Chemistry - Coordination Chemistry Question with Solution | TestHub

To find the maximum value of $(X+Y)$, we need to determine the maximum total number of geometrical isomers for the octahedral complex $M{a}_2{b}_p{c}_q$.

Identify the formula: Since the coordination number is 6, $2+p+q=6⟹p+q=4$. For maximum isomers, we choose $p=2$ and $q=2$, giving the formula $M{a}_2{b}_2{c}_2$.

Find trans isomers $(Y)$: The structures with 'a' ligands opposite to each other are $(aa)(bb)(cc)$ and $(aa)(bc)(bc)$, so $Y=2$.

Find cis isomers $(X)$: The structures with 'a' ligands adjacent to each other are $(bb)(ac)(ac)$, $(cc)(ab)(ab)$, and $(ab)(ac)(bc)$, so $X=3$.

Calculate the final answer: Combining both types gives the total number of geometrical isomers: $X+Y=3+2=5.00$.