Final answer:
The energy used to pump hydrogen ions is derived from the electrons released from NADH and FADH2. This energy is used to pump H+ ions across the inner membrane, creating a concentration gradient. The flow of these ions back into the matrix through ATP synthase powers the production of ATP.
Step-by-step explanation:
The energy used to pump hydrogen ions from the mitochondrial matrix across the inner membrane and into the intermembrane space is derived from the electrons released from NADH and FADH2. These electrons pass along an electron transport chain on the inner membrane, and with each step, a small amount of energy is released. This energy is used to pump H+ ions across the inner membrane, creating a concentration gradient. The flow of these ions back into the matrix through ATP synthase powers the production of ATP.