Complete the missing lnks (X), (Y) and (Z) by making an appropriate choice.
`CH_(3)COOH overset(PBr_(3)//Br_(2))toXoverset(KCN)toYoverset(H_(3)O^(+))toZ`

Options

A. `{:(" X"," Y"," Z"),(CH_(3)COBr,CH_(3)COCN,CH_(3)COOH):}`
B. `{:(" X"," Y"," Z"),(BrCH_(2)COOH,underset(CN)underset(|)CH_(2)COOH,HOOC-CH_(2)COOH):}`
C. `{:(" X"," Y"," Z"),(BrCH_(2)COOH,CH_(2)(CN)COOH,overset(" COOH")underset(" COOH")("|")):}`
D. `{:(" X"," Y"," Z"),(Br_(2)CHCOOH,Br_(2)C(CN)COOH,CH_(3)CH_(2)COOH):}`

Explanation

To solve the question, we need to identify the compounds X, Y, and Z in the reaction sequence starting from acetic acid (CH₃COOH) and going through the given reagents.

### Step-by-Step Solution:

1. **Identify the starting compound:**
The starting compound is acetic acid, which has the structure CH₃COOH.

2. **Reaction with PBr₃ and Br₂:**
Acetic acid reacts with phosphorus tribromide (PBr₃) and bromine (Br₂). This reaction will convert the hydroxyl (-OH) group of acetic acid into a bromine atom, resulting in the formation of brominated acetic acid.
- **Product X:** The product formed is brominated acetic acid, which can be represented as BrCH₂COOH.

3. **Reaction with KCN:**
The brominated acetic acid (X) then reacts with potassium cyanide (KCN). In this step, the cyanide ion (CN⁻) acts as a nucleophile and attacks the carbon atom bonded to the bromine atom, leading to the substitution of the bromine atom with the cyanide group.
- **Product Y:** The product formed is 2-cyanoacetic acid, which can be represented as CNCH₂COOH.

4. **Reaction with H₃O⁺:**
The 2-cyanoacetic acid (Y) then undergoes acidic hydrolysis when treated with hydronium ions (H₃O⁺). During this reaction, the cyano group (CN) is converted into a carboxylic acid group (-COOH) through hydrolysis.
- **Product Z:** The final product formed is 2-carboxyacetic acid, which can be represented as HOOC-CH₂-COOH.

### Summary of Products:
- **X:** BrCH₂COOH (Brominated acetic acid)
- **Y:** CNCH₂COOH (2-Cyanoacetic acid)
- **Z:** HOOC-CH₂-COOH (2-Carboxyacetic acid)

Thus, the missing links are:
- (X) = BrCH₂COOH
- (Y) = CNCH₂COOH
- (Z) = HOOC-CH₂-COOH