Identify the final product (Z) in the following sequence of reactions :
`Me_2C=O+HCNrarr(X) overset(H_3O^+)rarr(Y)overset(H_2SO_4)rarr`

Options

A. `(CH_3)_2C(OH) COOH`
B. `CH_2=C(CH_3)COOH`
C. `HOCH_2CH(CH_3)COOH`
D. `CH_3CH=CHCOOH`

Answer

To identify the final product (Z) in the given sequence of reactions, let's break down the steps involved:

### Step 1: Identify the starting compound
The starting compound is dimethyl ketone, which can be represented as:
\[ \text{Me}_2C=O \]
This can be written as:
\[ \text{CH}_3C(=O)\text{CH}_3 \]

### Step 2: Reaction with HCN
When dimethyl ketone reacts with hydrogen cyanide (HCN), the nucleophilic cyanide ion (CN⁻) attacks the carbonyl carbon. The reaction can be represented as follows:
\[ \text{CH}_3C(=O)\text{CH}_3 + HCN \rightarrow \text{CH}_3C(\text{CN})(\text{OH})\text{CH}_3 \]
This results in the formation of a cyanohydrin (X):
\[ X = \text{CH}_3C(\text{CN})(\text{OH})\text{CH}_3 \]

### Step 3: Hydrolysis of X
Next, when the cyanohydrin (X) is treated with hydronium ions (H₃O⁺), the cyanide group (CN) is hydrolyzed to a carboxylic acid (COOH):
\[ \text{CH}_3C(\text{CN})(\text{OH})\text{CH}_3 + H_3O^+ \rightarrow \text{CH}_3C(\text{COOH})(\text{OH})\text{CH}_3 \]
This product is denoted as Y:
\[ Y = \text{CH}_3C(\text{COOH})(\text{OH})\text{CH}_3 \]

### Step 4: Reaction with H₂SO₄
When Y is treated with sulfuric acid (H₂SO₄), dehydration occurs. The hydroxyl group (OH) can be protonated, leading to the formation of a carbocation:
\[ \text{CH}_3C(\text{COOH})(\text{OH})\text{CH}_3 \overset{H_2SO_4}{\rightarrow} \text{CH}_3C^+(\text{COOH})\text{CH}_3 + H_2O \]
After the loss of water, we obtain a double bond:
\[ \text{CH}_3C(=C)\text{CH}_3\text{COOH} \]

### Step 5: Final product Z
The final product Z after the dehydration process is:
\[ Z = \text{CH}_3C(=C)\text{CH}_3\text{COOH} \]
This can also be represented as:
\[ Z = \text{CH}_2=CH\text{COOH} \text{ (with a methyl group attached)} \]

### Summary of Products
- **X**: \(\text{CH}_3C(\text{CN})(\text{OH})\text{CH}_3\)
- **Y**: \(\text{CH}_3C(\text{COOH})(\text{OH})\text{CH}_3\)
- **Z**: \(\text{CH}_2=CH\text{COOH}\)