How many pair(s) of geometrical isomers are possible with`C_(5) H_(10)` (only open chain structues)

Answer

To determine how many pairs of geometrical isomers are possible for the molecular formula \( C_5H_{10} \) (considering only open-chain structures), we can follow these steps:

### Step 1: Calculate the Degree of Unsaturation
The degree of unsaturation can be calculated using the formula:

\[ \text{Degree of Unsaturation} = \frac{C + 1 - H}{2} \]

Where:
- \( C \) = number of carbon atoms
- \( H \) = number of hydrogen atoms

For \( C_5H_{10} \):
- \( C = 5 \)
- \( H = 10 \)

Substituting the values:

\[ \text{Degree of Unsaturation} = \frac{5 + 1 - 10}{2} = \frac{-4}{2} = -2 \]

Since the degree of unsaturation cannot be negative, we must have at least one double bond or a ring structure. In this case, we will consider the presence of a double bond.

### Step 2: Identify Possible Structures with a Double Bond
We can have several structural isomers that contain a double bond. The possible structures for \( C_5H_{10} \) with a double bond include:

1. **1-Pentene**: \( CH_2=CH-CH_2-CH_2-CH_3 \)
2. **2-Pentene**: \( CH_3-CH=CH-CH_2-CH_3 \)

### Step 3: Determine Geometrical Isomers
Geometrical isomers (cis-trans isomers) occur when there are different groups attached to the carbons involved in the double bond.

1. **1-Pentene**:
- This compound does not have geometrical isomers because the double bond is at the terminal position, and both ends have hydrogen atoms.

2. **2-Pentene**:
- This compound can have geometrical isomers:
- **Cis-2-pentene**: The two methyl groups (CH3) are on the same side of the double bond.
- **Trans-2-pentene**: The two methyl groups (CH3) are on opposite sides of the double bond.

### Step 4: Count the Pairs of Geometrical Isomers
From the analysis:
- 1-Pentene has no geometrical isomers.
- 2-Pentene has 1 pair of geometrical isomers (cis and trans).

Thus, the total number of pairs of geometrical isomers for \( C_5H_{10} \) is **1 pair**.

### Final Answer
The number of pairs of geometrical isomers possible for \( C_5H_{10} \) is **1**.

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