Let 'A ' be the methyl ester of an organic monocarboxylic acid. The vapour density of 'A' is 37. What is the molecular weight of the acid ?

Options

A. 46
B. 60
C. 70
D. 74

Answer

To solve the problem, we need to find the molecular weight of the organic monocarboxylic acid given that the vapor density of its methyl ester is 37.

### Step-by-Step Solution:

1. **Understanding the Methyl Ester**:
- The methyl ester of a carboxylic acid can be represented as RCOOCH3, where R is the hydrocarbon part of the acid.

2. **Vapor Density Formula**:
- The vapor density (VD) is defined as the ratio of the molecular weight of the substance to the molecular weight of hydrogen (H2).
- The formula for vapor density is:
\[ \text{Vapor Density} = \frac{\text{Molecular Weight of A}}{\text{Molecular Weight of H2}} \]

3. **Molecular Weight of Hydrogen**:
- The molecular weight of hydrogen (H2) is 2 g/mol (since H has an atomic weight of approximately 1 g/mol).

4. **Calculating the Molecular Weight of Methyl Ester (A)**:
- Rearranging the vapor density formula gives us:
\[ \text{Molecular Weight of A} = \text{Vapor Density} \times \text{Molecular Weight of H2} \]
- Substituting the values:
\[ \text{Molecular Weight of A} = 37 \times 2 = 74 \text{ g/mol} \]

5. **Finding the Molecular Weight of the Carboxylic Acid**:
- The molecular weight of the methyl ester (A) is 74 g/mol. The structure of the methyl ester can be broken down into the components of the carboxylic acid and the methyl group:
- Methyl group (CH3) contributes: 12 (C) + 3 (H) = 15 g/mol
- The carboxylic acid (RCOOH) contributes: 1 (C) + 1 (O) + 1 (O) + 1 (H) = 45 g/mol
- Therefore, the molecular weight of the acid can be calculated as:
\[ \text{Molecular Weight of Acid} = \text{Molecular Weight of A} - \text{Molecular Weight of Methyl Group} \]
- Substituting the values:
\[ \text{Molecular Weight of Acid} = 74 - 15 = 59 \text{ g/mol} \]

6. **Final Result**:
- The molecular weight of the organic monocarboxylic acid is approximately 60 g/mol.

### Conclusion:
The molecular weight of the organic monocarboxylic acid is **60 g/mol**.