Total number of compounds with molecular formula `C_(5) H_(10)`which can show geometrical isomerism are (only cyclic)?

Answer

To determine the total number of cyclic compounds with the molecular formula \(C_5H_{10}\) that can show geometrical isomerism, we will follow these steps:

### Step 1: Determine the Degree of Unsaturation
The degree of unsaturation can be calculated using the formula:
\[ \text{Degree of Unsaturation} = \frac{(2C + 2 + N - H - X)}{2} \]
Where:
- \(C\) = number of carbon atoms
- \(H\) = number of hydrogen atoms
- \(N\) = number of nitrogen atoms
- \(X\) = number of halogen atoms

For \(C_5H_{10}\):
- \(C = 5\)
- \(H = 10\)
- \(N = 0\)
- \(X = 0\)

Plugging in the values:
\[ \text{Degree of Unsaturation} = \frac{(2 \times 5 + 2 - 10)}{2} = \frac{(10 + 2 - 10)}{2} = \frac{2}{2} = 1 \]

### Step 2: Identify Possible Cyclic Structures
A degree of unsaturation of 1 indicates either a double bond or a ring structure. Since we are only considering cyclic compounds, we will focus on cyclic structures.

For \(C_5H_{10}\), we can form a cyclopentane structure or other cyclic structures with substituents.

1. **Cyclopentane (C5H10)**: A simple ring with no substituents.
2. **Methylcyclobutane**: A four-membered ring with one methyl group.
3. **Cyclobutylmethyl**: A three-membered ring with two methyl groups.

### Step 3: Analyze for Geometrical Isomerism
Geometrical isomerism (cis-trans isomerism) occurs when there are two different groups attached to the same carbon atoms in a ring structure.

1. **Cyclopentane**: Does not show geometrical isomerism as all carbon atoms are equivalent.
2. **Methylcyclobutane**: Can show geometrical isomerism. The two methyl groups can be positioned either on the same side (cis) or opposite sides (trans).
3. **Cyclobutylmethyl**: Also can show geometrical isomerism with the two substituents being either on the same side or opposite sides.

### Step 4: Count the Compounds
From the analysis:
- **Methylcyclobutane**: 1 compound showing geometrical isomerism.
- **Cyclobutylmethyl**: 1 compound showing geometrical isomerism.

Thus, the total number of cyclic compounds with the molecular formula \(C_5H_{10}\) that can show geometrical isomerism is **2**.

### Final Answer
The total number of cyclic compounds with the molecular formula \(C_5H_{10}\) that can show geometrical isomerism is **2**.

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