Step 1: Understand precipitation in coordination compounds.
When silver nitrate (AgNO\(_3\)) is added to a solution of a coordination complex, it only reacts with the halide ions that are outside the coordination sphere (the square brackets). These are known as counter-ions. Ions inside the coordination sphere are covalently bonded to the central metal atom and do not dissociate.
Step 2: Relate the amount of precipitate to the number of counter-ions.
The problem states that one mole of silver chloride (AgCl) is precipitated per mole of the complex. This means there must be exactly one chloride ion (\(\text{Cl}^-\)) available as a counter-ion in the formula.
Step 3: Examine the given formulas.
- \(\text{[CoCl}_2\text{(NH}_3)_4\text{]Cl}\): Has one \(\text{Cl}^-\) outside the brackets. Will precipitate 1 mole of AgCl.
- \(\text{[CoCl(NH}_3)_5\text{]Cl}_2\): Has two \(\text{Cl}^-\) outside the brackets. Will precipitate 2 moles of AgCl.
- \(\text{[CoCl}_3\text{(NH}_3)_3\text{]}\): Has zero \(\text{Cl}^-\) outside the brackets. Will precipitate 0 moles of AgCl.
- \(\text{[Co(NH}_3)_6\text{]Cl}_3\): Has three \(\text{Cl}^-\) outside the brackets. Will precipitate 3 moles of AgCl.
Based on this analysis, formula is the correct answer.