of 6, as seen in \([\mathrm{Mn(NH_3)_6}]^{2+}\), denotes a typical octahedral geometry.
These complexes possess unique properties such as color and magnetism due to the electron transitions in their d orbitals. This quality makes them crucial in industrial applications and biological systems, like hemoglobin in the human body.

Ligands and Charges

Ligands are atoms, ions, or molecules that donate pairs of electrons to the central metal ion in a coordination complex. The effectiveness of a ligand is often determined by its charge and the availability of electrons to share.

• Neutral ligands, like \(\mathrm{NH_3}\) (ammonia) and \(\mathrm{en}\) (ethylenediamine), carry no net charge and thus do not contribute to the net charge of the complex.
• Anionic ligands, such as \(\mathrm{Cl^-}\) (chloride) and \(\mathrm{CN^-}\) (cyanide), carry negative charges and will increase the net charge of the complex negatively.

The role of these ligands extends beyond charge balance; they significantly affect the metal's oxidation state, geometry, and overall reactivity. In complex \([\mathrm{Co(NH_3)_4Cl_2}^+]\), the ammonia ligands are neutral, while chloride ions contribute negatively, influencing the cobalt's oxidation state. Thus, understanding ligands and their charges is crucial for predicting the stability and chemical behavior of coordination complexes.