Consider the different types of isomerism in coordination compounds, such as linkage isomerism, ionization isomerism, geometrical isomerism, and optical isomerism.
\(\left[ Co \left( H _2 O \right)_6\right]^{3+}\)
\(\left[ Co \left( NH _3\right)_5 Cl \right]^{+}\)
\(\left[ Co \left( NH _3\right)_5 NO _2\right]^{2+}\)
\(\left[ Co \left( NH _3\right)_5 Cl \right]^{2+}\)
Step 1: Analyze the Complexes for Isomerism
We are looking for a complex cation that exhibits two isomers. Let’s analyze each option:
\([ \text{Co}(\text{H}_2\text{O})_6 ]^{3+}\):
This complex has only one possible structure, as all ligands are the same (\(\text{H}_2\text{O}\)). So, it does not have isomers.
\([ \text{Co}(\text{NH}_3)_5\text{Cl} ]^{2+}\):
This complex can only exhibit ionization isomerism if another counter ion is present within the complex to exchange positions with the \(\text{Cl}\) ligand. With only one \(\text{Cl}\), there’s no possibility of isomerism here.
\([ \text{Co}(\text{NH}_3)_5\text{NO}_2 ]^{2+}\):
This complex can exhibit linkage isomerism because the \(\text{NO}_2\) ligand can coordinate to the metal ion through either the nitrogen atom (nitro isomer) or the oxygen atom (nitrito isomer). Thus, it has two isomers.
\([ \text{Co}(\text{NH}_3)_5\text{Cl} ]^{+}\):
Same explanation as (2), no isomerism is possible
Conclusion
The correct option is (3): \([ \text{Co}(\text{NH}_3)_5\text{NO}_2 ]^{2+}\), which exhibits two isomers (nitro and nitrito isomers).
Method used for separation of mixture of products (B and C) obtained in the following reaction is: 
In the following \(p\text{–}V\) diagram, the equation of state along the curved path is given by \[ (V-2)^2 = 4ap, \] where \(a\) is a constant. The total work done in the closed path is: 
Let \( ABC \) be a triangle. Consider four points \( p_1, p_2, p_3, p_4 \) on the side \( AB \), five points \( p_5, p_6, p_7, p_8, p_9 \) on the side \( BC \), and four points \( p_{10}, p_{11}, p_{12}, p_{13} \) on the side \( AC \). None of these points is a vertex of the triangle \( ABC \). Then the total number of pentagons that can be formed by taking all the vertices from the points \( p_1, p_2, \ldots, p_{13} \) is ___________.
A coordination compound holds a central metal atom or ion surrounded by various oppositely charged ions or neutral molecules. These molecules or ions are re-bonded to the metal atom or ion by a coordinate bond.
A coordination entity composes of a central metal atom or ion bonded to a fixed number of ions or molecules.
A molecule, ion, or group which is bonded to the metal atom or ion in a complex or coordination compound by a coordinate bond is commonly called a ligand. It may be either neutral, positively, or negatively charged.