This problem involves determining the correct formula of a cobalt complex based on the number of chloride ions precipitated when treated with silver nitrate. The key concept is that only the chloride ions outside the coordination sphere (not bonded to the central metal ion) will be precipitated as AgCl. The chloride ions inside the coordination sphere (acting as ligands) will not be precipitated.

Given Data:

• Volume of solution = 100 mL = 0.1 L
• Molarity of CoCl₃.6H₂O solution = 0.1 M
• Number of ions precipitated = 1.2 × 10²²
• Precipitating agent = Excess AgNO₃

Step 1: Calculate the total moles of the complex compound.

Moles of complex = Molarity × Volume (in L) = 0.1 mol/L × 0.1 L = 0.01 mol.

Step 2: Calculate the number of moles of ions precipitated.

The ions precipitated are Cl⁻ ions. We are given the number of ions. $\text{Number of moles of Cl}{}^{-<!--\; -\; -->}\text{ ions precipitated =}\frac{\text{Number of ions}}{N_A}\text{ =}\frac{1.2\times {10}^{22}}{6.022\times {10}^{23}}\text{ = 0.02 mol}$ (where N_A is Avogadro's number, 6.022 × 10²³).

Step 3: Relate the moles of Cl⁻ precipitated to the moles of the complex.

These 0.02 moles of Cl⁻ ions come from 0.01 moles of the complex. $\text{Therefore, number of Cl}{}^{-<!--\; -\; -->}\text{ ions precipitated per mole of complex =}\frac{0.02}{0.01}\text{ = 2}$.

This means 2 chloride ions per formula unit are outside the coordination sphere and are free to be precipitated.

Step 4: Analyze the options.

We need to find the complex where exactly 2 Cl⁻ ions are present as counter ions (outside the sphere).

• Option A: [Co(H₂O)₆]Cl₃ → 3 Cl⁻ ions outside the sphere.
• Option B: [Co(H₂O)₅Cl]Cl₂.H₂O → 2 Cl⁻ ions outside the sphere. (One Cl is inside as a ligand).
• Option C: [Co(H₂O)₃Cl₃].3H₂O → 0 Cl⁻ ions outside the sphere. (All 3 Cl are ligands inside the sphere).
• Option D: [Co(H₂O)₄Cl₂]Cl.2H₂O → 1 Cl⁻ ion outside the sphere. (Two Cl are ligands inside the sphere).

Final Answer: The complex is [Co(H₂O)₅Cl]Cl₂.H₂O (Option B), as it is the only formula with exactly 2 chloride ions outside the coordination sphere.

Related Topic: Werner's Theory of Coordination Compounds

This concept is fundamental to coordination chemistry. Alfred Werner proposed that in a coordination compound, the metal atom has two types of valencies: primary (ionic) and secondary (non-ionic, directional). The primary valencies are satisfied by negative ions (counter ions), which are ionizable. The secondary valencies are satisfied by ligands (ions or molecules) and are non-ionizable. These ligands are written inside the square brackets, forming the coordination sphere. Only the ions outside this sphere are precipitated in reactions with AgNO₃.

Key Formula

The number of ions precipitated is directly related to the number of counter ions (n) per formula unit of the complex. $\text{Moles of ions precipitated = n × Moles of complex}$