Final answer:
The direct energy source for chemiosmosis in ATP production is the movement of hydrogen ions across a membrane, using ATP synthase.
Step-by-step explanation:
In chemiosmosis, the most direct source of energy used to convert ADP + Pi to ATP is energy released from the exergonic movement of hydrogen ions (protons) across a membrane through a specialized protein channel known as ATP synthase. This movement of hydrogen ions is down their electrochemical gradient from an area of high concentration to an area of low concentration. As these ions flow through ATP synthase, their kinetic energy is harnessed to synthesize ATP from ADP and inorganic phosphate (Pi) by the process of oxidative phosphorylation in the mitochondria or photophosphorylation in chloroplasts.