This is a subject that usually generates some confusion when I talk about it in my classes. The reason is very simple... many of my students have learned that when a NADH molecule transfers the electrons to the mitochondrial respiratory chain, it is formed 3 ATP, and when it is the FADH2 the donor of the electrons it is produced 2 ATP. When I say in my classes that are in fact 2.5 ATP produced when the electron donor is NADH, and 1.5 when it is the FADH2, there are many students who make a puzzled face. By the way, let me just make a correction to something that I hear very often. It is not correct to say that NADH is converted in 2.5 ATP, instead it should be said that NADH leads to the production of 2.5 ATP, since NADH is not spent on the process and it only gives two electrons. But back to the energy efficiency... another thing that often causes confusion when I talk about the production of 2.5 ATP, is the fact that you are talking about "one half of an ATP". But how do we produce "half ATP"? And what does the chemical point of view of "half ATP"? In reality it is a strange and confusing idea but the justification is very simple. As it is logical, no one produces “half ATP”, what is happening is that the energy released during the transport of electrons along the mitochondrial respiratory chain is sufficient to produce in average ATP 2.5 or 1.5 (depending if the donor of the electrons is NADH or FADH2, respectively). As the process is continuous, the sum of the energy released per a second electron donor is sufficient to ensure one ATP together.
But back to the total amount of ATP, how it gets to the value of 2.5 or 1.5 ATP, and why the 3 and 2 ATP that many learn is wrong? To recap the operation of the mitochondrial respiratory chain, when NADH is the electron donor, it gives two electrons to the complex I, and 4 protons are pumped into the intermembrane space. The electrons pass to the complex II, which pumps more 4 protons into the intermembrane space. Afterwords, the electrons cross the complex IV until they reach the O2, leading to the pumping of 2 more protons into the intermembrane space, which makes a total of 10 protons pumped into the intermembrane space per NADH that transfers the electrons to the respiratory chain. If the electron donor is the FADH2, these are delivered to complex II, which does not pump protons. Then go to complex III, which pumps 4 protons into the intermembrane space, and finally to the compound IV, which pumps more 2 protons, that means, in total are pumped 6 protons. According to the chemiosmotic theory, the protons will return to the matrix in favor of the concentration gradient, releasing energy. It has been shown experimentally that for every 4 protons returning the matrix, it is released sufficient energy to produce an ATP molecule. Thus, when the electron donor is NADH, it is produced 10/4 = 2.5 ATP molecules, and when it is FADH2 it is produced 6/4 = 1.5 ATP!