Number of structurally isomeric ether with molecular formula `C_(5)H_(12)O`.

Options

A. 4
B. 5
C. 6
D. 7

Answer

To determine the number of structurally isomeric ethers with the molecular formula \( C_5H_{12}O \), we can follow these steps:

### Step 1: Understand the General Structure of Ethers
Ethers have the general structure \( R-O-R' \), where \( R \) and \( R' \) are alkyl groups. The oxygen atom is bonded to two carbon atoms.

### Step 2: Calculate the Degree of Unsaturation
The degree of unsaturation (or double bond equivalent) can be calculated using the formula:
\[ \text{DBE} = \frac{(2C + 2 + N - H)}{2} \]
For \( C_5H_{12}O \):
- \( C = 5 \)
- \( H = 12 \)
- \( N = 0 \)

Plugging in the values:
\[ \text{DBE} = \frac{(2 \times 5 + 2 + 0 - 12)}{2} = \frac{(10 + 2 - 12)}{2} = \frac{0}{2} = 0 \]
This indicates that the compound is acyclic and does not contain any double bonds.

### Step 3: Identify Possible Alkyl Groups
Since we have 5 carbon atoms, we can form different combinations of alkyl groups. The possible combinations of \( R \) and \( R' \) can be derived from the different ways to arrange the carbon atoms.

### Step 4: Draw the Isomeric Structures
1. **Isomer 1**: \( CH_3-CH_2-CH_2-CH_2-O-CH_3 \) (Diethyl ether)
2. **Isomer 2**: \( CH_3-CH_2-O-CH_2-CH_3 \) (Ethyl methyl ether)
3. **Isomer 3**: \( CH_3-O-CH_2-CH_2-CH_3 \) (Methyl butyl ether)
4. **Isomer 4**: \( CH_3-CH(O)-CH_2-CH_3 \) (Isobutyl methyl ether)
5. **Isomer 5**: \( CH_3-CH_2-CH(O)-CH_3 \) (Sec-butyl methyl ether)
6. **Isomer 6**: \( CH_3-O-CH(CH_3)-CH_2-CH_3 \) (Tert-butyl methyl ether)

### Step 5: Count the Isomers
After drawing all possible structures, we find that there are a total of **6 structurally isomeric ethers** for the molecular formula \( C_5H_{12}O \).

### Final Answer
The number of structurally isomeric ethers with the molecular formula \( C_5H_{12}O \) is **6**.

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