Problem 57 - Chemistry: An Atoms-Focused Approach

Question

Does the complex \(\mathrm{Co}(\mathrm{en})\left(\mathrm{H}_{2} \mathrm{O}\right)_{2} \mathrm{Cl}_{2}\) have stereoisomers?

Step-by-Step Solution

Answer

Answer: The complex \(\mathrm{Co}(\mathrm{en})\left(\mathrm{H}_{2}\mathrm{O}\right)_{2}\mathrm{Cl}_{2}\) has one stereoisomer, which is the cis isomer in octahedral geometry. This is because only a cis configuration, with two chloride ligands and two water molecules occupying adjacent positions, is possible, while the trans configuration doesn't yield a new isomer due to the presence of the ethylenediamine ligand. Enantiomers are absent in this complex as well.

Step 1: Identify the central metal atom and ligands

The central metal atom is Cobalt (Co) and the ligands are ethylenediamine (en), water (H2O), and chloride (Cl).

Step 2: Determine the coordination number

Each ethylenediamine (en) ligand contributes 2 coordination sites (since it is a bidentate ligand), and each H2O and Cl ligand contributes 1 coordination site. So, the coordination number of the complex is 2 (from en) + 2 (from H2O) + 2 (from Cl) = 6.

Step 3: Identify the geometry of the complex

Since the complex has a coordination number of 6, its geometry can be either octahedral or trigonal prismatic. However, the most common coordination geometry for transition metal complexes with a coordination number of 6 is octahedral.

Step 4: Look for possible stereoisomers

In an octahedral complex, we should explore both cis and trans isomer possibilities for the given ligands. We start by looking at the cis isomer, where the two chloride ligands are in the cis position, and the two water molecules are also in the cis position with the ethylenediamine occupying the remaining two sites. This yields a possible isomer. Next, we consider the trans isomer, where two chloride ligands are in a trans position. However, in this case, the ethylenediamine ligand is fixed in its position, and the two water molecules are already cis to each other as well as to the ethylenediamine ligand. Therefore, we don't have any new isomer in the trans configuration. Additionally, since the octahedral complex doesn't possess a center of symmetry or a plane of symmetry (except for the ones involving the ethylenediamine ligand), the complex doesn't have enantiomers. (a pair of non-superimposable mirror images)

Step 5: Conclusion

The complex \(\mathrm{Co}(\mathrm{en})\left(\mathrm{H}_{2}\mathrm{O}\right)_{2}\mathrm{Cl}_{2}\) indeed has one stereoisomer, which is the cis isomer in octahedral geometry. There are no additional stereoisomers, and enantiomers are also absent in this particular complex.