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Which of the following complexes will NOT conduct electricity?
(A) $[CrCl{({H_2}O)_5}]C{l_2}.{H_2}O$
(B) $[Pt{(N{H_3})_6}]C{l_4}$
(C) $[CrC{l_3}{({H_2}O)_3}].3{H_2}O$
(D) $[Co{(N{H_3})_4}]C{l_2}$

Answer
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Hint: To conduct electricity, there must be a flow of ions in an aqueous solution of a complex compound hence, we will first check whether the complex (in aqueous form) can be dissociated into ions or not. If the complex can dissociate, analyse the total number of ions produced by the compound and then choose the suitable option from the given question.

Complete Step by Step Solution:
Let us consider all the four options given into consideration and write their balanced chemical equation for dissociation one by one. The factors for dissociation can vary with the physical and chemical properties of compounds but on taking the general dissociation reaction, we get:
$[CrCl{({H_2}O)_5}]C{l_2}.{H_2}O \to {[CrCl{({H_2}O)_5}]^{2 + }} + 2C{l^ - } + {H_2}O$
i.e., $[CrCl{({H_2}O)_5}]C{l_2}.{H_2}O$dissociates into $3$ions. It means it will conduct electricity.
$[Pt{(N{H_3})_6}]C{l_4} \to {[Pt{(N{H_3})_6}]^{4 + }} + 4C{l^ - }$
i.e., $[Pt{(N{H_3})_6}]C{l_4}$ dissociates into $5$ ions. It means it will also conduct electricity.

The complex $[CrC{l_3}{({H_2}O)_3}].3{H_2}O$ cannot be dissociated in an aqueous solution.
i.e., $[CrC{l_3}{({H_2}O)_3}].3{H_2}O$ gives $0$ ions. It means it will NOT conduct electricity.

$[Co{(N{H_3})_4}]C{l_2} \to {[Co{(N{H_3})_4}]^{2 + }} + 2C{l^ - }$
i.e., $[Co{(N{H_3})_4}]C{l_2}$dissociates into $3$ions. It means it will also conduct electricity.
Thus, it can be clearly identified that $[CrC{l_3}{({H_2}O)_3}].3{H_2}O$ complex will NOT conduct electricity due to its deficiency of ions in an aqueous solution.
Hence, the correct option is (C) $[CrC{l_3}{({H_2}O)_3}].3{H_2}O$ .

Note: Since this is a conceptual-based problem hence, it is essential that the options are given in the question be analysed very carefully to give an accurate solution. Also, remember the atomic numbers of atoms and the lone pair availability while dissociating complex compounds. Reactions given must be in a balanced form.