Find the number of geometrical isomers of the given compound .
`C_(6)H_(5) - CH = CH - CH-CH = CH - CH = CH - COOH`

Answer

To find the number of geometrical isomers of the compound \( C_6H_5 - CH = CH - CH - CH = CH - CH = CH - COOH \), we will follow these steps:

### Step 1: Identify the Structure
The given compound has a phenyl group (\( C_6H_5 \)) attached to a chain of carbon atoms with multiple double bonds, and a carboxylic acid group (\( -COOH \)) at the end. The structure can be represented as follows:

\[ C_6H_5 - CH = CH - CH - CH = CH - CH = CH - COOH \]

### Step 2: Count the Number of Double Bonds
In the structure, we can identify the number of double bonds present. The compound has three double bonds:

1. Between the first and second carbon atoms.
2. Between the third and fourth carbon atoms.
3. Between the fifth and sixth carbon atoms.

Thus, \( n = 3 \) (where \( n \) is the number of double bonds).

### Step 3: Determine if the Compound is Symmetrical or Unsymmetrical
Next, we need to determine whether the compound is symmetrical or unsymmetrical. A symmetrical compound has the same groups at both ends, while an unsymmetrical compound has different groups.

In this case, the starting group is a phenyl group (\( C_6H_5 \)) and the ending group is a carboxylic acid group (\( -COOH \)). Since these two groups are different, the compound is unsymmetrical.

### Step 4: Apply the Formula for Unsymmetrical Compounds
For unsymmetrical compounds, the formula to calculate the number of geometrical isomers is:

\[ \text{Number of geometrical isomers} = 2^n \]

### Step 5: Calculate the Number of Geometrical Isomers
Now, substituting the value of \( n \) into the formula:

\[ \text{Number of geometrical isomers} = 2^3 = 8 \]

### Conclusion
Thus, the number of geometrical isomers of the given compound is **8**.

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