ATP synthase phosphorylates ADP to make ATP. This enzyme is embedded in the inner membrane of the mitochondria. ATP synthase is also called F0F1-ATPase because it consists of two parts: an F0 portion that sits in the membrane and an F1-ATPase section that lies in the matrix of the mitochondria.
To phosphorylate ADP, protons enter the ATP synthase complex from the region between the inner and outer membranes of the mitochondria. The process of protons entering the proton channel of the F0 portion of the enzyme creates energy to power the process of adding a phosphate group to ADP by the F1-ATPase portion.
Power from protons entering the proton channel also rotates a part of the F1-ATPase called the central stalk. When the central stalk turns, a phosphate group is added to ADP and then the newly synthesized ATP molecule is released.