Which of the following is correct order of esterification of following acids with `CH_(3)OH` :
`underset(I)(HCOOH)," "underset(II)(CH_(3)COOH)," "underset(III)(CH_(3)-CH_(2)-COOH)," "underset(IV)(CH_(3) - underset(CH_(3))underset(|)(CH) - COOH)`

Options

A. I = II = III = IV
B. `I gt II gt III gt IV`
C. `I lt II lt III lt IV`
D. `I gt IV gt III gt II`

Explanation

To determine the correct order of esterification of the given acids with methanol (CH₃OH), we need to analyze the structure of each acid and how the presence of electron-donating or electron-withdrawing groups affects the electrophilicity of the carbonyl carbon in the carboxylic acid. The higher the electrophilicity, the faster the esterification reaction will occur.

### Step-by-Step Solution:

1. **Identify the Acids**:
- (I) HCOOH (Formic Acid)
- (II) CH₃COOH (Acetic Acid)
- (III) CH₃-CH₂-COOH (Propanoic Acid)
- (IV) CH₃-CH(CH₃)-COOH (Isobutyric Acid)

2. **Understand the Mechanism of Esterification**:
- Esterification involves the reaction of a carboxylic acid with an alcohol, resulting in the formation of an ester and the release of water. The electrophilicity of the carbonyl carbon in the carboxylic acid is crucial for the reaction rate.

3. **Evaluate Electrophilicity**:
- **Formic Acid (I)**: Has no alkyl groups, making it more electrophilic due to less steric hindrance and no electron-donating groups.
- **Acetic Acid (II)**: Contains one methyl group (electron-donating), which slightly decreases electrophilicity compared to formic acid.
- **Propanoic Acid (III)**: Contains an ethyl group (more electron-donating than a methyl group), further decreasing electrophilicity.
- **Isobutyric Acid (IV)**: Contains two methyl groups, which significantly reduce electrophilicity due to increased steric hindrance and electron donation.

4. **Rank the Acids Based on Electrophilicity**:
- The order of decreasing electrophilicity (and thus increasing reactivity towards methanol) is:
- (I) HCOOH > (II) CH₃COOH > (III) CH₃-CH₂-COOH > (IV) CH₃-CH(CH₃)-COOH

5. **Conclusion**:
- The correct order of esterification of the acids with methanol is:
- HCOOH > CH₃COOH > CH₃-CH₂-COOH > CH₃-CH(CH₃)-COOH

### Final Answer:
The correct order of esterification with CH₃OH is:
**(I) > (II) > (III) > (IV)**