Step 1: Understanding the Concept:
In coordination chemistry, a complex consists of a coordination sphere (inside the square brackets) and an ionization sphere (outside the square brackets).
Step 2: Key Formula or Approach:
Write the dissociation equation for the complex in water. The coordination sphere does not break apart, acting as a single intact polyatomic ion, while the counter-ions dissociate completely.
Step 3: Detailed Explanation:
The given complex is $[Co(NH_{3})_{6}]Cl_{3}$.
The entity inside the square brackets, $[Co(NH_{3})_{6}]$, is the complex cation. The three chlorine atoms outside are the ionizable counter-anions.
When dissolved in water, the dissociation reaction is:
\[ [Co(NH_{3})_{6}]Cl_{3} \xrightarrow{H_{2}O} [Co(NH_{3})_{6}]^{3+} + 3Cl^{-} \]
Total number of ions produced = $1$ (complex cation) + $3$ (chloride anions) = $4$ ions.
Step 4: Final Answer:
A total of 4 ions are produced per molecule.