The question tests the understanding of nucleophilic substitution reactions, specifically focusing on the reactivity of nucleophiles towards \( \text{CH}_3\text{Br} \) in methanol. This reaction involves a nucleophile attacking an electrophilic carbon, displacing the leaving group (bromide ion in this case).
To determine the reactivity order, we must consider the factors affecting nucleophilicity, which include:
- Charge: Negatively charged nucleophiles are generally more reactive than their neutral counterparts.
- Electronegativity: Less electronegative atoms tend to share electrons more readily, increasing nucleophilicity.
- Solvent Effects: In polar protic solvents like methanol, larger anions are more nucleophilic because they are less solvated than smaller anions.
Given the nucleophiles in the question:
- \( \text{F}^- \): Small, highly electronegative, and strongly solvated in polar protic solvents like methanol.
- \( \text{I}^- \): Larger anion, less electronegative, and weakly solvated, thus more reactive.
- \( \text{C}_2\text{H}_5\text{O}^- \): Larger than \( \text{F}^- \), negatively charged, and less solvated due to its alkoxide nature.
- \( \text{C}_6\text{H}_5\text{O}^- \): Phenoxide ion, resonant stabilized and therefore less reactive than the alkoxide.
Comparing the reactivity in methanol (polar protic solvent), the order is determined by the interplay of these factors:
- \( \text{I}^- \) is the most reactive due to its size and less solvation, leading to higher nucleophilicity.
- \( \text{C}_2\text{H}_5\text{O}^- \) is next as alkoxides are strong nucleophiles and larger than fluoride.
- \( \text{C}_6\text{H}_5\text{O}^- \) comes next due to resonance stabilization reducing its reactivity compared to the ethoxide.
- \( \text{F}^- \) is the least reactive due to strong solvation and high electronegativity.
Thus, the correct reactivity order when reacting with \( \text{CH}_3\text{Br} \) in methanol is:
\( \text{I}^- > \text{C}_2\text{H}_5\text{O}^- > \text{C}_6\text{H}_5\text{O}^- > \text{F}^- \)
This corresponds to the answer option:
\( \text{I}^- > \text{C}_2\text{H}_5\text{O}^- > \text{C}_6\text{H}_5\text{O}^- > \text{F}^- \)