Step 1: Understanding the role of substituents.
The rate of electrophilic substitution reactions such as nitration is influenced by the electron-donating or electron-withdrawing effects of substituents on the aromatic ring. Electron-donating groups increase the electron density on the ring, facilitating the attack by the nitronium ion (NO\(_2\)\(^+\)), thus increasing the rate of nitration.
Step 2: Analyzing the substituents.
- OMe (Methoxy group): A strong electron-donating group via resonance, which significantly increases the nucleophilicity of the aromatic ring, making nitration faster.
- F (Fluorine): An electron-withdrawing group via induction, which decreases the electron density on the ring and slows down nitration.
- Br (Bromine): A weaker electron-donating group via resonance, which slightly increases the electron density and promotes the nitration reaction, but not as strongly as OMe.
Step 3: Conclusion.
The correct order of the rate of mononitration is: OMe>F>Br, as OMe is the strongest electron-donating group, followed by Br, and F is the electron-withdrawing group.
Final Answer:
\[
\boxed{\text{OMe>F>Br}}
\]