The order of reactivity of following alcohols with halogen acids is _______.
`CH_3CH_2-CH_2-OH`
`CH_3CH_2-underset(CH_3)underset(|)"CH"-OH`
`CH_3CH_2-underset(CH_3)underset(|)overset(CH_3)overset(|)C-OH`

Options

A. (I)gt(II)gt(III)
B. `(III)gt(II)gt(I)`
C. (II)gt(I)gt(III)
D. (I)gt(III)gt(II)

Explanation

To determine the order of reactivity of the given alcohols with halogen acids, we need to analyze the structure of each alcohol and understand how their reactivity is influenced by their classification (primary, secondary, or tertiary) and the stability of the carbocation formed during the reaction.

### Step-by-Step Solution:

1. **Identify the Types of Alcohols**:
- The first alcohol, `CH3CH2-CH2-OH`, is a **primary alcohol** (1°).
- The second alcohol, `CH3CH2-(CH3)C(OH)`, is a **secondary alcohol** (2°).
- The third alcohol, `CH3CH2-(CH3)2C(OH)`, is a **tertiary alcohol** (3°).

2. **Understand the Mechanism of Reaction**:
- Alcohols react with halogen acids (like HCl) through an **SN1 mechanism** for secondary and tertiary alcohols. This involves the formation of a carbocation intermediate.
- The stability of the carbocation is crucial: tertiary carbocations are more stable than secondary, which are more stable than primary.

3. **Analyze the Carbocation Stability**:
- For the primary alcohol (1°), the carbocation formed is less stable.
- For the secondary alcohol (2°), the carbocation formed is more stable than that of the primary.
- For the tertiary alcohol (3°), the carbocation formed is the most stable.

4. **Determine the Order of Reactivity**:
- Since the rate of reaction is directly related to the stability of the carbocation, we can conclude:
- Tertiary alcohol (3°) > Secondary alcohol (2°) > Primary alcohol (1°).
- Therefore, the order of reactivity with halogen acids is:
- **3° > 2° > 1°**.

5. **Final Answer**:
- The order of reactivity of the given alcohols with halogen acids is **3° > 2° > 1°**.