A complex has a composition corresponding to the formula `CoBr_(2)Cl.4NH_(3)`. What is the structural formula if conductance measurements show two ions per formula unit ? Silver nitrate solution given an immediate precipitate of AgCl but AgBr :-

Options

A. `[CoBrCl(NH_(3))_(4)]Br`
B. `[CoCl(NH_(3))_(4)]Br_(2)`
C. `[CoBr_(2)Cl(NH_(3))_(4)]`
D. `[CoBr_(2)(NH_(3))_(4)]Cl`

Answer

To solve the problem, we need to analyze the given complex and the information provided about its behavior in solution. The complex is represented by the formula \(CoBr_2Cl \cdot 4NH_3\). Let's break down the steps to find the structural formula.

### Step 1: Identify the Components of the Complex
The complex consists of:
- Cobalt (Co) as the central metal atom.
- Two bromide ions (Br\(^-\)).
- One chloride ion (Cl\(^-\)).
- Four ammonia molecules (NH\(_3\)) acting as ligands.

### Step 2: Determine the Charge of the Complex
Cobalt typically has a +3 oxidation state in coordination complexes. The charges from the anions and ligands need to be balanced:
- The two bromide ions contribute a total charge of -2.
- The one chloride ion contributes a charge of -1.
- The four ammonia molecules are neutral (0 charge).

Thus, the total charge from the anions is -3. To balance this, cobalt must be in the +3 oxidation state:
\[ +3 + (-2) + (-1) = 0 \]

### Step 3: Analyze Conductance Measurements
The conductance measurements indicate that the complex dissociates into two ions in solution. This suggests that the complex can be represented as:
\[ [Co(NH_3)_4Br_2]^+ + Cl^- \]

Here, the complex ion \([Co(NH_3)_4Br_2]^+\) is the cation, and the chloride ion (Cl\(^-\)) is the anion. This gives a total of two ions when the complex is dissolved in solution.

### Step 4: Precipitation with Silver Nitrate
When silver nitrate (AgNO\(_3\)) is added to the solution, an immediate precipitate of AgCl forms. This indicates that Cl\(^-\) is free in solution and can react with Ag\(^+\) to form AgCl. The absence of a precipitate with AgBr suggests that the bromide ions are still coordinated to the cobalt and do not dissociate in solution.

### Step 5: Write the Structural Formula
Given the information, the structural formula of the complex can be represented as:
\[ [Co(NH_3)_4Br_2]Cl \]

This indicates that the complex ion \([Co(NH_3)_4Br_2]^+\) is associated with one chloride ion as the counter ion.

### Final Structural Formula
The final structural formula is:
\[ [Co(NH_3)_4Br_2]Cl \]