Problem 71 - Chemistry and Chemical Reactivity

Question

Three geometric isomers are possible for \(\left[\mathrm{Co (\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right]^{3+} .\) One of the three is chiral; that is, it has a non-superimposable mirror image. Draw the structures of the three isomers. Which one is chiral?

Step-by-Step Solution

Answer

The cis-cis isomer of \([\text{Co(en)}(\text{NH}_3)_2(\text{H}_2\text{O})_2]^{3+}\) is chiral.

Step 1: Understand the Coordination Complex

The complex given is \( [\text{Co(en)}(\text{NH}_3)_2(\text{H}_2\text{O})_2]^{3+} \). In this complex, Co is the central metal atom, 'en' is ethylenediamine (a bidentate ligand), and \(\text{NH}_3\) and \(\text{H}_2\text{O}\) are monodentate ligands. Ethylenediamine can bind to the metal at two positions, making it a bidentate ligand, which is important for determining the isomers.

Step 2: Determine Possible Geometric Isomers

The number of possible isomers is determined by the arrangement of ligands around the central metal. The complex is of the type \([\text{MABC}_2]\), where ethylenediamine (\text{en}) plays a crucial role.- **cis-\(\text{cis}\)** configuration: Both ammine ligands and both water molecules are adjacent to each other.- **trans-\(\text{cis}\)** configuration: Both ammine ligands are adjacent (cis), and both water molecules are opposite each other (trans).- **trans complex**: When both pairs of ligands have their own bonds positioned farthest from the other pairs (trans-positioned).

Step 3: Visualizing the Isomers

To represent these geometries, consider that the \(\text{Co}(III)\) has an octahedral coordination geometry. Draw the structure:\1. For the **cis-cis** isomer, place the two \(\text{NH}_3\) molecules cis to each other and likewise for the \(\text{H}_2\text{O}\).2. For the **trans-cis** isomer, place the two \(\text{NH}_3\) cis to each other and the two \(\text{H}_2\text{O}\) trans to each other.3. For the **trans** complex, arrange the ligands such that each ligand pair type is across from its pair type partner (both \(\text{NH}_3\) and \(\text{H}_2\text{O}\) are trans to each other).

Step 4: Identify the Chiral Isomer

A chiral complex lacks a plane of symmetry and is not superimposable with its mirror image. Among the three, the **cis-cis** arrangement results in a chiral compound because there is no internal line of symmetry that will make its mirror image superimposable. The other configurations (trans-cis and trans) have symmetry planes, thus making them achiral.

Key Concepts

Geometric Isomers

In coordination chemistry, geometric isomers are isomers that have the same types and numbers of atoms, but differ in their spatial arrangement around a central metal ion. This is particularly important in complexes with multiple types of ligands, like those with octahedral coordination. In the given complex,

• "cis" configuration means ligands are adjacent to each other, and
• "trans" configuration means ligands are opposite each other.

For the complex \([\mathrm{Co(\mathrm{en})(\mathrm{NH}_{3})_{2}(\mathrm{H}_{2} \mathrm{O})_{2}]^{3+}\), the isomers manifest as follows:

• **cis-cis**: Adjacent \(\mathrm{NH}_3\) and \(\mathrm{H}_2\mathrm{O}\) molecules, providing opportunities for chiral arrangements.
• **trans-cis**: Adjacent \(\mathrm{NH}_3\) molecules, with \(\mathrm{H}_2\mathrm{O}\) on opposite sides, eliminating chirality due to symmetry.
• **trans**: Each ligand type across from the other type, resulting in symmetrical and achiral geometry.

Chirality

Chirality in coordination compounds refers to the property where a complex is not superimposable on its mirror image, much like left and right hands. This characteristic is essential for determining which geometric isomers are chiral. In the context of octahedral coordination,

• a chiral complex does not possess a plane of symmetry.
• The structure appears asidesuitably arranged in a manner that the mirror images are distinct objects.

In the exercise, the cis-cis isomer of \( [\text{Co(en)}(\text{NH}_3)_2(\text{H}_2\text{O})_2]^{3+} \) emerges as chiral because it doesn't have a symmetry plane that could overlap the isomer with its mirror image upon reflection. This absence of a symmetry plane is the hallmark of chirality for this particular isomer.

Bidentate Ligands

Bidentate ligands are special types of ligands that can attach to a central metal at two separate locations simultaneously. This makes such ligands particularly influential in determining the possibilities of geometric isomers and chirality in coordination complexes. The complex in the exercise,

• involves ethylenediamine ("en"), a classic bidentate ligand known for forming stable chelate rings around central metal ions.

When a bidentate ligand like ethylenediamine participates in a coordination complex, it can result in enhanced structural stability due to the chelate effect. The ligand wraps around the metal ion, making it difficult for the coordinating atoms to displace and increasing the overall kinetic and thermodynamic stability of the complex.

Octahedral Coordination

Octahedral coordination geometry involves a central metal ion surrounded by ligands in a symmetrical six-ligand arrangement. In this specific geometric arrangement, ligands occupy the vertices of an octahedron. This geometry is predominant for coordination complexes involving transition metals because

• it allows for maximum spatial distribution and coordination number increase.
• The presence of multiple instances of geometric isomerism such as cis and trans formations is possible.

In our exercise, the octahedral geometry of the \(\mathrm{Co(\mathrm{en})(\mathrm{NH}_{3})_{2}(\mathrm{H}_{2} \mathrm{O})_{2}]^{3+}\) complex allows for different geometric isomers through ligand arrangement modification around the central cobalt ion. Not only does octahedral coordination allow multiple isomers, but it also influences the potential for chirality based on the lack of symmetry in the **cis-cis** isomer, making it particularly versatile and fascinating in coordination chemistry.