In the following sequence of reactions
`CH_(3)-Br overset(KCN) to A overset(H_(3)O^(+)) to B overset(LiAlH_(4))underset("ether") to C`
How many `sp^(3)` hybridized atoms are present in product C

Explanation

To solve the problem, we will go through the sequence of reactions step by step, identifying the products and determining the number of sp³ hybridized atoms in product C.

### Step 1: Identify Product A
The starting compound is CH₃-Br (methyl bromide). When it reacts with KCN, the cyanide ion (CN⁻) acts as a nucleophile and attacks the carbon atom bonded to bromine, leading to the substitution of bromine.

**Reaction:**
\[ \text{CH}_3\text{-Br} + \text{KCN} \rightarrow \text{CH}_3\text{-CN} + \text{Br}^- \]

**Product A:**
- A = CH₃-CN (methyl cyanide)

### Step 2: Identify Product B
Next, product A (CH₃-CN) undergoes hydrolysis in the presence of H₃O⁺ (acidic conditions). The cyanide group is converted to a carboxylic acid.

**Reaction:**
\[ \text{CH}_3\text{-CN} + \text{H}_3\text{O}^+ \rightarrow \text{CH}_3\text{-COOH} \]

**Product B:**
- B = CH₃-COOH (acetic acid)

### Step 3: Identify Product C
Product B (acetic acid) is then reduced by lithium aluminum hydride (LiAlH₄) in ether, which is a strong reducing agent. It reduces the carboxylic acid to an alcohol.

**Reaction:**
\[ \text{CH}_3\text{-COOH} + \text{LiAlH}_4 \rightarrow \text{CH}_3\text{-CH}_2\text{OH} \]

**Product C:**
- C = CH₃-CH₂-OH (ethanol)

### Step 4: Count sp³ Hybridized Atoms in Product C
In product C (ethanol, CH₃-CH₂-OH), we need to identify the sp³ hybridized atoms.

1. **Carbon Atoms:**
- The first carbon (C1) in CH₃ is bonded to three hydrogens and one carbon (C2), which gives it 4 sigma bonds (sp³ hybridized).
- The second carbon (C2) in CH₂ is bonded to two hydrogens and one carbon (C1) and one oxygen (O), which also gives it 4 sigma bonds (sp³ hybridized).

2. **Oxygen Atom:**
- The oxygen (O) in the hydroxyl group (OH) has two lone pairs and one bond to carbon (C2). This gives it a total of 4 (2 lone pairs + 1 bond), which makes it sp³ hybridized as well.

### Summary of Hybridization:
- C1 (from CH₃) - sp³
- C2 (from CH₂) - sp³
- O (from OH) - sp³

### Total Count of sp³ Hybridized Atoms:
- 2 Carbon atoms + 1 Oxygen atom = 3 sp³ hybridized atoms.

### Final Answer:
The number of sp³ hybridized atoms present in product C is **3**.

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