The carboxylic acid that does not undergo Hell-Velhard Zelinsky reaction, is

$(CH_3)_3C-COOH$

The correct answer is Option (4) → $(CH_3)_3C-COOH$

The Hell-Volhard-Zelinsky (HVZ) reaction is a method for the α-halogenation of carboxylic acids. This reaction involves the formation of an acyl halide intermediate, which can then be halogenated at the α-position. Here is a detailed breakdown of the reaction and an analysis of the given options.

Overview of the Hell-Volhard-Zelinsky Reaction

Mechanism: The reaction typically starts with a carboxylic acid reacting with a phosphorus halide (like phosphorus tribromide, \(PBr_3\)) to form an acyl halide.

The acyl halide can then be treated with a halogen (\(Br_2\) or \(Cl_2)\) to halogenate the α-carbon, where the \(\alpha \)-hydrogen is replaced by a halogen atom.

Analyzing Each Carboxylic Acid

1. \(CH_3COOH\) (Acetic Acid):

A simple carboxylic acid with one α-hydrogen.

Can undergo HVZ because it has an accessible α-hydrogen. The reaction would yield α-bromoacetic acid upon halogenation.

2. \(CH_3CH_2CH_2CH_2COOH\) (Butanoic Acid):

A straight-chain carboxylic acid with two α-hydrogens.

Can undergo HVZ. Both α-hydrogens are accessible for halogenation, leading to α-bromobutanoic acid.

3. \((CH_3)_2CHCOOH\) (Isobutyric Acid):

A branched carboxylic acid with two methyl groups on the α-carbon.

Can also undergo HVZ, but the steric hindrance from the two methyl groups can affect the reaction rate. It is still capable of halogenation due to the presence of an α-hydrogen.

4. \((CH_3)_3C−COOH\) (tert-Butyric Acid):

This carboxylic acid has a tert-butyl group at the α-carbon, which is heavily branched.

The steric hindrance from the three methyl groups makes it very difficult for the reaction to proceed. The α-carbon does not have any accessible hydrogen atoms due to the tert-butyl group's bulky nature, preventing the formation of the acyl halide or the halogenation step.

Conclusion

Given this analysis, the carboxylic acid that does not undergo the Hell-Volhard-Zelinsky reaction is: \((CH_3)_3C−COOH\) (tert-Butyric Acid).

The tert-butyl group provides significant steric hindrance, effectively blocking the α-hydrogens from participating in the reaction, which is why this compound cannot undergo the HVZ reaction.