Question

For the low-spin complex [Co(en)(NHs)_SCl_{2} ] \mathrm { ClO } _ { 4 } \text { , } identify the following: (a) the coordination number of cobalt (b) the coordination geometry for cobalt (c) the oxidation number of cobalt (d) the number of unpaired electrons (e) whether the complex is diamagnetic or paramagnetic (f) Draw any geometric isomers.

Short answer

(a) 8; (b) square antiprismatic; (c) +3; (d) 0 unpaired electrons; (e) diamagnetic.

Step-by-step solution

Determine the Ligands and Coordination Number

In the complex \([Co(en)(NH_3)_5Cl_2]ClO_4\), 'en' stands for ethylenediamine, which is a bidentate ligand. It coordinates through two donor atoms. The NH3 and Cl ligands are monodentate. Therefore, the coordination number of cobalt is calculated as follows: ethylenediamine contributes 2, each NH3 contributes 1, and Cl contributes 1. Total: 2 (from en) + 5 (from NH3) + 1 (from Cl) = 8.

Determine Coordination Geometry

A coordination number of 8 typically corresponds to a coordination geometry of a square antiprism or dodecahedron. However, in many coordination complexes, such as this one, the usual geometry is square antiprismatic.

Calculate Oxidation Number

Let the oxidation number of cobalt be \(x\). The charged species can be represented as \( [Co(en)(NH_3)_5Cl_2]^{+}\) because there is one counter ion \(ClO_4^-\). The total charge can be calculated: \(2(0) + 5(0) + 2(-1) + x = +1\). Solving for \(x\), we find: \(x = 3\). Therefore, the oxidation number of cobalt is +3.

Count Unpaired Electrons and Identify Magnetism

\([Co(en)(NH_3)_5Cl_2]ClO_4\) is a low-spin complex due to the presence of strong field ligands \((en, NH_3)\). Cobalt (III) \((3+)\) in a low-spin state has no unpaired electrons in its \(d^6\) configuration, as all electrons are paired in the lower energy orbitals.

Determine Magnetic Property

Since the complex has no unpaired electrons, it is diamagnetic.

Draw Geometric Isomers

For complexes with this structure, we can have geometric isomers based on the spatial arrangement of ligands. Arrange NH3, Cl, and en such that they form different spatial orientations. The presence of strong field ligands (like ethylenediamine) commonly leads to optical isomerism.

Key concepts

Coordination Number

In coordination chemistry, the coordination number refers to the total number of ligand atoms that are directly bonded to the central metal atom or ion in a complex.
This number is crucial because it determines the shape and size of the coordination complex.

In the complex \[ [Co(en)(NH_3)_5Cl_2]ClO_4 \], we have multiple types of ligands:

• 'en' which stands for ethylenediamine and is a bidentate ligand, meaning it attaches to the central metal at two points. So, it contributes 2 to the coordination number.
• Five NH3 ligands, each being monodentate, contributing 1 each.
• A single Cl is also monodentate, contributing 1.

When totaled, the coordination number for cobalt in this complex is \[ 2 (from \, en) + 5 (from \, NH_3) + 1 (from \, Cl) = 8 \]. Understanding the coordination number helps predict the possible spatial arrangement of the ligands around the metal center.

Coordination Geometry

Coordination geometry refers to the spatial arrangement of ligands around a central metal atom in a coordination complex.
It heavily depends on the coordination number. A coordination geometry influences the physical and chemical properties of the complex, such as color and reactivity.

For a coordination number of eight, which we see in the complex \[ [Co(en)(NH_3)_5Cl_2]ClO_4 \], typical geometries include square antiprismatic and dodecahedral formations.
In many cases, specifically with a coordination number of 8, the structure leans towards a square antiprism formation.
This means that ligands will be arranged in a way to minimize repulsion and maximize stability in the three-dimensional space around the metal center.
Envision trying to fit all the ligands around a central point, much like pieces fitting within a puzzle, ensuring each has optimal space.

Oxidation Number

The oxidation number of an element in a complex is an indicator of the degree of oxidation of an atom. It can provide insight into the electron distribution and can influence the compound's reactivity and properties.

For cobalt in \[ [Co(en)(NH_3)_5Cl_2]ClO_4 \], calculating the oxidation number involves setting up an equation based on known charges:

• Ethylenediamine (en) and NH3 are neutral, contributing zero to the charge.
• Each Cl contributes a charge of -1.
• The overall charge of the complex ion is +1, considering the counter ion \[ ClO_4^- \].

The equation linking these is:\[ 2(0) + 5(0) + 2(-1) + x = +1 \], where \(x\) is the oxidation number of cobalt.
Solving this gives \(x = 3\).
Thus, cobalt is in the +3 oxidation state.

Unpaired Electrons

Unpaired electrons in a complex play a significant role in determining its magnetic properties. The number of unpaired electrons directly reflects the electron configuration in the d-orbitals of the metal ion.

In the case of the complex \[ [Co(en)(NH_3)_5Cl_2]ClO_4 \], cobalt is in the +3 oxidation state, which gives it a \(d^6 \) electron configuration. Due to the strong-field ligands present, which are ethylenediamine and NH3, the complex operates as a low-spin complex.
This arrangement pairs electrons within the lower energy t2g orbitals, resulting in no unpaired electrons.
When assessing electron pairing, it’s understanding of ligand strength and configurations that shape whether the complex spins and thus impacts its magnetic properties.

Magnetic Properties

Magnetic properties in coordination complexes arise largely due to the presence or absence of unpaired electrons.
A complex can be either diamagnetic or paramagnetic based on this.

Diamagnetic substances have all their electrons paired, and as a result, they are not attracted to a magnetic field. On the other hand, paramagnetic substances have one or more unpaired electrons and are attracted to a magnetic field.

For the low-spin cobalt complex \[ [Co(en)(NH_3)_5Cl_2]ClO_4 \], strong field ligands like ethylenediamine cause all electrons to pair up in the lower energy d orbitals, resulting in no unpaired electrons.
Thus, this specific complex is noted as being diamagnetic.
This understanding solidifies the idea that strong field ligands decrease the number of unpaired electrons, affecting the magnetism of the complex.

Geometric Isomerism

Geometric isomerism in coordination complexes occurs when the ligands can attach to the metal center in different spatial arrangements, resulting in different isomers with distinct properties even though they have the same formula.

This type of isomerism is highly impactful in terms of the complex's physical and chemical attributes.

For the complex \[ [Co(en)(NH_3)_5Cl_2]ClO_4 \], geometric isomers can form based on various spatial arrangements of the NH3, Cl, and ethylenediamine ligands around the cobalt ion.
While ligands like ethylenediamine often lead to optical isomerism, they also have roles in geometric isomerism, particularly in large coordination numbers like 8.
Understanding how ligands can position themselves offers insights into the diverse characteristics and behaviors in coordination chemistry.