Final answer:
True, hydrogen ions diffuse back through ATP synthase, allowing it to add a phosphate group to ADP, thus forming ATP. The process is powered by the electrochemical gradient across the mitochondrial membrane.
Step-by-step explanation:
The statement that hydrogen ions diffuse back into the matrix through a carrier protein that adds a phosphate group to ADP, making ATP, is true. The protein responsible for this process is called ATP synthase. As hydrogen ions move back across the inner mitochondrial membrane, they pass through ATP synthase, which operates like a tiny turbine. The flow of protons through ATP synthase is known as chemiosmosis. This mechanical energy is then used by ATP synthase to phosphorylate ADP, adding a phosphate group to it and transforming it into ATP. This conversion is a critical part of cellular respiration, specifically the electron transport chain, and the generation of ATP in this manner is called oxidative phosphorylation. The electrochemical gradient created by the pumping of hydrogen ions into the intermembrane space is essential for ATP synthesis as it provides the necessary energy for ATP synthase to function.