The enzyme that harnesses the energy of h+ diffusion down its concentration gradient within a mitochondrion to make high-energy molecules for the cell is

The enzyme is: ATP synthase.

ATP synthase is an enzymatic protein complex found in the mitochondrial ridges, the thylakoid membrane, and the plasma membrane of bacteria and archaea. The role of this membrane protein is to synthesize adenosine triphosphate (ATP) from the proton electrochemical gradient of protons maintained by the respiratory chain and adenosine diphosphate (ADP), as well as inorganic phosphate, according to the following reaction:ADP + Pi → ATP.
The synthesis of ATP is based on energy conversion, via conformational changes of the subunits.A proton gradient on either side of the membrane into which the ATP synthases are inserted is necessary for their operation, which implies that the synthesis of ATP can not be done independently of a membrane. Within the mitochondrial inner membrane, it is the respiratory chain that provides the pH gradient by injecting protons into the intermembrane space during the transfer of electrons from one complex to another.