A solution containing 2.675 g of `CoCl_(3).6NH_(3)` (molar mass = 267.5 g `mol^(-1)` is passed through a cation exchanger. The chloride ions obtained in solution are treated with excess of `AgNO_(3)` to give 4.78 g of AgCl (molar mass = 143.5 g `mol^(-1)` ). The formula of the complex is (At.mass of Ag = 108 u ) .

Options

A. `[CoCl(NH_(3))_(5)]Cl_(2)`
B. `[Co(NH_(3))_(6)Cl_(3)`
C. `[CoCl_(2) (NH_(3))_(4)]Cl`
D. `[CoCl_(3) (NH_(3))_(3)]`

Explanation

To solve the problem step by step, we will follow the outlined procedure:

### Step 1: Calculate the number of moles of the complex `CoCl3.6NH3`
Given:
- Mass of `CoCl3.6NH3` = 2.675 g
- Molar mass of `CoCl3.6NH3` = 267.5 g/mol

**Calculation:**
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{2.675 \, \text{g}}{267.5 \, \text{g/mol}} = 0.01 \, \text{mol} \]

### Step 2: Calculate the number of moles of `AgCl` produced
Given:
- Mass of `AgCl` = 4.78 g
- Molar mass of `AgCl` = 143.5 g/mol

**Calculation:**
\[ \text{Number of moles of AgCl} = \frac{\text{mass}}{\text{molar mass}} = \frac{4.78 \, \text{g}}{143.5 \, \text{g/mol}} \approx 0.033 \, \text{mol} \]

### Step 3: Determine the number of moles of `Cl-` ions produced
From the stoichiometry of the reaction, each mole of `CoCl3.6NH3` produces 3 moles of `Cl-` ions. Therefore, if we have 0.01 moles of `CoCl3.6NH3`, the number of moles of `Cl-` produced is:
\[ \text{Moles of Cl-} = 3 \times \text{moles of CoCl3.6NH3} = 3 \times 0.01 \, \text{mol} = 0.03 \, \text{mol} \]

### Step 4: Verify the moles of `AgCl` produced
Since we have determined that 0.03 moles of `Cl-` ions are produced, and each `Cl-` reacts with `AgNO3` to form `AgCl`, the number of moles of `AgCl` produced should also be 0.03 moles.

### Step 5: Identify the formula of the complex
From the calculations:
- The complex is `CoCl3.6NH3`.
- The coordination number of `Co` is 6 (from the 6 ammonia ligands).
- There are 3 chloride ions.

Thus, the formula of the complex is:
\[ \text{Co(NH}_3\text{)}_6\text{Cl}_3 \]

### Final Answer:
The formula of the complex is `Co(NH3)6Cl3`.

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