The aqueous solution containing one mole of `CoCl_(3).5NH_3` consumed 2 mol of silver nitrate solution for precipitation of free chloride ions. The formula of the compound should be

Options

A. `[Co(NH_3)_5Cl]Cl_2`
B. `[Co(NH_3)_6Cl]Cl_2`
C. `[Co(NH_3)_5Cl_2]Cl`
D. `[Co(NH_3)_5Cl_3]`

Answer

To solve the given problem, we need to analyze the information provided and determine the correct formula for the compound based on the precipitation reaction with silver nitrate (AgNO3). Here’s a step-by-step solution:

### Step 1: Understand the Reaction
The compound in question is `CoCl3.5NH3`, which indicates that cobalt (Co) is coordinated with 5 ammonia (NH3) ligands and 3 chloride (Cl) ions. When this compound reacts with silver nitrate, it will precipitate the free chloride ions as silver chloride (AgCl).

### Step 2: Write the Reaction
The reaction can be represented as:
\[ \text{CoCl}_3.5\text{NH}_3 + 3\text{AgNO}_3 \rightarrow 3\text{AgCl} + \text{Co(NO}_3)_2 + 5\text{NH}_3 \]

### Step 3: Analyze the Given Information
According to the problem, 2 moles of AgNO3 were consumed. Since each mole of AgNO3 reacts to precipitate one mole of AgCl, this means:
- 2 moles of AgNO3 will produce 2 moles of AgCl.

### Step 4: Determine the Free Chloride Ions
From the precipitation of 2 moles of AgCl, we can deduce that:
- 2 moles of Cl⁻ ions are released.

### Step 5: Identify the Ionizable Chloride Ions
The 2 moles of Cl⁻ ions must come from the coordination complex. Since the original formula `CoCl3.5NH3` suggests that there are 3 chloride ions, we need to determine how many of these are ionizable.

### Step 6: Conclusion About the Structure
Since 2 moles of Cl⁻ ions are available as ionizable ions outside the coordination sphere, we can conclude that:
- 1 of the Cl⁻ ions is coordinated (not free) and 2 are free.

### Step 7: Write the Correct Formula
Given that there are 2 free Cl⁻ ions, the correct formula for the compound should be:
\[ \text{Co(NH}_3\text{)}_5\text{Cl}_2\text{Cl} \]
This indicates that there are 5 ammonia ligands, 2 chloride ions are part of the coordination sphere, and 1 chloride ion is free.

### Final Answer
The formula of the compound should be:
\[ \text{Co(NH}_3\text{)}_5\text{Cl}_2\text{Cl} \]

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