To determine the correct order of stoichiometries of AgCl formed when AgNO_3 is added in excess to the complexes CoCl_3.6NH_3, CoCl_3.5NH_3, and CoCl_3.4NH_3, we need to identify the number of chloride ions available for reaction from each complex.
Complex: CoCl_3.6NH_3
In this complex, all three chloride ions are bound as ligands inside the coordination sphere. Therefore, none are available to react with Ag^+ to form AgCl. Thus, no AgCl will be precipitated from this complex.
Complex: CoCl_3.5NH_3\]
In this complex, the formula suggests that one Cl^-\] is outside the coordination sphere, while the other two are inside along with 5NH_3 ligands. Therefore, one AgCl will be formed.
Complex: CoCl_3.4NH_3
For this complex, two chloride ions are outside the coordination sphere, allowing them to react with \[AgNO_3\] to form \[2\ AgCl\].
Summarizing the stoichiometries, we have:
Thus, when referring to "3 AgCl, 2 AgCl, 1 AgCl" in the options, they must mean for comparative purposes among larger collections of complexes (e.g., when scale is involved, or a mistake in wording), as each does not strictly yield those results, but rather:
The correct order according to the stoichiometry from actual reactions of yielding AgCl respectively would simply refer to increasing orders of availability: 2\ AgCl\, 1\ AgCl\, 0\ AgCl.