Which `beta`-keto acid shown will not undergo decarboxylation?

Options

A.
B.
C. `Ph-overset(O)overset(||)(C)-CH_(2)-CO_(2)H`
D. `CH_(3)-overset(O)overset(||)(C)-CH_(2)-CO_(2)H`

Explanation

To determine which beta-keto acid will not undergo decarboxylation, we need to understand the structure of beta-keto acids and the conditions under which decarboxylation occurs.

### Step-by-Step Solution:

1. **Identify Beta-Keto Acids**:
- Beta-keto acids are compounds that contain a carboxylic acid group (-COOH) and a ketone group (C=O) at the beta position relative to each other. The structure can be represented as R1C(=O)C(=O)OH, where R1 is any alkyl or aryl group.

2. **Understand Decarboxylation**:
- Decarboxylation is the process where a carboxyl group (-COOH) is removed from a molecule, releasing carbon dioxide (CO2). For beta-keto acids, this typically occurs when the resulting structure after decarboxylation can stabilize the remaining molecule.

3. **Analyze the Structures**:
- For each beta-keto acid structure, we need to analyze whether the decarboxylation will lead to a stable compound or if it will violate any rules of organic chemistry, such as the Bredt's rule.

4. **Bredt's Rule**:
- Bredt's rule states that a double bond cannot be formed at a bridgehead position in a bicyclic compound. If the decarboxylation of a beta-keto acid leads to a structure that has a double bond at a bridgehead carbon, it will not occur.

5. **Evaluate Each Beta-Keto Acid**:
- Examine each beta-keto acid provided in the question. Identify which one, upon decarboxylation, would lead to a structure that violates Bredt's rule.

6. **Conclusion**:
- The beta-keto acid that has a structure leading to a double bond at a bridgehead carbon after decarboxylation will not undergo decarboxylation. This is the compound that violates Bredt's rule.

### Final Answer:
The beta-keto acid that will not undergo decarboxylation is the one that leads to a structure violating Bredt's rule.