The number of ether metamers represented by the formula `C_4H_(10)O` is

Options

A. 2
B. 3
C. 4
D. 1

Explanation

To determine the number of ether metamers represented by the formula C₄H₁₀O, we can follow these steps:

### Step 1: Understand the Structure of Ethers
Ethers have the general formula R-O-R', where R and R' can be different alkyl groups. In the case of C₄H₁₀O, we need to identify the different possible combinations of R and R' that can yield ethers.

**Hint:** Remember that R and R' can be the same or different, leading to different structural isomers.

### Step 2: Identify Possible Alkyl Groups
The molecular formula C₄H₁₀O indicates that we have 4 carbon atoms. The possible alkyl groups that can be formed with 4 carbon atoms are:
- Butyl (C₄H₉)
- Propyl (C₃H₇)
- Ethyl (C₂H₅)
- Methyl (C₁H₃)

**Hint:** Think about how many different combinations of these alkyl groups can be formed while keeping the total number of carbon atoms equal to 4.

### Step 3: Generate Ether Structures
Now, we can create different ether structures (metamers) by varying the combinations of the alkyl groups:

1. **Methoxypropane**: CH₃-O-CH₂-CH₂-CH₃ (where R = CH₃ and R' = C₃H₇)
2. **Ethoxyethane**: CH₃-CH₂-O-CH₂-CH₃ (where R = C₂H₅ and R' = C₂H₅)
3. **Dimethyl ether**: CH₃-O-CH₃ (where R = R' = CH₃)

**Hint:** For each combination of R and R', ensure that the total number of carbon atoms adds up to 4.

### Step 4: Count the Unique Ethers
After generating the structures, we can count the unique ethers we have formed:
- Methoxypropane
- Ethoxyethane
- Dimethyl ether

Thus, there are **3 unique ether metamers** that can be formed from the molecular formula C₄H₁₀O.

### Final Answer
The number of ether metamers represented by the formula C₄H₁₀O is **3**.

---