What is the proper name for vinegar?

Acetic acid is the scientific name for vinegar

The word "vinegar" derives from the French vin aigre, meaning "sour wine." Its called Acetic acid or Ethanoic acid.
Its chemical formula is : CH3COOH or HC2H3O2.

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The proper name for vinegar is vinegar.
It consists of roughly 15% acetic acid and 85% water, with a small amount of natural vegetable colorants and volatiles (hence the differences in colours and odours between brown vinegar, white vinegar, cider vinegar, balsamic vinegar, etc.)

The acid in vinegar is indeed acetic acid; however, 90 percent of all the acetic acid on the market is made in chemical plants. Almost all of that - 83 percent of the total - is made by reacting methanol and carbon monoxide in the formula

CH3OH + CO -> CH3COOH

The rest is made by oxidizing either acetaldehyde or ethylene.

Vinegar is always made by fermenting fruit juices. It is a two-stage process, in which yeasts convert fruit juice to wine, then acetobacter bacteria convert the alcohol in wine to acetic acid. Because many nations' food laws prohibit the use of vinegar in edibles that is not made through the fermentation of fruit juice, they are very careful to only call fruit juice-derived acetic acid "vinegar."