The correct answer is Option C: Cold, dilute, aqueous solution of potassium permanganate. Here's why:

Baeyer's reagent is a chemical test used to detect the presence of unsaturation in organic compounds, particularly the presence of carbon-carbon double bonds (C=C). It relies on the oxidizing power of potassium permanganate (KMnO₄).

Here's a breakdown of why the other options are incorrect:

• Option A: Acidic potassium permanganate solution - While acidic potassium permanganate is a strong oxidizing agent, it is too reactive and would oxidize other functional groups present in the molecule, making it unsuitable for specifically detecting unsaturation.
• Option B: Acidic potassium dichromate solution - Acidic potassium dichromate is another strong oxidizing agent, but it is not typically used for detecting unsaturation. It is commonly used for oxidizing alcohols to aldehydes or ketones.
• Option D: Hot, concentrated solution of potassium permanganate - A hot, concentrated solution of potassium permanganate would be too harsh and could lead to over-oxidation, making it unreliable for detecting unsaturation.

Why Cold, Dilute, Aqueous Potassium Permanganate Works

In Baeyer's test, the cold, dilute, aqueous solution of potassium permanganate acts as a mild oxidant. The purple color of the permanganate solution disappears as it reacts with the double bond, forming a brown precipitate of manganese dioxide (MnO₂).

The reaction can be represented as follows:

$$ 3R-CH=CH-R' + 2KMnO_4 + 4H_2O \longrightarrow 3R-CH(OH)-CH(OH)-R' + 2MnO_2 + 2KOH $$

The disappearance of the purple color and the formation of the brown precipitate indicate the presence of an unsaturated compound. This reaction is highly specific to alkenes and alkynes because they are readily oxidized by the permanganate ion.