Question

For the high-spin coordination compound \(\mathrm{Mn}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\) 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

Short answer

Oxidation number: +2, Coordination number: 6, Geometry: Octahedral, Unpaired electrons: 5, Paramagnetic, 2 isomers.

Step-by-step solution

Determine the oxidation number of manganese

In the complex \( \mathrm{Mn(NH}_3)_4 \mathrm{Cl}_2 \), ammonia (\( \mathrm{NH}_3 \)) is a neutral ligand and chloride (\( \mathrm{Cl}^- \)) has a charge of -1. The compound is neutral, so the sum of all charges must be zero. Let the oxidation state of Mn be \( x \). Thus,\[ x + 4(0) + 2(-1) = 0 \] Simplifying gives \( x = +2 \). Therefore, the oxidation number of manganese is +2.

Determine the coordination number

The coordination number is defined by the number of ligand atoms directly bonded to the central metal atom. In \( \mathrm{Mn(NH}_3)_4 \mathrm{Cl}_2 \), manganese is directly bonded to four ammonia ligands and two chloride ions, totaling a coordination number of 6.

Determine the coordination geometry

With a coordination number of 6, the typical geometry is octahedral, which is common for transition metals with this coordination number. Therefore, the coordination geometry for manganese in this compound is octahedral.

Determine the number of unpaired electrons

Manganese has an electron configuration of \([\text{Ar}] 3d^5 4s^2\). With an oxidation state of +2, it loses 2 electrons, resulting in \([\text{Ar}] 3d^5\). In a high-spin octahedral complex, the electrons will remain unpaired in the \(3d\) orbitals, yielding 5 unpaired electrons.

Determine if the complex is diamagnetic or paramagnetic

Since \( \mathrm{Mn(NH}_3)_4 \mathrm{Cl}_2 \) has 5 unpaired electrons, it is paramagnetic. Paramagnetic compounds contain unpaired electrons and are attracted to magnetic fields.

Determine the number of geometric isomers

In an octahedral complex like \( \mathrm{Mn(NH}_3)_4 \mathrm{Cl}_2 \), geometric isomers arise from different arrangements of ligands. Possible arrangements include having the two chloride ions adjacent (cis) or opposite (trans) to each other. Thus, there are 2 geometric isomers.

Key concepts

Oxidation State

Understanding the oxidation state in coordination compounds is crucial for predicting their reactivity and properties. The oxidation state indicates the charge of the central metal atom when all bonds are broken, assuming all ligands are removed as neutral fragments. In chemistry, oxidation state helps in understanding the electron count, and thus the electron configuration, of the metal ion.

For the complex \( \mathrm{Mn(NH}_3)_4 \mathrm{Cl}_2 \), manganese is the central metal. Ammonia (\( \mathrm{NH}_3 \)) is a neutral ligand, contributing zero charge, while each chloride ion (\( \mathrm{Cl}^- \)) carries a \(-1\) charge. To find the oxidation state of manganese, let's assume it is \( x \). The compound is neutral, hence \( x + 4(0) + 2(-1) = 0 \). Solving this gives us \( x = +2 \). This means manganese has an oxidation state of +2, having lost two electrons. This loss of electrons affects its electron configuration and properties, making this information particularly useful for further analysis of the compound's behavior.

Coordination Number

The coordination number is a fundamental concept in understanding the structure of coordination compounds. It is defined as the number of ligand atoms directly attached to the central metal ion. This number provides insights into the geometry and overall shape of the compound.

In the \ coordination compound \( \mathrm{Mn(NH}_3)_4 \mathrm{Cl}_2 \), manganese is coordinated to four ammonia molecules and two chloride ions. Each of these ligands occupies a coordination site. Consequently, the coordination number for manganese in this compound is calculated as 4 (ammonia) + 2 (chloride) = 6. A coordination number of 6 is common in transition metals and typically leads to an octahedral geometry, which will be discussed in the next sections.

Knowing the coordination number is essential for predicting not only the compound's structure but also its reactivity and potential uses in various chemical applications.

Magnetism in Complexes

Magnetism is a fascinating property that hinges on the electron configuration of a compound. In coordination chemistry, the presence of unpaired electrons in d-orbitals dictates whether a complex is paramagnetic or diamagnetic.

For \( \mathrm{Mn(NH}_3)_4 \mathrm{Cl}_2 \), manganese has a base electron configuration of \([\text{Ar}] 3d^5 4s^2\). In its +2 oxidation state, it loses two electrons, resulting in \([\text{Ar}] 3d^5\), where all five 3d electrons remain unpaired. Because this complex is described as high-spin, the electrons do not pair up, resulting in five unpaired electrons.

This results in a strong magnetic moment, making the complex paramagnetic. Paramagnetic compounds are attracted to magnetic fields, which is a stark contrast to diamagnetic compounds that have all electrons paired and are slightly repelled by magnetic fields. The magnetic property of these complexes is greatly significant in material science and technological applications, such as designing magnetic materials.

Geometric Isomerism

Geometric isomerism in coordination compounds occurs due to different possible spatial arrangements of ligands around the central metal ion. These arrangements lead to isomers having the same formula but distinct geometric configurations, influencing the compound’s properties.

In the case of \( \mathrm{Mn(NH}_3)_4 \mathrm{Cl}_2 \), which adopts an octahedral geometry due to its coordination number of 6, the chlorine ions can be positioned differently. The two primary geometric isomers here are the "cis" and "trans" arrangements. In the cis arrangement, the two chloride ligands are adjacent to each other, whereas in the trans arrangement, they are opposite each other. These configurations affect how each isomer interacts with other molecules, potentially leading to differences in reactivity and physical properties, such as solubility and boiling points.

Understanding geometric isomerism is vital in fields like pharmacology, where different isomers can have vastly different biological activities. It also plays a critical role in catalysis and materials design.