Step 1: Understanding pKa value.
pKa is a measure of the acidity of a compound, with a lower pKa indicating a stronger acid. The presence of electron-withdrawing groups (EWGs) typically lowers the pKa, making the acid stronger.
Step 2: Analysis of the options.
\begin{itemize}
\item (A) CH\(_3\)COOH: This is acetic acid, which is a weak acid. It has the highest pKa among the given options, indicating that it is the weakest acid.
\item (B) F-CH\(_2\)-COOH: The presence of the electronegative fluorine atom withdraws electron density from the carboxyl group, making it a stronger acid and lowering its pKa value.
\item (C) CN-CH\(_2\)-COOH: The nitrile group (CN) is an electron-withdrawing group, which lowers the pKa further, making this compound a stronger acid.
\item (D) Cl-CH\(_2\)-COOH: Chlorine is also an electron-withdrawing group, but it is less effective than fluorine or nitrile groups in lowering the pKa.
\item (E) NO\(_2\)-CH\(_2\)-COOH: The nitro group (NO\(_2\)) is a very strong electron-withdrawing group, which significantly lowers the pKa value, making this the strongest acid.
\end{itemize}
Step 3: Conclusion.
Therefore, the compound with the highest pKa value is acetic acid (CH\(_3\)COOH), as it has the weakest electron-withdrawing effect and is the least acidic.
Final Answer: CH\(_3\)COOH.