Calculate sum of structural methyl esters and carboxylic acids with molecular formula `C_(5)H_(10)O_(2)`.

Explanation

To solve the problem of calculating the sum of structural methyl esters and carboxylic acids with the molecular formula C5H10O2, we will follow these steps:

### Step 1: Identify the Functional Groups
The molecular formula C5H10O2 indicates that we are looking for compounds that contain either a methyl ester (RCOOCH3) or a carboxylic acid (RCOOH).

### Step 2: Draw Structural Formulas for Methyl Esters
1. **First Methyl Ester Structure**:
- Start with a straight-chain structure:
- CH3-CH2-CH2-C(=O)-O-CH3
- This can be written as:
- CH3-CH2-CH2-COOCH3

2. **Second Methyl Ester Structure**:
- Create a branched structure:
- CH3-CH(CH3)-C(=O)-O-CH3
- This can be written as:
- CH3-CH(CH3)-COOCH3

### Total Methyl Esters: 2

### Step 3: Draw Structural Formulas for Carboxylic Acids
1. **First Carboxylic Acid Structure**:
- Straight-chain structure:
- CH3-CH2-CH2-COOH

2. **Second Carboxylic Acid Structure**:
- Branched structure:
- CH3-CH(CH3)-CH2-COOH

3. **Third Carboxylic Acid Structure**:
- Another branched structure:
- CH3-CH2-CH(CH3)-COOH

4. **Fourth Carboxylic Acid Structure**:
- Another variation:
- CH3-C(CH3)-CH2-COOH

5. **Fifth Carboxylic Acid Structure**:
- Final branched structure:
- CH3-C(CH3)-COOH

### Total Carboxylic Acids: 5

### Step 4: Calculate the Total Structures
- Total Methyl Esters = 2
- Total Carboxylic Acids = 5
- **Sum of Structures** = 2 (methyl esters) + 5 (carboxylic acids) = **7**

### Final Answer
The total number of structural methyl esters and carboxylic acids with the molecular formula C5H10O2 is **7**.

---