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The type of isomerism exhibited in \[{{\rm{K}}_{\rm{3}}}\left[ {{\rm{Co}}{{\left( {{\rm{N}}{{\rm{O}}_{\rm{2}}}} \right)}_{\rm{6}}}} \right]\] and \[{{\rm{K}}_{\rm{3}}}\left[ {{\rm{Co}}{{\left( {{\rm{ONO}}} \right)}_{\rm{6}}}} \right]\]is
A. Linkage
B. Coordination
C. Ionisation
D. Geometrical

Answer
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Hint: A set of molecules possessing the same molecular formula but their structures are different is termed isomers. And this phenomenon is termed isomerism. The different isomerism types are linkage, ionisation, etc.

Complete Step by Step Answer:
Let's first understand what is an ambidentate ligand. They are the ligands that possess more than one donor atoms, such as \[{\rm{N}}{{\rm{O}}_{\rm{2}}},\,{\rm{C}}{{\rm{N}}^ - },{\rm{SC}}{{\rm{N}}^ - }\] .
Now, we will discuss linkage isomerism. This isomerism is observed in complexes containing ambidentate ligands. In the given question, the two complexes contain \[{\rm{N}}{{\rm{O}}_{\rm{2}}}\] as ligands whose nature is ambidentate that is, they can bind through N and O atom. Therefore, in \[{{\rm{K}}_{\rm{3}}}\left[ {{\rm{Co}}{{\left( {{\rm{N}}{{\rm{O}}_{\rm{2}}}} \right)}_{\rm{6}}}} \right]\] and \[{{\rm{K}}_{\rm{3}}}\left[ {{\rm{Co}}{{\left( {{\rm{ONO}}} \right)}_{\rm{6}}}} \right]\], linkage isomerism is observed.
Hence, option A is right.

Additional Information: In coordination isomerism, the exchange of ligands of anions and cations occurs. This isomerism occurs in those coordination compounds which possess both anionic and cationic complex ions. For example, \[\left[ {{\rm{Pt}}{{\left( {{\rm{N}}{{\rm{H}}_{\rm{3}}}} \right)}_{\rm{4}}}} \right]\left[ {{\rm{CuC}}{{\rm{l}}_{\rm{4}}}} \right]\] and \[\left[ {{\rm{Cu}}{{\left( {{\rm{N}}{{\rm{H}}_{\rm{3}}}} \right)}_{\rm{4}}}} \right]\left[ {{\rm{PtC}}{{\rm{l}}_{\rm{4}}}} \right]\]. Let's understand what ionisation isomerism is. This isomerism occurs due to the production of different ions by the coordination compounds in the solution.
\[{\rm{[Co(N}}{{\rm{H}}_{\rm{3}}}{{\rm{)}}_{\rm{5}}}{\rm{Br]S}}{{\rm{O}}_{\rm{4}}} \to {[{\rm{Co(N}}{{\rm{H}}_{\rm{3}}}{{\rm{)}}_{\rm{5}}}{\rm{Br}}]^{2 + }} - {\rm{Cobalt(III)ion}} + {\rm{S}}{{\rm{O}}_4}^{2 - }\]
This isomer gives white coloured precipitate of \[{\rm{BaS}}{{\rm{O}}_{\rm{4}}}\] in a solution of \[{\rm{BaC}}{{\rm{l}}_{\rm{2}}}\] .
\[{\rm{[Co(N}}{{\rm{H}}_{\rm{3}}}{{\rm{)}}_{\rm{5}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}{\rm{]Br}} \to {[{\rm{Co(N}}{{\rm{H}}_{\rm{3}}}{{\rm{)}}_{\rm{5}}}{\rm{S}}{{\rm{O}}_4}]^ + } - {\rm{Cobalt(III)ion}} + {\rm{B}}{{\rm{r}}^ - }\]
The above isomer gives a light yellow coloured precipitate.

Note: There are two other types of defect namely Frenkel and Schottky defect. In ionic solids, the Frenkel defect is seen in ionic solids where smaller ions (cations) are dislocated such as in AgBr, AgCl etc. Schottky defect is observed in potassium chloride, sodium chloride.