The fraction of chlorine precipitated by `AgNO_3` solution from `[Co(NH_3)_5Cl]Cl_2` is _________.

Options

A. `(1)/(2)`
B. `(2)/(3)`
C. `(1)/(3)`
D. `(1)/(4)`

Answer

To solve the problem of finding the fraction of chlorine precipitated by `AgNO3` solution from the complex `[Co(NH3)5Cl]Cl2`, we can follow these steps:

### Step 1: Identify the Components of the Complex
The complex `[Co(NH3)5Cl]Cl2` consists of:
- Cobalt (Co) as the central metal atom.
- Five ammonia (NH3) ligands.
- One chloride (Cl) ligand that is part of the coordination sphere.
- Two chloride (Cl) ions that are counter ions.

### Step 2: Determine the Charges
The overall charge of the complex is +2, as indicated by the formula. The two chloride ions outside the coordination sphere contribute a total charge of -2 (since each Cl has a charge of -1). Therefore, the charge balance can be represented as follows:
- Charge of Co complex: +2
- Charge from 2 Cl counter ions: -2
- Charge from 1 Cl ligand: -1
- Total charge = +2 from Co - 2 from 2 Cl counter ions - 1 from 1 Cl ligand = 0 (which is balanced).

### Step 3: Reaction with `AgNO3`
When the complex reacts with `AgNO3`, the counter ions (the two Cl ions) will precipitate as silver chloride (AgCl). The ammonia ligands do not participate in this reaction because they are bonded to the cobalt through coordinate bonds.

### Step 4: Calculate the Amount of Chlorine Precipitated
From the complex, we have:
- 2 Cl counter ions that precipitate with `AgNO3`.
- 1 Cl ligand that remains in the coordination sphere.

Thus, the total number of Cl atoms initially present is:
- 2 (from counter ions) + 1 (from ligand) = 3 Cl atoms.

### Step 5: Determine the Fraction of Chlorine Precipitated
The fraction of chlorine that has precipitated can be calculated as:
\[ \text{Fraction of Cl precipitated} = \frac{\text{Number of Cl precipitated}}{\text{Total number of Cl}} = \frac{2}{3} \]

### Final Answer
The fraction of chlorine precipitated by `AgNO3` solution from `[Co(NH3)5Cl]Cl2` is **\(\frac{2}{3}\)**.

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