Decreasing order of reactivity of HX in the reaction
`ROH + HX to RX + H_(2)O`

Options

A. `HIgt HBr gt HCl gt HF`
B. `HBr gt HCl gt Hl gt HF`
C. `HCl gt HBr gt HI gt HF`
D. `HF gt HBr gt HCl gt HI`

Answer

To determine the decreasing order of reactivity of HX in the reaction \( ROH + HX \rightarrow RX + H_2O \), we need to analyze the nucleophilicity of the halides (X) involved in the reaction.

### Step-by-Step Solution:

1. **Identify the Halides**: The halides involved in the reaction are Fluorine (F), Chlorine (Cl), Bromine (Br), and Iodine (I). These correspond to the acids HF, HCl, HBr, and HI.

2. **Understand Nucleophilicity**: Nucleophilicity is a measure of how readily a species donates an electron pair to form a bond. In this reaction, the halide ion (X-) acts as a nucleophile.

3. **Trends in Nucleophilicity**: In the halogen group (Group 17), nucleophilicity increases as we move down the group from Fluorine to Iodine. This is due to the following reasons:
- **Size of the Atom**: As we move down the group, the size of the halogen increases. Larger atoms have more electron shells, which means the valence electrons are further from the nucleus.
- **Effective Nuclear Charge**: The effective nuclear charge experienced by the outermost electrons decreases down the group, making it easier for the larger halide ions to donate their electrons.

4. **Order of Nucleophilicity**: Based on the above understanding, the order of nucleophilicity for the halides is:
\[ I^- > Br^- > Cl^- > F^- \]
This means that Iodide (I-) is the most nucleophilic and Fluoride (F-) is the least nucleophilic.

5. **Relate Nucleophilicity to Reactivity**: Since the reactivity of HX in the given reaction is directly related to the nucleophilicity of the halide ion, we can conclude that:
- HI (Iodine) will be the most reactive.
- HBr (Bromine) will be next.
- HCl (Chlorine) will follow.
- HF (Fluorine) will be the least reactive.

6. **Final Order of Reactivity**: Therefore, the decreasing order of reactivity of HX in the reaction \( ROH + HX \rightarrow RX + H_2O \) is:
\[ HI > HBr > HCl > HF \]

### Final Answer:
The decreasing order of reactivity of HX is:
\[ HI > HBr > HCl > HF \]