For the reaction `C_2H_5OH+HXoverset(ZCl_2)rarrC_2H_5X` , the decreasing order of reactivity of halogen acids is

Options

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

Answer

To determine the decreasing order of reactivity of halogen acids (HX) in the reaction \( C_2H_5OH + HX \overset{ZnCl_2}{\rightarrow} C_2H_5X \), we need to analyze the bond strength of the hydrogen-halogen bonds in the halogen acids HCl, HBr, and HI.

### Step-by-Step Solution:

1. **Identify the Halogen Acids**: The halogen acids involved in this reaction are HCl, HBr, and HI.

2. **Understand the Reaction Mechanism**:
- The reaction involves the conversion of ethanol (\( C_2H_5OH \)) to haloalkane (\( C_2H_5X \)) in the presence of a Lewis acid, ZnCl2.
- The Lewis acid helps in forming a carbocation intermediate by protonating the alcohol.

3. **Formation of Carbocation**:
- The oxygen in the alcohol donates a lone pair to ZnCl2, resulting in a positively charged oxygen and the formation of a carbocation.
- The bond between hydrogen and halogen in HX needs to break for the halogen to attack the carbocation.

4. **Bond Strength Consideration**:
- The strength of the H-X bond is crucial. A weaker bond will break more easily, leading to higher reactivity.
- The bond strengths generally decrease in the order: HCl > HBr > HI.
- This is because as you move down the group in the periodic table, the size of the halogen increases, leading to a weaker bond with hydrogen due to less effective orbital overlap.

5. **Reactivity Order**:
- Since HI has the weakest bond, it will be the most reactive.
- HBr is next, followed by HCl, which has the strongest bond and is therefore the least reactive.
- Thus, the decreasing order of reactivity of halogen acids is:
\[ HI > HBr > HCl \]

### Final Answer:
The decreasing order of reactivity of halogen acids in the given reaction is:
\[ HI > HBr > HCl \]