The gradient created by this drives hydrogen back through the membrane, through ATP synthase. As this happens, the enzymatic activity of ATP synthase synthesiszes ATP from ADP. Mitochondria are ...

which is synthesized from ADP and phosphate through the enzymatic action of a special protein (ATP synthase). Naturally, since this process is essential for the functioning of any organism, ATP ...

which certainly lacked such sophisticated protein machinery as the ATP synthase. There are a few possible abiotic mechanisms, presently under scrutiny in Russell's lab and elsewhere. But ...