Why do long chain fatty acids have low saponification number? What is the relation of fatty acid chain( R) with saponification number?
The saponification number, or saponification value, can be described as...
the measure of the amount of alkali required to saponify a definite weight of fat. It is expressed in milligrams of potassium hydroxide required to saponify 1g of fat.
Notice that, in the definition, we're talking about grams and milligrams, not mols.
Now comes the important information: in the saponification, the base reacts with the ester group, and any triglyceride, regardless its chain length, has exactly three ester groups.
Let's see this is an oversimplified example:
Suppose we have two triglycerides, A and B. A has a chain twice as long as B. So, suppose that a given number of mols of A weights around two times the weight of the same number of mols of B.
However, they have the same number of esters, and they will require the same amount of potassium hydroxide. As A has a greater weight (which is in the denominator on our equation), it will have a lower saponification number compared to B.