The reason we usually need soap to clean ourselves is that we produce an oil on our skin called sebum. Stuff like dirt sticks to it, and if you just use water, it won’t get the dirt from the oil.
The main feature of soap is that it can stick to water and oil. so when you wash the soap off your body, it takes the sebum with it.
Soap itself is not oils and fats, but it’s made when oils/fats undergo a process called saponification.
Saponification turns oils and fats into soap, and soap is a surfactant which is a special molecule that allows water and oil to stick to each other when they normally don’t.
So when you use soap, the oil in your skin sticks to the water you’re washing with and gets washed away leaving your skin dried out.
Soaps are made of *saponified* oils. This is a chemical reaction where a strong base (such as lye) reacts with a fatty material (such as vegetable oil or animal fat) to create alcohol and soap. So, soap is a whole different kind of molecule than the oil that you make it out of, with different properties. It will lift oil out of your skin rather than add oil to it.
Soap is made from oil that’s been chemically modified so it can dissolve in water. The oils on whatever object you’re cleaning dissolve into the soap, and then it carries them into the water and away from the object.
It’s possible to make soaps less drying, but that makes them weaker cleansers too. I use a bath soap made from beef tallow (which makes relatively mild soap) where 8% of the fat wasn’t modified to make it dissolve. It hardly dries out my skin at all. But it wouldn’t be very good for cleaning oil off of dishes.
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