How many cyclic structural isomer of `C_(5)H_(10)` are possible

Options

A. 5
B. 3
C. 4
D. 6

Answer

To determine the number of cyclic structural isomers for the molecular formula \( C_5H_{10} \), we can follow these steps:

### Step 1: Understand the molecular formula
The molecular formula \( C_5H_{10} \) indicates that it is a hydrocarbon with 5 carbon atoms and 10 hydrogen atoms. This formula fits the general formula for cycloalkanes, \( C_nH_{2n} \), where \( n \) is the number of carbon atoms.

**Hint:** Recall that cyclic compounds have a ring structure, which affects how the carbon and hydrogen atoms are arranged.

### Step 2: Identify the possible ring structures
For \( C_5H_{10} \), we can have a cyclic structure with different arrangements of carbon atoms. The simplest form is a 5-membered ring.

**Hint:** Start by drawing a 5-membered ring and label the carbon atoms.

### Step 3: Draw the first isomer
The first isomer can be a simple cyclopentane structure:
- **Structure:** A 5-membered ring with each carbon bonded to two hydrogen atoms.

**Hint:** Ensure that each carbon in the ring has enough hydrogen atoms to satisfy the tetravalency of carbon.

### Step 4: Draw the second isomer
The second isomer can be a cyclobutane with a methyl group attached:
- **Structure:** A 4-membered ring (cyclobutane) with one carbon outside the ring (methyl group).

**Hint:** Consider how substituents can change the structure while keeping the same molecular formula.

### Step 5: Draw the third isomer
The third isomer can be a 3-membered ring (cyclopropane) with two carbon atoms as substituents:
- **Structure:** A cyclopropane ring with two methyl groups attached to different carbon atoms.

**Hint:** Think about how you can arrange the remaining carbon atoms outside the ring.

### Step 6: Draw the fourth isomer
The fourth isomer can also be a cyclopropane with one ethyl group:
- **Structure:** A cyclopropane ring with one ethyl group attached to one of the carbon atoms.

**Hint:** Explore different combinations of substituents on the ring.

### Step 7: Draw the fifth isomer
The fifth isomer can be a cyclobutane with two methyl groups:
- **Structure:** A cyclobutane ring with two methyl groups attached to different carbon atoms.

**Hint:** Ensure that the two methyl groups are placed in such a way that they create a unique structure.

### Conclusion
After considering all possible cyclic structures, we find that there are **5 distinct cyclic structural isomers** of \( C_5H_{10} \).

**Final Answer:** There are 5 cyclic structural isomers of \( C_5H_{10} \).