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How do mitochondria produce ATP for cells?

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Fluorescent confocal image of HeLa cells with green microtubules outlining cell shapes, red mitochondria, and blue nuclei. — mitochondrion Mitochondria (red) are found throughout the cytoplasm of almost all eukaryotic cells (cell nucleus is shown in blue; cytoskeleton is shown in yellow).

Mitochondria produce ATP through a process known as oxidative phosphorylation, which relies on the chemiosmotic theory proposed by Peter Mitchell.12

The Mechanism of ATP Synthesis

The production of ATP occurs in several key stages within the mitochondrion:

Electron Transport: During cellular respiration, reduced coenzymes (NADH and FADH $_{2}$ ) donate electrons to the electron-transport chain located in the inner mitochondrial membrane (cristae).12
Proton Pumping: As electrons move through the protein complexes of the chain, the energy released is used to pump protons (H $^{+}$ ions) from the mitochondrial matrix into the intermembrane space.12
Gradient Formation: This pumping action creates an electrochemical gradient—a high concentration of protons outside the membrane and an electrical potential across it—because the inner membrane is impermeable to protons.12
ATP Synthesis: Protons flow back into the matrix through a specialized enzyme complex called ATP synthase. The energy released by this flow drives the conversion of ADP and inorganic phosphate (P $_{i}$ ) into ATP.12

Ultimately, the electrons are transferred to oxygen, which combines with protons to form water, completing the process.2