Short answers, pulled from the story.
A carboxylic acid is a polar organic compound containing a carboxyl group, which consists of a carbonyl and a hydroxyl group joined to the same carbon. The hydroxyl end donates a proton, making the compound acidic; the resulting carboxylate anion is stabilized by resonance, with the negative charge delocalized across both oxygen atoms.
Carboxylic acids are weak acids that only partially dissociate in water. Acetic acid, with a pKa of 4.76, dissociates at a rate of only 0.001 percent in a one-molar solution at room temperature, meaning just one in roughly a hundred thousand molecules releases its proton.
Vinegar contains acetic acid, butter contains butyric acid, coconut oil contains lauric acid and caprylic acid, and citrus fruits contain citric acid. Soaps are sodium or potassium salts of fatty acids, which are long-chain carboxylic acids.
Amino acids, the building blocks of proteins, are carboxylic acids with an attached amino group. Fatty acids, which form the main components of lipids, are long-chain carboxylic acids. The enzyme RuBisCo, the most abundant protein on Earth, produces carboxylic acids during the carbon-fixation step of photosynthesis.
Carboxylic acids with one to five carbons are soluble in water, while longer-chain acids become increasingly hydrophobic and dissolve in less-polar solvents such as ethers and alcohols. For example, enanthic acid, a seven-carbon acid, dissolves in water at only 0.2 grams per liter, though its sodium salt is very water-soluble.
Acetic acid is a precursor to solvents and coatings, acrylic acid feeds into polymers and adhesives, adipic acid is used to produce nylon, terephthalic acid is a polymer building block, citric acid serves as a flavor and preservative in food and beverages, and propionic acid preserves stored grains.