How many carboxylic acids (structural isomers only ) of molecular formula `C_5H_10O_2` is possible

Answer

To determine the number of structural isomers of carboxylic acids with the molecular formula \( C_5H_{10}O_2 \), we can follow these steps:

### Step 1: Understand the Structure of Carboxylic Acids
Carboxylic acids contain a carboxyl group (-COOH) and can be represented as \( R-COOH \), where \( R \) is a hydrocarbon chain. The molecular formula \( C_5H_{10}O_2 \) indicates that we have a total of 5 carbon atoms, 10 hydrogen atoms, and 2 oxygen atoms.

### Step 2: Determine the Carbon Skeleton
We need to consider different carbon skeletons that can accommodate the carboxylic acid functional group. The carbon skeleton can be either straight-chain or branched.

### Step 3: Identify Possible Structures
1. **Straight-chain Carboxylic Acids**:
- **Pentanoic Acid**: \( CH_3(CH_2)_3COOH \) (1 straight chain)

2. **Branched Carboxylic Acids**:
- **2-Methylbutanoic Acid**: \( (CH_3)_2CH(CH_2)COOH \) (1 branched structure)
- **3-Methylbutanoic Acid**: \( CH_3CH(CH_3)CH_2COOH \) (1 branched structure)
- **2,2-Dimethylpropanoic Acid**: \( (CH_3)_3C-COOH \) (1 branched structure)

### Step 4: Count the Isomers
From the structures identified:
1. Pentanoic Acid
2. 2-Methylbutanoic Acid
3. 3-Methylbutanoic Acid
4. 2,2-Dimethylpropanoic Acid

Thus, we have a total of **4 structural isomers** of carboxylic acids for the molecular formula \( C_5H_{10}O_2 \).

### Final Answer
The number of structural isomers of carboxylic acids with the molecular formula \( C_5H_{10}O_2 \) is **4**.

---