`R-OH + HX to R -X + H_(2)O`
In the above reaction the reactivity of different alcohols is

Options

A. `1^(@) gt 2^(@) gt 3^(@)`
B. `1^(@) lt 2^(@) gt 3^(@)`
C. `3^(@) gt 2^(@) gt 1^(@)`
D. `3^(@) gt 1^(@) gt 2^(@)`

Explanation

To determine the reactivity of different alcohols (R-OH) when they react with hydrogen halides (HX) to form alkyl halides (R-X) and water (H₂O), we need to analyze the mechanism of the reaction and the stability of the intermediates formed.

### Step-by-Step Solution:

1. **Understanding the Reaction**:
The reaction can be represented as:
\[ R-OH + HX \rightarrow R-X + H_2O \]
Here, R-OH is an alcohol, HX is a hydrogen halide, R-X is an alkyl halide, and H₂O is water. The hydroxyl group (OH) is replaced by a halide ion (X⁻).

2. **Identifying the Mechanism**:
This reaction is a nucleophilic substitution reaction. Depending on the type of alcohol, the mechanism can follow either SN1 or SN2 pathways. In this case, it predominantly follows the SN1 mechanism because it involves the formation of a carbocation intermediate.

3. **Formation of Carbocation**:
When the alcohol reacts with HX, the hydroxyl group leaves, forming a carbocation (R⁺). The stability of this carbocation is crucial for the reactivity of the alcohol:
- **Tertiary Carbocation (3°)**: Most stable due to hyperconjugation and inductive effects from three alkyl groups.
- **Secondary Carbocation (2°)**: Moderately stable, supported by two alkyl groups.
- **Primary Carbocation (1°)**: Least stable, as it is supported by only one alkyl group.

4. **Reactivity Order Based on Carbocation Stability**:
Since the reactivity of the alcohols depends on the stability of the carbocations formed, we can establish the following order:
- Tertiary alcohols (3°) will form the most stable carbocations and are therefore the most reactive.
- Secondary alcohols (2°) will form moderately stable carbocations and are less reactive than tertiary.
- Primary alcohols (1°) will form the least stable carbocations and are the least reactive.

5. **Final Reactivity Order**:
Based on the stability of the carbocations, the order of reactivity of the alcohols in the reaction with HX is:
\[ \text{Tertiary (3°) > Secondary (2°) > Primary (1°)} \]

### Summary:
The reactivity of different alcohols in the reaction with HX is as follows:
- **Tertiary Alcohols (3°)**: Most reactive
- **Secondary Alcohols (2°)**: Moderately reactive
- **Primary Alcohols (1°)**: Least reactive