Question

The total number of all possible isomers of \( [\text{Co}( \text{H}_2\text{NCH}_2\text{CH}_2\text{NH}_2)_2 ]^{2+} \) and \( [\text{Co}( \text{H}_2\text{NCH}_2\text{CH}_2\text{NH}_2)_3 ]^{3+} \) together is ............
 

Hint:

For coordination complexes with ligands having multiple donor atoms, count the possible ways the ligands can be arranged around the central metal to determine the total number of isomers.

Answer 1

Correct Answer: 5

1. Isomers of $\mathbf{[\text{Co}(\text{en})_2\text{Cl}_2]^{+}}$ ($\text{M}(\text{AA})_2\text{X}_2$ type)

The complex $\mathbf{[\text{Co}(\text{H}_2\text{NCH}_2\text{CH}_2\text{NH}_2)_2\text{Cl}_2]^{+}}$ has the general form $\text{M}(\text{AA})_2\text{X}_2$, where $\text{AA}$ is the bidentate ligand ethylenediamine ($\text{en}$) and $\text{X}$ is $\text{Cl}^{-}$. This octahedral complex exhibits two types of stereoisomerism: geometrical and optical.

Geometrical Isomers: Two are possible:

$\text{cis}$ isomer: The two chloride ligands ($\text{Cl}$) are adjacent to each other.

$\text{trans}$ isomer: The two chloride ligands ($\text{Cl}$) are opposite to each other.

Optical Isomers (Enantiomers):

The $\text{trans}$ isomer has a plane of symmetry and is achiral (no optical isomers).

The $\text{cis}$ isomer lacks a plane of symmetry and is chiral, existing as a pair of non-superimposable mirror images (a pair of enantiomers).

Isomer Type	Number of Forms
$\text{trans}$ (achiral)	1
$\text{cis}$ (chiral)	2 (enantiomers)
Total Isomers for $\mathbf{[\text{Co}(\text{en})_2\text{Cl}_2]^{+}}$	$\mathbf{3}$

 

2. Isomers of $\mathbf{[\text{Co}(\text{en})_3]^{3+}}$ ($\text{M}(\text{AA})_3$ type)

The complex $\mathbf{[\text{Co}(\text{H}_2\text{NCH}_2\text{CH}_2\text{NH}_2)_3]^{3+}}$ has the general form $\text{M}(\text{AA})_3$. This octahedral complex has only one possible geometrical arrangement (no $\text{cis}/\text{trans}$ isomerism), but it is inherently chiral due to the arrangement of the three bidentate ligands.

Geometrical Isomers: Only one geometrical form is possible.

Optical Isomers (Enantiomers): This form lacks a plane of symmetry and is chiral, existing as a pair of non-superimposable mirror images.

Isomer Type	Number of Forms
$\text{fac}$ (only form) (chiral)	2 (enantiomers)
Total Isomers for $\mathbf{[\text{Co}(\text{en})_3]^{3+}}$	$\mathbf{2}$

3. Total Number of Isomers

The total number of all possible isomers (geometrical and optical) for both complexes together is the sum of the isomers for each complex:

$$\text{Total Isomers} = \text{Isomers for } [\text{Co}(\text{en})_2\text{Cl}_2]^{+} + \text{Isomers for } [\text{Co}(\text{en})_3]^{3+}$$

$$\text{Total Isomers} = 3 + 2 = \mathbf{5}$$

Answer: 5