The number of isomers of `c_(3) H_(5) Br_(3)` (including stereoisomers )

Options

A. 4
B. 5
C. 6
D. 7

Answer

To determine the number of isomers of \( C_3H_5Br_3 \) including stereoisomers, we can follow these steps:

### Step 1: Identify the Molecular Formula
The molecular formula is \( C_3H_5Br_3 \). This indicates that we have three carbon atoms, five hydrogen atoms, and three bromine atoms.

### Step 2: Determine Possible Structures
We can start by drawing the possible structural isomers based on the arrangement of carbon and bromine atoms.

1. **Straight-chain structure**: The simplest structure is a straight chain of three carbon atoms (propane).
- **Isomer 1**: \( CH_3-CHBr-CH_2Br \) (with bromine on the second carbon)
- **Isomer 2**: \( CH_2Br-CHBr-CH_3 \) (with bromine on the first and second carbons)
- **Isomer 3**: \( CHBr_2-CH_2-CH_3 \) (with two bromines on the first carbon)

### Step 3: Consider Positional Isomers
Next, we can consider different positions for the bromine atoms on the carbon chain:
- **Isomer 4**: \( CH_3-CH_2-CHBr_2 \) (bromine on the last carbon)
- **Isomer 5**: \( CH_2Br-CH_2-CHBr \) (bromine on the first and second carbons)

### Step 4: Identify Stereoisomers
Now, we need to check for stereoisomers. Stereoisomers occur when there is a chiral center in the molecule. A chiral center is typically a carbon atom that is attached to four different groups.

- In the structure \( CH_3-CHBr-CH_2Br \), the second carbon (attached to \( CH_3 \), \( CH_2Br \), and \( Br \)) can be a chiral center, leading to two stereoisomers (R and S configurations).

### Step 5: Count All Isomers
Now, let's summarize the isomers:
1. \( CH_3-CHBr-CH_2Br \) (1 chiral center, 2 stereoisomers)
2. \( CH_2Br-CHBr-CH_3 \) (1 chiral center, 2 stereoisomers)
3. \( CHBr_2-CH_2-CH_3 \) (no chiral centers)
4. \( CH_3-CH_2-CHBr_2 \) (no chiral centers)
5. \( CH_2Br-CH_2-CHBr \) (1 chiral center, 2 stereoisomers)

### Final Count
- Total isomers: 5 structural isomers + 4 stereoisomers (2 from each chiral structure) = 9 isomers.

### Conclusion
The total number of isomers of \( C_3H_5Br_3 \), including stereoisomers, is **9**.

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