A compound [A] with molecular formula `C_(4)H_(10)O` reacts rapidly with metallic sodium but very slowly with Lucas reagent. When [A] treated with hot concentrated `H_(2)SO_(4)`, it gives a compound [B] `C_(4)H_(8)` which upon hydration with aqueous `H_(2)SO_(4)` forms a compound [C] with molecular formula `C_(4)H_(10)O`. The compound [C] is almost unert to metallic sodium but reacts rapidly with Lucas reagent. What are the compounds [A], [B] and [C] ? Explain the reaction involved.

Answer

To solve the problem, we need to identify the compounds A, B, and C based on the given information about their molecular formulas and their reactivity.

### Step-by-Step Solution:

1. **Identify Compound A**:
- Given: Compound A has the molecular formula C₄H₁₀O, reacts rapidly with metallic sodium, but slowly with Lucas reagent.
- Since it reacts rapidly with sodium, it is likely a primary or secondary alcohol (not tertiary).
- The structure of A can be isobutyl alcohol (2-methyl-1-propanol), which is a primary alcohol:
\[ \text{A: } \text{CH}_3\text{CH}_2\text{CH(CH}_3)\text{OH} \]

2. **Identify Compound B**:
- Given: When A is treated with hot concentrated H₂SO₄, it forms compound B (C₄H₈).
- This indicates a dehydration reaction where water is removed to form an alkene.
- The likely product B is isobutylene (2-methylpropene):
\[ \text{B: } \text{CH}_3\text{C(CH}_3)=\text{CH}_2 \]

3. **Identify Compound C**:
- Given: Compound C is formed by the hydration of compound B with aqueous H₂SO₄ and has the formula C₄H₁₀O.
- The hydration of isobutylene (B) leads to the formation of tertiary butyl alcohol (C):
\[ \text{C: } \text{(CH}_3)_3\text{COH} \]
- This compound is tertiary butyl alcohol, which is inert to sodium but reacts rapidly with Lucas reagent.

### Summary of Compounds:
- **Compound A**: Isobutyl alcohol (2-methyl-1-propanol) - CH₃CH₂CH(CH₃)OH
- **Compound B**: Isobutylene (2-methylpropene) - CH₃C(CH₃)=CH₂
- **Compound C**: Tertiary butyl alcohol - (CH₃)₃COH

### Reactions Involved:
1. **Dehydration of A to B**:
\[ \text{A (Isobutyl alcohol)} \xrightarrow{\text{H}_2\text{SO}_4, \text{heat}} \text{B (Isobutylene)} + \text{H}_2\text{O} \]

2. **Hydration of B to C**:
\[ \text{B (Isobutylene)} + \text{H}_2\text{O} \xrightarrow{\text{H}_2\text{SO}_4} \text{C (Tertiary butyl alcohol)} \]