Before we get to the actual saponification reaction, there is one more chemical concept we need to explore. This is the ester. Remember from the last chemistry post that the reaction of an acid and a base produces a salt and water. Alcohols will also react with acids, but instead of producing a salt and water, they create an ester and water. This is a kind of condensation reaction, because of the formation of a water molecule from the original reactants. Esters are essentially insoluble in water, a property that we will come back to later. This is because the carbon/hydrogen tail is long enough that it counteracts the solubility of the head formed from the alcohol. If you mix an ester and a base, you get back the original alcohol and a salt in a type of hydrolysis reaction. If you look at the different parts of that word, you can see the hydro, meaning water, and lysis, which is to break apart. A hydrolysis reaction reinserts the water molecule lost in the condensation reaction to break apart the molecule. If the base is sodium hydroxide (lye) you will get a sodium salt. An important alcohol in soapmaking is glycerol, better known to soapmakers as glycerin. We'll talk much more about glycerin below.
Now that we've covered the chemistry of water and oils, acids and bases, fatty acids, and a little bit about esters, we're ready to tackle the reaction that creates soap: saponification. Though we talk about the fatty acids found in oils, in reality it isn't the fatty acids that are in coconut and olive oils, for example, but their esters. The fatty acid ester structure found in oils consists of three fatty acids attached to one glycerol molecule, formed by a condensation reaction. Chemists call these molecules triacylglycerides, the acyl part (or group) being the part that is formed from the fatty acids. The three fatty acids don't have to be all of the same type, either. Olive oil contains stearic, ricinoleic, linoleic, and linolenic fatty acids, and the triacylglyceride molecules can contain any combination of those fatty acids as the acyl parts of the molecule. The proportion, however, of all the acyl groups matches the proportion you find on Soapcalc for the fatty acids. You've heard of triacylglycerides as triglycerides, the very fatty molecules that you don't want a lot of in your blood. Trigylcerides, being esters, have non-polar covalent bonds and are not soluble, which explains why oils do not mix with water. I mentioned above that if you mix an ester and a base, a hydrolysis reaction occurs, resulting in a salt and the original alcohol. Therefore, when you add lye (sodium hydroxide), to your oils when making soap, the reaction forms glycerol and sodium salts of the fatty acids in the esters. That's the source of the glycerin in handcrafted soap. Fatty acid salts are soaps. Remember, the fatty acid has a water soluble head, and an insoluble tail. They are also alkalis, which have a basic (greater than 7) pH. Knowing how the saponification works also gives us the information on how to calculate the amount of glycerin formed from the reaction. For every three fatty acid molecules produced, one glycerol molecule will be produced. So the ratio of glycerin to fatty acid molecules is 1:3. You can actually calculate the weight of glycerin in a batch of soap. I refer you to Kevin Dunn's Scientific Soapmaking, pages 218 and 219 if you want to calculate the weight (or more correctly, mass) of glycerin in your finished soap.
We aren't finished with soap chemistry. To come later: how and why some FO's accelerate trace, why FO's often change in the finished soap, soaps versus detergents, soap scum, and those dreaded orange spots (DOS).