For the following acids the rate of decarboxylation on heating would be
`I. CH_(6)H_(5)-overset(O)overset(||)(C)-CH_(2)-COOH " " (II) C_(6)H_(5)-overset(O)overset(||)(C)-COOH`
`III. CH_(3)-CH_(2)-COOH " " IV. HOOC-CH_(2)-COOH`

Options

A. III>I>IV>II
B. I>III>IV>II
C. III>IV>I>II
D. I>IV>II>III

Explanation

To determine the rate of decarboxylation of the given acids upon heating, we need to analyze the stability of the carbanion that forms during the decarboxylation process. The more stable the carbanion, the faster the decarboxylation will occur.

### Step-by-Step Solution:

1. **Understanding Decarboxylation**:
- Decarboxylation is the process of removing a carboxyl group (-COOH) from a compound, resulting in the release of carbon dioxide (CO2). The stability of the intermediate carbanion formed during this process is crucial in determining the rate of decarboxylation.

2. **Analyzing the Compounds**:
- **Compound I**: C₆H₅-C(=O)-CH₂-COOH
- Upon heating, the carboxylic acid group will lose CO2, forming a carbanion at the CH₂ position. The negative charge can resonate with the adjacent carbonyl group (C=O) and the phenyl ring, providing significant stabilization. Thus, this compound is expected to decarboxylate rapidly.

- **Compound II**: C₆H₅-C(=O)-COOH
- Here, the carboxylic acid group is directly attached to a carbonyl group. Upon heating, the carbanion formed will be less stable because it is not as effectively stabilized by resonance as in Compound I. Therefore, the rate of decarboxylation will be slower compared to Compound I.

- **Compound III**: CH₃-CH₂-COOH
- In this case, the carbanion formed after decarboxylation will be CH₃-CH₂⁻. The methyl group (CH₃) is an electron-donating group (+I effect), which destabilizes the carbanion. Thus, this compound will have a slower rate of decarboxylation.

- **Compound IV**: HOOC-CH₂-COOH
- This compound has two carboxylic acid groups. When heated, the carbanion formed will be CH₂⁻, which is destabilized by the presence of the adjacent carboxylic acid group (due to the -I effect). Therefore, this compound will decarboxylate the slowest.

3. **Ranking the Compounds**:
- Based on the stability of the carbanions formed:
- **Fastest Decarboxylation**: Compound I (most stable carbanion)
- **Next**: Compound II (less stable than I)
- **Next**: Compound III (unstable due to +I effect)
- **Slowest**: Compound IV (most unstable due to two -COOH groups)

4. **Final Order**:
- The order of decarboxylation rates from fastest to slowest is:
- I > II > III > IV

### Conclusion:
The correct order of decarboxylation rates upon heating for the given acids is:
**I > II > III > IV**.