The number of cyclic isomers of molecular formula `C_(3)H_(4)Cl_(2)` are:

Options

A. 1
B. 2
C. 3
D. 4

Answer

To determine the number of cyclic isomers for the molecular formula \( C_3H_4Cl_2 \), we can follow these steps:

### Step 1: Identify the Structure
The molecular formula \( C_3H_4Cl_2 \) indicates that we have three carbon atoms, four hydrogen atoms, and two chlorine atoms. Since we are looking for cyclic isomers, we can form a cyclic structure with the three carbon atoms.

### Step 2: Draw the Cyclic Structure
The only possible cyclic structure with three carbon atoms is a cyclopropane ring. This means we will have a triangle-shaped structure with three carbon atoms.

### Step 3: Attach Chlorine Atoms
Now we need to consider how to attach the two chlorine atoms to the cyclopropane ring. There are different ways to do this:

1. **Isomer 1**: Attach one chlorine atom to one carbon and the second chlorine atom to a different carbon. For example, if we label the carbon atoms as C1, C2, and C3, we can have Cl on C1 and Cl on C2.

2. **Isomer 2**: Attach both chlorine atoms to the same carbon atom. For example, we can attach both Cl atoms to C1.

### Step 4: Consider the Positioning
- In Isomer 1, we can have Cl on C1 and Cl on C2, or Cl on C2 and Cl on C3, but since the ring is symmetrical, these arrangements will not lead to new isomers.
- In Isomer 2, having both Cl atoms on C1 is a distinct arrangement.

### Step 5: Count the Isomers
From the above arrangements, we can conclude that there are two distinct cyclic isomers for the molecular formula \( C_3H_4Cl_2 \):

1. One chlorine on C1 and one on C2.
2. Both chlorines on C1.

Thus, the total number of cyclic isomers is **2**.

### Final Answer
The number of cyclic isomers of the molecular formula \( C_3H_4Cl_2 \) is **2**.

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