If 4 -bromo-1-butanol is treated with sodium, a product of molecular formula \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}\) is formed. Arrive at the structure and propose a mechanism.

Understanding the reaction mechanism of 4-bromo-1-butanol is pivotal in grasping how its molecular structure is altered to produce different compounds. Here, we dissect how this compound reacts when sodium is introduced. Initially, the presence of sodium initiates a displacement reaction. This happens because sodium, an alkali metal, is highly reactive and donates an electron to the bromine atom in the 4-bromo-1-butanol.

This electron donation is the first step that creates a carbanion, an important intermediate in many organic reactions. The resulting structure now contains a negatively charged oxygen atom, which is highly reactive and is the driving force behind subsequent steps in the mechanism.

The intramolecular nucleophilic substitution is a fascinating reaction where a nucleophile within the same molecule attacks an electrophilic center, leading to a rearrangement of the molecular structure. In the context of our 4-bromo-1-butanol, once the reactive carbanion is formed, the negatively charged oxygen now takes center stage as it behaves as a nucleophile.

It seeks out a positively charged carbon atom adjacent to it, to which it can donate its pair of electrons, thereby forming a new bond. This S_N2 reaction is 'intramolecular' because the nucleophile and the electrophile are in the same molecule, leading to the formation of a new cyclic or ring structure. The ability of the nucleophile to attack from the 'backside' of the electrophilic carbon is a classic characteristic of S_N2 reactions, resulting in the inversion of stereochemistry at the carbon where substitution occurs.

Carbanions are intriguing species in organic chemistry; they are carbon atoms bearing a negative charge due to an extra pair of electrons. In our exercise with 4-bromo-1-butanol, the carbanion is formed by the removal of bromine atom when sodium donates an electron.

This negatively charged carbanion is highly reactive and readily seeks to stabilize itself by engaging in further chemical reactions. For instance, it finds a proton (H+) to form an alcohol or can reorganize internally to create a new compound, as seen in intramolecular nucleophilic substitution. Carbanions are also notable in various organic syntheses, acting as nucleophiles in many reactions including alkylation and condensation, highlighting their versatile role in organic chemistry.