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

The correct option is [Co(NH₃)₃Cl₃].

Explanation:
The electrical conductance of an aqueous solution of a coordination complex depends directly on the number of free ions it produces when dissolved in water. A higher number of mobile ions in the solution leads to higher electrical conductance, whereas fewer ions result in lower conductance. A neutral complex that does not dissociate into ions will exhibit the minimum (practically zero) conductance.

Let's analyze the dissociation behavior of each of the given complex compounds in aqueous solution:

1. [Co(NH₃)₃Cl₃]:
This is a neutral coordination sphere. Because all three chloride ligands and the three ammonia ligands are inside the coordination sphere (within the square brackets), they are directly coordinated to the central cobalt ion and do not ionize in solution.
$[Co(NH3)3Cl3]\; \backslash Rightarrow\; \backslash text\{No\; ionization\; (0\; ions)\}$ Since it produces zero ions in solution, it has the minimum conductance.

2. [Co(NH₃)₄Cl₂]Cl:
This complex dissociates in solution to give a complex cation and a chloride anion:
$[Co(NH3)4Cl2]Cl\; \backslash Rightarrow\; [Co(NH3)4Cl2]^+\; +\; Cl^-\; \backslash text\{\; (2\; ions)\}$

3. [Co(NH₃)₆]Cl₃:
This complex dissociates completely in water to yield one complex cation and three chloride anions:
$[Co(NH3)6]Cl3\; \backslash Rightarrow\; [Co(NH3)6]^3+\; +\; 3Cl^-\; \backslash text\{\; (4\; ions)\}$

4. [Co(NH₃)₅Cl]Cl₂:
This complex dissociates in solution to produce one complex cation and two chloride anions:
$[Co(NH3)5Cl]Cl2\; \backslash Rightarrow\; [Co(NH3)5Cl]^2+\; +\; 2Cl^-\; \backslash text\{\; (3\; ions)\}$

Conclusion:
Comparing the number of ions produced by each compound, $[Co(NH3)3Cl3]$ does not ionize at all and thus possesses the minimum electrical conductance in solution.