The reaction of glycerol (C₃H₈O₃) with sodium metal (Na) is a vigorous reaction that produces sodium glyceroxide (C₃H₇O₃Na) and hydrogen gas (H₂).

Here's the balanced chemical equation:

2 C₃H₈O₃ + 6 Na → 2 C₃H₇O₃Na + 3 H₂

Explanation:

* Glycerol (C₃H₈O₃): Glycerol has three hydroxyl groups (-OH) that can react with sodium.

* Sodium (Na): Sodium is a highly reactive alkali metal that readily loses an electron to form a cation (Na⁺).

* Sodium glyceroxide (C₃H₇O₃Na): The sodium ions (Na⁺) replace the hydrogen ions (H⁺) in the hydroxyl groups of glycerol, forming sodium glyceroxide.

* Hydrogen gas (H₂): The displaced hydrogen atoms combine to form hydrogen gas.

Important Note: This reaction is highly exothermic and can be dangerous if not handled properly. It should only be carried out by experienced chemists in a controlled environment.