For a given alcohol the order of reactivity of halogen acids is :

Options

A. `HI gt HBr gt HCl`
B. `HCl gt HBr lt HI`
C. `HI lt HBr lt HCl`
D. `HCl lt HI lt HBr`

Explanation

To determine the order of reactivity of halogen acids with a given alcohol, we can follow these steps:

### Step 1: Understand the Reaction Mechanism
When an alcohol reacts with a halogen acid (HX), the alcohol first protonates, forming a carbocation. The reaction can be represented as:
\[ \text{R-OH} + \text{HX} \rightarrow \text{R-OH}_2^+ + \text{X}^- \]
Here, the oxygen in the alcohol donates a lone pair to the hydrogen ion (H+), resulting in a positively charged oxonium ion.

**Hint:** Focus on the role of the alcohol's oxygen and how it interacts with the halogen acid.

### Step 2: Formation of Carbocation
Once the alcohol is protonated, it forms a carbocation (R-OH₂⁺). The stability of this carbocation is crucial for the subsequent reaction with the halide ion (X⁻).

**Hint:** Remember that the stability of the carbocation influences the reaction rate.

### Step 3: Attack of Halide Ion
The halide ion (X⁻) then attacks the carbocation, resulting in the formation of the alkyl halide:
\[ \text{R-OH}_2^+ + \text{X}^- \rightarrow \text{R-X} + \text{H}_2\text{O} \]

**Hint:** Consider how the stability of the halide ion affects the speed of this step.

### Step 4: Compare Halogen Acids
The reactivity of halogen acids (HX) can be compared based on the bond strength of H-X. As we move down the group in the periodic table from HF to HI, the bond strength decreases due to increasing atomic size and bond length:
- H-F (strongest bond)
- H-Cl
- H-Br
- H-I (weakest bond)

**Hint:** Think about how bond strength relates to the ease of bond breaking during the reaction.

### Step 5: Determine Order of Reactivity
Based on the bond strengths, the order of reactivity of halogen acids with alcohols is:
\[ \text{HI} > \text{HBr} > \text{HCl} \]
This means that HI is the most reactive, followed by HBr, and then HCl.

**Hint:** Recall that weaker bonds break more easily, leading to faster reactions.

### Final Answer
The order of reactivity of halogen acids with a given alcohol is:
\[ \text{HI} > \text{HBr} > \text{HCl} \]