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 find the molecular weight of the organic monocarboxylic acid from the given vapor density of its methyl ester, we can follow these steps:

### Step 1: Understand the relationship between vapor density and molecular weight
The vapor density (VD) of a substance is defined as the ratio of the molecular weight (MW) of that substance to the molecular weight of hydrogen (H2). The formula is:
\[ \text{Vapor Density} = \frac{\text{Molecular Weight of A}}{\text{Molecular Weight of H2}} \]

### Step 2: Use the given vapor density to find the molecular weight of the methyl ester (A)
We know the vapor density of the methyl ester (A) is 37. The molecular weight of hydrogen (H2) is 2 g/mol. Using the formula:
\[ 37 = \frac{\text{Molecular Weight of A}}{2} \]
To find the molecular weight of A, we rearrange the equation:
\[ \text{Molecular Weight of A} = 37 \times 2 = 74 \, \text{g/mol} \]

### Step 3: Determine the molecular weight of the monocarboxylic acid
The methyl ester of a monocarboxylic acid can be represented as RCOOCH3. The molecular weight of the methyl ester consists of the molecular weight of the acid plus the molecular weight of the methyl group (CH3).

The methyl group (CH3) has a molecular weight of:
- Carbon (C) = 12 g/mol
- Hydrogen (H) = 1 g/mol × 3 = 3 g/mol
- Total for CH3 = 12 + 3 = 15 g/mol

Since the methyl ester is formed from the acid by replacing the -OH group with -OCH3, we need to subtract the molecular weight of the methyl group from the molecular weight of the ester to find the molecular weight of the acid.

### Step 4: Calculate the molecular weight of the acid
To find the molecular weight of the monocarboxylic acid, we subtract the molecular weight of the methyl group from the molecular weight of the methyl ester:
\[ \text{Molecular Weight of Acid} = \text{Molecular Weight of A} - \text{Molecular Weight of CH3} \]
\[ \text{Molecular Weight of Acid} = 74 - 15 = 59 \, \text{g/mol} \]

### Final Answer
The molecular weight of the organic monocarboxylic acid is **59 g/mol**.

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