`ROH + HX to RX + H_(2)O`
In the above reaction , the reactivity of different alcohols is :

Options

A. `"Tertiary" gt "Secondary" gt "Primary"`
B. `"Tertiary" lt "Secondary" lt "Primary"`
C. `"Tertiary" lt "Secondary" gt "Primary"`
D. `"Secondary" lt "Primary" lt "Tertiary"`

Answer

To determine the reactivity order of different alcohols in the reaction \(ROH + HX \rightarrow RX + H_2O\), we need to analyze the stability of the carbocations formed during the reaction.

### Step-by-Step Solution:

1. **Identify the Reaction**: The reaction involves an alcohol \(ROH\) reacting with a hydrogen halide \(HX\) to form an alkyl halide \(RX\) and water \(H_2O\).

2. **Formation of Carbocation**: When the alcohol reacts with \(HX\), the hydroxyl group (\(-OH\)) is protonated by \(H^+\) from \(HX\), leading to the formation of a better leaving group (water) and a carbocation \(R^+\).

3. **Carbocation Stability**: The stability of the carbocation \(R^+\) is crucial for the reactivity of the alcohol. The order of stability for carbocations is:
- Tertiary (3°) > Secondary (2°) > Primary (1°)

4. **Tertiary Carbocation**: In a tertiary carbocation, the positive charge is on a carbon atom that is bonded to three other carbon atoms. This structure provides greater stability due to hyperconjugation and inductive effects from the surrounding alkyl groups.

5. **Secondary Carbocation**: A secondary carbocation has the positive charge on a carbon atom that is bonded to two other carbon atoms. It is less stable than a tertiary carbocation but more stable than a primary one.

6. **Primary Carbocation**: A primary carbocation has the positive charge on a carbon atom that is bonded to only one other carbon atom. This structure is the least stable due to the lack of stabilizing effects from surrounding alkyl groups.

7. **Reactivity Order**: Since the rate of the reaction depends on the stability of the carbocation formed, the reactivity order of alcohols in this reaction is:
- Tertiary alcohols > Secondary alcohols > Primary alcohols

### Conclusion:
The reactivity order of alcohols in the reaction \(ROH + HX \rightarrow RX + H_2O\) is:
- **Tertiary > Secondary > Primary**