Out of the following complex compounds, which of the compound will be having the minimum conductance in solution?

The correct answer is [Co(NH₃)₃Cl₃].

Explanation:
The electrical conductance of an aqueous solution of a coordination compound depends directly on the number of ions produced when the compound dissolves in water. A higher number of ions in solution leads to a higher electrical conductance, whereas a compound that does not dissociate into ions will show minimum (essentially zero) conductance.

Let us analyze the dissociation of the given complex compounds in aqueous solution:

1. [Co(NH₃)₆]Cl₃: This compound dissociates to give four ions:
$\left[\mathrm{Co}\right({\mathrm{NH}}_3{)}_6]{\mathrm{Cl}}_3\to [\mathrm{Co}({\mathrm{NH}}_3{)}_6{]}^{3+}+3{\mathrm{Cl}}^{-}$
It produces 4 ions in total, resulting in high conductance.

2. [Co(NH₃)₅Cl]Cl (or [Co(NH₃)₅Cl]Cl₂): Assuming a standard cobalt(III) oxidation state, this complex dissociates to release free chloride ions into the solution, producing multiple ions and thus showing significant conductance.

3. [Co(NH₃)₄Cl₂] (or [Co(NH₃)₄Cl₂]Cl): This complex also dissociates in solution to yield ions, contributing to electrical conductance.

4. [Co(NH₃)₃Cl₃]: This is a neutral coordination complex. All three chloride ligands and three ammonia ligands are directly coordinated to the central cobalt ion within the coordination sphere (indicated by the square brackets). Since there are no counter-ions present outside the coordination sphere, this compound does not dissociate into ions when dissolved in water:
$\left[\mathrm{Co}\right({\mathrm{NH}}_3{)}_3{\mathrm{Cl}}_3]\to \text{No dissociation (0 ions)}$
Because it behaves as a non-electrolyte, it has the minimum conductance in solution.