The conductivity of a solution of complex with formula $$CoCl_3(NH_3)_4$$ corresponds to $$1:1$$ electrolyte, then the primary valency of central metal ion is ______.

The complex has the formula $$CoCl_3(NH_3)_4$$, which can be written as $$[Co(NH_3)_4Cl_x]Cl_{3-x}$$.

The conductivity corresponds to a 1:1 electrolyte, which means the complex dissociates into 2 ions (one cation and one anion).

For a 1:1 electrolyte:

$$[Co(NH_3)_4Cl_2]Cl \rightarrow [Co(NH_3)_4Cl_2]^+ + Cl^-$$

This gives 2 ions, confirming a 1:1 electrolyte.

In the complex ion $$[Co(NH_3)_4Cl_2]^+$$, we have:

- 4 $$NH_3$$ molecules (neutral ligands)

- 2 $$Cl^-$$ ions (inside coordination sphere, acting as secondary valency)

- 1 $$Cl^-$$ ion (outside coordination sphere, acting as primary valency/ionizable)

The primary valency (ionization valency) of the central metal ion equals the total number of ions outside the coordination sphere, which determines the charge on the complex ion.

The charge on Co: Let the oxidation state of Co be $$x$$.

$$x + 4(0) + 2(-1) = +1$$

$$x = +3$$

The primary valency equals the oxidation state of the central metal ion, which is the total ionic charge it satisfies. Since Co is in +3 oxidation state, the primary valency is 3.

Therefore, the primary valency of the central metal ion is $$\textbf{3}$$.