What Exactly are Oil and Vinegar?
To understand why oil and vinegar don't mix, you have to understand their individual compositions. Vinegar is about 95 percent water, with just a small amount of acetic acid and some other compounds. Oil is made up of fats called lipids. There is a widely held belief that oil and vinegar don't mix because they are of different densities, but this is not true.
Polarity
The true cause is the difference in the polarity of the water in the vinegar and the lipids in the oil. Water molecules have a positively and a negatively charged end. Molecules of this nature are called "polar" molecules, and easily bond with one another. Lipids, on the other hand, are non-polar; they have no separation of charge. This means it is much easier for water to bind with more water than for it to bond with oil, and nature much prefers the path of least resistance. In the end, the oil is less dense, which is why it floats to the top, but not why it won't combine.
Emulsion
There is a way to make oil and vinegar combine. For example, if you were to get grease on your hands, it would be very difficult to wash off with just water due to the polarity of the water and the grease. But once you use soap, it becomes very easy. This is because soap is an "emulsifier;" soap contains certain special compounds which surround the non-polar molecules in the grease and allow them to bond with the water. You can do this with oil and vinegar too, but it's much more tasty to use egg yolk than soap. Combine oil, vinegar and egg yolk together and you'll have a homemade mayonnaise.
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