Problem 43 - Chemistry and Chemical Reactivity

Question

For the high-spin complex \(\mathrm{Mn}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2},\) identify the following. (a) the oxidation number of manganese (b) the coordination number for manganese (c) the coordination geometry for manganese (d) the number of unpaired electrons per metal atom (e) whether the complex is diamagnetic or paramagnetic (f) the number of geometric isomers

Step-by-Step Solution

Answer

(a) +2, (b) 6, (c) octahedral, (d) 5, (e) paramagnetic, (f) 2.

Step 1: Determine the Oxidation Number of Manganese

To find the oxidation number of manganese in the complex \(\text{Mn(NH}_3\text{)}_4\text{Cl}_2\), consider the charges. Ammonia \((\text{NH}_3)\) is a neutral ligand, and chloride \((\text{Cl}^-)\) carries a \(-1\) charge. The complex is neutral, thus the sum of all charges in the complex must equal zero. The oxidation state of manganese can be represented as \(x\). We can write the equation: \[x + 4(0) + 2(-1) = 0\]Solving gives:\[x - 2 = 0\]Therefore, the oxidation number of manganese is \(+2\).

Step 2: Determine the Coordination Number of Manganese

The coordination number refers to the number of ligand atoms that are bonded directly to the central metal. In \(\text{Mn(NH}_3\text{)}_4\text{Cl}_2\), there are four ammonia molecules and potentially up to six coordination sites. Given typical bonding, the two chlorides and four amines typically make a coordination number of 6.

Step 3: Determine the Coordination Geometry of Manganese

With a coordination number of 6, the common geometry is octahedral. This complex, with four \(\text{NH}_3\) groups and two \(\text{Cl}^-\) ions, will likely adopt this geometry.

Step 4: Find the Number of Unpaired Electrons

We know the oxidation state of manganese is \(+2\), so its electron configuration is [Ar] \(3d^5\). For a high-spin complex, all \(d\)-orbitals are singly occupied to minimize electron repulsion. Therefore, there are 5 unpaired electrons.

Step 5: Assess Magnetism of the Complex

A complex with unpaired electrons is paramagnetic, while one with all paired electrons is diamagnetic. In this case, \(\text{Mn}^{2+}\) has 5 unpaired electrons, so the complex is paramagnetic.

Step 6: Determine the Number of Geometric Isomers

Geometric isomers are possible when different arrangements of ligands provide distinct structures. This complex has an octahedral geometry with two different types of ligands. Two types of isomerism are possible: cis and trans, resulting in 2 geometric isomers.

Key Concepts

Oxidation Number

The oxidation number indicates how many electrons an atom has gained or lost compared to its elemental state. It's crucial in understanding how atoms bond within a compound. In coordination complexes like \( \text{Mn(NH}_3\text{)}_4\text{Cl}_2 \), calculating the oxidation number involves looking at the charges of the ligands. Ammonia \((\text{NH}_3)\) is a neutral ligand, contributing zero to the charge balance, while each chloride ion \((\text{Cl}^-)\) contributes a charge of \(-1\).
To find the oxidation number of manganese, we sum these contributions to equal the neutral charge of the entire complex, leading us to the equation \( x + 4(0) + 2(-1) = 0 \). Solving for \( x \), the oxidation number for manganese is \(+2\).
Understanding oxidation numbers helps us predict the behavior of substances in chemical reactions, as they often hint at how molecules might interact or rearrange.

Coordination Number

The coordination number is the total number of ligand atoms directly attached to the central metal ion in a complex. It gives us insight into the spatial structure of coordination compounds. For \( \text{Mn(NH}_3\text{)}_4\text{Cl}_2 \), the manganese atom, as the central metal, connects to six ligand atoms: four from ammonia and two from chloride ions.
This setup follows a common coordination number of 6, typically resulting in an octahedral geometry. Calculating the coordination number helps determine how a metal will interact with ligands and predicts the geometry and stability of the complex. Knowing this can be essential in fields like medicinal chemistry, where the shape of a molecule affects its biological activity.

Unpaired Electrons

Unpaired electrons in an atom or a molecule show up when not all electrons are paired in an orbital. In coordination chemistry, the number of unpaired electrons affects the magnetic properties of a compound.
For the manganese complex \( \text{Mn(NH}_3\text{)}_4\text{Cl}_2 \), with an oxidation state of \(+2\), manganese has a \(3d^5\) electron configuration. In a high-spin scenario, this means all five \(d\)-orbitals contain unpaired electrons, as is usual when minimizing electron repulsion. Identifying unpaired electrons helps in determining the paramagnetic or diamagnetic nature of a compound and can further predict reactivity and interaction tendencies.

Paramagnetism

Paramagnetism is a form of magnetism that occurs due to unpaired electrons in a chemical species. Compounds with unpaired electrons are attracted by external magnetic fields, which is the case for our example, \( \text{Mn(NH}_3\text{)}_4\text{Cl}_2 \).
Manganese in this complex has 5 unpaired electrons, making it paramagnetic. This means an external magnetic field can influence the compound, aligning these unpaired electrons and generating a magnetic effect. Paramagnetic compounds often play roles in various applications, such as magnetic resonance imaging (MRI), where their magnetic properties are crucial.
Recognizing whether a compound is paramagnetic or diamagnetic provides insight into its potential uses and behaviors in experimental and technological contexts.