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

Mn oxidation number is +2, coordination number is 6, geometry is octahedral, 5 unpaired electrons, it is paramagnetic, and has 2 geometric isomers.

Step-by-step solution

Identify the Oxidation Number of Manganese

The compound is given as \( \mathrm{Mn}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2} \). Ammonia \((\mathrm{NH}_3)\) is a neutral ligand, so it does not contribute to the oxidation state. Each chloride ion \((\mathrm{Cl}^-)\) carries a -1 charge. To find the oxidation state of Mn, set the sum of the charges to zero: \( \text{oxidation number of Mn} + 4(0) + 2(-1) = 0 \). Thus, the oxidation state of Mn is +2.

Determine the Coordination Number for Manganese

The coordination number is determined by counting the number of ligand donor atoms directly bonded to the metal center. In \( \mathrm{Mn}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2} \), there are four ammonia ligands and two chloride ions, yielding a total coordination number of 6 for Mn.

Establish the Coordination Geometry for Manganese

For a coordination number of 6, the most common geometry is octahedral. Thus, the coordination geometry of manganese in this compound is octahedral.

Find the Number of Unpaired Electrons per Metal Atom

Manganese in this compound is in the +2 oxidation state, which means it has the electron configuration \([\mathrm{Ar}] 3d^5\). In a high-spin octahedral complex, all five 3d orbitals are singly occupied, resulting in 5 unpaired electrons.

Determine if the Complex is Diamagnetic or Paramagnetic

A paramagnetic complex contains unpaired electrons, while a diamagnetic complex does not. With 5 unpaired electrons, \(\mathrm{Mn}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\) is paramagnetic.

Count the Number of Geometric Isomers

For octahedral complexes such as this, consider the number of ways ligands can be arranged. In \( \mathrm{Mn}(\mathrm{NH}_3)_4 \mathrm{Cl}_2 \), the \(\mathrm{NH}_3\) and \(\mathrm{Cl}\) ligands can exist in either trans (opposite sides) or cis (adjacent) configurations, leading to two geometric isomers.

Key concepts

Oxidation Number

The oxidation number of an atom in a compound represents the total number of electrons it has gained or lost to form that compound. In our high-spin coordination compound, \( \mathrm{Mn(\mathrm{NH}_3)_4\mathrm{Cl}_2} \), finding the oxidation number of manganese involves analyzing the charges of the ligands attached to it. Here's how you calculate:

• Ammonia (\(\mathrm{NH}_3\)) is neutral and does not contribute to the oxidation state.
• Chloride ions (\(\mathrm{Cl}^-\)) are charged negatively at -1 each.

Set the equation to zero, considering two negative charges from chloride: \ \[ \text{oxidation number of Mn} + 2(-1) = 0 \]By solving, you find that manganese must have an oxidation number of +2. This step helps zero in on the electronic environment of manganese and how it interacts with its surrounding atoms.

Coordination Number

The coordination number determines how many ligand atoms are bonded directly to the central metal atom in a complex. For our coordination compound, \( \mathrm{Mn(\mathrm{NH}_3)_4\mathrm{Cl}_2} \), the coordination number is found by counting the ligands around manganese.

• There are four ammonia ligands, each contributing one donor atom to bind to the metal.
• There are two chloride ions, each also providing a single donor atom.

Adding these gives a coordination number of 6 for manganese. This number is crucial for understanding the spatial arrangement and potential reactivity of the complex.

Coordination Geometry

Coordination geometry refers to the spatial arrangement of ligand atoms around the central metal atom in a complex. For a coordination number of 6, the most prevalent geometry is octahedral. In the compound \( \mathrm{Mn(\mathrm{NH}_3)_4\mathrm{Cl}_2} \), manganese sits at the center with ligands forming the vertices of an octahedron. This arrangement:

• Maximizes ligand interactions around the metal.
• Optimizes the stability and symmetry of the compound.

Understanding this geometry helps predict the chemical behavior and reactivity patterns of the complex.

Unpaired Electrons

In coordination chemistry, the number of unpaired electrons in a metal atom significantly influences properties like magnetism. Manganese in \( \mathrm{Mn(\mathrm{NH}_3)_4\mathrm{Cl}_2} \) is in the +2 oxidation state, leading to an electronic configuration of \ \[ [\mathrm{Ar}] 3d^5 \]In a high-spin octahedral field, these d-orbitals remain singly occupied due to weak ligand field splitting, having:

• Five unpaired electrons.

Unpaired electrons are essential for explaining magnetic properties and transitions in these compounds.

Paramagnetic vs Diamagnetic Properties

The magnetic behavior of coordination complexes depends on their electronic structure. A complex is paramagnetic if it contains unpaired electrons, and diamagnetic if all electrons are paired. In our compound \( \mathrm{Mn(\mathrm{NH}_3)_4\mathrm{Cl}_2} \), the presence of five unpaired electrons means it is paramagnetic.

• Paramagnetic substances are attracted to magnetic fields.
• Diamagnetic substances are repelled by magnetic fields.

Knowing whether a compound is paramagnetic or diamagnetic informs us about its interactions with magnetic fields, which is crucial in various applications, from materials science to medicine.

Geometric Isomers

Geometric isomerism occurs when ligands in a coordination complex can be positioned differently around the central atom. In \( \mathrm{Mn(\mathrm{NH}_3)_4\mathrm{Cl}_2} \), the presence of four ammonia and two chloride ligands leads to possibilities of cis and trans arrangements:

• "Cis" isomers have similar ligands adjacent to each other.
• "Trans" isomers have these ligands positioned opposite each other.

This results in two geometric isomers. Identifying these isomers is vital for understanding the different physical and chemical properties they may exhibit, such as differences in ligand reactivities or optical activities.