The sum of stereoisomers of comple-A, complex-B and complex-C in following reaction is ………..
`[PtCl_(4)]^(2-) underset(-2Cl^(-)) overset(+2("pyridine"))to"[Complex-A]" underset(-Cl^(-))overset(+NH_(3)) to"[Complex-B]" underset("-(Pyridine)")overset(+Br^(-))to "[Complex-C]"`

Explanation

To solve the question regarding the sum of stereoisomers of complexes A, B, and C, we will analyze each complex step by step.

### Step 1: Identify Complex A
The first complex formed is from the reaction of `[PtCl4]^(2-)` with `2 pyridine`. The resulting complex is denoted as Complex A, which can be represented as `Pt(Py)2Cl2`.

**Hint for Step 1:** Look for the coordination number and the ligands to identify the structure of the complex.

### Step 2: Determine Stereoisomers of Complex A
Complex A has the formula `Ma2B2`, where M is the metal (Pt), a is the number of one type of ligand (pyridine), and b is the number of another type of ligand (chloride). This type of complex can exhibit geometrical isomerism. For `Ma2B2`, there are 2 geometrical isomers (cis and trans).

**Hint for Step 2:** Remember that geometrical isomers arise from different arrangements of the ligands around the central metal atom.

### Step 3: Identify Complex B
Complex A reacts with `NH3` and `Cl^-` to form Complex B. The resulting complex can be represented as `Pt(Py)2(NH3)Cl`.

**Hint for Step 3:** Pay attention to how the ligands are replaced in the reaction to identify the new complex.

### Step 4: Determine Stereoisomers of Complex B
Complex B also has the formula `Ma2Bc`, which allows for geometrical isomerism. This complex can also exhibit 2 geometrical isomers (cis and trans).

**Hint for Step 4:** Consider the positions of the ligands when determining the possible isomers.

### Step 5: Identify Complex C
Complex B then reacts with `Br^-` to form Complex C, represented as `Pt(Py)2(NH3)(Br)`.

**Hint for Step 5:** Follow the same approach as before to identify the new complex formed after the reaction.

### Step 6: Determine Stereoisomers of Complex C
Complex C can be represented as `Pt(Py)2(NH3)(Br)`, which has the formula `Ma2Bc`. This complex can exhibit 3 geometrical isomers due to the presence of two types of bidentate ligands.

**Hint for Step 6:** Analyze the possible arrangements of the ligands to find the number of isomers.

### Step 7: Sum of Stereoisomers
Now, we can sum the stereoisomers from each complex:
- Complex A: 2 stereoisomers
- Complex B: 2 stereoisomers
- Complex C: 3 stereoisomers

Total = 2 + 2 + 3 = 7 stereoisomers.

**Final Answer:** The sum of stereoisomers of Complex A, Complex B, and Complex C is **7**.