Question

Which of the following complex has the least conductivity? ________.

• A. $[Co(NH_{3})_{5}Cl]Cl_{2}$
• B. $Cis-[Co(NH_{3})_{4}Cl_{2}]Cl$
• C. $[Co(NH_{3})_{6}]Cl_{3}$
• D. $[Co(NH_{3})_{3}Cl_{3}]$
• E. $trans-[Co(NH_{3})_{4}Cl_{2}]Cl$

Hint:

The more ions outside the square brackets, the higher the conductivity.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
The molar conductivity of a solution of an ionic complex depends on the number of ions it dissociates into when dissolved. A higher number of ions leads to a higher conductivity, as there are more charge carriers available to move through the solution. To find the complex with the least conductivity, we must find the one that produces the fewest ions in solution.
Step 2: Detailed Explanation
We need to analyze how each coordination compound ionizes in an aqueous solution. The part of the complex inside the square brackets, the coordination sphere, acts as a single ion, while the ions outside the brackets are counter-ions.
(A) \([Co(NH_3)_5Cl]Cl_2\):
This compound dissociates into one complex cation, \([Co(NH_3)_5Cl]^{2+}\), and two chloride anions, \(2Cl^-\). \[ [\text{Co(NH}_3)_5\text{Cl}]\text{Cl}_2 \to [\text{Co(NH}_3)_5\text{Cl}]^{2+}(aq) + 2\text{Cl}^-(aq) \] Total ions produced = 1 + 2 = 3.
(B) and (E) cis- and trans-\([Co(NH_3)_4Cl_2]Cl\):
These are geometric isomers, but they dissociate in the same way. They produce one complex cation, \([Co(NH_3)_4Cl_2]^+\), and one chloride anion, \(Cl^-\). \[ [\text{Co(NH}_3)_4\text{Cl}_2]\text{Cl} \to [\text{Co(NH}_3)_4\text{Cl}_2]^{+}(aq) + \text{Cl}^-(aq) \] Total ions produced = 1 + 1 = 2.
(C) \([Co(NH_3)_6]Cl_3\):
This compound dissociates into one complex cation, \([Co(NH_3)_6]^{3+}\), and three chloride anions, \(3Cl^-\). \[ [\text{Co(NH}_3)_6]\text{Cl}_3 \to [\text{Co(NH}_3)_6]^{3+}(aq) + 3\text{Cl}^-(aq) \] Total ions produced = 1 + 3 = 4.
(D) \([Co(NH_3)_3Cl_3]\):
This compound has no counter-ions outside the coordination sphere. It is a neutral complex. As a neutral molecule, it does not dissociate into ions when dissolved in water. \[ [\text{Co(NH}_3)_3\text{Cl}_3] \to \text{No ions} \] Since it produces no ions, it is a non-electrolyte and its solution will have nearly zero (or the least) conductivity.
Step 4: Final Answer
The complex \([Co(NH_3)_3Cl_3]\) produces the fewest ions (zero) and therefore has the least conductivity.