In the given reaction
`CH_3-overset(Br)overset(|)(C )H-CH_2-COOH overset(NaOH)(rarr)(X)`.
'X' will be

Options

A. `CH_3-underset(OH)underset(|)OH(C )H-CH_2-COOH`
B. `CH_3-underset(OH)underset(|)(C )H-CH_2-COOH`
C. `CH_3-underset(OH)underset(|)(C )H-CH_2-COONa`
D. `CH_3-CH=CH-COOH`

Answer

To solve the given reaction step by step, we will analyze the structure and the reaction conditions provided.

### Step 1: Identify the Reactants
The reactant is given as:
\[ CH_3-CH(Br)-CH_2-COOH \]
This molecule contains a bromine atom (Br) attached to a carbon atom, and it also has a carboxylic acid group (-COOH).

### Step 2: Understand the Reaction Conditions
The reaction is treated with sodium hydroxide (NaOH), which is a strong base. In this reaction, the hydroxide ion (OH⁻) from NaOH will act as a nucleophile.

### Step 3: Nucleophilic Substitution Reaction
In the presence of NaOH, a nucleophilic substitution reaction (SN2 mechanism) will occur. The hydroxide ion (OH⁻) will attack the carbon atom that is bonded to the bromine atom (Br).

1. The OH⁻ ion will attack the carbon atom from the opposite side of the Br atom, leading to the displacement of the Br atom.
2. The Br atom will leave as Br⁻.

### Step 4: Formation of the Product
After the nucleophilic attack and the leaving of the Br atom, the product will be:
\[ CH_3-CH(OH)-CH_2-COO^- \]
This product will also have a sodium ion (Na⁺) from the dissociation of NaOH, resulting in:
\[ CH_3-CH(OH)-CH_2-COO^- \cdot Na^+ \]

### Step 5: Final Product Representation
The final product can be represented as:
\[ CH_3-CH(OH)-CH_2-COONa \]
This indicates that we have a sodium salt of the carboxylic acid.

### Conclusion
The product 'X' formed in the reaction is:
\[ CH_3-CH(OH)-CH_2-COONa \]

### Answer
Thus, the correct answer is option C: \( CH_3-CH(OH)-CH_2-COONa \).

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