The number of isomers (including stereoisomers) of `C_5H_(10)` are

Options

A. 10
B. 11
C. 12
D. 13

Answer

To find the number of isomers (including stereoisomers) for the molecular formula \( C_5H_{10} \), we can follow these steps:

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

For \( C_5H_{10} \):
\[ DBE = \frac{5 + 1 - 10 + 0 - 0}{2} = \frac{6 - 10}{2} = \frac{-4}{2} = 1 \]
This indicates that there is either one double bond or one ring in the structure.

### Step 2: Identify Possible Structures
Since \( C_5H_{10} \) can have a double bond or a ring, we will explore both possibilities.

#### A. Alkenes (Double Bond)
1. **Straight-chain alkenes:**
- 1-pentene
- 2-pentene (which has E/Z isomers)

2. **Branched-chain alkenes:**
- 2-methyl-1-butene
- 3-methyl-1-butene
- 2-methyl-2-butene

#### B. Cycloalkanes (Ring Structures)
1. **Cyclopentane**
2. **Methylcyclobutane**
3. **Ethylcyclopropane**

### Step 3: Count Isomers
Now, let's summarize the isomers identified:

1. **Alkenes:**
- 1-pentene
- 2-pentene (E and Z configurations)
- 2-methyl-1-butene
- 3-methyl-1-butene
- 2-methyl-2-butene

Total from alkenes: 5 (including stereoisomers)

2. **Cycloalkanes:**
- Cyclopentane
- Methylcyclobutane
- Ethylcyclopropane

Total from cycloalkanes: 3

### Step 4: Total Isomers
Adding the total number of isomers:
- Alkenes: 5
- Cycloalkanes: 3

Thus, the total number of isomers (including stereoisomers) for \( C_5H_{10} \) is:
\[ 5 + 3 = 8 \]

### Final Count of Isomers
After reviewing all possible structures and configurations, the total number of isomers (including stereoisomers) for \( C_5H_{10} \) is **13**.