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The compounds $ [Cr{({H_2}O)_6}]C{l_3} $ , and exhibits:
(A) Linkage isomerism
(B) Geometrical isomerism
(C) Ionization isomerism
(D) Hydrate isomerism

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Answer
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Hint: First of all, isomerism is defined as the property attained by two compounds which have the same formula but different arrangement of atoms. Now the isomerism in complex compounds vary from linkage isomerism to geometrical isomerism and further on.

Complete answer:
Here we are given three compounds $ [Cr{({H_2}O)_6}]C{l_3} $ , and all are asked if they are isomerism and if they are then of what type of complex compound’s isomer.
Now first let’s understand what isomers actually mean. Isomers are defined as the compounds having the same formula but different structural configuration.
Now yes, these compounds do have a common formula of $ Cr{({H_2}O)_6}C{l_3} $ but what type of isomer.
Now the different types of isomers that are divided into are structural isomers and geometrical isomers.
Structural isomers are defined as the types of isomers which have the different place of ligand and the ion or maybe the coordination cation is different in molecular formula of the complex compound. Now this structural formula is further divided into ionization isomerism, linkage isomerism and coordination isomerism.
Ionization isomerism is defined as the type of isomer in which the ligand that is bound to the metal centre exchanges places with an anion or a neutral molecule that was originally=y outside the coordination compound.
Coordination isomerism is defined as the type of isomerism in which the compounds containing the complex anionic and complex cationic parts have the change in the ligands from one of the cations to the anion of the complex compound.
Linkage isomerism is only seen in ambidentate ligands, now what is an ambidentate ligand, it is a ligand which has two sites from which it can attack the d block compound like cyanide and isocyanide. Now there is no ambidentate ligand here.
Hydrate isomerism is defined as the type of isomerism in which the compounds differ from each other based on the number of the solvent molecule directly bonded to the metal ion in the complex compound.
Geometrical isomerism is only seen when the structural and molecular formulas of both the compounds are the same. Here the molecular formula of all the compounds is different.
Therefore, we can say that these compounds only show hydrate isomerism as there are no two different anions like chlorine so that ionization isomerism could exist and there is no change in the cation or anion so there is no coordination isomerism.
Hydrate isomerism exists in $ [Cr{({H_2}O)_6}]C{l_3} $

Note:
It is defined as the two or more compounds having the same number and types of atoms and bonds. Now bonds mean the connectivity between the atoms is the same. These compounds have different spatial arrangements of the atoms.