The total number of cyclic structure as well as stereoisomers
possible for a compound with the molecular formula `C_(5)H_(10)` is:

Options

A. (a) 7
B. (b) 9
C. (c) 12
D. (d) 13

Explanation

To determine the total number of cyclic structures and stereoisomers for a compound with the molecular formula C₅H₁₀, we can follow these steps:

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

For C₅H₁₀:
\[ DU = \frac{2(5) + 2 - 10}{2} = \frac{10 + 2 - 10}{2} = \frac{2}{2} = 1 \]
This means there is one degree of unsaturation, indicating the presence of either a ring or a double bond.

### Step 2: Identify Possible Cyclic Structures
With one degree of unsaturation, we can have cyclic structures. For five carbon atoms, we can form:
- A **cyclopentane** (5-membered ring).
- A **cyclobutane** (4-membered ring) with a methyl group attached.
- A **cyclopropane** (3-membered ring) with two methyl groups attached.

### Step 3: Draw and Count the Isomers
1. **Cyclopentane**: This is a single structure.
2. **Cyclobutane with Methyl Group**: The methyl group can be attached in different positions, but due to symmetry, they are not unique. This gives us one unique isomer.
3. **Cyclopropane with Two Methyl Groups**: The two methyl groups can be positioned either on adjacent carbons (cis) or on opposite carbons (trans). This gives us two unique isomers.

### Step 4: Count the Total Cyclic Structures
From the above:
- 1 (Cyclopentane)
- 1 (Cyclobutane with a methyl group)
- 2 (Cyclopropane with two methyl groups)

Total cyclic structures = \(1 + 1 + 2 = 4\)

### Step 5: Identify Stereoisomers
Now, we need to consider stereoisomers:
- For the cyclopropane with two methyl groups, we have cis and trans forms, which are stereoisomers.
- The cyclobutane with a methyl group can also exhibit stereoisomerism depending on the orientation of the methyl group.

### Step 6: Total Count of Isomers
Combining all the isomers:
- Cyclopentane: 1
- Cyclobutane: 1
- Cyclopropane (cis and trans): 2

Thus, the total number of isomers (including stereoisomers) is:
\[ 1 + 1 + 2 = 4 \]

### Final Answer
The total number of cyclic structures and stereoisomers possible for a compound with the molecular formula C₅H₁₀ is **4**.

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