Final answer:
Complex II does not pump hydrogen ions into the inner membrane space of the mitochondria during the electron transport chain process; it receives electrons from FADH2 and transfers them to ubiquinone without pumping protons.
Step-by-step explanation:
In the electron transport chain (ETC), the complex that does not pump hydrogen ions into the inner membrane space of the mitochondria is Complex II. Unlike Complex I, III, and IV, Complex II extends to the matrix from the inner membrane but does not cross the membrane to the intermembrane space and therefore cannot pump protons. Complex II receives electrons from FADH2 and passes them to ubiquinone (Q), which then transfers the electrons to Complex III. However, since these electrons bypass the first complex, fewer ATP molecules are produced from these FADH2 electrons compared to NADH electrons.