Find the number of structural isomers of fully saturated cycloalkane of molecular formulae `C_(6)H_(12)` which give three monochloro structural products.

Answer

To find the number of structural isomers of fully saturated cycloalkanes with the molecular formula \( C_6H_{12} \) that can yield three monochloro structural products, we can follow these steps:

### Step 1: Identify the Molecular Formula
The molecular formula given is \( C_6H_{12} \). This indicates that we are dealing with a fully saturated compound, which is a cycloalkane.

### Step 2: Determine the Structure of Cycloalkanes
Cycloalkanes are cyclic hydrocarbons. For \( C_6H_{12} \), the simplest cycloalkane is cyclohexane, but we need to consider other possible structures that can provide different types of hydrogens.

### Step 3: Analyze Cyclohexane
Cyclohexane (C6H12) has all carbon atoms equivalent, meaning it has only one type of hydrogen. Therefore, it can only produce one monochloro product. This does not satisfy the requirement for three monochloro products.

### Step 4: Consider Other Cycloalkanes
We need to find cycloalkanes that have at least three different types of hydrogen atoms, which would allow for three different monochloro products.

1. **Cyclobutane with two methyl groups (1,1-dimethylcyclobutane)**:
- Structure:
```
CH3
|
CH2-CH2
|
CH3
```
- Types of hydrogens:
- 2 equivalent CH2 (from the cyclobutane)
- 2 equivalent CH3 (methyl groups)
- 2 equivalent CH2 (adjacent to the methyl groups)
- This structure has three different types of hydrogen atoms, allowing for three monochloro products.

2. **1,2-Dimethylcyclobutane**:
- Structure:
```
CH3
|
CH-CH
|
CH2
```
- This structure also has three different types of hydrogen atoms.

3. **1,3-Dimethylcyclobutane**:
- Structure:
```
CH3
|
CH2-CH2
|
CH3
```
- This structure also has three different types of hydrogen atoms.

### Step 5: Count the Isomers
From the analysis, we find:
- 1,1-Dimethylcyclobutane
- 1,2-Dimethylcyclobutane
- 1,3-Dimethylcyclobutane
- 1,4-Dimethylcyclobutane

Each of these structures has three different types of hydrogen atoms, allowing for three different monochloro products.

### Conclusion
The number of structural isomers of fully saturated cycloalkanes \( C_6H_{12} \) that can give three monochloro structural products is **4**.

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