Identify the complex and use Werner’s theory

The compound is written as: $\mathrm{CoCl_3(NH_3)_4}$

Here:

• $\mathrm{NH_3}$ is a neutral ligand.
• $\mathrm{Cl^-}$ may be either inside or outside the coordination sphere.

Use the conductivity information

The solution behaves as a 1 : 1 electrolyte.

A $1:1$ electrolyte produces 2 ions in solution, like: $[\text{complex}]^+ + \mathrm{Cl^-}$ or $[\text{complex}]^- + \mathrm{K^+}$

Since the given compound contains only cobalt, ammonia, and chloride, the suitable form is: $[\mathrm{Co(NH_3)_4Cl_2}]\mathrm{Cl}$

On ionization: $[\mathrm{Co(NH_3)_4Cl_2}]\mathrm{Cl} \rightarrow [\mathrm{Co(NH_3)_4Cl_2}]^+ + \mathrm{Cl^-}$

So, one chloride ion is outside the coordination sphere and two chloride ions are inside.

Find the primary valency

According to Werner’s theory:

• Primary valency of the metal = oxidation state of the metal = number of ionizable anions required to satisfy charge.

Let oxidation state of Co be $x$ in the complex ion $[\mathrm{Co(NH_3)_4Cl_2}]^+$.

Since $\mathrm{NH_3}$ is neutral and each coordinated $\mathrm{Cl}$ is $-1$: $x + 4(0) + 2(-1) = +1$ $x - 2 = 1$ $x = +3$

Therefore, the primary valency of cobalt is 3.

Final answer

$\boxed{3}$

Comparison with stored answer

Stored correct answer = $3$

Our derived answer matches it.