Step 1: Understand gas phase acidity.
Gas phase acidity depends on how easily an alcohol loses \(H^+\) to form its conjugate base.
\[
ROH \rightarrow RO^- + H^+
\]
Step 2: Relate acidity with conjugate base stability.
Greater stability of the conjugate base means greater acidity of the parent alcohol.
\[
\text{More stable } RO^- \Rightarrow \text{more acidic } ROH
\]
Step 3: Compare methanol.
For \(CH_3OH\), the \(CH_3\) group has \(+I\) effect, which destabilizes the conjugate base \(CH_3O^-\).
Therefore, \(CH_3OH\) is the least acidic among the given alcohols.
Step 4: Effect of halogen substitution.
In \(XCH_2OH\), the halogen atom withdraws electron density through the \(-I\) effect and stabilizes the conjugate base.
Thus, haloalcohols are more acidic than methanol.
Step 5: Compare halogen effects in gas phase.
In the gas phase, both electronegativity and polarizability affect conjugate base stabilization.
Fluorine gives the strongest electron-withdrawing effect, so \(FCH_2OH\) is the most acidic.
Step 6: Compare \(BrCH_2OH\) and \(ClCH_2OH\).
In the gas phase, bromine stabilizes the negative charge better than chlorine due to greater polarizability.
Hence,
\[
BrCH_2OH > ClCH_2OH
\]
Step 7: Final order.
Therefore, the correct gas phase acidity order is
\[
FCH_2OH > BrCH_2OH > ClCH_2OH > CH_3OH
\]
\[
\boxed{FCH_2OH > BrCH_2OH > ClCH_2OH > CH_3OH}
\]
Hence, the correct answer is option (B).