Concept:
Acidic strength depends on the stability of the conjugate base. Stronger acids have conjugate bases stabilized by resonance, electronegativity, or inductive effects.
Step 1: Identify the products.
\(\mathbf{A}\): From PhNH\(_2\) via diazotization and Sandmeyer reaction, followed by hydrolysis, the product is benzoic acid (\(\ce{C6H5COOH}\)).
\(\mathbf{B}\): From CH\(_3\)CH\(_2\)CHO (propanal) under Tollens’ reagent, the product is propanoic acid (\(\ce{CH3CH2COOH}\)).
\(\mathbf{C}\): From CH\(_4\) oxidation under MoO\(_3\) and Na\(_2\)Cr\(_2\)O\(_7\)/H\(^+\), the product is carbonic acid (\(\ce{H2CO3}\)).
\(\mathbf{D}\): From PhCH\(_2\)MgBr + CO\(_2\), followed by hydrolysis, the product is phenylacetic acid (\(\ce{C6H5CH2COOH}\)).
Step 2: Compare acidic strengths.
\(\ce{H2CO3}\) (C): Strongest acid among the given, as it is a mineral acid with high ionization tendency.
\(\ce{CH3CH2COOH}\) (B): Aliphatic carboxylic acid, weaker than carbonic acid but stronger than aromatic acids.
\(\ce{C6H5COOH}\) (A): Benzoic acid, weaker than aliphatic acids due to resonance stabilization reducing polarity of the \(\ce{COOH}\) group.
\(\ce{C6H5CH2COOH}\) (D): Phenylacetic acid, weakest among these because the \(\ce{-CH2-}\) group reduces the electron-withdrawing effect of the phenyl ring, lowering acidity compared to benzoic acid.
\[
\text{Order of acidic strength: } C>B>A>D
\]