Which of the following reactions of phenol is used for its quantitative estimation? (a) Reaction with bromine (b) Reaction with con. \(\mathrm{HNO}_{3}\) (c) Reaction with \(\mathrm{FeCl}_{3}\) solution (d) Reaction with \(\mathrm{CO}_{2}\)

Phenol is an aromatic compound with a hydroxyl group (-OH) attached to its benzene ring. Due to its resonance structure, phenol is a weak acid compared to ordinary alcohols. It forms phenoxide ion when it loses a proton from its -OH group.

Let's analyze each reaction given in the question: (a) Reaction with Bromine: When phenol reacts with bromine at room temperature, a white precipitate of 2,4,6-tribromophenol is formed. However, this reaction does not provide a quantitative measurement of phenol. (b) Reaction with con. \(\mathrm{HNO}_{3}\): Phenol reacts with concentrated nitric acid to form 2,4,6-trinitrophenol, also known as picric acid. This reaction is a nitration reaction and does not directly aid in the quantitative estimation of phenol. (c) Reaction with \(\mathrm{FeCl}_{3}\) solution: Phenol reacts with a solution of ferric chloride (\(\mathrm{FeCl}_{3}\)) to form a colored complex which can be used to determine the concentration of phenol in the solution. This reaction is based on the property that phenols form colored complexes with \(\mathrm{FeCl}_{3}\), known as the "Ferric chloride test". (d) Reaction with \(\mathrm{CO}_{2}\): Reaction of phenol with \(\mathrm{CO}_{2}\) results in the formation of salicylic acid, but this reaction does not provide a way to estimate the quantity of phenol.

Based on the analysis above, reaction (c) with \(\mathrm{FeCl}_{3}\) solution is used for the quantitative estimation of phenol as it forms a colored complex based on the concentration of phenol present in the sample. Thus, the correct answer is (c).