A compound has the formula `C_2HCl_2Br.` The number of non - identical structures that are possible is

Options

A. one
B. two
C. three
D. four

Answer

To determine the number of non-identical structures (isomers) possible for the compound with the formula \( C_2HCl_2Br \), we can follow these steps:

### Step 1: Identify the Molecular Formula
The molecular formula given is \( C_2HCl_2Br \).

### Step 2: Calculate the Degree of Unsaturation
The degree of unsaturation (DU) can be calculated using the formula:
\[ DU = C - \frac{H + X}{2} + \frac{N}{2} + 1 \]
where:
- \( C \) = number of carbon atoms
- \( H \) = number of hydrogen atoms
- \( X \) = number of halogens (Cl, Br)
- \( N \) = number of nitrogen atoms

For \( C_2HCl_2Br \):
- \( C = 2 \)
- \( H = 2 \)
- \( X = 2 \) (1 Cl and 1 Br)
- \( N = 0 \)

Substituting these values into the formula:
\[ DU = 2 - \frac{2 + 2}{2} + 0 + 1 = 2 - 2 + 1 = 1 \]
Thus, the degree of unsaturation is 1, indicating that there is one double bond or one ring present.

### Step 3: Determine the Structure
Since we have a degree of unsaturation of 1, we can deduce that the compound is likely an alkene with a carbon-carbon double bond.

### Step 4: Draw Possible Structures
We can draw the structures based on the placement of the substituents (Cl and Br) around the double bond:

1. **Structure 1**:
- \( C=C \)
- Cl on one carbon and H on the other carbon, with Br on the same carbon as Cl.
- Structure:
\[ Cl - C = C - H \]
(Br is on the other carbon)

2. **Structure 2**:
- \( C=C \)
- Cl on one carbon and Br on the other carbon, with H on the same carbon as Cl.
- Structure:
\[ Cl - C = C - Br \]

3. **Geometric Isomers**:
- **Cis Isomer**: Both Cl atoms on the same side.
- **Trans Isomer**: Cl atoms on opposite sides.

- **Cis Structure**:
\[ Cl - C = C - Cl \]
(Br and H can be on the same carbon as Cl)

- **Trans Structure**:
\[ Cl - C = C - Br \]

### Step 5: Count Non-Identical Structures
From the above analysis, we can summarize the non-identical structures:
1. Cl on one carbon, H on the other (with Br on the same carbon as Cl).
2. Cl on one carbon, Br on the other (with H on the same carbon as Cl).
3. Geometric isomers (Cis and Trans).

Thus, we find that there are **three non-identical structures** possible for \( C_2HCl_2Br \).

### Final Answer
The number of non-identical structures that are possible is **3**.

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