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Vegetable oil is made of nonpolar molecules and vinegar (which is a solution of approximately 5% acetic acid and water) is made of polar molecules. Where solubility is concerned, the rule is usually "like dissolves like", or materials with similar types of intermolecular forces tend to be soluble in one another.

The carbon and hydrogen atoms in its fatty acid chains have similar electronegativities, so the electrons aren't pulled to any one part of the molecule. This makes it attracted to other materials that are nonpolar (have no negative or positive charges), but not to materials that are polar. Vinegar contains oxygen-hydrogen bonds that are quite polar--the oxygen pulls electrons away from the hydrogen, giving oxygen a partial negative and hydrogen a partial positive charge. That results in molecules that are attracted to other substances with full or partial charges.

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