Compound having molecular formula `C_(5)H_(12)O` cannot show

Options

A. Tautomerism
B. Position isomerism
C. Metamerism
D. Functional isomerism

Answer

To determine which type of isomerism the compound with the molecular formula \( C_5H_{12}O \) cannot exhibit, we will analyze each option provided in the question.

### Step-by-Step Solution:

1. **Understanding the Molecular Formula**:
- The molecular formula \( C_5H_{12}O \) indicates that the compound contains 5 carbon atoms, 12 hydrogen atoms, and 1 oxygen atom.

2. **Analyzing Tautomerism**:
- Tautomerism involves the interconversion between two isomers, typically a keto form and an enol form.
- For a compound to exhibit tautomerism, it usually needs to have a carbonyl group (C=O) present, which is characteristic of ketones and aldehydes.
- Since \( C_5H_{12}O \) does not contain a carbonyl group (as it can only be an alcohol or ether), it cannot exhibit tautomerism.

3. **Analyzing Position Isomerism**:
- Position isomerism occurs when the position of a functional group changes within the same carbon skeleton.
- For example, different alcohols can be formed by varying the position of the hydroxyl group (-OH) in the carbon chain.
- Given that \( C_5H_{12}O \) can represent various alcohols (like pentanol) with the hydroxyl group in different positions, it can show position isomerism.

4. **Analyzing Metamerism**:
- Metamerism occurs in compounds with the same functional group but different alkyl groups on either side of the functional group.
- In the case of ethers derived from \( C_5H_{12}O \), different arrangements of alkyl groups around the oxygen can lead to metamerism.
- Thus, \( C_5H_{12}O \) can exhibit metamerism.

5. **Analyzing Functional Isomerism**:
- Functional isomerism occurs when compounds have the same molecular formula but different functional groups.
- For \( C_5H_{12}O \), it can exist as both an alcohol and an ether, which are functional isomers.
- Therefore, it can exhibit functional isomerism.

### Conclusion:
Based on the analysis, the compound with the molecular formula \( C_5H_{12}O \) **cannot show tautomerism**.

### Final Answer:
The compound having molecular formula \( C_5H_{12}O \) cannot show **tautomerism**.