Write the chemical reactions for the following conversions:
$1.$ Phenol to Anisole and Phenetole
$2.$ Chlorobenzene to $p$-Bromoanisole

(N/A) $1.$ Conversion of Phenol to Anisole and Phenetole:
Phenol reacts with $NaOH$ to form Sodium phenoxide. Sodium phenoxide then undergoes Williamson ether synthesis with alkyl halides:
- Phenol $+ NaOH \rightarrow$ Sodium phenoxide $+ H_2O$
- Sodium phenoxide $+ CH_3Br \rightarrow$ Anisole $+ NaBr$
- Sodium phenoxide $+ CH_3CH_2Br \rightarrow$ Phenetole $+ NaBr$
$2.$ Conversion of Chlorobenzene to $p$-Bromoanisole:
- Chlorobenzene is converted to Sodium phenoxide using $NaOH$ at $623 \ K$ and $300 \ atm$ (Dow's process).
- Sodium phenoxide reacts with $CH_3Br$ to form Anisole.
- Anisole undergoes electrophilic aromatic substitution (bromination) with $Br_2$ in ethanoic acid to yield $p$-Bromoanisole as the major product.