The number of isomers possible for the molecular formula `C_(2)` FCIBrl is

Options

A. 2
B. 3
C. 4
D. 6

Answer

To determine the number of isomers possible for the molecular formula C₂FClBrI, we will follow these steps:

### Step 1: Determine the Structure
The molecular formula C₂FClBrI indicates that we have 2 carbon atoms and 4 halogen atoms (F, Cl, Br, I).

### Step 2: Calculate the Double Bond Equivalent (DBE)
The formula for calculating the Double Bond Equivalent (DBE) is:
\[ \text{DBE} = C + 1 - \frac{H + N + X}{2} \]
Where:
- \(C\) = number of carbon atoms
- \(H\) = number of hydrogen atoms
- \(N\) = number of nitrogen atoms
- \(X\) = number of halogen atoms

For C₂FClBrI:
- \(C = 2\)
- \(H = 0\) (since there are no hydrogen atoms in the formula)
- \(N = 0\) (no nitrogen atoms)
- \(X = 4\) (F, Cl, Br, I)

Substituting the values:
\[ \text{DBE} = 2 + 1 - \frac{0 + 0 + 4}{2} = 3 - 2 = 1 \]

### Step 3: Identify Possible Structures
A DBE of 1 indicates that there is either a double bond or a ring. However, since we only have 2 carbon atoms, a ring structure is not feasible. Therefore, we will have a carbon-carbon double bond.

### Step 4: Draw Possible Isomers
With the carbon-carbon double bond, we can arrange the halogens around the double bond. The possible arrangements can be:
1. **C=C with different halogens on each carbon**:
- C1: F, C2: Cl
- C1: F, C2: Br
- C1: F, C2: I
- C1: Cl, C2: Br
- C1: Cl, C2: I
- C1: Br, C2: I

### Step 5: Consider Geometric Isomers
Since we have different halogens attached to the double bond, we can also have cis/trans isomers:
- For example, if we take F and Cl on one carbon and Br and I on the other, we can have:
- **Cis Isomer**: Both higher priority groups (based on atomic number) on the same side.
- **Trans Isomer**: Higher priority groups on opposite sides.

### Step 6: Count the Isomers
From the arrangements, we can derive the following isomers:
1. **Cis and Trans Isomers** for each arrangement of halogens.

After analyzing all possible configurations, we find that there are a total of **6 unique isomers** (considering cis and trans).

### Final Answer
The number of isomers possible for the molecular formula C₂FClBrI is **6**.

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