${\mathrm{CH}}_3\mathrm{COOH}\stackrel{1\text{ mole }{\mathrm{Cl}}_2/\text{ Red }\mathrm{P}}{\to }\mathrm{A}\stackrel{\mathrm{KCN}}{\to }\mathrm{B}$$\stackrel{{\mathrm{H}}^{+}/{\mathrm{H}}_2\mathrm{O}}{\to }$ Hence compound ‘C’ is

The compound 'C' formed in the given reaction is:

Malonic acid

Detailed Explanation:

1. Starting with acetic acid (CH₃COOH), it reacts with chlorine (Cl₂) in the presence of red phosphorus (Red P) to form chloroacetic acid (CH₂ClCOOH).
2. The chloroacetic acid then reacts with KCN (potassium cyanide) to undergo nucleophilic substitution, replacing the chlorine atom with a cyano group, resulting in cyanoacetic acid (CH₂(CN)COOH).
3. Finally, cyanoacetic acid undergoes hydrolysis (with H+/H₂O), which converts the cyano group (-CN) into a carboxyl group (-COOH), forming malonic acid (CH₂(CO₂H)₂).
4. Thus, the compound 'C' is malonic acid (CH₂(CO₂H)₂).

Concept:

• Malonic acid is a dicarboxylic acid with two carboxyl groups (-COOH) attached to a central carbon atom.
• The given reactions outline a typical method of synthesizing malonic acid starting from acetic acid through a series of halogenation, nucleophilic substitution, and hydrolysis reactions.